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Stan Math Library
2.11.0
reverse mode automatic differentiation
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Matrices and templated mathematical functions. More...
Namespaces | |
detail | |
Classes | |
struct | abs_fun |
Structure to wrap abs() so it can be vectorized. More... | |
class | accumulator |
Class to accumulate values and eventually return their sum. More... | |
struct | acos_fun |
Structure to wrap acos() so it can be vectorized. More... | |
struct | apply_scalar_unary |
Base template class for vectorization of unary scalar functions defined by a template class F to a scalar, standard library vector, or Eigen dense matrix expression template. More... | |
struct | apply_scalar_unary< F, double > |
Template specialization for vectorized functions applying to double arguments. More... | |
struct | apply_scalar_unary< F, int > |
Template specialization for vectorized functions applying to integer arguments. More... | |
struct | apply_scalar_unary< F, stan::math::fvar< T > > |
Template specialization to fvar for vectorizing a unary scalar function. More... | |
struct | apply_scalar_unary< F, stan::math::var > |
Template specialization to var for vectorizing a unary scalar function. More... | |
struct | apply_scalar_unary< F, std::vector< T > > |
Template specialization for vectorized functions applying to standard vector containers. More... | |
struct | array_builder |
Structure for building up arrays in an expression (rather than in statements) using an argumentchaining add() method and a getter method array() to return the result. More... | |
struct | asin_fun |
Structure to wrap asin() so it can be vectorized. More... | |
struct | asinh_fun |
Structure to wrap asinh() so it can be vectorized. More... | |
struct | atan_fun |
Structure to wrap atan() so it can be vectorized. More... | |
struct | AutodiffStackStorage |
struct | cbrt_fun |
Structure to wrap cbrt() so it can be vectorized. More... | |
struct | ceil_fun |
Structure to wrap ceil() so it can be vectorized. More... | |
class | chainable_alloc |
A chainable_alloc is an object which is constructed and destructed normally but the memory lifespan is managed along with the arena allocator for the gradient calculation. More... | |
struct | child_type |
Primary template class for metaprogram to compute child type of T. More... | |
struct | child_type< T_struct< T_child > > |
Specialization for template classes / structs. More... | |
class | cholesky_decompose_v_vari |
struct | common_type |
struct | common_type< Eigen::Matrix< T1, R, C >, Eigen::Matrix< T2, R, C > > |
struct | common_type< std::vector< T1 >, std::vector< T2 > > |
class | container_view |
Primary template class for container view of array y with same structure as T1 and size as x. More... | |
class | container_view< dummy, T2 > |
Dummy type specialization, used in conjunction with struct dummy as described above. More... | |
class | container_view< Eigen::Matrix< T1, R, C >, Eigen::Matrix< T2, R, C > > |
Template specialization for Eigen::Map view of array with scalar type T2 with size inferred from input Eigen::Matrix. More... | |
class | container_view< Eigen::Matrix< T1, R, C >, T2 > |
Template specialization for scalar view of array y with scalar type T2. More... | |
class | container_view< std::vector< Eigen::Matrix< T1, R, C > >, Eigen::Matrix< T2, R, C > > |
Template specialization for matrix view of array y with scalar type T2 with shape equal to x. More... | |
class | container_view< std::vector< T1 >, T2 > |
Template specialization for scalar view of array y with scalar type T2 with proper indexing inferred from input vector x of scalar type T1. More... | |
struct | cos_fun |
Structure to wrap cos() so it can be vectorized. More... | |
struct | cosh_fun |
Structure to wrap cosh() so it can be vectorized. More... | |
struct | coupled_ode_observer |
Observer for the coupled states. More... | |
struct | coupled_ode_system |
Base template class for a coupled ordinary differential equation system, which adds sensitivities to the base system. More... | |
class | coupled_ode_system< F, double, double > |
The coupled ode system for known initial values and known parameters. More... | |
struct | coupled_ode_system< F, double, stan::math::var > |
The coupled ODE system for known initial values and unknown parameters. More... | |
struct | coupled_ode_system< F, stan::math::var, double > |
The coupled ODE system for unknown initial values and known parameters. More... | |
struct | coupled_ode_system< F, stan::math::var, stan::math::var > |
The coupled ode system for unknown intial values and unknown parameters. More... | |
class | cvodes_ode_data |
CVODES ode data holder object which is used during CVODES integration for CVODES callbacks. More... | |
struct | digamma_fun |
Structure to wrap digamma() so it can be vectorized. More... | |
struct | dummy |
Empty struct for use in boost::condtional<is_constant_struct<T1>::value, T1, dummy>::type as false condtion for safe indexing. More... | |
struct | erf_fun |
Structure to wrap erf() so it can be vectorized. More... | |
struct | erfc_fun |
Structure to wrap erfc() so that it can be vectorized. More... | |
struct | exp_fun |
Structure to wrap exp() so that it can be vectorized. More... | |
struct | expm1_fun |
Structure to wrap expm1() so that it can be vectorized. More... | |
struct | fabs_fun |
Structure to wrap fabs() so that it can be vectorized. More... | |
struct | floor_fun |
Structure to wrap floor() so that it can be vectorized. More... | |
struct | fvar |
class | gevv_vvv_vari |
struct | include_summand |
Template metaprogram to calculate whether a summand needs to be included in a proportional (log) probability calculation. More... | |
struct | index_type |
Primary template class for the metaprogram to compute the index type of a container. More... | |
struct | index_type< const T > |
Template class for metaprogram to compute the type of indexes used in a constant container type. More... | |
struct | index_type< Eigen::Matrix< T, R, C > > |
Template metaprogram defining typedef for the type of index for an Eigen matrix, vector, or row vector. More... | |
struct | index_type< std::vector< T > > |
Template metaprogram class to compute the type of index for a standard vector. More... | |
struct | inv_cloglog_fun |
Structure to wrap inv_cloglog() so that it can be vectorized. More... | |
struct | inv_fun |
Structure to wrap inv() so that it can be vectorized. More... | |
struct | inv_logit_fun |
Structure to wrap inv_logit() so that it can be vectorized. More... | |
struct | inv_Phi_fun |
Structure to wrap inv_Phi() so it can be vectorized. More... | |
struct | inv_sqrt_fun |
Structure to wrap inv_sqrt() so that it can be vectorized. More... | |
struct | inv_square_fun |
Structure to wrap inv_square() so that it can be vectorized. More... | |
class | LDLT_alloc |
This object stores the actual (double typed) LDLT factorization of an Eigen::Matrix<var> along with pointers to its vari's which allow the *_ldlt functions to save memory. More... | |
class | LDLT_factor |
class | LDLT_factor< stan::math::var, R, C > |
A template specialization of src/stan/math/matrix/LDLT_factor.hpp for stan::math::var which can be used with all the *_ldlt functions. More... | |
class | LDLT_factor< T, R, C > |
LDLT_factor is a thin wrapper on Eigen::LDLT to allow for reusing factorizations and efficient autodiff of things like log determinants and solutions to linear systems. More... | |
struct | lgamma_fun |
Structure to wrap lgamma() so that it can be vectorized. More... | |
struct | log10_fun |
Structure to wrap log10() so it can be vectorized. More... | |
struct | log1m_exp_fun |
Structure to wrap log1m_exp() so it can be vectorized. More... | |
struct | log1m_fun |
Structure to wrap log1m() so it can be vectorized. More... | |
struct | log1p_exp_fun |
Structure to wrap log1m_exp() so that it can be vectorized. More... | |
struct | log_fun |
Structure to wrap log() so that it can be vectorized. More... | |
class | ode_system |
Internal representation of an ODE model object which provides convenient Jacobian functions to obtain gradients wrt to states and parameters. More... | |
class | op_ddv_vari |
class | op_dv_vari |
class | op_dvd_vari |
class | op_dvv_vari |
class | op_matrix_vari |
class | op_v_vari |
class | op_vd_vari |
class | op_vdd_vari |
class | op_vdv_vari |
class | op_vector_vari |
class | op_vv_vari |
class | op_vvd_vari |
class | op_vvv_vari |
struct | OperandsAndPartials |
This class builds partial derivatives with respect to a set of operands. More... | |
struct | OperandsAndPartials< T1, T2, T3, T4, T5, T6, typename stan::math::fvar< T_partials_return > > |
This class builds partial derivatives with respect to a set of operands. More... | |
struct | OperandsAndPartials< T1, T2, T3, T4, T5, T6, stan::math::var > |
This class builds partial derivatives with respect to a set of operands. More... | |
struct | pass_type |
struct | pass_type< double > |
struct | pass_type< int > |
struct | Phi_fun |
Structure to wrap Phi() so it can be vectorized. More... | |
class | precomp_v_vari |
class | precomp_vv_vari |
class | precomp_vvv_vari |
class | precomputed_gradients_vari |
A variable implementation taking a sequence of operands and partial derivatives with respect to the operands. More... | |
struct | promote_scalar_struct |
General struct to hold static function for promoting underlying scalar types. More... | |
struct | promote_scalar_struct< T, Eigen::Matrix< S, 1,-1 > > |
Struct to hold static function for promoting underlying scalar types. More... | |
struct | promote_scalar_struct< T, Eigen::Matrix< S,-1, 1 > > |
Struct to hold static function for promoting underlying scalar types. More... | |
struct | promote_scalar_struct< T, Eigen::Matrix< S,-1,-1 > > |
Struct to hold static function for promoting underlying scalar types. More... | |
struct | promote_scalar_struct< T, std::vector< S > > |
Struct to hold static function for promoting underlying scalar types. More... | |
struct | promote_scalar_struct< T, T > |
Struct to hold static function for promoting underlying scalar types. More... | |
struct | promote_scalar_type |
Template metaprogram to calculate a type for converting a convertible type. More... | |
struct | promote_scalar_type< T, Eigen::Matrix< S, 1, Eigen::Dynamic > > |
Template metaprogram to calculate a type for a row vector whose underlying scalar is converted from the second template parameter type to the first. More... | |
struct | promote_scalar_type< T, Eigen::Matrix< S, Eigen::Dynamic, Eigen::Dynamic > > |
Template metaprogram to calculate a type for a matrix whose underlying scalar is converted from the second template parameter type to the first. More... | |
struct | promote_scalar_type< T, Eigen::Matrix< S, Eigen::Dynamic, 1 > > |
Template metaprogram to calculate a type for a vector whose underlying scalar is converted from the second template parameter type to the first. More... | |
struct | promote_scalar_type< T, std::vector< S > > |
Template metaprogram to calculate a type for a container whose underlying scalar is converted from the second template parameter type to the first. More... | |
struct | promoter |
struct | promoter< Eigen::Matrix< F, R, C >, Eigen::Matrix< T, R, C > > |
struct | promoter< Eigen::Matrix< T, R, C >, Eigen::Matrix< T, R, C > > |
struct | promoter< std::vector< F >, std::vector< T > > |
struct | promoter< std::vector< T >, std::vector< T > > |
struct | promoter< T, T > |
struct | round_fun |
Structure to wrap round() so it can be vectorized. More... | |
class | scal_squared_distance_dv_vari |
class | scal_squared_distance_vd_vari |
class | scal_squared_distance_vv_vari |
class | seq_view |
class | seq_view< double, std::vector< int > > |
class | seq_view< T, Eigen::Matrix< S, 1, Eigen::Dynamic > > |
class | seq_view< T, Eigen::Matrix< S, Eigen::Dynamic, 1 > > |
class | seq_view< T, Eigen::Matrix< S, Eigen::Dynamic, Eigen::Dynamic > > |
class | seq_view< T, std::vector< S > > |
class | seq_view< T, std::vector< std::vector< T > > > |
class | seq_view< T, std::vector< T > > |
struct | sin_fun |
Structure to wrap sin() so it can be vectorized. More... | |
struct | sinh_fun |
Structure to wrap sinh() so that it can be vectorized. More... | |
struct | sqrt_fun |
Structure to wrap sqrt() so that it can be vectorized. More... | |
struct | square_fun |
Structure to wrap square() so that it can be vectorized. More... | |
class | stack_alloc |
An instance of this class provides a memory pool through which blocks of raw memory may be allocated and then collected simultaneously. More... | |
struct | store_type |
struct | store_type< double > |
struct | store_type< int > |
class | stored_gradient_vari |
A var implementation that stores the daughter variable implementation pointers and the partial derivative with respect to the result explicitly in arrays constructed on the auto-diff memory stack. More... | |
class | sum_eigen_v_vari |
Class for representing sums with constructors for Eigen. More... | |
class | sum_v_vari |
Class for sums of variables constructed with standard vectors. More... | |
struct | tan_fun |
Structure to wrap tan() so that it can be vectorized. More... | |
struct | tanh_fun |
Structure to wrap tanh() so that it can be vectorized. More... | |
struct | tgamma_fun |
Structure to wrap tgamma() so that it can be vectorized. More... | |
struct | value_type |
Primary template class for metaprogram to compute the type of values stored in a container. More... | |
struct | value_type< const T > |
Template class for metaprogram to compute the type of values stored in a constant container. More... | |
struct | value_type< Eigen::Matrix< T, R, C > > |
Template metaprogram defining the type of values stored in an Eigen matrix, vector, or row vector. More... | |
struct | value_type< std::vector< T > > |
Template metaprogram class to compute the type of values stored in a standard vector. More... | |
class | var |
Independent (input) and dependent (output) variables for gradients. More... | |
class | vari |
The variable implementation base class. More... | |
class | welford_covar_estimator |
class | welford_var_estimator |
Typedefs | |
typedef Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic >::Index | size_type |
Type for sizes and indexes in an Eigen matrix with double e. More... | |
typedef Eigen::Matrix< fvar< double >, Eigen::Dynamic, Eigen::Dynamic > | matrix_fd |
typedef Eigen::Matrix< fvar< fvar< double > >, Eigen::Dynamic, Eigen::Dynamic > | matrix_ffd |
typedef Eigen::Matrix< fvar< double >, Eigen::Dynamic, 1 > | vector_fd |
typedef Eigen::Matrix< fvar< fvar< double > >, Eigen::Dynamic, 1 > | vector_ffd |
typedef Eigen::Matrix< fvar< double >, 1, Eigen::Dynamic > | row_vector_fd |
typedef Eigen::Matrix< fvar< fvar< double > >, 1, Eigen::Dynamic > | row_vector_ffd |
typedef Eigen::Matrix< fvar< var >, Eigen::Dynamic, Eigen::Dynamic > | matrix_fv |
typedef Eigen::Matrix< fvar< fvar< var > >, Eigen::Dynamic, Eigen::Dynamic > | matrix_ffv |
typedef Eigen::Matrix< fvar< var >, Eigen::Dynamic, 1 > | vector_fv |
typedef Eigen::Matrix< fvar< fvar< var > >, Eigen::Dynamic, 1 > | vector_ffv |
typedef Eigen::Matrix< fvar< var >, 1, Eigen::Dynamic > | row_vector_fv |
typedef Eigen::Matrix< fvar< fvar< var > >, 1, Eigen::Dynamic > | row_vector_ffv |
typedef Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > | matrix_d |
Type for matrix of double values. More... | |
typedef Eigen::Matrix< double, Eigen::Dynamic, 1 > | vector_d |
Type for (column) vector of double values. More... | |
typedef Eigen::Matrix< double, 1, Eigen::Dynamic > | row_vector_d |
Type for (row) vector of double values. More... | |
typedef AutodiffStackStorage< vari, chainable_alloc > | ChainableStack |
typedef Eigen::Matrix< var, Eigen::Dynamic, Eigen::Dynamic > | matrix_v |
The type of a matrix holding stan::math::var values. More... | |
typedef Eigen::Matrix< var, Eigen::Dynamic, 1 > | vector_v |
The type of a (column) vector holding stan::math::var values. More... | |
typedef Eigen::Matrix< var, 1, Eigen::Dynamic > | row_vector_v |
The type of a row vector holding stan::math::var values. More... | |
Functions | |
template<typename T > | |
fvar< T > | log_sum_exp (const std::vector< fvar< T > > &v) |
template<typename T > | |
fvar< T > | sum (const std::vector< fvar< T > > &m) |
Return the sum of the entries of the specified standard vector. More... | |
template<typename T > | |
std::vector< fvar< T > > | to_fvar (const std::vector< T > &v) |
template<typename T > | |
std::vector< fvar< T > > | to_fvar (const std::vector< T > &v, const std::vector< T > &d) |
template<typename T > | |
std::vector< fvar< T > > | to_fvar (const std::vector< fvar< T > > &v) |
template<typename T > | |
fvar< T > | operator+ (const fvar< T > &x1, const fvar< T > &x2) |
template<typename T > | |
fvar< T > | operator+ (const double x1, const fvar< T > &x2) |
template<typename T > | |
fvar< T > | operator+ (const fvar< T > &x1, const double x2) |
template<typename T > | |
fvar< T > | operator/ (const fvar< T > &x1, const fvar< T > &x2) |
template<typename T > | |
fvar< T > | operator/ (const fvar< T > &x1, const double x2) |
template<typename T > | |
fvar< T > | operator/ (const double x1, const fvar< T > &x2) |
template<typename T > | |
bool | operator== (const fvar< T > &x, const fvar< T > &y) |
template<typename T > | |
bool | operator== (const fvar< T > &x, double y) |
template<typename T > | |
bool | operator== (double x, const fvar< T > &y) |
template<typename T > | |
bool | operator> (const fvar< T > &x, const fvar< T > &y) |
template<typename T > | |
bool | operator> (const fvar< T > &x, double y) |
template<typename T > | |
bool | operator> (double x, const fvar< T > &y) |
template<typename T > | |
bool | operator>= (const fvar< T > &x, const fvar< T > &y) |
template<typename T > | |
bool | operator>= (const fvar< T > &x, double y) |
template<typename T > | |
bool | operator>= (double x, const fvar< T > &y) |
template<typename T > | |
bool | operator< (const fvar< T > &x, double y) |
template<typename T > | |
bool | operator< (double x, const fvar< T > &y) |
template<typename T > | |
bool | operator< (const fvar< T > &x, const fvar< T > &y) |
template<typename T > | |
bool | operator<= (const fvar< T > &x, const fvar< T > &y) |
template<typename T > | |
bool | operator<= (const fvar< T > &x, double y) |
template<typename T > | |
bool | operator<= (double x, const fvar< T > &y) |
template<typename T > | |
fvar< T > | operator* (const fvar< T > &x1, const fvar< T > &x2) |
template<typename T > | |
fvar< T > | operator* (double x1, const fvar< T > &x2) |
template<typename T > | |
fvar< T > | operator* (const fvar< T > &x1, double x2) |
template<typename T > | |
bool | operator!= (const fvar< T > &x, const fvar< T > &y) |
template<typename T > | |
bool | operator!= (const fvar< T > &x, double y) |
template<typename T > | |
bool | operator!= (double x, const fvar< T > &y) |
template<typename T > | |
fvar< T > | operator- (const fvar< T > &x1, const fvar< T > &x2) |
template<typename T > | |
fvar< T > | operator- (const double x1, const fvar< T > &x2) |
template<typename T > | |
fvar< T > | operator- (const fvar< T > &x1, const double x2) |
template<typename T > | |
fvar< T > | operator- (const fvar< T > &x) |
template<typename T , int R1, int C1, int R2, int C2> | |
Eigen::Matrix< fvar< T >, 1, C1 > | columns_dot_product (const Eigen::Matrix< fvar< T >, R1, C1 > &v1, const Eigen::Matrix< fvar< T >, R2, C2 > &v2) |
template<typename T , int R1, int C1, int R2, int C2> | |
Eigen::Matrix< fvar< T >, 1, C1 > | columns_dot_product (const Eigen::Matrix< fvar< T >, R1, C1 > &v1, const Eigen::Matrix< double, R2, C2 > &v2) |
template<typename T , int R1, int C1, int R2, int C2> | |
Eigen::Matrix< fvar< T >, 1, C1 > | columns_dot_product (const Eigen::Matrix< double, R1, C1 > &v1, const Eigen::Matrix< fvar< T >, R2, C2 > &v2) |
template<typename T , int R, int C> | |
Eigen::Matrix< fvar< T >, 1, C > | columns_dot_self (const Eigen::Matrix< fvar< T >, R, C > &x) |
template<typename T , int R, int C> | |
Eigen::Matrix< fvar< T >, C, C > | crossprod (const Eigen::Matrix< fvar< T >, R, C > &m) |
template<typename T , int R, int C> | |
fvar< T > | determinant (const Eigen::Matrix< fvar< T >, R, C > &m) |
template<typename T , int R, int C> | |
Eigen::Matrix< fvar< T >, R, C > | divide (const Eigen::Matrix< fvar< T >, R, C > &v, const fvar< T > &c) |
template<typename T , int R, int C> | |
Eigen::Matrix< fvar< T >, R, C > | divide (const Eigen::Matrix< fvar< T >, R, C > &v, const double c) |
template<typename T , int R, int C> | |
Eigen::Matrix< fvar< T >, R, C > | divide (const Eigen::Matrix< double, R, C > &v, const fvar< T > &c) |
template<typename T , int R, int C> | |
Eigen::Matrix< fvar< T >, R, C > | operator/ (const Eigen::Matrix< fvar< T >, R, C > &v, const fvar< T > &c) |
template<typename T , int R, int C> | |
Eigen::Matrix< fvar< T >, R, C > | operator/ (const Eigen::Matrix< fvar< T >, R, C > &v, const double c) |
template<typename T , int R, int C> | |
Eigen::Matrix< fvar< T >, R, C > | operator/ (const Eigen::Matrix< double, R, C > &v, const fvar< T > &c) |
template<typename T , int R1, int C1, int R2, int C2> | |
fvar< T > | dot_product (const Eigen::Matrix< fvar< T >, R1, C1 > &v1, const Eigen::Matrix< fvar< T >, R2, C2 > &v2) |
template<typename T , int R1, int C1, int R2, int C2> | |
fvar< T > | dot_product (const Eigen::Matrix< fvar< T >, R1, C1 > &v1, const Eigen::Matrix< double, R2, C2 > &v2) |
template<typename T , int R1, int C1, int R2, int C2> | |
fvar< T > | dot_product (const Eigen::Matrix< double, R1, C1 > &v1, const Eigen::Matrix< fvar< T >, R2, C2 > &v2) |
template<typename T , int R1, int C1, int R2, int C2> | |
fvar< T > | dot_product (const Eigen::Matrix< fvar< T >, R1, C1 > &v1, const Eigen::Matrix< fvar< T >, R2, C2 > &v2, size_type &length) |
template<typename T , int R1, int C1, int R2, int C2> | |
fvar< T > | dot_product (const Eigen::Matrix< fvar< T >, R1, C1 > &v1, const Eigen::Matrix< double, R2, C2 > &v2, size_type &length) |
template<typename T , int R1, int C1, int R2, int C2> | |
fvar< T > | dot_product (const Eigen::Matrix< double, R1, C1 > &v1, const Eigen::Matrix< fvar< T >, R2, C2 > &v2, size_type &length) |
template<typename T > | |
fvar< T > | dot_product (const std::vector< fvar< T > > &v1, const std::vector< fvar< T > > &v2) |
template<typename T > | |
fvar< T > | dot_product (const std::vector< double > &v1, const std::vector< fvar< T > > &v2) |
template<typename T > | |
fvar< T > | dot_product (const std::vector< fvar< T > > &v1, const std::vector< double > &v2) |
template<typename T > | |
fvar< T > | dot_product (const std::vector< fvar< T > > &v1, const std::vector< fvar< T > > &v2, size_type &length) |
template<typename T > | |
fvar< T > | dot_product (const std::vector< double > &v1, const std::vector< fvar< T > > &v2, size_type &length) |
template<typename T > | |
fvar< T > | dot_product (const std::vector< fvar< T > > &v1, const std::vector< double > &v2, size_type &length) |
template<typename T , int R, int C> | |
fvar< T > | dot_self (const Eigen::Matrix< fvar< T >, R, C > &v) |
template<typename T , int R, int C> | |
Eigen::Matrix< fvar< T >, R, C > | inverse (const Eigen::Matrix< fvar< T >, R, C > &m) |
template<typename T , int R, int C> | |
fvar< T > | log_determinant (const Eigen::Matrix< fvar< T >, R, C > &m) |
template<typename T > | |
Eigen::Matrix< fvar< T >, Eigen::Dynamic, 1 > | log_softmax (const Eigen::Matrix< fvar< T >, Eigen::Dynamic, 1 > &alpha) |
template<typename T , int R, int C> | |
fvar< T > | log_sum_exp (const Eigen::Matrix< fvar< T >, R, C > &v) |
template<typename T , int R1, int C1, int R2, int C2> | |
Eigen::Matrix< fvar< T >, R1, C2 > | mdivide_left (const Eigen::Matrix< fvar< T >, R1, C1 > &A, const Eigen::Matrix< fvar< T >, R2, C2 > &b) |
template<typename T , int R1, int C1, int R2, int C2> | |
Eigen::Matrix< fvar< T >, R1, C2 > | mdivide_left (const Eigen::Matrix< double, R1, C1 > &A, const Eigen::Matrix< fvar< T >, R2, C2 > &b) |
template<typename T , int R1, int C1, int R2, int C2> | |
Eigen::Matrix< fvar< T >, R1, C2 > | mdivide_left (const Eigen::Matrix< fvar< T >, R1, C1 > &A, const Eigen::Matrix< double, R2, C2 > &b) |
template<int R1, int C1, int R2, int C2, typename T2 > | |
Eigen::Matrix< fvar< T2 >, R1, C2 > | mdivide_left_ldlt (const stan::math::LDLT_factor< double, R1, C1 > &A, const Eigen::Matrix< fvar< T2 >, R2, C2 > &b) |
Returns the solution of the system Ax=b given an LDLT_factor of A. More... | |
template<typename T , int R1, int C1, int R2, int C2> | |
Eigen::Matrix< fvar< T >, R1, C1 > | mdivide_left_tri_low (const Eigen::Matrix< fvar< T >, R1, C1 > &A, const Eigen::Matrix< fvar< T >, R2, C2 > &b) |
template<typename T , int R1, int C1, int R2, int C2> | |
Eigen::Matrix< fvar< T >, R1, C1 > | mdivide_left_tri_low (const Eigen::Matrix< double, R1, C1 > &A, const Eigen::Matrix< fvar< T >, R2, C2 > &b) |
template<typename T , int R1, int C1, int R2, int C2> | |
Eigen::Matrix< fvar< T >, R1, C1 > | mdivide_left_tri_low (const Eigen::Matrix< fvar< T >, R1, C1 > &A, const Eigen::Matrix< double, R2, C2 > &b) |
template<typename T , int R1, int C1, int R2, int C2> | |
Eigen::Matrix< fvar< T >, R1, C2 > | mdivide_right (const Eigen::Matrix< fvar< T >, R1, C1 > &A, const Eigen::Matrix< fvar< T >, R2, C2 > &b) |
template<typename T , int R1, int C1, int R2, int C2> | |
Eigen::Matrix< fvar< T >, R1, C2 > | mdivide_right (const Eigen::Matrix< fvar< T >, R1, C1 > &A, const Eigen::Matrix< double, R2, C2 > &b) |
template<typename T , int R1, int C1, int R2, int C2> | |
Eigen::Matrix< fvar< T >, R1, C2 > | mdivide_right (const Eigen::Matrix< double, R1, C1 > &A, const Eigen::Matrix< fvar< T >, R2, C2 > &b) |
template<typename T , int R1, int C1, int R2, int C2> | |
Eigen::Matrix< fvar< T >, R1, C1 > | mdivide_right_tri_low (const Eigen::Matrix< fvar< T >, R1, C1 > &A, const Eigen::Matrix< fvar< T >, R2, C2 > &b) |
template<typename T , int R1, int C1, int R2, int C2> | |
Eigen::Matrix< fvar< T >, R1, C2 > | mdivide_right_tri_low (const Eigen::Matrix< fvar< T >, R1, C1 > &A, const Eigen::Matrix< double, R2, C2 > &b) |
template<typename T , int R1, int C1, int R2, int C2> | |
Eigen::Matrix< fvar< T >, R1, C2 > | mdivide_right_tri_low (const Eigen::Matrix< double, R1, C1 > &A, const Eigen::Matrix< fvar< T >, R2, C2 > &b) |
template<typename T , int R1, int C1> | |
Eigen::Matrix< fvar< T >, R1, C1 > | multiply (const Eigen::Matrix< fvar< T >, R1, C1 > &m, const fvar< T > &c) |
template<typename T , int R2, int C2> | |
Eigen::Matrix< fvar< T >, R2, C2 > | multiply (const Eigen::Matrix< fvar< T >, R2, C2 > &m, const double c) |
template<typename T , int R1, int C1> | |
Eigen::Matrix< fvar< T >, R1, C1 > | multiply (const Eigen::Matrix< double, R1, C1 > &m, const fvar< T > &c) |
template<typename T , int R1, int C1> | |
Eigen::Matrix< fvar< T >, R1, C1 > | multiply (const fvar< T > &c, const Eigen::Matrix< fvar< T >, R1, C1 > &m) |
template<typename T , int R1, int C1> | |
Eigen::Matrix< fvar< T >, R1, C1 > | multiply (const double c, const Eigen::Matrix< fvar< T >, R1, C1 > &m) |
template<typename T , int R1, int C1> | |
Eigen::Matrix< fvar< T >, R1, C1 > | multiply (const fvar< T > &c, const Eigen::Matrix< double, R1, C1 > &m) |
template<typename T , int R1, int C1, int R2, int C2> | |
Eigen::Matrix< fvar< T >, R1, C2 > | multiply (const Eigen::Matrix< fvar< T >, R1, C1 > &m1, const Eigen::Matrix< fvar< T >, R2, C2 > &m2) |
template<typename T , int R1, int C1, int R2, int C2> | |
Eigen::Matrix< fvar< T >, R1, C2 > | multiply (const Eigen::Matrix< fvar< T >, R1, C1 > &m1, const Eigen::Matrix< double, R2, C2 > &m2) |
template<typename T , int R1, int C1, int R2, int C2> | |
Eigen::Matrix< fvar< T >, R1, C2 > | multiply (const Eigen::Matrix< double, R1, C1 > &m1, const Eigen::Matrix< fvar< T >, R2, C2 > &m2) |
template<typename T , int C1, int R2> | |
fvar< T > | multiply (const Eigen::Matrix< fvar< T >, 1, C1 > &rv, const Eigen::Matrix< fvar< T >, R2, 1 > &v) |
template<typename T , int C1, int R2> | |
fvar< T > | multiply (const Eigen::Matrix< fvar< T >, 1, C1 > &rv, const Eigen::Matrix< double, R2, 1 > &v) |
template<typename T , int C1, int R2> | |
fvar< T > | multiply (const Eigen::Matrix< double, 1, C1 > &rv, const Eigen::Matrix< fvar< T >, R2, 1 > &v) |
template<typename T , int R, int C> | |
Eigen::Matrix< fvar< T >, R, R > | multiply_lower_tri_self_transpose (const Eigen::Matrix< fvar< T >, R, C > &m) |
template<typename T > | |
Eigen::Matrix< fvar< T >, Eigen::Dynamic, Eigen::Dynamic > | qr_Q (const Eigen::Matrix< fvar< T >, Eigen::Dynamic, Eigen::Dynamic > &m) |
template<typename T > | |
Eigen::Matrix< fvar< T >, Eigen::Dynamic, Eigen::Dynamic > | qr_R (const Eigen::Matrix< fvar< T >, Eigen::Dynamic, Eigen::Dynamic > &m) |
template<int RA, int CA, int RB, int CB, typename T > | |
Eigen::Matrix< fvar< T >, CB, CB > | quad_form_sym (const Eigen::Matrix< fvar< T >, RA, CA > &A, const Eigen::Matrix< double, RB, CB > &B) |
template<int RA, int CA, int RB, typename T > | |
fvar< T > | quad_form_sym (const Eigen::Matrix< fvar< T >, RA, CA > &A, const Eigen::Matrix< double, RB, 1 > &B) |
template<int RA, int CA, int RB, int CB, typename T > | |
Eigen::Matrix< fvar< T >, CB, CB > | quad_form_sym (const Eigen::Matrix< double, RA, CA > &A, const Eigen::Matrix< fvar< T >, RB, CB > &B) |
template<int RA, int CA, int RB, typename T > | |
fvar< T > | quad_form_sym (const Eigen::Matrix< double, RA, CA > &A, const Eigen::Matrix< fvar< T >, RB, 1 > &B) |
template<typename T , int R1, int C1, int R2, int C2> | |
Eigen::Matrix< fvar< T >, R1, 1 > | rows_dot_product (const Eigen::Matrix< fvar< T >, R1, C1 > &v1, const Eigen::Matrix< fvar< T >, R2, C2 > &v2) |
template<typename T , int R1, int C1, int R2, int C2> | |
Eigen::Matrix< fvar< T >, R1, 1 > | rows_dot_product (const Eigen::Matrix< double, R1, C1 > &v1, const Eigen::Matrix< fvar< T >, R2, C2 > &v2) |
template<typename T , int R1, int C1, int R2, int C2> | |
Eigen::Matrix< fvar< T >, R1, 1 > | rows_dot_product (const Eigen::Matrix< fvar< T >, R1, C1 > &v1, const Eigen::Matrix< double, R2, C2 > &v2) |
template<typename T , int R, int C> | |
Eigen::Matrix< fvar< T >, R, 1 > | rows_dot_self (const Eigen::Matrix< fvar< T >, R, C > &x) |
template<typename T > | |
Eigen::Matrix< fvar< T >, Eigen::Dynamic, 1 > | softmax (const Eigen::Matrix< fvar< T >, Eigen::Dynamic, 1 > &alpha) |
template<typename T > | |
std::vector< fvar< T > > | sort_asc (std::vector< fvar< T > > xs) |
template<typename T , int R, int C> | |
Eigen::Matrix< fvar< T >, R, C > | sort_asc (Eigen::Matrix< fvar< T >, R, C > xs) |
template<typename T > | |
std::vector< fvar< T > > | sort_desc (std::vector< fvar< T > > xs) |
template<typename T , int R, int C> | |
Eigen::Matrix< fvar< T >, R, C > | sort_desc (Eigen::Matrix< fvar< T >, R, C > xs) |
template<typename T , int R, int C> | |
stan::math::fvar< T > | squared_distance (const Eigen::Matrix< stan::math::fvar< T >, R, C > &v1, const Eigen::Matrix< double, R, C > &v2) |
Returns the squared distance between the specified vectors of the same dimensions. More... | |
template<typename T , int R1, int C1, int R2, int C2> | |
stan::math::fvar< T > | squared_distance (const Eigen::Matrix< stan::math::fvar< T >, R1, C1 > &v1, const Eigen::Matrix< double, R2, C2 > &v2) |
Returns the squared distance between the specified vectors of the same dimensions. More... | |
template<typename T , int R, int C> | |
stan::math::fvar< T > | squared_distance (const Eigen::Matrix< double, R, C > &v1, const Eigen::Matrix< stan::math::fvar< T >, R, C > &v2) |
Returns the squared distance between the specified vectors of the same dimensions. More... | |
template<typename T , int R1, int C1, int R2, int C2> | |
stan::math::fvar< T > | squared_distance (const Eigen::Matrix< double, R1, C1 > &v1, const Eigen::Matrix< stan::math::fvar< T >, R2, C2 > &v2) |
Returns the squared distance between the specified vectors of the same dimensions. More... | |
template<typename T , int R, int C> | |
stan::math::fvar< T > | squared_distance (const Eigen::Matrix< stan::math::fvar< T >, R, C > &v1, const Eigen::Matrix< stan::math::fvar< T >, R, C > &v2) |
Returns the squared distance between the specified vectors of the same dimensions. More... | |
template<typename T , int R1, int C1, int R2, int C2> | |
stan::math::fvar< T > | squared_distance (const Eigen::Matrix< stan::math::fvar< T >, R1, C1 > &v1, const Eigen::Matrix< stan::math::fvar< T >, R2, C2 > &v2) |
Returns the squared distance between the specified vectors of the same dimensions. More... | |
template<typename T , int R, int C> | |
fvar< T > | sum (const Eigen::Matrix< fvar< T >, R, C > &m) |
Return the sum of the entries of the specified matrix. More... | |
template<typename T , int R, int C> | |
Eigen::Matrix< fvar< T >, R, R > | tcrossprod (const Eigen::Matrix< fvar< T >, R, C > &m) |
template<int R, int C, typename T > | |
Eigen::Matrix< T, R, C > | to_fvar (const Eigen::Matrix< T, R, C > &m) |
template<int R, int C> | |
Eigen::Matrix< fvar< double >, R, C > | to_fvar (const Eigen::Matrix< double, R, C > &m) |
template<typename T , int R, int C> | |
Eigen::Matrix< fvar< T >, R, C > | to_fvar (const Eigen::Matrix< T, R, C > &val, const Eigen::Matrix< T, R, C > &deriv) |
template<int RD, int CD, int RA, int CA, int RB, int CB, typename T > | |
fvar< T > | trace_gen_quad_form (const Eigen::Matrix< fvar< T >, RD, CD > &D, const Eigen::Matrix< fvar< T >, RA, CA > &A, const Eigen::Matrix< fvar< T >, RB, CB > &B) |
template<int RA, int CA, int RB, int CB, typename T > | |
fvar< T > | trace_quad_form (const Eigen::Matrix< fvar< T >, RA, CA > &A, const Eigen::Matrix< fvar< T >, RB, CB > &B) |
template<int RA, int CA, int RB, int CB, typename T > | |
fvar< T > | trace_quad_form (const Eigen::Matrix< fvar< T >, RA, CA > &A, const Eigen::Matrix< double, RB, CB > &B) |
template<int RA, int CA, int RB, int CB, typename T > | |
fvar< T > | trace_quad_form (const Eigen::Matrix< double, RA, CA > &A, const Eigen::Matrix< fvar< T >, RB, CB > &B) |
template<typename T , int R, int C> | |
Eigen::Matrix< fvar< T >, R, C > | unit_vector_constrain (const Eigen::Matrix< fvar< T >, R, C > &y) |
template<typename T , int R, int C> | |
Eigen::Matrix< fvar< T >, R, C > | unit_vector_constrain (const Eigen::Matrix< fvar< T >, R, C > &y, fvar< T > &lp) |
template<typename T , typename F > | |
void | gradient (const F &f, const Eigen::Matrix< T, Eigen::Dynamic, 1 > &x, T &fx, Eigen::Matrix< T, Eigen::Dynamic, 1 > &grad_fx) |
Calculate the value and the gradient of the specified function at the specified argument. More... | |
template<typename T , typename F > | |
void | jacobian (const F &f, const Eigen::Matrix< T, Eigen::Dynamic, 1 > &x, Eigen::Matrix< T, Eigen::Dynamic, 1 > &fx, Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &J) |
template<typename T > | |
fvar< T > | abs (const fvar< T > &x) |
template<typename T > | |
fvar< T > | acos (const fvar< T > &x) |
template<typename T > | |
fvar< T > | acosh (const fvar< T > &x) |
template<typename T > | |
fvar< T > | asin (const fvar< T > &x) |
template<typename T > | |
fvar< T > | asinh (const fvar< T > &x) |
template<typename T > | |
fvar< T > | atan (const fvar< T > &x) |
template<typename T > | |
fvar< T > | atan2 (const fvar< T > &x1, const fvar< T > &x2) |
template<typename T > | |
fvar< T > | atan2 (const double x1, const fvar< T > &x2) |
template<typename T > | |
fvar< T > | atan2 (const fvar< T > &x1, const double x2) |
template<typename T > | |
fvar< T > | atanh (const fvar< T > &x) |
template<typename T > | |
fvar< T > | bessel_first_kind (int v, const fvar< T > &z) |
template<typename T > | |
fvar< T > | bessel_second_kind (int v, const fvar< T > &z) |
template<typename T > | |
fvar< T > | binary_log_loss (const int y, const fvar< T > &y_hat) |
template<typename T > | |
fvar< T > | binomial_coefficient_log (const fvar< T > &x1, const fvar< T > &x2) |
template<typename T > | |
fvar< T > | binomial_coefficient_log (const fvar< T > &x1, const double x2) |
template<typename T > | |
fvar< T > | binomial_coefficient_log (const double x1, const fvar< T > &x2) |
template<typename T > | |
fvar< T > | cbrt (const fvar< T > &x) |
template<typename T > | |
fvar< T > | ceil (const fvar< T > &x) |
template<typename T > | |
fvar< T > | cos (const fvar< T > &x) |
template<typename T > | |
fvar< T > | cosh (const fvar< T > &x) |
template<typename T > | |
fvar< T > | digamma (const fvar< T > &x) |
template<typename T > | |
fvar< T > | erf (const fvar< T > &x) |
template<typename T > | |
fvar< T > | erfc (const fvar< T > &x) |
template<typename T > | |
fvar< T > | exp (const fvar< T > &x) |
template<typename T > | |
fvar< T > | exp2 (const fvar< T > &x) |
template<typename T > | |
fvar< T > | expm1 (const fvar< T > &x) |
template<typename T > | |
fvar< T > | fabs (const fvar< T > &x) |
template<typename T > | |
fvar< T > | falling_factorial (const fvar< T > &x, const fvar< T > &n) |
template<typename T > | |
fvar< T > | falling_factorial (const fvar< T > &x, const double n) |
template<typename T > | |
fvar< T > | falling_factorial (const double x, const fvar< T > &n) |
template<typename T > | |
fvar< T > | fdim (const fvar< T > &x1, const fvar< T > &x2) |
template<typename T > | |
fvar< T > | fdim (const fvar< T > &x1, const double x2) |
template<typename T > | |
fvar< T > | fdim (const double x1, const fvar< T > &x2) |
template<typename T > | |
fvar< T > | floor (const fvar< T > &x) |
template<typename T1 , typename T2 , typename T3 > | |
fvar< typename stan::return_type< T1, T2, T3 >::type > | fma (const fvar< T1 > &x1, const fvar< T2 > &x2, const fvar< T3 > &x3) |
The fused multiply-add operation (C99). More... | |
template<typename T1 , typename T2 , typename T3 > | |
fvar< typename stan::return_type< T1, T2, T3 >::type > | fma (const T1 &x1, const fvar< T2 > &x2, const fvar< T3 > &x3) |
See all-var input signature for details on the function and derivatives. More... | |
template<typename T1 , typename T2 , typename T3 > | |
fvar< typename stan::return_type< T1, T2, T3 >::type > | fma (const fvar< T1 > &x1, const T2 &x2, const fvar< T3 > &x3) |
See all-var input signature for details on the function and derivatives. More... | |
template<typename T1 , typename T2 , typename T3 > | |
fvar< typename stan::return_type< T1, T2, T3 >::type > | fma (const fvar< T1 > &x1, const fvar< T2 > &x2, const T3 &x3) |
See all-var input signature for details on the function and derivatives. More... | |
template<typename T1 , typename T2 , typename T3 > | |
fvar< typename stan::return_type< T1, T2, T3 >::type > | fma (const T1 &x1, const T2 &x2, const fvar< T3 > &x3) |
See all-var input signature for details on the function and derivatives. More... | |
template<typename T1 , typename T2 , typename T3 > | |
fvar< typename stan::return_type< T1, T2, T3 >::type > | fma (const fvar< T1 > &x1, const T2 &x2, const T3 &x3) |
See all-var input signature for details on the function and derivatives. More... | |
template<typename T1 , typename T2 , typename T3 > | |
fvar< typename stan::return_type< T1, T2, T3 >::type > | fma (const T1 &x1, const fvar< T2 > &x2, const T3 &x3) |
See all-var input signature for details on the function and derivatives. More... | |
template<typename T > | |
fvar< T > | fmax (const fvar< T > &x1, const fvar< T > &x2) |
template<typename T > | |
fvar< T > | fmax (const double x1, const fvar< T > &x2) |
template<typename T > | |
fvar< T > | fmax (const fvar< T > &x1, const double x2) |
template<typename T > | |
fvar< T > | fmin (const fvar< T > &x1, const fvar< T > &x2) |
template<typename T > | |
fvar< T > | fmin (const double x1, const fvar< T > &x2) |
template<typename T > | |
fvar< T > | fmin (const fvar< T > &x1, const double x2) |
template<typename T > | |
fvar< T > | fmod (const fvar< T > &x1, const fvar< T > &x2) |
template<typename T > | |
fvar< T > | fmod (const fvar< T > &x1, const double x2) |
template<typename T > | |
fvar< T > | fmod (const double x1, const fvar< T > &x2) |
template<typename T > | |
fvar< T > | gamma_p (const fvar< T > &x1, const fvar< T > &x2) |
template<typename T > | |
fvar< T > | gamma_p (const fvar< T > &x1, const double x2) |
template<typename T > | |
fvar< T > | gamma_p (const double x1, const fvar< T > &x2) |
template<typename T > | |
fvar< T > | gamma_q (const fvar< T > &x1, const fvar< T > &x2) |
template<typename T > | |
fvar< T > | gamma_q (const fvar< T > &x1, const double x2) |
template<typename T > | |
fvar< T > | gamma_q (const double x1, const fvar< T > &x2) |
template<typename T > | |
void | grad_inc_beta (stan::math::fvar< T > &g1, stan::math::fvar< T > &g2, stan::math::fvar< T > a, stan::math::fvar< T > b, stan::math::fvar< T > z) |
template<typename T > | |
fvar< T > | hypot (const fvar< T > &x1, const fvar< T > &x2) |
template<typename T > | |
fvar< T > | hypot (const fvar< T > &x1, const double x2) |
template<typename T > | |
fvar< T > | hypot (const double x1, const fvar< T > &x2) |
template<typename T > | |
fvar< T > | inc_beta (const fvar< T > &a, const fvar< T > &b, const fvar< T > &x) |
template<typename T > | |
fvar< T > | inv (const fvar< T > &x) |
template<typename T > | |
fvar< T > | inv_cloglog (const fvar< T > &x) |
template<typename T > | |
fvar< T > | inv_logit (const fvar< T > &x) |
template<typename T > | |
fvar< T > | inv_Phi (const fvar< T > &p) |
template<typename T > | |
fvar< T > | inv_sqrt (const fvar< T > &x) |
template<typename T > | |
fvar< T > | inv_square (const fvar< T > &x) |
template<typename T > | |
int | is_inf (const fvar< T > &x) |
Returns 1 if the input's value is infinite and 0 otherwise. More... | |
template<typename T > | |
int | is_nan (const fvar< T > &x) |
Returns 1 if the input's value is NaN and 0 otherwise. More... | |
template<typename T > | |
fvar< T > | lbeta (const fvar< T > &x1, const fvar< T > &x2) |
template<typename T > | |
fvar< T > | lbeta (const double x1, const fvar< T > &x2) |
template<typename T > | |
fvar< T > | lbeta (const fvar< T > &x1, const double x2) |
template<typename T > | |
fvar< T > | lgamma (const fvar< T > &x) |
template<typename T > | |
fvar< typename stan::return_type< T, int >::type > | lmgamma (int x1, const fvar< T > &x2) |
template<typename T > | |
fvar< T > | log (const fvar< T > &x) |
template<typename T > | |
fvar< T > | log10 (const fvar< T > &x) |
template<typename T > | |
fvar< T > | log1m (const fvar< T > &x) |
template<typename T > | |
fvar< T > | log1m_exp (const fvar< T > &x) |
template<typename T > | |
fvar< T > | log1m_inv_logit (const fvar< T > &x) |
template<typename T > | |
fvar< T > | log1p (const fvar< T > &x) |
template<typename T > | |
fvar< T > | log1p_exp (const fvar< T > &x) |
template<typename T > | |
fvar< T > | log2 (const fvar< T > &x) |
template<typename T > | |
fvar< T > | log_diff_exp (const fvar< T > &x1, const fvar< T > &x2) |
template<typename T1 , typename T2 > | |
fvar< T2 > | log_diff_exp (const T1 &x1, const fvar< T2 > &x2) |
template<typename T1 , typename T2 > | |
fvar< T1 > | log_diff_exp (const fvar< T1 > &x1, const T2 &x2) |
template<typename T > | |
fvar< T > | log_falling_factorial (const fvar< T > &x, const fvar< T > &n) |
template<typename T > | |
fvar< T > | log_falling_factorial (const double x, const fvar< T > &n) |
template<typename T > | |
fvar< T > | log_falling_factorial (const fvar< T > &x, const double n) |
template<typename T > | |
fvar< T > | log_inv_logit (const fvar< T > &x) |
template<typename T_theta , typename T_lambda1 , typename T_lambda2 , int N> | |
void | log_mix_partial_helper (const T_theta &theta, const T_lambda1 &lambda1, const T_lambda2 &lambda2, typename boost::math::tools::promote_args< T_theta, T_lambda1, T_lambda2 >::type(&partials_array)[N]) |
template<typename T > | |
fvar< T > | log_mix (const fvar< T > &theta, const fvar< T > &lambda1, const fvar< T > &lambda2) |
Return the log mixture density with specified mixing proportion and log densities and its derivative at each. More... | |
template<typename T > | |
fvar< T > | log_mix (const fvar< T > &theta, const fvar< T > &lambda1, const double lambda2) |
template<typename T > | |
fvar< T > | log_mix (const fvar< T > &theta, const double lambda1, const fvar< T > &lambda2) |
template<typename T > | |
fvar< T > | log_mix (const double theta, const fvar< T > &lambda1, const fvar< T > &lambda2) |
template<typename T > | |
fvar< T > | log_mix (const fvar< T > &theta, const double lambda1, const double lambda2) |
template<typename T > | |
fvar< T > | log_mix (const double theta, const fvar< T > &lambda1, const double lambda2) |
template<typename T > | |
fvar< T > | log_mix (const double theta, const double lambda1, const fvar< T > &lambda2) |
template<typename T > | |
fvar< T > | log_rising_factorial (const fvar< T > &x, const fvar< T > &n) |
template<typename T > | |
fvar< T > | log_rising_factorial (const fvar< T > &x, const double n) |
template<typename T > | |
fvar< T > | log_rising_factorial (const double x, const fvar< T > &n) |
template<typename T > | |
fvar< T > | log_sum_exp (const fvar< T > &x1, const fvar< T > &x2) |
template<typename T > | |
fvar< T > | log_sum_exp (const double x1, const fvar< T > &x2) |
template<typename T > | |
fvar< T > | log_sum_exp (const fvar< T > &x1, const double x2) |
template<typename T > | |
fvar< T > | logit (const fvar< T > &x) |
template<typename T > | |
fvar< T > | modified_bessel_first_kind (int v, const fvar< T > &z) |
template<typename T > | |
fvar< T > | modified_bessel_second_kind (int v, const fvar< T > &z) |
template<typename T > | |
fvar< T > | multiply_log (const fvar< T > &x1, const fvar< T > &x2) |
template<typename T > | |
fvar< T > | multiply_log (const double x1, const fvar< T > &x2) |
template<typename T > | |
fvar< T > | multiply_log (const fvar< T > &x1, const double x2) |
template<typename T > | |
fvar< T > | owens_t (const fvar< T > &x1, const fvar< T > &x2) |
template<typename T > | |
fvar< T > | owens_t (const double x1, const fvar< T > &x2) |
template<typename T > | |
fvar< T > | owens_t (const fvar< T > &x1, const double x2) |
template<typename T > | |
fvar< T > | Phi (const fvar< T > &x) |
template<typename T > | |
fvar< T > | pow (const fvar< T > &x1, const fvar< T > &x2) |
template<typename T > | |
fvar< T > | pow (const double x1, const fvar< T > &x2) |
template<typename T > | |
fvar< T > | pow (const fvar< T > &x1, const double x2) |
template<typename T > | |
double | primitive_value (const fvar< T > &v) |
Return the primitive value of the specified forward-mode autodiff variable. More... | |
template<typename T > | |
fvar< T > | rising_factorial (const fvar< T > &x, const fvar< T > &n) |
template<typename T > | |
fvar< T > | rising_factorial (const fvar< T > &x, const double n) |
template<typename T > | |
fvar< T > | rising_factorial (const double x, const fvar< T > &n) |
template<typename T > | |
fvar< T > | round (const fvar< T > &x) |
template<typename T > | |
fvar< T > | sin (const fvar< T > &x) |
template<typename T > | |
fvar< T > | sinh (const fvar< T > &x) |
template<typename T > | |
fvar< T > | sqrt (const fvar< T > &x) |
template<typename T > | |
fvar< T > | square (const fvar< T > &x) |
template<typename T > | |
fvar< T > | tan (const fvar< T > &x) |
template<typename T > | |
fvar< T > | tanh (const fvar< T > &x) |
template<typename T > | |
fvar< T > | tgamma (const fvar< T > &x) |
template<typename T > | |
fvar< T > | to_fvar (const T &x) |
template<typename T > | |
fvar< T > | to_fvar (const fvar< T > &x) |
template<typename T > | |
fvar< T > | trunc (const fvar< T > &x) |
template<typename T > | |
T | value_of (const fvar< T > &v) |
Return the value of the specified variable. More... | |
template<typename T > | |
double | value_of_rec (const fvar< T > &v) |
Return the value of the specified variable. More... | |
template<typename T > | |
bool | is_aligned (T *ptr, unsigned int bytes_aligned) |
Return true if the specified pointer is aligned on the number of bytes. More... | |
template<typename T , typename F > | |
void | derivative (const F &f, const T &x, T &fx, T &dfx_dx) |
Return the derivative of the specified univariate function at the specified argument. More... | |
template<typename F > | |
void | finite_diff_grad_hessian (const F &f, const Eigen::Matrix< double,-1, 1 > &x, double &fx, Eigen::Matrix< double,-1,-1 > &hess, std::vector< Eigen::Matrix< double,-1,-1 > > &grad_hess_fx, const double epsilon=1e-04) |
Calculate the value and the gradient of the hessian of the specified function at the specified argument using second-order autodiff and first-order finite difference. More... | |
template<typename F > | |
void | grad_hessian (const F &f, const Eigen::Matrix< double, Eigen::Dynamic, 1 > &x, double &fx, Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > &H, std::vector< Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > > &grad_H) |
Calculate the value, the Hessian, and the gradient of the Hessian of the specified function at the specified argument. More... | |
template<typename F > | |
void | grad_tr_mat_times_hessian (const F &f, const Eigen::Matrix< double, Eigen::Dynamic, 1 > &x, const Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > &M, Eigen::Matrix< double, Eigen::Dynamic, 1 > &grad_tr_MH) |
template<typename T1 , typename T2 , typename F > | |
void | gradient_dot_vector (const F &f, const Eigen::Matrix< T1, Eigen::Dynamic, 1 > &x, const Eigen::Matrix< T2, Eigen::Dynamic, 1 > &v, T1 &fx, T1 &grad_fx_dot_v) |
template<typename F > | |
void | hessian (const F &f, const Eigen::Matrix< double, Eigen::Dynamic, 1 > &x, double &fx, Eigen::Matrix< double, Eigen::Dynamic, 1 > &grad, Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > &H) |
Calculate the value, the gradient, and the Hessian, of the specified function at the specified argument in O(N^2) time and O(N^2) space. More... | |
template<typename T , typename F > | |
void | hessian (const F &f, const Eigen::Matrix< T, Eigen::Dynamic, 1 > &x, T &fx, Eigen::Matrix< T, Eigen::Dynamic, 1 > &grad, Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &H) |
template<typename F > | |
void | hessian_times_vector (const F &f, const Eigen::Matrix< double, Eigen::Dynamic, 1 > &x, const Eigen::Matrix< double, Eigen::Dynamic, 1 > &v, double &fx, Eigen::Matrix< double, Eigen::Dynamic, 1 > &Hv) |
template<typename T , typename F > | |
void | hessian_times_vector (const F &f, const Eigen::Matrix< T, Eigen::Dynamic, 1 > &x, const Eigen::Matrix< T, Eigen::Dynamic, 1 > &v, T &fx, Eigen::Matrix< T, Eigen::Dynamic, 1 > &Hv) |
template<typename T , typename F > | |
void | partial_derivative (const F &f, const Eigen::Matrix< T, Eigen::Dynamic, 1 > &x, int n, T &fx, T &dfx_dxn) |
Return the partial derivative of the specified multiivariate function at the specified argument. More... | |
template<typename T_y > | |
bool | check_nonzero_size (const char *function, const char *name, const T_y &y) |
Return true if the specified matrix/vector is of non-zero size. More... | |
template<typename T_y > | |
bool | check_ordered (const char *function, const char *name, const std::vector< T_y > &y) |
Return true if the specified vector is sorted into strictly increasing order. More... | |
double | dot (const std::vector< double > &x, const std::vector< double > &y) |
double | dot_self (const std::vector< double > &x) |
template<typename T , typename S > | |
void | fill (std::vector< T > &x, const S &y) |
Fill the specified container with the specified value. More... | |
double | log_sum_exp (const std::vector< double > &x) |
Return the log of the sum of the exponentiated values of the specified sequence of values. More... | |
template<typename T > | |
std::vector< T > | rep_array (const T &x, int n) |
template<typename T > | |
std::vector< std::vector< T > > | rep_array (const T &x, int m, int n) |
template<typename T > | |
std::vector< std::vector< std::vector< T > > > | rep_array (const T &x, int k, int m, int n) |
void | scaled_add (std::vector< double > &x, const std::vector< double > &y, const double lambda) |
void | sub (std::vector< double > &x, std::vector< double > &y, std::vector< double > &result) |
template<typename T > | |
T | sum (const std::vector< T > &xs) |
Return the sum of the values in the specified standard vector. More... | |
template<typename T > | |
std::vector< typename child_type< T >::type > | value_of (const std::vector< T > &x) |
Convert a std::vector of type T to a std::vector of child_type<T>::type. More... | |
template<> | |
std::vector< double > | value_of (const std::vector< double > &x) |
Return the specified argument. More... | |
template<typename T > | |
std::vector< double > | value_of_rec (const std::vector< T > &x) |
Convert a std::vector of type T to a std::vector of doubles. More... | |
template<> | |
std::vector< double > | value_of_rec (const std::vector< double > &x) |
Return the specified argument. More... | |
template<typename F , typename T1 , typename T2 > | |
std::vector< std::vector< typename stan::return_type< T1, T2 >::type > > | integrate_ode_rk45 (const F &f, const std::vector< T1 > y0, const double t0, const std::vector< double > &ts, const std::vector< T2 > &theta, const std::vector< double > &x, const std::vector< int > &x_int, std::ostream *msgs=0, double relative_tolerance=1e-6, double absolute_tolerance=1e-6, int max_num_steps=1E6) |
Return the solutions for the specified system of ordinary differential equations given the specified initial state, initial times, times of desired solution, and parameters and data, writing error and warning messages to the specified stream. More... | |
template<typename T_y > | |
bool | check_cholesky_factor (const char *function, const char *name, const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &y) |
Return true if the specified matrix is a valid Cholesky factor. More... | |
template<typename T_y > | |
bool | check_cholesky_factor_corr (const char *function, const char *name, const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &y) |
Return true if the specified matrix is a valid Cholesky factor of a correlation matrix. More... | |
template<typename T_y , int R, int C> | |
bool | check_column_index (const char *function, const char *name, const Eigen::Matrix< T_y, R, C > &y, const size_t i) |
Return true if the specified index is a valid column of the matrix. More... | |
template<typename T_y > | |
bool | check_corr_matrix (const char *function, const char *name, const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &y) |
Return true if the specified matrix is a valid correlation matrix. More... | |
template<typename T_y > | |
bool | check_cov_matrix (const char *function, const char *name, const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &y) |
Return true if the specified matrix is a valid covariance matrix. More... | |
template<typename T , int R, int C> | |
bool | check_ldlt_factor (const char *function, const char *name, stan::math::LDLT_factor< T, R, C > &A) |
Return true if the argument is a valid stan::math::LDLT_factor . More... | |
template<typename T_y > | |
bool | check_lower_triangular (const char *function, const char *name, const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &y) |
Return true if the specified matrix is lower triangular. More... | |
template<typename T1 , typename T2 , int R1, int C1, int R2, int C2> | |
bool | check_matching_dims (const char *function, const char *name1, const Eigen::Matrix< T1, R1, C1 > &y1, const char *name2, const Eigen::Matrix< T2, R2, C2 > &y2) |
Return true if the two matrices are of the same size. More... | |
template<typename T_y1 , typename T_y2 > | |
bool | check_matching_sizes (const char *function, const char *name1, const T_y1 &y1, const char *name2, const T_y2 &y2) |
Return true if two structures at the same size. More... | |
template<typename T1 , typename T2 > | |
bool | check_multiplicable (const char *function, const char *name1, const T1 &y1, const char *name2, const T2 &y2) |
Return true if the matrices can be multiplied. More... | |
template<typename T_y > | |
bool | check_ordered (const char *function, const char *name, const Eigen::Matrix< T_y, Eigen::Dynamic, 1 > &y) |
Return true if the specified vector is sorted into strictly increasing order. More... | |
template<typename T_y > | |
bool | check_pos_definite (const char *function, const char *name, const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &y) |
Return true if the specified square, symmetric matrix is positive definite. More... | |
template<typename Derived > | |
bool | check_pos_definite (const char *function, const char *name, const Eigen::LDLT< Derived > &cholesky) |
Return true if the specified LDLT transform of a matrix is positive definite. More... | |
template<typename Derived > | |
bool | check_pos_definite (const char *function, const char *name, const Eigen::LLT< Derived > &cholesky) |
Return true if the specified LLT transform of a matrix is positive definite. More... | |
template<typename T_y > | |
bool | check_pos_semidefinite (const char *function, const char *name, const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &y) |
Return true if the specified matrix is positive definite. More... | |
template<typename T_y > | |
bool | check_positive_ordered (const char *function, const char *name, const Eigen::Matrix< T_y, Eigen::Dynamic, 1 > &y) |
Return true if the specified vector contains non-negative values and is sorted into strictly increasing order. More... | |
bool | check_range (const char *function, const char *name, const int max, const int index, const int nested_level, const char *error_msg) |
Return true if specified index is within range. More... | |
bool | check_range (const char *function, const char *name, const int max, const int index, const char *error_msg) |
Return true if specified index is within range. More... | |
bool | check_range (const char *function, const char *name, const int max, const int index) |
Return true if specified index is within range. More... | |
template<typename T_y , int R, int C> | |
bool | check_row_index (const char *function, const char *name, const Eigen::Matrix< T_y, R, C > &y, size_t i) |
Return true if the specified index is a valid row of the matrix. More... | |
template<typename T_prob > | |
bool | check_simplex (const char *function, const char *name, const Eigen::Matrix< T_prob, Eigen::Dynamic, 1 > &theta) |
Return true if the specified vector is simplex. More... | |
template<typename T_y > | |
bool | check_spsd_matrix (const char *function, const char *name, const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &y) |
Return true if the specified matrix is a square, symmetric, and positive semi-definite. More... | |
template<typename T_y > | |
bool | check_square (const char *function, const char *name, const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &y) |
Return true if the specified matrix is square. More... | |
template<typename T > | |
bool | check_std_vector_index (const char *function, const char *name, const std::vector< T > &y, int i) |
Return true if the specified index is valid in std vector. More... | |
template<typename T_y > | |
bool | check_symmetric (const char *function, const char *name, const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &y) |
Return true if the specified matrix is symmetric. More... | |
template<typename T_prob > | |
bool | check_unit_vector (const char *function, const char *name, const Eigen::Matrix< T_prob, Eigen::Dynamic, 1 > &theta) |
Return true if the specified vector is unit vector. More... | |
template<typename T , int R, int C> | |
bool | check_vector (const char *function, const char *name, const Eigen::Matrix< T, R, C > &x) |
Return true if the matrix is either a row vector or column vector. More... | |
void | validate_non_negative_index (const char *var_name, const char *expr, int val) |
template<typename T > | |
apply_scalar_unary< abs_fun, T >::return_t | abs (const T &x) |
Vectorized version of abs(). More... | |
template<typename T > | |
apply_scalar_unary< acos_fun, T >::return_t | acos (const T &x) |
Vectorized version of acos(). More... | |
template<typename T1 , typename T2 , int R, int C> | |
Eigen::Matrix< typename boost::math::tools::promote_args< T1, T2 >::type, R, C > | add (const Eigen::Matrix< T1, R, C > &m1, const Eigen::Matrix< T2, R, C > &m2) |
Return the sum of the specified matrices. More... | |
template<typename T1 , typename T2 , int R, int C> | |
Eigen::Matrix< typename boost::math::tools::promote_args< T1, T2 >::type, R, C > | add (const Eigen::Matrix< T1, R, C > &m, const T2 &c) |
Return the sum of the specified matrix and specified scalar. More... | |
template<typename T1 , typename T2 , int R, int C> | |
Eigen::Matrix< typename boost::math::tools::promote_args< T1, T2 >::type, R, C > | add (const T1 &c, const Eigen::Matrix< T2, R, C > &m) |
Return the sum of the specified scalar and specified matrix. More... | |
template<typename T1 , typename T2 , int R1, int C1, int R2, int C2> | |
Eigen::Matrix< typename return_type< T1, T2 >::type, Eigen::Dynamic, Eigen::Dynamic > | append_col (const Eigen::Matrix< T1, R1, C1 > &A, const Eigen::Matrix< T2, R2, C2 > &B) |
Return the result of appending the second argument matrix after the first argument matrix, that is, putting them side by side, with the first matrix followed by the second matrix. More... | |
template<typename T1 , typename T2 , int C1, int C2> | |
Eigen::Matrix< typename return_type< T1, T2 >::type, 1, Eigen::Dynamic > | append_col (const Eigen::Matrix< T1, 1, C1 > &A, const Eigen::Matrix< T2, 1, C2 > &B) |
Return the result of concatenaing the first row vector followed by the second row vector side by side, with the result being a row vector. More... | |
template<typename T , int R1, int C1, int R2, int C2> | |
Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > | append_col (const Eigen::Matrix< T, R1, C1 > &A, const Eigen::Matrix< T, R2, C2 > &B) |
Return the result of appending the second argument matrix after the first argument matrix, that is, putting them side by side, with the first matrix followed by the second matrix. More... | |
template<typename T , int C1, int C2> | |
Eigen::Matrix< T, 1, Eigen::Dynamic > | append_col (const Eigen::Matrix< T, 1, C1 > &A, const Eigen::Matrix< T, 1, C2 > &B) |
Return the result of concatenaing the first row vector followed by the second row vector side by side, with the result being a row vector. More... | |
template<typename T1 , typename T2 , int R, int C> | |
Eigen::Matrix< typename return_type< T1, T2 >::type, 1, Eigen::Dynamic > | append_col (const T1 &A, const Eigen::Matrix< T2, R, C > &B) |
Return the result of stacking an scalar on top of the a row vector, with the result being a row vector. More... | |
template<typename T1 , typename T2 , int R, int C> | |
Eigen::Matrix< typename return_type< T1, T2 >::type, 1, Eigen::Dynamic > | append_col (const Eigen::Matrix< T1, R, C > &A, const T2 &B) |
Return the result of stacking a row vector on top of the an scalar, with the result being a row vector. More... | |
template<typename T1 , typename T2 , int R1, int C1, int R2, int C2> | |
Eigen::Matrix< typename return_type< T1, T2 >::type, Eigen::Dynamic, Eigen::Dynamic > | append_row (const Eigen::Matrix< T1, R1, C1 > &A, const Eigen::Matrix< T2, R2, C2 > &B) |
Return the result of stacking the rows of the first argument matrix on top of the second argument matrix. More... | |
template<typename T1 , typename T2 , int R1, int R2> | |
Eigen::Matrix< typename return_type< T1, T2 >::type, Eigen::Dynamic, 1 > | append_row (const Eigen::Matrix< T1, R1, 1 > &A, const Eigen::Matrix< T2, R2, 1 > &B) |
Return the result of stacking the first vector on top of the second vector, with the result being a vector. More... | |
template<typename T , int R1, int C1, int R2, int C2> | |
Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > | append_row (const Eigen::Matrix< T, R1, C1 > &A, const Eigen::Matrix< T, R2, C2 > &B) |
Return the result of stacking the rows of the first argument matrix on top of the second argument matrix. More... | |
template<typename T , int R1, int R2> | |
Eigen::Matrix< T, Eigen::Dynamic, 1 > | append_row (const Eigen::Matrix< T, R1, 1 > &A, const Eigen::Matrix< T, R2, 1 > &B) |
Return the result of stacking the first vector on top of the second vector, with the result being a vector. More... | |
template<typename T1 , typename T2 , int R, int C> | |
Eigen::Matrix< typename return_type< T1, T2 >::type, Eigen::Dynamic, 1 > | append_row (const T1 &A, const Eigen::Matrix< T2, R, C > &B) |
Return the result of stacking an scalar on top of the a vector, with the result being a vector. More... | |
template<typename T1 , typename T2 , int R, int C> | |
Eigen::Matrix< typename return_type< T1, T2 >::type, Eigen::Dynamic, 1 > | append_row (const Eigen::Matrix< T1, R, C > &A, const T2 &B) |
Return the result of stacking a vector on top of the an scalar, with the result being a vector. More... | |
template<typename T > | |
apply_scalar_unary< asin_fun, T >::return_t | asin (const T &x) |
Vectorized version of asin(). More... | |
template<typename T > | |
apply_scalar_unary< asinh_fun, T >::return_t | asinh (const T &x) |
Vectorized version of acos(). More... | |
void | print_mat_size (int n, std::ostream &o) |
Helper function to return the matrix size as either "dynamic" or "1". More... | |
template<typename LHS , typename RHS > | |
void | assign (LHS &lhs, const RHS &rhs) |
Copy the right-hand side's value to the left-hand side variable. More... | |
template<typename LHS , typename RHS , int R1, int C1, int R2, int C2> | |
void | assign (Eigen::Matrix< LHS, R1, C1 > &x, const Eigen::Matrix< RHS, R2, C2 > &y) |
Copy the right-hand side's value to the left-hand side variable. More... | |
template<typename LHS , typename RHS , int R, int C> | |
void | assign (Eigen::Matrix< LHS, R, C > &x, const Eigen::Matrix< RHS, R, C > &y) |
Copy the right-hand side's value to the left-hand side variable. More... | |
template<typename LHS , typename RHS , int R, int C> | |
void | assign (Eigen::Block< LHS > x, const Eigen::Matrix< RHS, R, C > &y) |
Copy the right-hand side's value to the left-hand side variable. More... | |
template<typename LHS , typename RHS > | |
void | assign (std::vector< LHS > &x, const std::vector< RHS > &y) |
Copy the right-hand side's value to the left-hand side variable. More... | |
template<typename T > | |
apply_scalar_unary< atan_fun, T >::return_t | atan (const T &x) |
Vectorized version of asinh(). More... | |
template<typename T > | |
void | autocorrelation (const std::vector< T > &y, std::vector< T > &ac, Eigen::FFT< T > &fft) |
Write autocorrelation estimates for every lag for the specified input sequence into the specified result using the specified FFT engine. More... | |
template<typename T > | |
void | autocorrelation (const std::vector< T > &y, std::vector< T > &ac) |
Write autocorrelation estimates for every lag for the specified input sequence into the specified result. More... | |
template<typename T > | |
void | autocovariance (const std::vector< T > &y, std::vector< T > &acov, Eigen::FFT< T > &fft) |
Write autocovariance estimates for every lag for the specified input sequence into the specified result using the specified FFT engine. More... | |
template<typename T > | |
void | autocovariance (const std::vector< T > &y, std::vector< T > &acov) |
Write autocovariance estimates for every lag for the specified input sequence into the specified result. More... | |
template<typename T > | |
Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > | block (const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &m, size_t i, size_t j, size_t nrows, size_t ncols) |
Return a nrows x ncols submatrix starting at (i-1, j-1). More... | |
template<typename T > | |
apply_scalar_unary< cbrt_fun, T >::return_t | cbrt (const T &x) |
Vectorized version of cbrt(). More... | |
template<typename T > | |
apply_scalar_unary< ceil_fun, T >::return_t | ceil (const T &x) |
Vectorized version of ceil(). More... | |
template<typename T > | |
Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > | cholesky_corr_constrain (const Eigen::Matrix< T, Eigen::Dynamic, 1 > &y, int K) |
template<typename T > | |
Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > | cholesky_corr_constrain (const Eigen::Matrix< T, Eigen::Dynamic, 1 > &y, int K, T &lp) |
template<typename T > | |
Eigen::Matrix< T, Eigen::Dynamic, 1 > | cholesky_corr_free (const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &x) |
template<typename T > | |
Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > | cholesky_decompose (const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &m) |
Return the lower-triangular Cholesky factor (i.e., matrix square root) of the specified square, symmetric matrix. More... | |
template<typename T > | |
Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > | cholesky_factor_constrain (const Eigen::Matrix< T, Eigen::Dynamic, 1 > &x, int M, int N) |
Return the Cholesky factor of the specified size read from the specified vector. More... | |
template<typename T > | |
Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > | cholesky_factor_constrain (const Eigen::Matrix< T, Eigen::Dynamic, 1 > &x, int M, int N, T &lp) |
Return the Cholesky factor of the specified size read from the specified vector and increment the specified log probability reference with the log Jacobian adjustment of the transform. More... | |
template<typename T > | |
Eigen::Matrix< T, Eigen::Dynamic, 1 > | cholesky_factor_free (const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &y) |
Return the unconstrained vector of parameters correspdonding to the specified Cholesky factor. More... | |
template<typename T > | |
Eigen::Matrix< T, Eigen::Dynamic, 1 > | col (const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &m, size_t j) |
Return the specified column of the specified matrix using start-at-1 indexing. More... | |
template<typename T , int R, int C> | |
int | cols (const Eigen::Matrix< T, R, C > &m) |
Return the number of columns in the specified matrix, vector, or row vector. More... | |
template<int R1, int C1, int R2, int C2> | |
Eigen::Matrix< double, 1, C1 > | columns_dot_product (const Eigen::Matrix< double, R1, C1 > &v1, const Eigen::Matrix< double, R2, C2 > &v2) |
Returns the dot product of the specified vectors. More... | |
template<typename T , int R, int C> | |
Eigen::Matrix< T, 1, C > | columns_dot_self (const Eigen::Matrix< T, R, C > &x) |
Returns the dot product of each column of a matrix with itself. More... | |
template<typename T > | |
Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > | corr_matrix_constrain (const Eigen::Matrix< T, Eigen::Dynamic, 1 > &x, typename math::index_type< Eigen::Matrix< T, Eigen::Dynamic, 1 > >::type k) |
Return the correlation matrix of the specified dimensionality derived from the specified vector of unconstrained values. More... | |
template<typename T > | |
Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > | corr_matrix_constrain (const Eigen::Matrix< T, Eigen::Dynamic, 1 > &x, typename math::index_type< Eigen::Matrix< T, Eigen::Dynamic, 1 > >::type k, T &lp) |
Return the correlation matrix of the specified dimensionality derived from the specified vector of unconstrained values. More... | |
template<typename T > | |
Eigen::Matrix< T, Eigen::Dynamic, 1 > | corr_matrix_free (const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &y) |
Return the vector of unconstrained partial correlations that define the specified correlation matrix when transformed. More... | |
template<typename T > | |
apply_scalar_unary< cos_fun, T >::return_t | cos (const T &x) |
Vectorized version of cos(). More... | |
template<typename T > | |
apply_scalar_unary< cosh_fun, T >::return_t | cosh (const T &x) |
Vectorized version of cosh(). More... | |
template<typename T_x , typename T_sigma , typename T_l > | |
Eigen::Matrix< typename stan::return_type< T_x, T_sigma, T_l >::type, Eigen::Dynamic, Eigen::Dynamic > | cov_exp_quad (const std::vector< T_x > &x, T_sigma &sigma, T_l &l) |
Returns a squared exponential kernel. More... | |
template<typename T_x1 , typename T_x2 , typename T_sigma , typename T_l > | |
Eigen::Matrix< typename stan::return_type< T_x1, T_x2, T_sigma, T_l >::type, Eigen::Dynamic, Eigen::Dynamic > | cov_exp_quad (const std::vector< T_x1 > &x1, const std::vector< T_x2 > &x2, T_sigma &sigma, T_l &l) |
Returns a squared exponential kernel. More... | |
template<typename T > | |
Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > | cov_matrix_constrain (const Eigen::Matrix< T, Eigen::Dynamic, 1 > &x, typename math::index_type< Eigen::Matrix< T, Eigen::Dynamic, 1 > >::type K) |
Return the symmetric, positive-definite matrix of dimensions K by K resulting from transforming the specified finite vector of size K plus (K choose 2). More... | |
template<typename T > | |
Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > | cov_matrix_constrain (const Eigen::Matrix< T, Eigen::Dynamic, 1 > &x, typename math::index_type< Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > >::type K, T &lp) |
Return the symmetric, positive-definite matrix of dimensions K by K resulting from transforming the specified finite vector of size K plus (K choose 2). More... | |
template<typename T > | |
Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > | cov_matrix_constrain_lkj (const Eigen::Matrix< T, Eigen::Dynamic, 1 > &x, size_t k) |
Return the covariance matrix of the specified dimensionality derived from constraining the specified vector of unconstrained values. More... | |
template<typename T > | |
Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > | cov_matrix_constrain_lkj (const Eigen::Matrix< T, Eigen::Dynamic, 1 > &x, size_t k, T &lp) |
Return the covariance matrix of the specified dimensionality derived from constraining the specified vector of unconstrained values and increment the specified log probability reference with the log absolute Jacobian determinant. More... | |
template<typename T > | |
Eigen::Matrix< T, Eigen::Dynamic, 1 > | cov_matrix_free (const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &y) |
The covariance matrix derived from the symmetric view of the lower-triangular view of the K by K specified matrix is freed to return a vector of size K + (K choose 2). More... | |
template<typename T > | |
Eigen::Matrix< T, Eigen::Dynamic, 1 > | cov_matrix_free_lkj (const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &y) |
Return the vector of unconstrained partial correlations and deviations that transform to the specified covariance matrix. More... | |
matrix_d | crossprod (const matrix_d &M) |
Returns the result of pre-multiplying a matrix by its own transpose. More... | |
template<typename T > | |
const std::vector< int > | csr_extract_u (const Eigen::SparseMatrix< T, Eigen::RowMajor > &A) |
Extract the NZE index for each entry from a sparse matrix. More... | |
template<typename T , int R, int C> | |
const std::vector< int > | csr_extract_u (const Eigen::Matrix< T, R, C > &A) |
Extract the NZE index for each entry from a sparse matrix. More... | |
template<typename T > | |
const std::vector< int > | csr_extract_v (const Eigen::SparseMatrix< T, Eigen::RowMajor > &A) |
Extract the column indexes for non-zero value from a sparse matrix. More... | |
template<typename T , int R, int C> | |
const std::vector< int > | csr_extract_v (const Eigen::Matrix< T, R, C > &A) |
Extract the column indexes for non-zero values from a dense matrix by converting to sparse and calling the sparse matrix extractor. More... | |
template<typename T > | |
const Eigen::Matrix< T, Eigen::Dynamic, 1 > | csr_extract_w (const Eigen::SparseMatrix< T, Eigen::RowMajor > &A) |
template<typename T , int R, int C> | |
const Eigen::Matrix< T, Eigen::Dynamic, 1 > | csr_extract_w (const Eigen::Matrix< T, R, C > &A) |
template<typename T1 , typename T2 > | |
Eigen::Matrix< typename boost::math::tools::promote_args< T1, T2 >::type, Eigen::Dynamic, 1 > | csr_matrix_times_vector (const int &m, const int &n, const Eigen::Matrix< T1, Eigen::Dynamic, 1 > &w, const std::vector< int > &v, const std::vector< int > &u, const Eigen::Matrix< T2, Eigen::Dynamic, 1 > &b) |
template<typename T > | |
Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > | csr_to_dense_matrix (const int &m, const int &n, const Eigen::Matrix< T, Eigen::Dynamic, 1 > &w, const std::vector< int > &v, const std::vector< int > &u) |
Construct a dense Eigen matrix from the CSR format components. More... | |
int | csr_u_to_z (const std::vector< int > &u, int i) |
Return the z vector computed from the specified u vector at the index for the z vector. More... | |
template<typename T > | |
std::vector< T > | cumulative_sum (const std::vector< T > &x) |
Return the cumulative sum of the specified vector. More... | |
template<typename T , int R, int C> | |
Eigen::Matrix< T, R, C > | cumulative_sum (const Eigen::Matrix< T, R, C > &m) |
Return the cumulative sum of the specified matrix. More... | |
template<typename T , int R, int C> | |
T | determinant (const Eigen::Matrix< T, R, C > &m) |
Returns the determinant of the specified square matrix. More... | |
template<typename T > | |
Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > | diag_matrix (const Eigen::Matrix< T, Eigen::Dynamic, 1 > &v) |
Return a square diagonal matrix with the specified vector of coefficients as the diagonal values. More... | |
template<typename T1 , typename T2 , int R1, int C1, int R2, int C2> | |
Eigen::Matrix< typename boost::math::tools::promote_args< T1, T2 >::type, R1, C1 > | diag_post_multiply (const Eigen::Matrix< T1, R1, C1 > &m1, const Eigen::Matrix< T2, R2, C2 > &m2) |
template<typename T1 , typename T2 , int R1, int C1, int R2, int C2> | |
Eigen::Matrix< typename boost::math::tools::promote_args< T1, T2 >::type, R2, C2 > | diag_pre_multiply (const Eigen::Matrix< T1, R1, C1 > &m1, const Eigen::Matrix< T2, R2, C2 > &m2) |
template<typename T > | |
Eigen::Matrix< T, Eigen::Dynamic, 1 > | diagonal (const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &m) |
Return a column vector of the diagonal elements of the specified matrix. More... | |
template<typename T > | |
apply_scalar_unary< digamma_fun, T >::return_t | digamma (const T &x) |
Vectorized version of digamma(). More... | |
template<typename T > | |
void | dims (const T &x, std::vector< int > &result) |
template<typename T , int R, int C> | |
void | dims (const Eigen::Matrix< T, R, C > &x, std::vector< int > &result) |
template<typename T > | |
void | dims (const std::vector< T > &x, std::vector< int > &result) |
template<typename T > | |
std::vector< int > | dims (const T &x) |
template<typename T1 , int R1, int C1, typename T2 , int R2, int C2> | |
boost::math::tools::promote_args< T1, T2 >::type | distance (const Eigen::Matrix< T1, R1, C1 > &v1, const Eigen::Matrix< T2, R2, C2 > &v2) |
Returns the distance between the specified vectors. More... | |
template<int R, int C, typename T > | |
boost::enable_if_c< boost::is_arithmetic< T >::value, Eigen::Matrix< double, R, C > >::type | divide (const Eigen::Matrix< double, R, C > &m, T c) |
Return specified matrix divided by specified scalar. More... | |
template<int R1, int C1, int R2, int C2> | |
double | dot_product (const Eigen::Matrix< double, R1, C1 > &v1, const Eigen::Matrix< double, R2, C2 > &v2) |
Returns the dot product of the specified vectors. More... | |
double | dot_product (const double *v1, const double *v2, size_t length) |
Returns the dot product of the specified arrays of doubles. More... | |
double | dot_product (const std::vector< double > &v1, const std::vector< double > &v2) |
Returns the dot product of the specified arrays of doubles. More... | |
template<int R, int C> | |
double | dot_self (const Eigen::Matrix< double, R, C > &v) |
Returns the dot product of the specified vector with itself. More... | |
template<typename T > | |
Eigen::Matrix< T, Eigen::Dynamic, 1 > | eigenvalues_sym (const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &m) |
Return the eigenvalues of the specified symmetric matrix in descending order of magnitude. More... | |
template<typename T > | |
Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > | eigenvectors_sym (const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &m) |
template<typename T1 , typename T2 , int R, int C> | |
Eigen::Matrix< typename boost::math::tools::promote_args< T1, T2 >::type, R, C > | elt_divide (const Eigen::Matrix< T1, R, C > &m1, const Eigen::Matrix< T2, R, C > &m2) |
Return the elementwise division of the specified matrices. More... | |
template<typename T1 , typename T2 , int R, int C> | |
Eigen::Matrix< typename boost::math::tools::promote_args< T1, T2 >::type, R, C > | elt_divide (const Eigen::Matrix< T1, R, C > &m, T2 s) |
Return the elementwise division of the specified matrix by the specified scalar. More... | |
template<typename T1 , typename T2 , int R, int C> | |
Eigen::Matrix< typename boost::math::tools::promote_args< T1, T2 >::type, R, C > | elt_divide (T1 s, const Eigen::Matrix< T2, R, C > &m) |
Return the elementwise division of the specified scalar by the specified matrix. More... | |
template<typename T1 , typename T2 , int R, int C> | |
Eigen::Matrix< typename boost::math::tools::promote_args< T1, T2 >::type, R, C > | elt_multiply (const Eigen::Matrix< T1, R, C > &m1, const Eigen::Matrix< T2, R, C > &m2) |
Return the elementwise multiplication of the specified matrices. More... | |
template<typename T > | |
apply_scalar_unary< erf_fun, T >::return_t | erf (const T &x) |
Vectorized version of erf(). More... | |
template<typename T > | |
apply_scalar_unary< erfc_fun, T >::return_t | erfc (const T &x) |
Vectorized version of erfc(). More... | |
template<typename T > | |
apply_scalar_unary< exp_fun, T >::return_t | exp (const T &x) |
Vectorized version of exp(). More... | |
template<typename T > | |
apply_scalar_unary< expm1_fun, T >::return_t | expm1 (const T &x) |
Vectorized version of expm1(). More... | |
template<typename T > | |
apply_scalar_unary< fabs_fun, T >::return_t | fabs (const T &x) |
Vectorized version of fabs(). More... | |
template<typename T > | |
bool | factor_cov_matrix (const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &Sigma, Eigen::Array< T, Eigen::Dynamic, 1 > &CPCs, Eigen::Array< T, Eigen::Dynamic, 1 > &sds) |
This function is intended to make starting values, given a covariance matrix Sigma. More... | |
template<typename T > | |
void | factor_U (const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &U, Eigen::Array< T, Eigen::Dynamic, 1 > &CPCs) |
This function is intended to make starting values, given a unit upper-triangular matrix U such that U'DU is a correlation matrix. More... | |
template<typename T , int R, int C, typename S > | |
void | fill (Eigen::Matrix< T, R, C > &x, const S &y) |
Fill the specified container with the specified value. More... | |
template<typename T > | |
apply_scalar_unary< floor_fun, T >::return_t | floor (const T &x) |
Vectorized version of floor(). More... | |
template<typename T > | |
const T & | get_base1 (const std::vector< T > &x, size_t i, const char *error_msg, size_t idx) |
Return a reference to the value of the specified vector at the specified base-one index. More... | |
template<typename T > | |
const T & | get_base1 (const std::vector< std::vector< T > > &x, size_t i1, size_t i2, const char *error_msg, size_t idx) |
Return a reference to the value of the specified vector at the specified base-one indexes. More... | |
template<typename T > | |
const T & | get_base1 (const std::vector< std::vector< std::vector< T > > > &x, size_t i1, size_t i2, size_t i3, const char *error_msg, size_t idx) |
Return a reference to the value of the specified vector at the specified base-one indexes. More... | |
template<typename T > | |
const T & | get_base1 (const std::vector< std::vector< std::vector< std::vector< T > > > > &x, size_t i1, size_t i2, size_t i3, size_t i4, const char *error_msg, size_t idx) |
Return a reference to the value of the specified vector at the specified base-one indexes. More... | |
template<typename T > | |
const T & | get_base1 (const std::vector< std::vector< std::vector< std::vector< std::vector< T > > > > > &x, size_t i1, size_t i2, size_t i3, size_t i4, size_t i5, const char *error_msg, size_t idx) |
Return a reference to the value of the specified vector at the specified base-one indexes. More... | |
template<typename T > | |
const T & | get_base1 (const std::vector< std::vector< std::vector< std::vector< std::vector< std::vector< T > > > > > > &x, size_t i1, size_t i2, size_t i3, size_t i4, size_t i5, size_t i6, const char *error_msg, size_t idx) |
Return a reference to the value of the specified vector at the specified base-one indexes. More... | |
template<typename T > | |
const T & | get_base1 (const std::vector< std::vector< std::vector< std::vector< std::vector< std::vector< std::vector< T > > > > > > > &x, size_t i1, size_t i2, size_t i3, size_t i4, size_t i5, size_t i6, size_t i7, const char *error_msg, size_t idx) |
Return a reference to the value of the specified vector at the specified base-one indexes. More... | |
template<typename T > | |
const T & | get_base1 (const std::vector< std::vector< std::vector< std::vector< std::vector< std::vector< std::vector< std::vector< T > > > > > > > > &x, size_t i1, size_t i2, size_t i3, size_t i4, size_t i5, size_t i6, size_t i7, size_t i8, const char *error_msg, size_t idx) |
Return a reference to the value of the specified vector at the specified base-one indexes. More... | |
template<typename T > | |
Eigen::Matrix< T, 1, Eigen::Dynamic > | get_base1 (const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &x, size_t m, const char *error_msg, size_t idx) |
Return a copy of the row of the specified vector at the specified base-one row index. More... | |
template<typename T > | |
const T & | get_base1 (const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &x, size_t m, size_t n, const char *error_msg, size_t idx) |
Return a reference to the value of the specified matrix at the specified base-one row and column indexes. More... | |
template<typename T > | |
const T & | get_base1 (const Eigen::Matrix< T, Eigen::Dynamic, 1 > &x, size_t m, const char *error_msg, size_t idx) |
Return a reference to the value of the specified column vector at the specified base-one index. More... | |
template<typename T > | |
const T & | get_base1 (const Eigen::Matrix< T, 1, Eigen::Dynamic > &x, size_t n, const char *error_msg, size_t idx) |
Return a reference to the value of the specified row vector at the specified base-one index. More... | |
template<typename T > | |
T & | get_base1_lhs (std::vector< T > &x, size_t i, const char *error_msg, size_t idx) |
Return a reference to the value of the specified vector at the specified base-one index. More... | |
template<typename T > | |
T & | get_base1_lhs (std::vector< std::vector< T > > &x, size_t i1, size_t i2, const char *error_msg, size_t idx) |
Return a reference to the value of the specified vector at the specified base-one indexes. More... | |
template<typename T > | |
T & | get_base1_lhs (std::vector< std::vector< std::vector< T > > > &x, size_t i1, size_t i2, size_t i3, const char *error_msg, size_t idx) |
Return a reference to the value of the specified vector at the specified base-one indexes. More... | |
template<typename T > | |
T & | get_base1_lhs (std::vector< std::vector< std::vector< std::vector< T > > > > &x, size_t i1, size_t i2, size_t i3, size_t i4, const char *error_msg, size_t idx) |
Return a reference to the value of the specified vector at the specified base-one indexes. More... | |
template<typename T > | |
T & | get_base1_lhs (std::vector< std::vector< std::vector< std::vector< std::vector< T > > > > > &x, size_t i1, size_t i2, size_t i3, size_t i4, size_t i5, const char *error_msg, size_t idx) |
Return a reference to the value of the specified vector at the specified base-one indexes. More... | |
template<typename T > | |
T & | get_base1_lhs (std::vector< std::vector< std::vector< std::vector< std::vector< std::vector< T > > > > > > &x, size_t i1, size_t i2, size_t i3, size_t i4, size_t i5, size_t i6, const char *error_msg, size_t idx) |
Return a reference to the value of the specified vector at the specified base-one indexes. More... | |
template<typename T > | |
T & | get_base1_lhs (std::vector< std::vector< std::vector< std::vector< std::vector< std::vector< std::vector< T > > > > > > > &x, size_t i1, size_t i2, size_t i3, size_t i4, size_t i5, size_t i6, size_t i7, const char *error_msg, size_t idx) |
Return a reference to the value of the specified vector at the specified base-one indexes. More... | |
template<typename T > | |
T & | get_base1_lhs (std::vector< std::vector< std::vector< std::vector< std::vector< std::vector< std::vector< std::vector< T > > > > > > > > &x, size_t i1, size_t i2, size_t i3, size_t i4, size_t i5, size_t i6, size_t i7, size_t i8, const char *error_msg, size_t idx) |
Return a reference to the value of the specified vector at the specified base-one indexes. More... | |
template<typename T > | |
Eigen::Block< Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > > | get_base1_lhs (Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &x, size_t m, const char *error_msg, size_t idx) |
Return a copy of the row of the specified vector at the specified base-one row index. More... | |
template<typename T > | |
T & | get_base1_lhs (Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &x, size_t m, size_t n, const char *error_msg, size_t idx) |
Return a reference to the value of the specified matrix at the specified base-one row and column indexes. More... | |
template<typename T > | |
T & | get_base1_lhs (Eigen::Matrix< T, Eigen::Dynamic, 1 > &x, size_t m, const char *error_msg, size_t idx) |
Return a reference to the value of the specified column vector at the specified base-one index. More... | |
template<typename T > | |
T & | get_base1_lhs (Eigen::Matrix< T, 1, Eigen::Dynamic > &x, size_t n, const char *error_msg, size_t idx) |
Return a reference to the value of the specified row vector at the specified base-one index. More... | |
template<typename T_lp , typename T_lp_accum > | |
boost::math::tools::promote_args< T_lp, T_lp_accum >::type | get_lp (const T_lp &lp, const stan::math::accumulator< T_lp_accum > &lp_accum) |
template<typename T > | |
Eigen::Matrix< T, Eigen::Dynamic, 1 > | head (const Eigen::Matrix< T, Eigen::Dynamic, 1 > &v, size_t n) |
Return the specified number of elements as a vector from the front of the specified vector. More... | |
template<typename T > | |
Eigen::Matrix< T, 1, Eigen::Dynamic > | head (const Eigen::Matrix< T, 1, Eigen::Dynamic > &rv, size_t n) |
Return the specified number of elements as a row vector from the front of the specified row vector. More... | |
template<typename T > | |
std::vector< T > | head (const std::vector< T > &sv, size_t n) |
Return the specified number of elements as a standard vector from the front of the specified standard vector. More... | |
template<typename T > | |
void | initialize (T &x, const T &v) |
template<typename T , typename V > | |
boost::enable_if_c< boost::is_arithmetic< V >::value, void >::type | initialize (T &x, V v) |
template<typename T , int R, int C, typename V > | |
void | initialize (Eigen::Matrix< T, R, C > &x, const V &v) |
template<typename T , typename V > | |
void | initialize (std::vector< T > &x, const V &v) |
template<typename T > | |
apply_scalar_unary< inv_fun, T >::return_t | inv (const T &x) |
Vectorized version of inv(). More... | |
template<typename T > | |
apply_scalar_unary< inv_cloglog_fun, T >::return_t | inv_cloglog (const T &x) |
Vectorized version of inv_cloglog(). More... | |
template<typename T > | |
apply_scalar_unary< inv_logit_fun, T >::return_t | inv_logit (const T &x) |
Vectorized version of inv_logit(). More... | |
template<typename T > | |
apply_scalar_unary< inv_Phi_fun, T >::return_t | inv_Phi (const T &x) |
Vectorized version of inv_Phi(). More... | |
template<typename T > | |
apply_scalar_unary< inv_sqrt_fun, T >::return_t | inv_sqrt (const T &x) |
Vectorized version of inv_sqrt(). More... | |
template<typename T > | |
apply_scalar_unary< inv_square_fun, T >::return_t | inv_square (const T &x) |
Vectorized version of inv_square(). More... | |
template<typename T , int R, int C> | |
Eigen::Matrix< T, R, C > | inverse (const Eigen::Matrix< T, R, C > &m) |
Returns the inverse of the specified matrix. More... | |
template<typename T > | |
Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > | inverse_spd (const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &m) |
Returns the inverse of the specified symmetric, pos/neg-definite matrix. More... | |
template<typename T > | |
apply_scalar_unary< lgamma_fun, T >::return_t | lgamma (const T &x) |
Vectorized version of lgamma(). More... | |
template<typename T > | |
apply_scalar_unary< log_fun, T >::return_t | log (const T &x) |
Vectorized version of log(). More... | |
template<typename T > | |
apply_scalar_unary< log10_fun, T >::return_t | log10 (const T &x) |
Vectorized version of log10(). More... | |
template<typename T > | |
apply_scalar_unary< log1m_fun, T >::return_t | log1m (const T &x) |
Vectorized version of log1m(). More... | |
template<typename T > | |
apply_scalar_unary< log1m_exp_fun, T >::return_t | log1m_exp (const T &x) |
Vectorized version of log1m_exp(). More... | |
template<typename T > | |
apply_scalar_unary< log1p_exp_fun, T >::return_t | log1p_exp (const T &x) |
Vectorized version of log1m_exp(). More... | |
template<typename T , int R, int C> | |
T | log_determinant (const Eigen::Matrix< T, R, C > &m) |
Returns the log absolute determinant of the specified square matrix. More... | |
template<int R, int C, typename T > | |
T | log_determinant_ldlt (stan::math::LDLT_factor< T, R, C > &A) |
template<typename T , int R, int C> | |
T | log_determinant_spd (const Eigen::Matrix< T, R, C > &m) |
Returns the log absolute determinant of the specified square matrix. More... | |
template<typename T > | |
Eigen::Matrix< T, Eigen::Dynamic, 1 > | log_softmax (const Eigen::Matrix< T, Eigen::Dynamic, 1 > &v) |
Return the natural logarithm of the softmax of the specified vector. More... | |
template<int R, int C> | |
double | log_sum_exp (const Eigen::Matrix< double, R, C > &x) |
Return the log of the sum of the exponentiated values of the specified matrix of values. More... | |
template<typename T > | |
const Eigen::Array< T, Eigen::Dynamic, 1 > | make_nu (const T eta, const size_t K) |
This function calculates the degrees of freedom for the t distribution that corresponds to the shape parameter in the Lewandowski et. More... | |
int | max (const std::vector< int > &x) |
Returns the maximum coefficient in the specified column vector. More... | |
template<typename T > | |
T | max (const std::vector< T > &x) |
Returns the maximum coefficient in the specified column vector. More... | |
template<typename T , int R, int C> | |
T | max (const Eigen::Matrix< T, R, C > &m) |
Returns the maximum coefficient in the specified vector, row vector, or matrix. More... | |
template<typename T1 , typename T2 , int R1, int C1, int R2, int C2> | |
Eigen::Matrix< typename boost::math::tools::promote_args< T1, T2 >::type, R1, C2 > | mdivide_left (const Eigen::Matrix< T1, R1, C1 > &A, const Eigen::Matrix< T2, R2, C2 > &b) |
Returns the solution of the system Ax=b. More... | |
template<int R1, int C1, int R2, int C2, typename T1 , typename T2 > | |
Eigen::Matrix< typename boost::math::tools::promote_args< T1, T2 >::type, R1, C2 > | mdivide_left_ldlt (const stan::math::LDLT_factor< T1, R1, C1 > &A, const Eigen::Matrix< T2, R2, C2 > &b) |
Returns the solution of the system Ax=b given an LDLT_factor of A. More... | |
template<typename T1 , typename T2 , int R1, int C1, int R2, int C2> | |
Eigen::Matrix< typename boost::math::tools::promote_args< T1, T2 >::type, R1, C2 > | mdivide_left_spd (const Eigen::Matrix< T1, R1, C1 > &A, const Eigen::Matrix< T2, R2, C2 > &b) |
Returns the solution of the system Ax=b where A is symmetric positive definite. More... | |
template<int TriView, typename T1 , typename T2 , int R1, int C1, int R2, int C2> | |
Eigen::Matrix< typename boost::math::tools::promote_args< T1, T2 >::type, R1, C2 > | mdivide_left_tri (const Eigen::Matrix< T1, R1, C1 > &A, const Eigen::Matrix< T2, R2, C2 > &b) |
Returns the solution of the system Ax=b when A is triangular. More... | |
template<int TriView, typename T , int R1, int C1> | |
Eigen::Matrix< T, R1, C1 > | mdivide_left_tri (const Eigen::Matrix< T, R1, C1 > &A) |
Returns the solution of the system Ax=b when A is triangular and b=I. More... | |
template<typename T1 , typename T2 , int R1, int C1, int R2, int C2> | |
Eigen::Matrix< typename boost::math::tools::promote_args< T1, T2 >::type, R1, C2 > | mdivide_left_tri_low (const Eigen::Matrix< T1, R1, C1 > &A, const Eigen::Matrix< T2, R2, C2 > &b) |
template<typename T , int R1, int C1> | |
Eigen::Matrix< T, R1, C1 > | mdivide_left_tri_low (const Eigen::Matrix< T, R1, C1 > &A) |
template<typename T1 , typename T2 , int R1, int C1, int R2, int C2> | |
Eigen::Matrix< typename boost::math::tools::promote_args< T1, T2 >::type, R1, C2 > | mdivide_right (const Eigen::Matrix< T1, R1, C1 > &b, const Eigen::Matrix< T2, R2, C2 > &A) |
Returns the solution of the system Ax=b. More... | |
template<typename T1 , typename T2 , int R1, int C1, int R2, int C2> | |
Eigen::Matrix< typename boost::math::tools::promote_args< T1, T2 >::type, R1, C2 > | mdivide_right_ldlt (const Eigen::Matrix< T1, R1, C1 > &b, const stan::math::LDLT_factor< T2, R2, C2 > &A) |
Returns the solution of the system xA=b given an LDLT_factor of A. More... | |
template<int R1, int C1, int R2, int C2> | |
Eigen::Matrix< double, R1, C2 > | mdivide_right_ldlt (const Eigen::Matrix< double, R1, C1 > &b, const stan::math::LDLT_factor< double, R2, C2 > &A) |
template<typename T1 , typename T2 , int R1, int C1, int R2, int C2> | |
Eigen::Matrix< typename boost::math::tools::promote_args< T1, T2 >::type, R1, C2 > | mdivide_right_spd (const Eigen::Matrix< T1, R1, C1 > &b, const Eigen::Matrix< T2, R2, C2 > &A) |
Returns the solution of the system Ax=b where A is symmetric positive definite. More... | |
template<int TriView, typename T1 , typename T2 , int R1, int C1, int R2, int C2> | |
Eigen::Matrix< typename boost::math::tools::promote_args< T1, T2 >::type, R1, C2 > | mdivide_right_tri (const Eigen::Matrix< T1, R1, C1 > &b, const Eigen::Matrix< T2, R2, C2 > &A) |
Returns the solution of the system Ax=b when A is triangular. More... | |
template<typename T1 , typename T2 , int R1, int C1, int R2, int C2> | |
Eigen::Matrix< typename boost::math::tools::promote_args< T1, T2 >::type, R1, C2 > | mdivide_right_tri_low (const Eigen::Matrix< T1, R1, C1 > &b, const Eigen::Matrix< T2, R2, C2 > &A) |
Returns the solution of the system tri(A)x=b when tri(A) is a lower triangular view of the matrix A. More... | |
template<typename T > | |
boost::math::tools::promote_args< T >::type | mean (const std::vector< T > &v) |
Returns the sample mean (i.e., average) of the coefficients in the specified standard vector. More... | |
template<typename T , int R, int C> | |
boost::math::tools::promote_args< T >::type | mean (const Eigen::Matrix< T, R, C > &m) |
Returns the sample mean (i.e., average) of the coefficients in the specified vector, row vector, or matrix. More... | |
int | min (const std::vector< int > &x) |
Returns the minimum coefficient in the specified column vector. More... | |
template<typename T > | |
T | min (const std::vector< T > &x) |
Returns the minimum coefficient in the specified column vector. More... | |
template<typename T , int R, int C> | |
T | min (const Eigen::Matrix< T, R, C > &m) |
Returns the minimum coefficient in the specified matrix, vector, or row vector. More... | |
template<typename T > | |
T | minus (const T &x) |
Returns the negation of the specified scalar or matrix. More... | |
template<int R, int C, typename T > | |
boost::enable_if_c< boost::is_arithmetic< T >::value, Eigen::Matrix< double, R, C > >::type | multiply (const Eigen::Matrix< double, R, C > &m, T c) |
Return specified matrix multiplied by specified scalar. More... | |
template<int R, int C, typename T > | |
boost::enable_if_c< boost::is_arithmetic< T >::value, Eigen::Matrix< double, R, C > >::type | multiply (T c, const Eigen::Matrix< double, R, C > &m) |
Return specified scalar multiplied by specified matrix. More... | |
template<int R1, int C1, int R2, int C2> | |
Eigen::Matrix< double, R1, C2 > | multiply (const Eigen::Matrix< double, R1, C1 > &m1, const Eigen::Matrix< double, R2, C2 > &m2) |
Return the product of the specified matrices. More... | |
template<int C1, int R2> | |
double | multiply (const Eigen::Matrix< double, 1, C1 > &rv, const Eigen::Matrix< double, R2, 1 > &v) |
Return the scalar product of the specified row vector and specified column vector. More... | |
matrix_d | multiply_lower_tri_self_transpose (const matrix_d &L) |
Returns the result of multiplying the lower triangular portion of the input matrix by its own transpose. More... | |
template<typename T > | |
int | num_elements (const T &x) |
Returns 1, the number of elements in a primitive type. More... | |
template<typename T , int R, int C> | |
int | num_elements (const Eigen::Matrix< T, R, C > &m) |
Returns the size of the specified matrix. More... | |
template<typename T > | |
int | num_elements (const std::vector< T > &v) |
Returns the number of elements in the specified vector. More... | |
template<typename T > | |
Eigen::Matrix< T, Eigen::Dynamic, 1 > | ordered_constrain (const Eigen::Matrix< T, Eigen::Dynamic, 1 > &x) |
Return an increasing ordered vector derived from the specified free vector. More... | |
template<typename T > | |
Eigen::Matrix< T, Eigen::Dynamic, 1 > | ordered_constrain (const Eigen::Matrix< T, Eigen::Dynamic, 1 > &x, T &lp) |
Return a positive valued, increasing ordered vector derived from the specified free vector and increment the specified log probability reference with the log absolute Jacobian determinant of the transform. More... | |
template<typename T > | |
Eigen::Matrix< T, Eigen::Dynamic, 1 > | ordered_free (const Eigen::Matrix< T, Eigen::Dynamic, 1 > &y) |
Return the vector of unconstrained scalars that transform to the specified positive ordered vector. More... | |
template<typename T > | |
apply_scalar_unary< Phi_fun, T >::return_t | Phi (const T &x) |
Vectorized version of Phi(). More... | |
template<typename T > | |
Eigen::Matrix< T, Eigen::Dynamic, 1 > | positive_ordered_constrain (const Eigen::Matrix< T, Eigen::Dynamic, 1 > &x) |
Return an increasing positive ordered vector derived from the specified free vector. More... | |
template<typename T > | |
Eigen::Matrix< T, Eigen::Dynamic, 1 > | positive_ordered_constrain (const Eigen::Matrix< T, Eigen::Dynamic, 1 > &x, T &lp) |
Return a positive valued, increasing positive ordered vector derived from the specified free vector and increment the specified log probability reference with the log absolute Jacobian determinant of the transform. More... | |
template<typename T > | |
Eigen::Matrix< T, Eigen::Dynamic, 1 > | positive_ordered_free (const Eigen::Matrix< T, Eigen::Dynamic, 1 > &y) |
Return the vector of unconstrained scalars that transform to the specified positive ordered vector. More... | |
template<typename T > | |
T | prod (const std::vector< T > &v) |
Returns the product of the coefficients of the specified standard vector. More... | |
template<typename T , int R, int C> | |
T | prod (const Eigen::Matrix< T, R, C > &v) |
Returns the product of the coefficients of the specified column vector. More... | |
template<typename T1 , typename T2 , typename F > | |
common_type< T1, T2 >::type | promote_common (const F &u) |
template<typename T > | |
Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > | qr_Q (const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &m) |
template<typename T > | |
Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > | qr_R (const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &m) |
template<int RA, int CA, int RB, int CB, typename T > | |
Eigen::Matrix< T, CB, CB > | quad_form (const Eigen::Matrix< T, RA, CA > &A, const Eigen::Matrix< T, RB, CB > &B) |
Compute B^T A B. More... | |
template<int RA, int CA, int RB, typename T > | |
T | quad_form (const Eigen::Matrix< T, RA, CA > &A, const Eigen::Matrix< T, RB, 1 > &B) |
template<typename T1 , typename T2 , int R, int C> | |
Eigen::Matrix< typename boost::math::tools::promote_args< T1, T2 >::type, Eigen::Dynamic, Eigen::Dynamic > | quad_form_diag (const Eigen::Matrix< T1, Eigen::Dynamic, Eigen::Dynamic > &mat, const Eigen::Matrix< T2, R, C > &vec) |
template<int RA, int CA, int RB, int CB, typename T > | |
Eigen::Matrix< T, CB, CB > | quad_form_sym (const Eigen::Matrix< T, RA, CA > &A, const Eigen::Matrix< T, RB, CB > &B) |
template<int RA, int CA, int RB, typename T > | |
T | quad_form_sym (const Eigen::Matrix< T, RA, CA > &A, const Eigen::Matrix< T, RB, 1 > &B) |
template<typename T > | |
int | rank (const std::vector< T > &v, int s) |
Return the number of components of v less than v[s]. More... | |
template<typename T , int R, int C> | |
int | rank (const Eigen::Matrix< T, R, C > &v, int s) |
Return the number of components of v less than v[s]. More... | |
template<typename T > | |
Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > | read_corr_L (const Eigen::Array< T, Eigen::Dynamic, 1 > &CPCs, const size_t K) |
Return the Cholesky factor of the correlation matrix of the specified dimensionality corresponding to the specified canonical partial correlations. More... | |
template<typename T > | |
Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > | read_corr_L (const Eigen::Array< T, Eigen::Dynamic, 1 > &CPCs, const size_t K, T &log_prob) |
Return the Cholesky factor of the correlation matrix of the specified dimensionality corresponding to the specified canonical partial correlations, incrementing the specified scalar reference with the log absolute determinant of the Jacobian of the transformation. More... | |
template<typename T > | |
Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > | read_corr_matrix (const Eigen::Array< T, Eigen::Dynamic, 1 > &CPCs, const size_t K) |
Return the correlation matrix of the specified dimensionality corresponding to the specified canonical partial correlations. More... | |
template<typename T > | |
Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > | read_corr_matrix (const Eigen::Array< T, Eigen::Dynamic, 1 > &CPCs, const size_t K, T &log_prob) |
Return the correlation matrix of the specified dimensionality corresponding to the specified canonical partial correlations, incrementing the specified scalar reference with the log absolute determinant of the Jacobian of the transformation. More... | |
template<typename T > | |
Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > | read_cov_L (const Eigen::Array< T, Eigen::Dynamic, 1 > &CPCs, const Eigen::Array< T, Eigen::Dynamic, 1 > &sds, T &log_prob) |
This is the function that should be called prior to evaluating the density of any elliptical distribution. More... | |
template<typename T > | |
Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > | read_cov_matrix (const Eigen::Array< T, Eigen::Dynamic, 1 > &CPCs, const Eigen::Array< T, Eigen::Dynamic, 1 > &sds, T &log_prob) |
A generally worse alternative to call prior to evaluating the density of an elliptical distribution. More... | |
template<typename T > | |
Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > | read_cov_matrix (const Eigen::Array< T, Eigen::Dynamic, 1 > &CPCs, const Eigen::Array< T, Eigen::Dynamic, 1 > &sds) |
Builds a covariance matrix from CPCs and standard deviations. More... | |
template<typename T > | |
Eigen::Matrix< typename boost::math::tools::promote_args< T >::type, Eigen::Dynamic, Eigen::Dynamic > | rep_matrix (const T &x, int m, int n) |
template<typename T > | |
Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > | rep_matrix (const Eigen::Matrix< T, Eigen::Dynamic, 1 > &v, int n) |
template<typename T > | |
Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > | rep_matrix (const Eigen::Matrix< T, 1, Eigen::Dynamic > &rv, int m) |
template<typename T > | |
Eigen::Matrix< typename boost::math::tools::promote_args< T >::type, 1, Eigen::Dynamic > | rep_row_vector (const T &x, int m) |
template<typename T > | |
Eigen::Matrix< typename boost::math::tools::promote_args< T >::type, Eigen::Dynamic, 1 > | rep_vector (const T &x, int n) |
template<typename T > | |
void | resize (T &x, std::vector< size_t > dims) |
Recursively resize the specified vector of vectors, which must bottom out at scalar values, Eigen vectors or Eigen matrices. More... | |
template<typename T > | |
apply_scalar_unary< round_fun, T >::return_t | round (const T &x) |
Vectorized version of round. More... | |
template<typename T > | |
Eigen::Matrix< T, 1, Eigen::Dynamic > | row (const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &m, size_t i) |
Return the specified row of the specified matrix, using start-at-1 indexing. More... | |
template<typename T , int R, int C> | |
int | rows (const Eigen::Matrix< T, R, C > &m) |
Return the number of rows in the specified matrix, vector, or row vector. More... | |
template<int R1, int C1, int R2, int C2> | |
Eigen::Matrix< double, R1, 1 > | rows_dot_product (const Eigen::Matrix< double, R1, C1 > &v1, const Eigen::Matrix< double, R2, C2 > &v2) |
Returns the dot product of the specified vectors. More... | |
template<typename T , int R, int C> | |
Eigen::Matrix< T, R, 1 > | rows_dot_self (const Eigen::Matrix< T, R, C > &x) |
Returns the dot product of each row of a matrix with itself. More... | |
template<typename T > | |
boost::math::tools::promote_args< T >::type | sd (const std::vector< T > &v) |
Returns the unbiased sample standard deviation of the coefficients in the specified column vector. More... | |
template<typename T , int R, int C> | |
boost::math::tools::promote_args< T >::type | sd (const Eigen::Matrix< T, R, C > &m) |
Returns the unbiased sample standard deviation of the coefficients in the specified vector, row vector, or matrix. More... | |
template<typename T > | |
Eigen::Matrix< T, Eigen::Dynamic, 1 > | segment (const Eigen::Matrix< T, Eigen::Dynamic, 1 > &v, size_t i, size_t n) |
Return the specified number of elements as a vector starting from the specified element - 1 of the specified vector. More... | |
template<typename T > | |
Eigen::Matrix< T, 1, Eigen::Dynamic > | segment (const Eigen::Matrix< T, 1, Eigen::Dynamic > &v, size_t i, size_t n) |
template<typename T > | |
std::vector< T > | segment (const std::vector< T > &sv, size_t i, size_t n) |
template<typename T > | |
Eigen::Matrix< T, Eigen::Dynamic, 1 > | simplex_constrain (const Eigen::Matrix< T, Eigen::Dynamic, 1 > &y) |
Return the simplex corresponding to the specified free vector. More... | |
template<typename T > | |
Eigen::Matrix< T, Eigen::Dynamic, 1 > | simplex_constrain (const Eigen::Matrix< T, Eigen::Dynamic, 1 > &y, T &lp) |
Return the simplex corresponding to the specified free vector and increment the specified log probability reference with the log absolute Jacobian determinant of the transform. More... | |
template<typename T > | |
Eigen::Matrix< T, Eigen::Dynamic, 1 > | simplex_free (const Eigen::Matrix< T, Eigen::Dynamic, 1 > &x) |
Return an unconstrained vector that when transformed produces the specified simplex. More... | |
template<typename T > | |
apply_scalar_unary< sin_fun, T >::return_t | sin (const T &x) |
Vectorized version of sin(). More... | |
template<typename T > | |
Eigen::Matrix< T, Eigen::Dynamic, 1 > | singular_values (const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &m) |
Return the vector of the singular values of the specified matrix in decreasing order of magnitude. More... | |
template<typename T > | |
apply_scalar_unary< sinh_fun, T >::return_t | sinh (const T &x) |
Vectorized version of sinh(). More... | |
template<typename T > | |
int | size (const std::vector< T > &x) |
Return the size of the specified standard vector. More... | |
template<typename T > | |
Eigen::Matrix< T, Eigen::Dynamic, 1 > | softmax (const Eigen::Matrix< T, Eigen::Dynamic, 1 > &v) |
Return the softmax of the specified vector. More... | |
template<typename T > | |
std::vector< T > | sort_asc (std::vector< T > xs) |
Return the specified standard vector in ascending order. More... | |
template<typename T > | |
std::vector< T > | sort_desc (std::vector< T > xs) |
Return the specified standard vector in descending order. More... | |
template<typename T , int R, int C> | |
Eigen::Matrix< T, R, C > | sort_asc (Eigen::Matrix< T, R, C > xs) |
Return the specified eigen vector in ascending order. More... | |
template<typename T , int R, int C> | |
Eigen::Matrix< T, R, C > | sort_desc (Eigen::Matrix< T, R, C > xs) |
Return the specified eigen vector in descending order. More... | |
template<typename C > | |
std::vector< int > | sort_indices_asc (const C &xs) |
Return a sorted copy of the argument container in ascending order. More... | |
template<typename C > | |
std::vector< int > | sort_indices_desc (const C &xs) |
Return a sorted copy of the argument container in ascending order. More... | |
template<typename T > | |
apply_scalar_unary< sqrt_fun, T >::return_t | sqrt (const T &x) |
Vectorized version of sqrt(). More... | |
template<typename T > | |
apply_scalar_unary< square_fun, T >::return_t | square (const T &x) |
Vectorized version of square(). More... | |
template<int R, int C> | |
double | squared_distance (const Eigen::Matrix< double, R, C > &v1, const Eigen::Matrix< double, R, C > &v2) |
Returns the squared distance between the specified vectors of the same dimensions. More... | |
template<int R1, int C1, int R2, int C2> | |
double | squared_distance (const Eigen::Matrix< double, R1, C1 > &v1, const Eigen::Matrix< double, R2, C2 > &v2) |
Returns the squared distance between the specified vectors of the same dimensions. More... | |
template<typename T > | |
void | stan_print (std::ostream *o, const T &x) |
template<typename T > | |
void | stan_print (std::ostream *o, const std::vector< T > &x) |
template<typename T > | |
void | stan_print (std::ostream *o, const Eigen::Matrix< T, Eigen::Dynamic, 1 > &x) |
template<typename T > | |
void | stan_print (std::ostream *o, const Eigen::Matrix< T, 1, Eigen::Dynamic > &x) |
template<typename T > | |
void | stan_print (std::ostream *o, const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &x) |
template<typename T > | |
Eigen::Matrix< T, Eigen::Dynamic, 1 > | sub_col (const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &m, size_t i, size_t j, size_t nrows) |
Return a nrows x 1 subcolumn starting at (i-1, j-1). More... | |
template<typename T > | |
Eigen::Matrix< T, 1, Eigen::Dynamic > | sub_row (const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &m, size_t i, size_t j, size_t ncols) |
Return a 1 x nrows subrow starting at (i-1, j-1). More... | |
template<typename T1 , typename T2 , int R, int C> | |
Eigen::Matrix< typename boost::math::tools::promote_args< T1, T2 >::type, R, C > | subtract (const Eigen::Matrix< T1, R, C > &m1, const Eigen::Matrix< T2, R, C > &m2) |
Return the result of subtracting the second specified matrix from the first specified matrix. More... | |
template<typename T1 , typename T2 , int R, int C> | |
Eigen::Matrix< typename boost::math::tools::promote_args< T1, T2 >::type, R, C > | subtract (const T1 &c, const Eigen::Matrix< T2, R, C > &m) |
template<typename T1 , typename T2 , int R, int C> | |
Eigen::Matrix< typename boost::math::tools::promote_args< T1, T2 >::type, R, C > | subtract (const Eigen::Matrix< T1, R, C > &m, const T2 &c) |
template<typename T , int R, int C> | |
double | sum (const Eigen::Matrix< T, R, C > &v) |
Returns the sum of the coefficients of the specified column vector. More... | |
template<typename T > | |
Eigen::Matrix< T, Eigen::Dynamic, 1 > | tail (const Eigen::Matrix< T, Eigen::Dynamic, 1 > &v, size_t n) |
Return the specified number of elements as a vector from the back of the specified vector. More... | |
template<typename T > | |
Eigen::Matrix< T, 1, Eigen::Dynamic > | tail (const Eigen::Matrix< T, 1, Eigen::Dynamic > &rv, size_t n) |
Return the specified number of elements as a row vector from the back of the specified row vector. More... | |
template<typename T > | |
std::vector< T > | tail (const std::vector< T > &sv, size_t n) |
template<typename T > | |
apply_scalar_unary< tan_fun, T >::return_t | tan (const T &x) |
Vectorized version of tan(). More... | |
template<typename T > | |
apply_scalar_unary< tanh_fun, T >::return_t | tanh (const T &x) |
Vectorized version of tanh(). More... | |
matrix_d | tcrossprod (const matrix_d &M) |
Returns the result of post-multiplying a matrix by its own transpose. More... | |
template<typename T > | |
apply_scalar_unary< tgamma_fun, T >::return_t | tgamma (const T &x) |
Vectorized version of tgamma(). More... | |
template<typename T , int R, int C> | |
std::vector< T > | to_array_1d (const Eigen::Matrix< T, R, C > &matrix) |
template<typename T > | |
std::vector< T > | to_array_1d (const std::vector< T > &x) |
template<typename T > | |
std::vector< typename scalar_type< T >::type > | to_array_1d (const std::vector< std::vector< T > > &x) |
template<typename T > | |
std::vector< std::vector< T > > | to_array_2d (const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &matrix) |
template<typename T , int R, int C> | |
Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > | to_matrix (Eigen::Matrix< T, R, C > matrix) |
template<typename T > | |
Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > | to_matrix (const std::vector< std::vector< T > > &vec) |
Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > | to_matrix (const std::vector< std::vector< int > > &vec) |
template<typename T , int R, int C> | |
Eigen::Matrix< T, 1, Eigen::Dynamic > | to_row_vector (const Eigen::Matrix< T, R, C > &matrix) |
template<typename T > | |
Eigen::Matrix< T, 1, Eigen::Dynamic > | to_row_vector (const std::vector< T > &vec) |
Eigen::Matrix< double, 1, Eigen::Dynamic > | to_row_vector (const std::vector< int > &vec) |
template<typename T , int R, int C> | |
Eigen::Matrix< T, Eigen::Dynamic, 1 > | to_vector (const Eigen::Matrix< T, R, C > &matrix) |
template<typename T > | |
Eigen::Matrix< T, Eigen::Dynamic, 1 > | to_vector (const std::vector< T > &vec) |
Eigen::Matrix< double, Eigen::Dynamic, 1 > | to_vector (const std::vector< int > &vec) |
template<typename T > | |
T | trace (const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &m) |
Returns the trace of the specified matrix. More... | |
template<typename T > | |
T | trace (const T &m) |
template<typename T1 , typename T2 , typename T3 , int R1, int C1, int R2, int C2, int R3, int C3> | |
boost::enable_if_c<!stan::is_var< T1 >::value &&!stan::is_var< T2 >::value &&!stan::is_var< T3 >::value, typename boost::math::tools::promote_args< T1, T2, T3 >::type >::type | trace_gen_inv_quad_form_ldlt (const Eigen::Matrix< T1, R1, C1 > &D, const stan::math::LDLT_factor< T2, R2, C2 > &A, const Eigen::Matrix< T3, R3, C3 > &B) |
template<int RD, int CD, int RA, int CA, int RB, int CB> | |
double | trace_gen_quad_form (const Eigen::Matrix< double, RD, CD > &D, const Eigen::Matrix< double, RA, CA > &A, const Eigen::Matrix< double, RB, CB > &B) |
Compute trace(D B^T A B). More... | |
template<typename T1 , typename T2 , int R2, int C2, int R3, int C3> | |
boost::enable_if_c<!stan::is_var< T1 >::value &&!stan::is_var< T2 >::value, typename boost::math::tools::promote_args< T1, T2 >::type >::type | trace_inv_quad_form_ldlt (const stan::math::LDLT_factor< T1, R2, C2 > &A, const Eigen::Matrix< T2, R3, C3 > &B) |
template<int RA, int CA, int RB, int CB> | |
double | trace_quad_form (const Eigen::Matrix< double, RA, CA > &A, const Eigen::Matrix< double, RB, CB > &B) |
Compute trace(B^T A B). More... | |
template<typename T , int R, int C> | |
Eigen::Matrix< T, C, R > | transpose (const Eigen::Matrix< T, R, C > &m) |
template<typename T , int R, int C> | |
Eigen::Matrix< T, R, C > | unit_vector_constrain (const Eigen::Matrix< T, R, C > &y) |
Return the unit length vector corresponding to the free vector y. More... | |
template<typename T , int R, int C> | |
Eigen::Matrix< T, R, C > | unit_vector_constrain (const Eigen::Matrix< T, R, C > &y, T &lp) |
Return the unit length vector corresponding to the free vector y. More... | |
template<typename T > | |
Eigen::Matrix< T, Eigen::Dynamic, 1 > | unit_vector_free (const Eigen::Matrix< T, Eigen::Dynamic, 1 > &x) |
Transformation of a unit length vector to a "free" vector However, we are just fixing the unidentified radius to 1. More... | |
template<typename T , int R, int C> | |
Eigen::Matrix< typename child_type< T >::type, R, C > | value_of (const Eigen::Matrix< T, R, C > &M) |
Convert a matrix of type T to a matrix of doubles. More... | |
template<int R, int C> | |
Eigen::Matrix< double, R, C > | value_of (const Eigen::Matrix< double, R, C > &x) |
Return the specified argument. More... | |
template<typename T , int R, int C> | |
Eigen::Matrix< double, R, C > | value_of_rec (const Eigen::Matrix< T, R, C > &M) |
Convert a matrix of type T to a matrix of doubles. More... | |
template<int R, int C> | |
Eigen::Matrix< double, R, C > | value_of_rec (const Eigen::Matrix< double, R, C > &x) |
Return the specified argument. More... | |
template<typename T > | |
boost::math::tools::promote_args< T >::type | variance (const std::vector< T > &v) |
Returns the sample variance (divide by length - 1) of the coefficients in the specified standard vector. More... | |
template<typename T , int R, int C> | |
boost::math::tools::promote_args< T >::type | variance (const Eigen::Matrix< T, R, C > &m) |
Returns the sample variance (divide by length - 1) of the coefficients in the specified column vector. More... | |
template<typename F > | |
void | finite_diff_gradient (const F &f, const Eigen::Matrix< double,-1, 1 > &x, double &fx, Eigen::Matrix< double,-1, 1 > &grad_fx, const double epsilon=1e-03) |
Calculate the value and the gradient of the specified function at the specified argument using finite difference. More... | |
template<typename F > | |
double | finite_diff_hess_helper (const F &f, const Eigen::Matrix< double, Eigen::Dynamic, 1 > &x, const int lambda, const double epsilon=1e-03) |
template<typename F > | |
void | finite_diff_hessian (const F &f, const Eigen::Matrix< double,-1, 1 > &x, double &fx, Eigen::Matrix< double,-1, 1 > &grad_fx, Eigen::Matrix< double,-1,-1 > &hess_fx, const double epsilon=1e-03) |
Calculate the value and the Hessian of the specified function at the specified argument using second-order finite difference. More... | |
template<bool propto, typename T_prob > | |
boost::math::tools::promote_args< T_prob >::type | categorical_log (int n, const Eigen::Matrix< T_prob, Eigen::Dynamic, 1 > &theta) |
template<typename T_prob > | |
boost::math::tools::promote_args< T_prob >::type | categorical_log (const typename math::index_type< Eigen::Matrix< T_prob, Eigen::Dynamic, 1 > >::type n, const Eigen::Matrix< T_prob, Eigen::Dynamic, 1 > &theta) |
template<bool propto, typename T_prob > | |
boost::math::tools::promote_args< T_prob >::type | categorical_log (const std::vector< int > &ns, const Eigen::Matrix< T_prob, Eigen::Dynamic, 1 > &theta) |
template<typename T_prob > | |
boost::math::tools::promote_args< T_prob >::type | categorical_log (const std::vector< int > &ns, const Eigen::Matrix< T_prob, Eigen::Dynamic, 1 > &theta) |
template<bool propto, typename T_prob > | |
boost::math::tools::promote_args< T_prob >::type | categorical_logit_log (int n, const Eigen::Matrix< T_prob, Eigen::Dynamic, 1 > &beta) |
template<typename T_prob > | |
boost::math::tools::promote_args< T_prob >::type | categorical_logit_log (int n, const Eigen::Matrix< T_prob, Eigen::Dynamic, 1 > &beta) |
template<bool propto, typename T_prob > | |
boost::math::tools::promote_args< T_prob >::type | categorical_logit_log (const std::vector< int > &ns, const Eigen::Matrix< T_prob, Eigen::Dynamic, 1 > &beta) |
template<typename T_prob > | |
boost::math::tools::promote_args< T_prob >::type | categorical_logit_log (const std::vector< int > &ns, const Eigen::Matrix< T_prob, Eigen::Dynamic, 1 > &beta) |
template<class RNG > | |
int | categorical_rng (const Eigen::Matrix< double, Eigen::Dynamic, 1 > &theta, RNG &rng) |
template<bool propto, typename T_prob , typename T_prior_sample_size > | |
boost::math::tools::promote_args< T_prob, T_prior_sample_size >::type | dirichlet_log (const Eigen::Matrix< T_prob, Eigen::Dynamic, 1 > &theta, const Eigen::Matrix< T_prior_sample_size, Eigen::Dynamic, 1 > &alpha) |
The log of the Dirichlet density for the given theta and a vector of prior sample sizes, alpha. More... | |
template<typename T_prob , typename T_prior_sample_size > | |
boost::math::tools::promote_args< T_prob, T_prior_sample_size >::type | dirichlet_log (const Eigen::Matrix< T_prob, Eigen::Dynamic, 1 > &theta, const Eigen::Matrix< T_prior_sample_size, Eigen::Dynamic, 1 > &alpha) |
template<class RNG > | |
Eigen::VectorXd | dirichlet_rng (const Eigen::Matrix< double, Eigen::Dynamic, 1 > &alpha, RNG &rng) |
Return a draw from a Dirichlet distribution with specified parameters and pseudo-random number generator. More... | |
template<bool propto, typename T_y , typename T_F , typename T_G , typename T_V , typename T_W , typename T_m0 , typename T_C0 > | |
return_type< T_y, typename return_type< T_F, T_G, T_V, T_W, T_m0, T_C0 >::type >::type | gaussian_dlm_obs_log (const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &y, const Eigen::Matrix< T_F, Eigen::Dynamic, Eigen::Dynamic > &F, const Eigen::Matrix< T_G, Eigen::Dynamic, Eigen::Dynamic > &G, const Eigen::Matrix< T_V, Eigen::Dynamic, Eigen::Dynamic > &V, const Eigen::Matrix< T_W, Eigen::Dynamic, Eigen::Dynamic > &W, const Eigen::Matrix< T_m0, Eigen::Dynamic, 1 > &m0, const Eigen::Matrix< T_C0, Eigen::Dynamic, Eigen::Dynamic > &C0) |
The log of a Gaussian dynamic linear model (GDLM). More... | |
template<typename T_y , typename T_F , typename T_G , typename T_V , typename T_W , typename T_m0 , typename T_C0 > | |
return_type< T_y, typename return_type< T_F, T_G, T_V, T_W, T_m0, T_C0 >::type >::type | gaussian_dlm_obs_log (const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &y, const Eigen::Matrix< T_F, Eigen::Dynamic, Eigen::Dynamic > &F, const Eigen::Matrix< T_G, Eigen::Dynamic, Eigen::Dynamic > &G, const Eigen::Matrix< T_V, Eigen::Dynamic, Eigen::Dynamic > &V, const Eigen::Matrix< T_W, Eigen::Dynamic, Eigen::Dynamic > &W, const Eigen::Matrix< T_m0, Eigen::Dynamic, 1 > &m0, const Eigen::Matrix< T_C0, Eigen::Dynamic, Eigen::Dynamic > &C0) |
template<bool propto, typename T_y , typename T_F , typename T_G , typename T_V , typename T_W , typename T_m0 , typename T_C0 > | |
return_type< T_y, typename return_type< T_F, T_G, T_V, T_W, T_m0, T_C0 >::type >::type | gaussian_dlm_obs_log (const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &y, const Eigen::Matrix< T_F, Eigen::Dynamic, Eigen::Dynamic > &F, const Eigen::Matrix< T_G, Eigen::Dynamic, Eigen::Dynamic > &G, const Eigen::Matrix< T_V, Eigen::Dynamic, 1 > &V, const Eigen::Matrix< T_W, Eigen::Dynamic, Eigen::Dynamic > &W, const Eigen::Matrix< T_m0, Eigen::Dynamic, 1 > &m0, const Eigen::Matrix< T_C0, Eigen::Dynamic, Eigen::Dynamic > &C0) |
The log of a Gaussian dynamic linear model (GDLM) with uncorrelated observation disturbances. More... | |
template<typename T_y , typename T_F , typename T_G , typename T_V , typename T_W , typename T_m0 , typename T_C0 > | |
return_type< T_y, typename return_type< T_F, T_G, T_V, T_W, T_m0, T_C0 >::type >::type | gaussian_dlm_obs_log (const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &y, const Eigen::Matrix< T_F, Eigen::Dynamic, Eigen::Dynamic > &F, const Eigen::Matrix< T_G, Eigen::Dynamic, Eigen::Dynamic > &G, const Eigen::Matrix< T_V, Eigen::Dynamic, 1 > &V, const Eigen::Matrix< T_W, Eigen::Dynamic, Eigen::Dynamic > &W, const Eigen::Matrix< T_m0, Eigen::Dynamic, 1 > &m0, const Eigen::Matrix< T_C0, Eigen::Dynamic, Eigen::Dynamic > &C0) |
template<bool propto, typename T_y , typename T_dof , typename T_scale > | |
boost::math::tools::promote_args< T_y, T_dof, T_scale >::type | inv_wishart_log (const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &W, const T_dof &nu, const Eigen::Matrix< T_scale, Eigen::Dynamic, Eigen::Dynamic > &S) |
The log of the Inverse-Wishart density for the given W, degrees of freedom, and scale matrix. More... | |
template<typename T_y , typename T_dof , typename T_scale > | |
boost::math::tools::promote_args< T_y, T_dof, T_scale >::type | inv_wishart_log (const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &W, const T_dof &nu, const Eigen::Matrix< T_scale, Eigen::Dynamic, Eigen::Dynamic > &S) |
template<class RNG > | |
Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > | inv_wishart_rng (const double nu, const Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > &S, RNG &rng) |
template<bool propto, typename T_covar , typename T_shape > | |
boost::math::tools::promote_args< T_covar, T_shape >::type | lkj_corr_cholesky_log (const Eigen::Matrix< T_covar, Eigen::Dynamic, Eigen::Dynamic > &L, const T_shape &eta) |
template<typename T_covar , typename T_shape > | |
boost::math::tools::promote_args< T_covar, T_shape >::type | lkj_corr_cholesky_log (const Eigen::Matrix< T_covar, Eigen::Dynamic, Eigen::Dynamic > &L, const T_shape &eta) |
template<class RNG > | |
Eigen::MatrixXd | lkj_corr_cholesky_rng (const size_t K, const double eta, RNG &rng) |
template<typename T_shape > | |
T_shape | do_lkj_constant (const T_shape &eta, const unsigned int &K) |
template<bool propto, typename T_y , typename T_shape > | |
boost::math::tools::promote_args< T_y, T_shape >::type | lkj_corr_log (const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &y, const T_shape &eta) |
template<typename T_y , typename T_shape > | |
boost::math::tools::promote_args< T_y, T_shape >::type | lkj_corr_log (const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &y, const T_shape &eta) |
template<class RNG > | |
Eigen::MatrixXd | lkj_corr_rng (const size_t K, const double eta, RNG &rng) |
template<bool propto, typename T_y , typename T_loc , typename T_scale , typename T_shape > | |
boost::math::tools::promote_args< T_y, T_loc, T_scale, T_shape >::type | lkj_cov_log (const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &y, const Eigen::Matrix< T_loc, Eigen::Dynamic, 1 > &mu, const Eigen::Matrix< T_scale, Eigen::Dynamic, 1 > &sigma, const T_shape &eta) |
template<typename T_y , typename T_loc , typename T_scale , typename T_shape > | |
boost::math::tools::promote_args< T_y, T_loc, T_scale, T_shape >::type | lkj_cov_log (const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &y, const Eigen::Matrix< T_loc, Eigen::Dynamic, 1 > &mu, const Eigen::Matrix< T_scale, Eigen::Dynamic, 1 > &sigma, const T_shape &eta) |
template<bool propto, typename T_y , typename T_loc , typename T_scale , typename T_shape > | |
boost::math::tools::promote_args< T_y, T_loc, T_scale, T_shape >::type | lkj_cov_log (const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &y, const T_loc &mu, const T_scale &sigma, const T_shape &eta) |
template<typename T_y , typename T_loc , typename T_scale , typename T_shape > | |
boost::math::tools::promote_args< T_y, T_loc, T_scale, T_shape >::type | lkj_cov_log (const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &y, const T_loc &mu, const T_scale &sigma, const T_shape &eta) |
template<bool propto, typename T_y , typename T_Mu , typename T_Sigma , typename T_D > | |
boost::math::tools::promote_args< T_y, T_Mu, T_Sigma, T_D >::type | matrix_normal_prec_log (const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &y, const Eigen::Matrix< T_Mu, Eigen::Dynamic, Eigen::Dynamic > &Mu, const Eigen::Matrix< T_Sigma, Eigen::Dynamic, Eigen::Dynamic > &Sigma, const Eigen::Matrix< T_D, Eigen::Dynamic, Eigen::Dynamic > &D) |
The log of the matrix normal density for the given y, mu, Sigma and D where Sigma and D are given as precision matrices, not covariance matrices. More... | |
template<typename T_y , typename T_Mu , typename T_Sigma , typename T_D > | |
boost::math::tools::promote_args< T_y, T_Mu, T_Sigma, T_D >::type | matrix_normal_prec_log (const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &y, const Eigen::Matrix< T_Mu, Eigen::Dynamic, Eigen::Dynamic > &Mu, const Eigen::Matrix< T_Sigma, Eigen::Dynamic, Eigen::Dynamic > &Sigma, const Eigen::Matrix< T_D, Eigen::Dynamic, Eigen::Dynamic > &D) |
template<bool propto, typename T_y , typename T_covar , typename T_w > | |
boost::math::tools::promote_args< T_y, T_covar, T_w >::type | multi_gp_cholesky_log (const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &y, const Eigen::Matrix< T_covar, Eigen::Dynamic, Eigen::Dynamic > &L, const Eigen::Matrix< T_w, Eigen::Dynamic, 1 > &w) |
The log of a multivariate Gaussian Process for the given y, w, and a Cholesky factor L of the kernel matrix Sigma. More... | |
template<typename T_y , typename T_covar , typename T_w > | |
boost::math::tools::promote_args< T_y, T_covar, T_w >::type | multi_gp_cholesky_log (const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &y, const Eigen::Matrix< T_covar, Eigen::Dynamic, Eigen::Dynamic > &L, const Eigen::Matrix< T_w, Eigen::Dynamic, 1 > &w) |
template<bool propto, typename T_y , typename T_covar , typename T_w > | |
boost::math::tools::promote_args< T_y, T_covar, T_w >::type | multi_gp_log (const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &y, const Eigen::Matrix< T_covar, Eigen::Dynamic, Eigen::Dynamic > &Sigma, const Eigen::Matrix< T_w, Eigen::Dynamic, 1 > &w) |
The log of a multivariate Gaussian Process for the given y, Sigma, and w. More... | |
template<typename T_y , typename T_covar , typename T_w > | |
boost::math::tools::promote_args< T_y, T_covar, T_w >::type | multi_gp_log (const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &y, const Eigen::Matrix< T_covar, Eigen::Dynamic, Eigen::Dynamic > &Sigma, const Eigen::Matrix< T_w, Eigen::Dynamic, 1 > &w) |
template<bool propto, typename T_y , typename T_loc , typename T_covar > | |
return_type< T_y, T_loc, T_covar >::type | multi_normal_cholesky_log (const T_y &y, const T_loc &mu, const T_covar &L) |
The log of the multivariate normal density for the given y, mu, and a Cholesky factor L of the variance matrix. More... | |
template<typename T_y , typename T_loc , typename T_covar > | |
return_type< T_y, T_loc, T_covar >::type | multi_normal_cholesky_log (const T_y &y, const T_loc &mu, const T_covar &L) |
template<class RNG > | |
Eigen::VectorXd | multi_normal_cholesky_rng (const Eigen::Matrix< double, Eigen::Dynamic, 1 > &mu, const Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > &S, RNG &rng) |
template<bool propto, typename T_y , typename T_loc , typename T_covar > | |
return_type< T_y, T_loc, T_covar >::type | multi_normal_log (const T_y &y, const T_loc &mu, const T_covar &Sigma) |
template<typename T_y , typename T_loc , typename T_covar > | |
return_type< T_y, T_loc, T_covar >::type | multi_normal_log (const T_y &y, const T_loc &mu, const T_covar &Sigma) |
template<bool propto, typename T_y , typename T_loc , typename T_covar > | |
return_type< T_y, T_loc, T_covar >::type | multi_normal_prec_log (const T_y &y, const T_loc &mu, const T_covar &Sigma) |
template<typename T_y , typename T_loc , typename T_covar > | |
return_type< T_y, T_loc, T_covar >::type | multi_normal_prec_log (const T_y &y, const T_loc &mu, const T_covar &Sigma) |
template<class RNG > | |
Eigen::VectorXd | multi_normal_rng (const Eigen::Matrix< double, Eigen::Dynamic, 1 > &mu, const Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > &S, RNG &rng) |
template<bool propto, typename T_y , typename T_dof , typename T_loc , typename T_scale > | |
return_type< T_y, T_dof, T_loc, T_scale >::type | multi_student_t_log (const T_y &y, const T_dof &nu, const T_loc &mu, const T_scale &Sigma) |
Return the log of the multivariate Student t distribution at the specified arguments. More... | |
template<typename T_y , typename T_dof , typename T_loc , typename T_scale > | |
return_type< T_y, T_dof, T_loc, T_scale >::type | multi_student_t_log (const T_y &y, const T_dof &nu, const T_loc &mu, const T_scale &Sigma) |
template<class RNG > | |
Eigen::VectorXd | multi_student_t_rng (const double nu, const Eigen::Matrix< double, Eigen::Dynamic, 1 > &mu, const Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > &s, RNG &rng) |
template<bool propto, typename T_prob > | |
boost::math::tools::promote_args< T_prob >::type | multinomial_log (const std::vector< int > &ns, const Eigen::Matrix< T_prob, Eigen::Dynamic, 1 > &theta) |
template<typename T_prob > | |
boost::math::tools::promote_args< T_prob >::type | multinomial_log (const std::vector< int > &ns, const Eigen::Matrix< T_prob, Eigen::Dynamic, 1 > &theta) |
template<class RNG > | |
std::vector< int > | multinomial_rng (const Eigen::Matrix< double, Eigen::Dynamic, 1 > &theta, const int N, RNG &rng) |
template<typename T > | |
T | log_inv_logit_diff (const T &alpha, const T &beta) |
template<bool propto, typename T_lambda , typename T_cut > | |
boost::math::tools::promote_args< T_lambda, T_cut >::type | ordered_logistic_log (int y, const T_lambda &lambda, const Eigen::Matrix< T_cut, Eigen::Dynamic, 1 > &c) |
Returns the (natural) log probability of the specified integer outcome given the continuous location and specified cutpoints in an ordered logistic model. More... | |
template<typename T_lambda , typename T_cut > | |
boost::math::tools::promote_args< T_lambda, T_cut >::type | ordered_logistic_log (int y, const T_lambda &lambda, const Eigen::Matrix< T_cut, Eigen::Dynamic, 1 > &c) |
template<class RNG > | |
int | ordered_logistic_rng (const double eta, const Eigen::Matrix< double, Eigen::Dynamic, 1 > &c, RNG &rng) |
template<bool propto, typename T_y , typename T_dof , typename T_scale > | |
boost::math::tools::promote_args< T_y, T_dof, T_scale >::type | wishart_log (const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &W, const T_dof &nu, const Eigen::Matrix< T_scale, Eigen::Dynamic, Eigen::Dynamic > &S) |
The log of the Wishart density for the given W, degrees of freedom, and scale matrix. More... | |
template<typename T_y , typename T_dof , typename T_scale > | |
boost::math::tools::promote_args< T_y, T_dof, T_scale >::type | wishart_log (const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &W, const T_dof &nu, const Eigen::Matrix< T_scale, Eigen::Dynamic, Eigen::Dynamic > &S) |
template<class RNG > | |
Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > | wishart_rng (const double nu, const Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > &S, RNG &rng) |
template<typename T_y , typename T_low , typename T_high > | |
bool | check_bounded (const char *function, const char *name, const T_y &y, const T_low &low, const T_high &high) |
Return true if the value is between the low and high values, inclusively. More... | |
template<typename T > | |
bool | check_consistent_size (const char *function, const char *name, const T &x, size_t expected_size) |
Return true if the dimension of x is consistent, which is defined to be expected_size if x is a vector or 1 if x is not a vector. More... | |
template<typename T1 , typename T2 > | |
bool | check_consistent_sizes (const char *function, const char *name1, const T1 &x1, const char *name2, const T2 &x2) |
Return true if the dimension of x1 is consistent with x2. More... | |
template<typename T1 , typename T2 , typename T3 > | |
bool | check_consistent_sizes (const char *function, const char *name1, const T1 &x1, const char *name2, const T2 &x2, const char *name3, const T3 &x3) |
Return true if the dimension of x1, x2, and x3 are consistent. More... | |
template<typename T1 , typename T2 , typename T3 , typename T4 > | |
bool | check_consistent_sizes (const char *function, const char *name1, const T1 &x1, const char *name2, const T2 &x2, const char *name3, const T3 &x3, const char *name4, const T4 &x4) |
Return true if the dimension of x1, x2, x3, and x4 are consistent. More... | |
template<typename T1 , typename T2 , typename T3 , typename T4 , typename T5 > | |
bool | check_consistent_sizes (const char *function, const char *name1, const T1 &x1, const char *name2, const T2 &x2, const char *name3, const T3 &x3, const char *name4, const T4 &x4, const char *name5, const T5 &x5) |
template<typename T_y , typename T_eq > | |
bool | check_equal (const char *function, const char *name, const T_y &y, const T_eq &eq) |
Return true if y is equal to eq . More... | |
template<typename T_y > | |
bool | check_finite (const char *function, const char *name, const T_y &y) |
Return true if y is finite. More... | |
template<typename T_y , typename T_low > | |
bool | check_greater (const char *function, const char *name, const T_y &y, const T_low &low) |
Return true if y is strictly greater than low . More... | |
template<typename T_y , typename T_low > | |
bool | check_greater_or_equal (const char *function, const char *name, const T_y &y, const T_low &low) |
Return true if y is greater or equal than low . More... | |
template<typename T_y , typename T_high > | |
bool | check_less (const char *function, const char *name, const T_y &y, const T_high &high) |
Return true if y is strictly less than high . More... | |
template<typename T_y , typename T_high > | |
bool | check_less_or_equal (const char *function, const char *name, const T_y &y, const T_high &high) |
Return true if y is less or equal to high . More... | |
template<typename T_y > | |
bool | check_nonnegative (const char *function, const char *name, const T_y &y) |
Return true if y is non-negative. More... | |
template<typename T_y > | |
bool | check_not_nan (const char *function, const char *name, const T_y &y) |
Return true if y is not NaN . More... | |
template<typename T_y > | |
bool | check_positive (const char *function, const char *name, const T_y &y) |
Return true if y is positive. More... | |
template<typename T_y > | |
bool | check_positive_finite (const char *function, const char *name, const T_y &y) |
Return true if y is positive and finite. More... | |
bool | check_positive_size (const char *function, const char *name, const char *expr, const int size) |
Return true if size is positive. More... | |
template<typename T_size1 , typename T_size2 > | |
bool | check_size_match (const char *function, const char *name_i, T_size1 i, const char *name_j, T_size2 j) |
Return true if the provided sizes match. More... | |
template<typename T_size1 , typename T_size2 > | |
bool | check_size_match (const char *function, const char *expr_i, const char *name_i, T_size1 i, const char *expr_j, const char *name_j, T_size2 j) |
Return true if the provided sizes match. More... | |
template<typename T > | |
void | domain_error (const char *function, const char *name, const T &y, const char *msg1, const char *msg2) |
Throw a domain error with a consistently formatted message. More... | |
template<typename T > | |
void | domain_error (const char *function, const char *name, const T &y, const char *msg1) |
Throw a domain error with a consistently formatted message. More... | |
template<typename T > | |
void | domain_error_vec (const char *function, const char *name, const T &y, const size_t i, const char *msg1, const char *msg2) |
Throw a domain error with a consistently formatted message. More... | |
template<typename T > | |
void | domain_error_vec (const char *function, const char *name, const T &y, const size_t i, const char *msg) |
Throw a domain error with a consistently formatted message. More... | |
template<typename T > | |
void | invalid_argument (const char *function, const char *name, const T &y, const char *msg1, const char *msg2) |
Throw an invalid_argument exception with a consistently formatted message. More... | |
template<typename T > | |
void | invalid_argument (const char *function, const char *name, const T &y, const char *msg1) |
Throw an invalid_argument exception with a consistently formatted message. More... | |
template<typename T > | |
void | invalid_argument_vec (const char *function, const char *name, const T &y, const size_t i, const char *msg1, const char *msg2) |
Throw an invalid argument exception with a consistently formatted message. More... | |
template<typename T > | |
void | invalid_argument_vec (const char *function, const char *name, const T &y, const size_t i, const char *msg) |
Throw an invalid argument exception with a consistently formatted message. More... | |
void | out_of_range (const char *function, const int max, const int index, const char *msg1="", const char *msg2="") |
Throw an out_of_range exception with a consistently formatted message. More... | |
double | abs (double x) |
Return floating-point absolute value. More... | |
template<typename T > | |
bool | as_bool (const T x) |
Return 1 if the argument is unequal to zero and 0 otherwise. More... | |
template<typename T2 > | |
T2 | bessel_first_kind (const int v, const T2 z) |
| |
template<typename T2 > | |
T2 | bessel_second_kind (const int v, const T2 z) |
| |
template<typename T > | |
boost::math::tools::promote_args< T >::type | binary_log_loss (const int y, const T y_hat) |
Returns the log loss function for binary classification with specified reference and response values. More... | |
template<typename T_N , typename T_n > | |
boost::math::tools::promote_args< T_N, T_n >::type | binomial_coefficient_log (const T_N N, const T_n n) |
Return the log of the binomial coefficient for the specified arguments. More... | |
double | pi () |
Return the value of pi. More... | |
double | e () |
Return the base of the natural logarithm. More... | |
double | sqrt2 () |
Return the square root of two. More... | |
double | log10 () |
Return natural logarithm of ten. More... | |
double | positive_infinity () |
Return positive infinity. More... | |
double | negative_infinity () |
Return negative infinity. More... | |
double | not_a_number () |
Return (quiet) not-a-number. More... | |
double | machine_precision () |
Returns the difference between 1.0 and the next value representable. More... | |
template<typename T > | |
T | corr_constrain (const T x) |
Return the result of transforming the specified scalar to have a valid correlation value between -1 and 1 (inclusive). More... | |
template<typename T > | |
T | corr_constrain (const T x, T &lp) |
Return the result of transforming the specified scalar to have a valid correlation value between -1 and 1 (inclusive). More... | |
template<typename T > | |
T | corr_free (const T y) |
Return the unconstrained scalar that when transformed to a valid correlation produces the specified value. More... | |
double | digamma (double x) |
| |
template<typename T1 , typename T2 > | |
stan::return_type< T1, T2 >::type | divide (const T1 &x, const T2 &y) |
Return the division of the first scalar by the second scalar. More... | |
int | divide (const int x, const int y) |
template<typename T > | |
boost::math::tools::promote_args< T >::type | exp2 (const T y) |
Return the exponent base 2 of the specified argument (C99). More... | |
template<typename T > | |
T | F32 (T a, T b, T c, T d, T e, T z, T precision=1e-6) |
template<typename T1 , typename T2 > | |
boost::math::tools::promote_args< T1, T2 >::type | falling_factorial (const T1 x, const T2 n) |
| |
template<typename T1 , typename T2 > | |
boost::math::tools::promote_args< T1, T2 >::type | fdim (T1 a, T2 b) |
The positive difference function (C99). More... | |
template<typename T , typename S > | |
void | fill (T &x, const S &y) |
Fill the specified container with the specified value. More... | |
double | gamma_p (double x, double a) |
| |
double | gamma_q (double x, double a) |
| |
template<typename T > | |
void | grad_2F1 (T &gradA, T &gradC, T a, T b, T c, T z, T precision=1e-6) |
template<typename T > | |
void | grad_F32 (T *g, T a, T b, T c, T d, T e, T z, T precision=1e-6) |
void | grad_inc_beta (double &g1, double &g2, double a, double b, double z) |
template<typename T > | |
void | grad_reg_inc_beta (T &g1, T &g2, T a, T b, T z, T digammaA, T digammaB, T digammaSum, T betaAB) |
template<typename T > | |
T | grad_reg_inc_gamma (T a, T z, T g, T dig, T precision=1e-6) |
double | ibeta (const double a, const double b, const double x) |
The normalized incomplete beta function of a, b, and x. More... | |
template<typename T > | |
T | identity_constrain (T x) |
Returns the result of applying the identity constraint transform to the input. More... | |
template<typename T > | |
T | identity_constrain (const T x, T &) |
Returns the result of applying the identity constraint transform to the input and increments the log probability reference with the log absolute Jacobian determinant. More... | |
template<typename T > | |
T | identity_free (const T y) |
Returns the result of applying the inverse of the identity constraint transform to the input. More... | |
template<typename T_true , typename T_false > | |
boost::math::tools::promote_args< T_true, T_false >::type | if_else (const bool c, const T_true y_true, const T_false y_false) |
Return the second argument if the first argument is true and otherwise return the second argument. More... | |
double | inc_beta (const double &a, const double &b, const double &x) |
template<typename T > | |
T | inc_beta_ddb (T a, T b, T z, T digamma_b, T digamma_ab) |
Returns the partial derivative of the regularized incomplete beta function, I_{z}(a, b) with respect to b. More... | |
template<typename T > | |
T | inc_beta_dda (T a, T b, T z, T digamma_a, T digamma_ab) |
Returns the partial derivative of the regularized incomplete beta function, I_{z}(a, b) with respect to a. More... | |
template<typename T > | |
T | inc_beta_ddz (T a, T b, T z) |
Returns the partial derivative of the regularized incomplete beta function, I_{z}(a, b) with respect to z. More... | |
template<> | |
double | inc_beta_ddz (double a, double b, double z) |
template<typename T > | |
unsigned int | int_step (const T y) |
The integer step, or Heaviside, function. More... | |
double | inv (const double x) |
double | inv_cloglog (const double x) |
The inverse complementary log-log function. More... | |
double | inv_logit (const double a) |
Returns the inverse logit function applied to the argument. More... | |
double | inv_Phi (double p) |
The inverse of the unit normal cumulative distribution function. More... | |
double | inv_sqrt (const double x) |
double | inv_square (const double x) |
template<typename Vector > | |
void | inverse_softmax (const Vector &simplex, Vector &y) |
Writes the inverse softmax of the simplex argument into the second argument. More... | |
int | is_inf (const double x) |
Returns 1 if the input is infinite and 0 otherwise. More... | |
bool | is_nan (double x) |
Returns 1 if the input is NaN and 0 otherwise. More... | |
template<typename T > | |
bool | is_uninitialized (T x) |
Returns true if the specified variable is uninitialized. More... | |
template<typename T , typename TL > | |
T | lb_constrain (const T x, const TL lb) |
Return the lower-bounded value for the specified unconstrained input and specified lower bound. More... | |
template<typename T , typename TL > | |
boost::math::tools::promote_args< T, TL >::type | lb_constrain (const T x, const TL lb, T &lp) |
Return the lower-bounded value for the speicifed unconstrained input and specified lower bound, incrementing the specified reference with the log absolute Jacobian determinant of the transform. More... | |
template<typename T , typename TL > | |
boost::math::tools::promote_args< T, TL >::type | lb_free (const T y, const TL lb) |
Return the unconstrained value that produces the specified lower-bound constrained value. More... | |
template<typename T1 , typename T2 > | |
boost::math::tools::promote_args< T1, T2 >::type | lbeta (const T1 a, const T2 b) |
Return the log of the beta function applied to the specified arguments. More... | |
double | lgamma (double x) |
| |
template<typename T > | |
boost::math::tools::promote_args< T >::type | lmgamma (const int k, T x) |
Return the natural logarithm of the multivariate gamma function with the speciifed dimensions and argument. More... | |
double | log1m (const double x) |
Return the natural logarithm of one minus the specified value. More... | |
double | log1m_exp (const double a) |
Calculates the log of 1 minus the exponential of the specified value without overflow log1m_exp(x) = log(1-exp(x)). More... | |
template<typename T > | |
boost::math::tools::promote_args< T >::type | log1m_inv_logit (const T u) |
Returns the natural logarithm of 1 minus the inverse logit of the specified argument. More... | |
template<typename T > | |
boost::math::tools::promote_args< T >::type | log1p (const T x) |
Return the natural logarithm of one plus the specified value. More... | |
double | log1p_exp (const double a) |
Calculates the log of 1 plus the exponential of the specified value without overflow. More... | |
template<typename T > | |
boost::math::tools::promote_args< T >::type | log2 (const T a) |
Returns the base 2 logarithm of the argument (C99). More... | |
double | log2 () |
Return natural logarithm of two. More... | |
template<typename T1 , typename T2 > | |
boost::math::tools::promote_args< T1, T2 >::type | log_diff_exp (const T1 x, const T2 y) |
The natural logarithm of the difference of the natural exponentiation of x1 and the natural exponentiation of x2. More... | |
template<typename T1 , typename T2 > | |
boost::math::tools::promote_args< T1, T2 >::type | log_falling_factorial (const T1 x, const T2 n) |
| |
template<typename T > | |
boost::math::tools::promote_args< T >::type | log_inv_logit (const T &u) |
Returns the natural logarithm of the inverse logit of the specified argument. More... | |
double | log_mix (double theta, double lambda1, double lambda2) |
Return the log mixture density with specified mixing proportion and log densities. More... | |
template<typename T1 , typename T2 > | |
boost::math::tools::promote_args< T1, T2 >::type | log_rising_factorial (const T1 x, const T2 n) |
| |
template<typename T1 , typename T2 > | |
boost::math::tools::promote_args< T1, T2 >::type | log_sum_exp (const T2 &a, const T1 &b) |
Calculates the log sum of exponetials without overflow. More... | |
template<typename T1 , typename T2 > | |
int | logical_and (const T1 x1, const T2 x2) |
The logical and function which returns 1 if both arguments are unequal to zero and 0 otherwise. More... | |
template<typename T1 , typename T2 > | |
int | logical_eq (const T1 x1, const T2 x2) |
Return 1 if the first argument is equal to the second. More... | |
template<typename T1 , typename T2 > | |
int | logical_gt (const T1 x1, const T2 x2) |
Return 1 if the first argument is strictly greater than the second. More... | |
template<typename T1 , typename T2 > | |
int | logical_gte (const T1 x1, const T2 x2) |
Return 1 if the first argument is greater than or equal to the second. More... | |
template<typename T1 , typename T2 > | |
int | logical_lt (T1 x1, T2 x2) |
Return 1 if the first argument is strictly less than the second. More... | |
template<typename T1 , typename T2 > | |
int | logical_lte (const T1 x1, const T2 x2) |
Return 1 if the first argument is less than or equal to the second. More... | |
template<typename T > | |
int | logical_negation (const T x) |
The logical negation function which returns 1 if the input is equal to zero and 0 otherwise. More... | |
template<typename T1 , typename T2 > | |
int | logical_neq (const T1 x1, const T2 x2) |
Return 1 if the first argument is unequal to the second. More... | |
template<typename T1 , typename T2 > | |
int | logical_or (T1 x1, T2 x2) |
The logical or function which returns 1 if either argument is unequal to zero and 0 otherwise. More... | |
template<typename T > | |
boost::math::tools::promote_args< T >::type | logit (const T a) |
Returns the logit function applied to the argument. More... | |
template<typename T , typename TL , typename TU > | |
boost::math::tools::promote_args< T, TL, TU >::type | lub_constrain (const T x, TL lb, TU ub) |
Return the lower- and upper-bounded scalar derived by transforming the specified free scalar given the specified lower and upper bounds. More... | |
template<typename T , typename TL , typename TU > | |
boost::math::tools::promote_args< T, TL, TU >::type | lub_constrain (const T x, const TL lb, const TU ub, T &lp) |
Return the lower- and upper-bounded scalar derived by transforming the specified free scalar given the specified lower and upper bounds and increment the specified log probability with the log absolute Jacobian determinant. More... | |
template<typename T , typename TL , typename TU > | |
boost::math::tools::promote_args< T, TL, TU >::type | lub_free (const T y, TL lb, TU ub) |
Return the unconstrained scalar that transforms to the specified lower- and upper-bounded scalar given the specified bounds. More... | |
template<typename T2 > | |
T2 | modified_bessel_first_kind (const int v, const T2 z) |
| |
template<typename T2 > | |
T2 | modified_bessel_second_kind (const int v, const T2 z) |
| |
int | modulus (const int x, const int y) |
template<typename T_a , typename T_b > | |
boost::math::tools::promote_args< T_a, T_b >::type | multiply_log (const T_a a, const T_b b) |
Calculated the value of the first argument times log of the second argument while behaving properly with 0 inputs. More... | |
double | owens_t (const double h, const double a) |
The Owen's T function of h and a. More... | |
double | Phi (const double x) |
The unit normal cumulative distribution function. More... | |
template<typename T > | |
boost::math::tools::promote_args< T >::type | Phi_approx (T x) |
Approximation of the unit normal CDF. More... | |
template<typename T > | |
T | positive_constrain (const T x) |
Return the positive value for the specified unconstrained input. More... | |
template<typename T > | |
T | positive_constrain (const T x, T &lp) |
Return the positive value for the specified unconstrained input, incrementing the scalar reference with the log absolute Jacobian determinant. More... | |
template<typename T > | |
T | positive_free (const T y) |
Return the unconstrained value corresponding to the specified positive-constrained value. More... | |
template<typename T > | |
boost::enable_if< boost::is_arithmetic< T >, T >::type | primitive_value (T x) |
Return the value of the specified arithmetic argument unmodified with its own declared type. More... | |
template<typename T > | |
boost::disable_if< boost::is_arithmetic< T >, double >::type | primitive_value (const T &x) |
Return the primitive value of the specified argument. More... | |
template<typename T > | |
T | prob_constrain (const T x) |
Return a probability value constrained to fall between 0 and 1 (inclusive) for the specified free scalar. More... | |
template<typename T > | |
T | prob_constrain (const T x, T &lp) |
Return a probability value constrained to fall between 0 and 1 (inclusive) for the specified free scalar and increment the specified log probability reference with the log absolute Jacobian determinant of the transform. More... | |
template<typename T > | |
T | prob_free (const T y) |
Return the free scalar that when transformed to a probability produces the specified scalar. More... | |
template<typename T , typename S > | |
promote_scalar_type< T, S >::type | promote_scalar (const S &x) |
This is the top-level function to call to promote the scalar types of an input of type S to type T. More... | |
template<typename T1 , typename T2 > | |
boost::math::tools::promote_args< T1, T2 >::type | rising_factorial (const T1 x, const T2 n) |
| |
template<typename T > | |
int | sign (const T &z) |
double | square (const double x) |
Return the square of the specified argument. More... | |
template<typename T1 , typename T2 > | |
boost::math::tools::promote_args< T1, T2 >::type | squared_distance (const T1 &x1, const T2 &x2) |
Returns the squared distance. More... | |
template<typename T > | |
int | step (const T y) |
The step, or Heaviside, function. More... | |
template<typename T > | |
T | trigamma (T x) |
| |
template<typename T , typename TU > | |
boost::math::tools::promote_args< T, TU >::type | ub_constrain (const T x, const TU ub) |
Return the upper-bounded value for the specified unconstrained scalar and upper bound. More... | |
template<typename T , typename TU > | |
boost::math::tools::promote_args< T, TU >::type | ub_constrain (const T x, const TU ub, T &lp) |
Return the upper-bounded value for the specified unconstrained scalar and upper bound and increment the specified log probability reference with the log absolute Jacobian determinant of the transform. More... | |
template<typename T , typename TU > | |
boost::math::tools::promote_args< T, TU >::type | ub_free (const T y, const TU ub) |
Return the free scalar that corresponds to the specified upper-bounded value with respect to the specified upper bound. More... | |
template<typename T > | |
double | value_of (const T x) |
Return the value of the specified scalar argument converted to a double value. More... | |
template<> | |
double | value_of< double > (const double x) |
Return the specified argument. More... | |
template<typename T > | |
double | value_of_rec (const T x) |
Return the value of the specified scalar argument converted to a double value. More... | |
template<> | |
double | value_of_rec< double > (const double x) |
Return the specified argument. More... | |
template<typename T_n , typename T_prob > | |
return_type< T_prob >::type | bernoulli_ccdf_log (const T_n &n, const T_prob &theta) |
template<typename T_n , typename T_prob > | |
return_type< T_prob >::type | bernoulli_cdf (const T_n &n, const T_prob &theta) |
template<typename T_n , typename T_prob > | |
return_type< T_prob >::type | bernoulli_cdf_log (const T_n &n, const T_prob &theta) |
template<bool propto, typename T_n , typename T_prob > | |
return_type< T_prob >::type | bernoulli_log (const T_n &n, const T_prob &theta) |
template<typename T_y , typename T_prob > | |
return_type< T_prob >::type | bernoulli_log (const T_y &n, const T_prob &theta) |
template<bool propto, typename T_n , typename T_prob > | |
return_type< T_prob >::type | bernoulli_logit_log (const T_n &n, const T_prob &theta) |
template<typename T_n , typename T_prob > | |
return_type< T_prob >::type | bernoulli_logit_log (const T_n &n, const T_prob &theta) |
template<class RNG > | |
int | bernoulli_rng (const double theta, RNG &rng) |
template<typename T_n , typename T_N , typename T_size1 , typename T_size2 > | |
return_type< T_size1, T_size2 >::type | beta_binomial_ccdf_log (const T_n &n, const T_N &N, const T_size1 &alpha, const T_size2 &beta) |
template<typename T_n , typename T_N , typename T_size1 , typename T_size2 > | |
return_type< T_size1, T_size2 >::type | beta_binomial_cdf (const T_n &n, const T_N &N, const T_size1 &alpha, const T_size2 &beta) |
template<typename T_n , typename T_N , typename T_size1 , typename T_size2 > | |
return_type< T_size1, T_size2 >::type | beta_binomial_cdf_log (const T_n &n, const T_N &N, const T_size1 &alpha, const T_size2 &beta) |
template<bool propto, typename T_n , typename T_N , typename T_size1 , typename T_size2 > | |
return_type< T_size1, T_size2 >::type | beta_binomial_log (const T_n &n, const T_N &N, const T_size1 &alpha, const T_size2 &beta) |
template<typename T_n , typename T_N , typename T_size1 , typename T_size2 > | |
return_type< T_size1, T_size2 >::type | beta_binomial_log (const T_n &n, const T_N &N, const T_size1 &alpha, const T_size2 &beta) |
template<class RNG > | |
int | beta_binomial_rng (const int N, const double alpha, const double beta, RNG &rng) |
template<typename T_y , typename T_scale_succ , typename T_scale_fail > | |
return_type< T_y, T_scale_succ, T_scale_fail >::type | beta_ccdf_log (const T_y &y, const T_scale_succ &alpha, const T_scale_fail &beta) |
template<typename T_y , typename T_scale_succ , typename T_scale_fail > | |
return_type< T_y, T_scale_succ, T_scale_fail >::type | beta_cdf (const T_y &y, const T_scale_succ &alpha, const T_scale_fail &beta) |
Calculates the beta cumulative distribution function for the given variate and scale variables. More... | |
template<typename T_y , typename T_scale_succ , typename T_scale_fail > | |
return_type< T_y, T_scale_succ, T_scale_fail >::type | beta_cdf_log (const T_y &y, const T_scale_succ &alpha, const T_scale_fail &beta) |
template<bool propto, typename T_y , typename T_scale_succ , typename T_scale_fail > | |
return_type< T_y, T_scale_succ, T_scale_fail >::type | beta_log (const T_y &y, const T_scale_succ &alpha, const T_scale_fail &beta) |
The log of the beta density for the specified scalar(s) given the specified sample size(s). More... | |
template<typename T_y , typename T_scale_succ , typename T_scale_fail > | |
return_type< T_y, T_scale_succ, T_scale_fail >::type | beta_log (const T_y &y, const T_scale_succ &alpha, const T_scale_fail &beta) |
template<class RNG > | |
double | beta_rng (const double alpha, const double beta, RNG &rng) |
template<typename T_n , typename T_N , typename T_prob > | |
return_type< T_prob >::type | binomial_ccdf_log (const T_n &n, const T_N &N, const T_prob &theta) |
template<typename T_n , typename T_N , typename T_prob > | |
return_type< T_prob >::type | binomial_cdf (const T_n &n, const T_N &N, const T_prob &theta) |
template<typename T_n , typename T_N , typename T_prob > | |
return_type< T_prob >::type | binomial_cdf_log (const T_n &n, const T_N &N, const T_prob &theta) |
template<bool propto, typename T_n , typename T_N , typename T_prob > | |
return_type< T_prob >::type | binomial_log (const T_n &n, const T_N &N, const T_prob &theta) |
template<typename T_n , typename T_N , typename T_prob > | |
return_type< T_prob >::type | binomial_log (const T_n &n, const T_N &N, const T_prob &theta) |
template<bool propto, typename T_n , typename T_N , typename T_prob > | |
return_type< T_prob >::type | binomial_logit_log (const T_n &n, const T_N &N, const T_prob &alpha) |
template<typename T_n , typename T_N , typename T_prob > | |
return_type< T_prob >::type | binomial_logit_log (const T_n &n, const T_N &N, const T_prob &alpha) |
template<class RNG > | |
int | binomial_rng (const int N, const double theta, RNG &rng) |
template<typename T_y , typename T_loc , typename T_scale > | |
return_type< T_y, T_loc, T_scale >::type | cauchy_ccdf_log (const T_y &y, const T_loc &mu, const T_scale &sigma) |
template<typename T_y , typename T_loc , typename T_scale > | |
return_type< T_y, T_loc, T_scale >::type | cauchy_cdf (const T_y &y, const T_loc &mu, const T_scale &sigma) |
Calculates the cauchy cumulative distribution function for the given variate, location, and scale. More... | |
template<typename T_y , typename T_loc , typename T_scale > | |
return_type< T_y, T_loc, T_scale >::type | cauchy_cdf_log (const T_y &y, const T_loc &mu, const T_scale &sigma) |
template<bool propto, typename T_y , typename T_loc , typename T_scale > | |
return_type< T_y, T_loc, T_scale >::type | cauchy_log (const T_y &y, const T_loc &mu, const T_scale &sigma) |
The log of the Cauchy density for the specified scalar(s) given the specified location parameter(s) and scale parameter(s). More... | |
template<typename T_y , typename T_loc , typename T_scale > | |
return_type< T_y, T_loc, T_scale >::type | cauchy_log (const T_y &y, const T_loc &mu, const T_scale &sigma) |
template<class RNG > | |
double | cauchy_rng (const double mu, const double sigma, RNG &rng) |
template<typename T_y , typename T_dof > | |
return_type< T_y, T_dof >::type | chi_square_ccdf_log (const T_y &y, const T_dof &nu) |
template<typename T_y , typename T_dof > | |
return_type< T_y, T_dof >::type | chi_square_cdf (const T_y &y, const T_dof &nu) |
Calculates the chi square cumulative distribution function for the given variate and degrees of freedom. More... | |
template<typename T_y , typename T_dof > | |
return_type< T_y, T_dof >::type | chi_square_cdf_log (const T_y &y, const T_dof &nu) |
template<bool propto, typename T_y , typename T_dof > | |
return_type< T_y, T_dof >::type | chi_square_log (const T_y &y, const T_dof &nu) |
The log of a chi-squared density for y with the specified degrees of freedom parameter. More... | |
template<typename T_y , typename T_dof > | |
return_type< T_y, T_dof >::type | chi_square_log (const T_y &y, const T_dof &nu) |
template<class RNG > | |
double | chi_square_rng (const double nu, RNG &rng) |
template<typename T_y , typename T_loc , typename T_scale > | |
return_type< T_y, T_loc, T_scale >::type | double_exponential_ccdf_log (const T_y &y, const T_loc &mu, const T_scale &sigma) |
template<typename T_y , typename T_loc , typename T_scale > | |
return_type< T_y, T_loc, T_scale >::type | double_exponential_cdf (const T_y &y, const T_loc &mu, const T_scale &sigma) |
Calculates the double exponential cumulative density function. More... | |
template<typename T_y , typename T_loc , typename T_scale > | |
return_type< T_y, T_loc, T_scale >::type | double_exponential_cdf_log (const T_y &y, const T_loc &mu, const T_scale &sigma) |
template<bool propto, typename T_y , typename T_loc , typename T_scale > | |
return_type< T_y, T_loc, T_scale >::type | double_exponential_log (const T_y &y, const T_loc &mu, const T_scale &sigma) |
template<typename T_y , typename T_loc , typename T_scale > | |
return_type< T_y, T_loc, T_scale >::type | double_exponential_log (const T_y &y, const T_loc &mu, const T_scale &sigma) |
template<class RNG > | |
double | double_exponential_rng (const double mu, const double sigma, RNG &rng) |
template<typename T_y , typename T_loc , typename T_scale , typename T_inv_scale > | |
return_type< T_y, T_loc, T_scale, T_inv_scale >::type | exp_mod_normal_ccdf_log (const T_y &y, const T_loc &mu, const T_scale &sigma, const T_inv_scale &lambda) |
template<typename T_y , typename T_loc , typename T_scale , typename T_inv_scale > | |
return_type< T_y, T_loc, T_scale, T_inv_scale >::type | exp_mod_normal_cdf (const T_y &y, const T_loc &mu, const T_scale &sigma, const T_inv_scale &lambda) |
template<typename T_y , typename T_loc , typename T_scale , typename T_inv_scale > | |
return_type< T_y, T_loc, T_scale, T_inv_scale >::type | exp_mod_normal_cdf_log (const T_y &y, const T_loc &mu, const T_scale &sigma, const T_inv_scale &lambda) |
template<bool propto, typename T_y , typename T_loc , typename T_scale , typename T_inv_scale > | |
return_type< T_y, T_loc, T_scale, T_inv_scale >::type | exp_mod_normal_log (const T_y &y, const T_loc &mu, const T_scale &sigma, const T_inv_scale &lambda) |
template<typename T_y , typename T_loc , typename T_scale , typename T_inv_scale > | |
return_type< T_y, T_loc, T_scale, T_inv_scale >::type | exp_mod_normal_log (const T_y &y, const T_loc &mu, const T_scale &sigma, const T_inv_scale &lambda) |
template<class RNG > | |
double | exp_mod_normal_rng (const double mu, const double sigma, const double lambda, RNG &rng) |
template<typename T_y , typename T_inv_scale > | |
return_type< T_y, T_inv_scale >::type | exponential_ccdf_log (const T_y &y, const T_inv_scale &beta) |
template<typename T_y , typename T_inv_scale > | |
return_type< T_y, T_inv_scale >::type | exponential_cdf (const T_y &y, const T_inv_scale &beta) |
Calculates the exponential cumulative distribution function for the given y and beta. More... | |
template<typename T_y , typename T_inv_scale > | |
return_type< T_y, T_inv_scale >::type | exponential_cdf_log (const T_y &y, const T_inv_scale &beta) |
template<bool propto, typename T_y , typename T_inv_scale > | |
return_type< T_y, T_inv_scale >::type | exponential_log (const T_y &y, const T_inv_scale &beta) |
The log of an exponential density for y with the specified inverse scale parameter. More... | |
template<typename T_y , typename T_inv_scale > | |
return_type< T_y, T_inv_scale >::type | exponential_log (const T_y &y, const T_inv_scale &beta) |
template<class RNG > | |
double | exponential_rng (const double beta, RNG &rng) |
template<typename T_y , typename T_shape , typename T_scale > | |
return_type< T_y, T_shape, T_scale >::type | frechet_ccdf_log (const T_y &y, const T_shape &alpha, const T_scale &sigma) |
template<typename T_y , typename T_shape , typename T_scale > | |
return_type< T_y, T_shape, T_scale >::type | frechet_cdf (const T_y &y, const T_shape &alpha, const T_scale &sigma) |
template<typename T_y , typename T_shape , typename T_scale > | |
return_type< T_y, T_shape, T_scale >::type | frechet_cdf_log (const T_y &y, const T_shape &alpha, const T_scale &sigma) |
template<bool propto, typename T_y , typename T_shape , typename T_scale > | |
return_type< T_y, T_shape, T_scale >::type | frechet_log (const T_y &y, const T_shape &alpha, const T_scale &sigma) |
template<typename T_y , typename T_shape , typename T_scale > | |
return_type< T_y, T_shape, T_scale >::type | frechet_log (const T_y &y, const T_shape &alpha, const T_scale &sigma) |
template<class RNG > | |
double | frechet_rng (const double alpha, const double sigma, RNG &rng) |
template<typename T_y , typename T_shape , typename T_inv_scale > | |
return_type< T_y, T_shape, T_inv_scale >::type | gamma_ccdf_log (const T_y &y, const T_shape &alpha, const T_inv_scale &beta) |
template<typename T_y , typename T_shape , typename T_inv_scale > | |
return_type< T_y, T_shape, T_inv_scale >::type | gamma_cdf (const T_y &y, const T_shape &alpha, const T_inv_scale &beta) |
The cumulative density function for a gamma distribution for y with the specified shape and inverse scale parameters. More... | |
template<typename T_y , typename T_shape , typename T_inv_scale > | |
return_type< T_y, T_shape, T_inv_scale >::type | gamma_cdf_log (const T_y &y, const T_shape &alpha, const T_inv_scale &beta) |
template<bool propto, typename T_y , typename T_shape , typename T_inv_scale > | |
return_type< T_y, T_shape, T_inv_scale >::type | gamma_log (const T_y &y, const T_shape &alpha, const T_inv_scale &beta) |
The log of a gamma density for y with the specified shape and inverse scale parameters. More... | |
template<typename T_y , typename T_shape , typename T_inv_scale > | |
return_type< T_y, T_shape, T_inv_scale >::type | gamma_log (const T_y &y, const T_shape &alpha, const T_inv_scale &beta) |
template<class RNG > | |
double | gamma_rng (const double alpha, const double beta, RNG &rng) |
template<typename T_y , typename T_loc , typename T_scale > | |
return_type< T_y, T_loc, T_scale >::type | gumbel_ccdf_log (const T_y &y, const T_loc &mu, const T_scale &beta) |
template<typename T_y , typename T_loc , typename T_scale > | |
return_type< T_y, T_loc, T_scale >::type | gumbel_cdf (const T_y &y, const T_loc &mu, const T_scale &beta) |
template<typename T_y , typename T_loc , typename T_scale > | |
return_type< T_y, T_loc, T_scale >::type | gumbel_cdf_log (const T_y &y, const T_loc &mu, const T_scale &beta) |
template<bool propto, typename T_y , typename T_loc , typename T_scale > | |
return_type< T_y, T_loc, T_scale >::type | gumbel_log (const T_y &y, const T_loc &mu, const T_scale &beta) |
template<typename T_y , typename T_loc , typename T_scale > | |
return_type< T_y, T_loc, T_scale >::type | gumbel_log (const T_y &y, const T_loc &mu, const T_scale &beta) |
template<class RNG > | |
double | gumbel_rng (const double mu, const double beta, RNG &rng) |
template<bool propto, typename T_n , typename T_N , typename T_a , typename T_b > | |
double | hypergeometric_log (const T_n &n, const T_N &N, const T_a &a, const T_b &b) |
template<typename T_n , typename T_N , typename T_a , typename T_b > | |
double | hypergeometric_log (const T_n &n, const T_N &N, const T_a &a, const T_b &b) |
template<class RNG > | |
int | hypergeometric_rng (int N, int a, int b, RNG &rng) |
template<typename T_y , typename T_dof > | |
return_type< T_y, T_dof >::type | inv_chi_square_ccdf_log (const T_y &y, const T_dof &nu) |
template<typename T_y , typename T_dof > | |
return_type< T_y, T_dof >::type | inv_chi_square_cdf (const T_y &y, const T_dof &nu) |
template<typename T_y , typename T_dof > | |
return_type< T_y, T_dof >::type | inv_chi_square_cdf_log (const T_y &y, const T_dof &nu) |
template<bool propto, typename T_y , typename T_dof > | |
return_type< T_y, T_dof >::type | inv_chi_square_log (const T_y &y, const T_dof &nu) |
The log of an inverse chi-squared density for y with the specified degrees of freedom parameter. More... | |
template<typename T_y , typename T_dof > | |
return_type< T_y, T_dof >::type | inv_chi_square_log (const T_y &y, const T_dof &nu) |
template<class RNG > | |
double | inv_chi_square_rng (const double nu, RNG &rng) |
template<typename T_y , typename T_shape , typename T_scale > | |
return_type< T_y, T_shape, T_scale >::type | inv_gamma_ccdf_log (const T_y &y, const T_shape &alpha, const T_scale &beta) |
template<typename T_y , typename T_shape , typename T_scale > | |
return_type< T_y, T_shape, T_scale >::type | inv_gamma_cdf (const T_y &y, const T_shape &alpha, const T_scale &beta) |
The CDF of an inverse gamma density for y with the specified shape and scale parameters. More... | |
template<typename T_y , typename T_shape , typename T_scale > | |
return_type< T_y, T_shape, T_scale >::type | inv_gamma_cdf_log (const T_y &y, const T_shape &alpha, const T_scale &beta) |
template<bool propto, typename T_y , typename T_shape , typename T_scale > | |
return_type< T_y, T_shape, T_scale >::type | inv_gamma_log (const T_y &y, const T_shape &alpha, const T_scale &beta) |
The log of an inverse gamma density for y with the specified shape and scale parameters. More... | |
template<typename T_y , typename T_shape , typename T_scale > | |
return_type< T_y, T_shape, T_scale >::type | inv_gamma_log (const T_y &y, const T_shape &alpha, const T_scale &beta) |
template<class RNG > | |
double | inv_gamma_rng (const double alpha, const double beta, RNG &rng) |
template<typename T_y , typename T_loc , typename T_scale > | |
return_type< T_y, T_loc, T_scale >::type | logistic_ccdf_log (const T_y &y, const T_loc &mu, const T_scale &sigma) |
template<typename T_y , typename T_loc , typename T_scale > | |
return_type< T_y, T_loc, T_scale >::type | logistic_cdf (const T_y &y, const T_loc &mu, const T_scale &sigma) |
template<typename T_y , typename T_loc , typename T_scale > | |
return_type< T_y, T_loc, T_scale >::type | logistic_cdf_log (const T_y &y, const T_loc &mu, const T_scale &sigma) |
template<bool propto, typename T_y , typename T_loc , typename T_scale > | |
return_type< T_y, T_loc, T_scale >::type | logistic_log (const T_y &y, const T_loc &mu, const T_scale &sigma) |
template<typename T_y , typename T_loc , typename T_scale > | |
return_type< T_y, T_loc, T_scale >::type | logistic_log (const T_y &y, const T_loc &mu, const T_scale &sigma) |
template<class RNG > | |
double | logistic_rng (const double mu, const double sigma, RNG &rng) |
template<typename T_y , typename T_loc , typename T_scale > | |
return_type< T_y, T_loc, T_scale >::type | lognormal_ccdf_log (const T_y &y, const T_loc &mu, const T_scale &sigma) |
template<typename T_y , typename T_loc , typename T_scale > | |
return_type< T_y, T_loc, T_scale >::type | lognormal_cdf (const T_y &y, const T_loc &mu, const T_scale &sigma) |
template<typename T_y , typename T_loc , typename T_scale > | |
return_type< T_y, T_loc, T_scale >::type | lognormal_cdf_log (const T_y &y, const T_loc &mu, const T_scale &sigma) |
template<bool propto, typename T_y , typename T_loc , typename T_scale > | |
return_type< T_y, T_loc, T_scale >::type | lognormal_log (const T_y &y, const T_loc &mu, const T_scale &sigma) |
template<typename T_y , typename T_loc , typename T_scale > | |
return_type< T_y, T_loc, T_scale >::type | lognormal_log (const T_y &y, const T_loc &mu, const T_scale &sigma) |
template<class RNG > | |
double | lognormal_rng (const double mu, const double sigma, RNG &rng) |
template<typename T_n , typename T_location , typename T_precision > | |
return_type< T_location, T_precision >::type | neg_binomial_2_ccdf_log (const T_n &n, const T_location &mu, const T_precision &phi) |
template<typename T_n , typename T_location , typename T_precision > | |
return_type< T_location, T_precision >::type | neg_binomial_2_cdf (const T_n &n, const T_location &mu, const T_precision &phi) |
template<typename T_n , typename T_location , typename T_precision > | |
return_type< T_location, T_precision >::type | neg_binomial_2_cdf_log (const T_n &n, const T_location &mu, const T_precision &phi) |
template<bool propto, typename T_n , typename T_location , typename T_precision > | |
return_type< T_location, T_precision >::type | neg_binomial_2_log (const T_n &n, const T_location &mu, const T_precision &phi) |
template<typename T_n , typename T_location , typename T_precision > | |
return_type< T_location, T_precision >::type | neg_binomial_2_log (const T_n &n, const T_location &mu, const T_precision &phi) |
template<bool propto, typename T_n , typename T_log_location , typename T_precision > | |
return_type< T_log_location, T_precision >::type | neg_binomial_2_log_log (const T_n &n, const T_log_location &eta, const T_precision &phi) |
template<typename T_n , typename T_log_location , typename T_precision > | |
return_type< T_log_location, T_precision >::type | neg_binomial_2_log_log (const T_n &n, const T_log_location &eta, const T_precision &phi) |
template<class RNG > | |
int | neg_binomial_2_log_rng (const double eta, const double phi, RNG &rng) |
template<class RNG > | |
int | neg_binomial_2_rng (const double mu, const double phi, RNG &rng) |
template<typename T_n , typename T_shape , typename T_inv_scale > | |
return_type< T_shape, T_inv_scale >::type | neg_binomial_ccdf_log (const T_n &n, const T_shape &alpha, const T_inv_scale &beta) |
template<typename T_n , typename T_shape , typename T_inv_scale > | |
return_type< T_shape, T_inv_scale >::type | neg_binomial_cdf (const T_n &n, const T_shape &alpha, const T_inv_scale &beta) |
template<typename T_n , typename T_shape , typename T_inv_scale > | |
return_type< T_shape, T_inv_scale >::type | neg_binomial_cdf_log (const T_n &n, const T_shape &alpha, const T_inv_scale &beta) |
template<bool propto, typename T_n , typename T_shape , typename T_inv_scale > | |
return_type< T_shape, T_inv_scale >::type | neg_binomial_log (const T_n &n, const T_shape &alpha, const T_inv_scale &beta) |
template<typename T_n , typename T_shape , typename T_inv_scale > | |
return_type< T_shape, T_inv_scale >::type | neg_binomial_log (const T_n &n, const T_shape &alpha, const T_inv_scale &beta) |
template<class RNG > | |
int | neg_binomial_rng (const double alpha, const double beta, RNG &rng) |
template<typename T_y , typename T_loc , typename T_scale > | |
return_type< T_y, T_loc, T_scale >::type | normal_ccdf_log (const T_y &y, const T_loc &mu, const T_scale &sigma) |
template<typename T_y , typename T_loc , typename T_scale > | |
return_type< T_y, T_loc, T_scale >::type | normal_cdf (const T_y &y, const T_loc &mu, const T_scale &sigma) |
Calculates the normal cumulative distribution function for the given variate, location, and scale. More... | |
template<typename T_y , typename T_loc , typename T_scale > | |
return_type< T_y, T_loc, T_scale >::type | normal_cdf_log (const T_y &y, const T_loc &mu, const T_scale &sigma) |
template<bool propto, typename T_y , typename T_loc , typename T_scale > | |
return_type< T_y, T_loc, T_scale >::type | normal_log (const T_y &y, const T_loc &mu, const T_scale &sigma) |
The log of the normal density for the specified scalar(s) given the specified mean(s) and deviation(s). More... | |
template<typename T_y , typename T_loc , typename T_scale > | |
return_type< T_y, T_loc, T_scale >::type | normal_log (const T_y &y, const T_loc &mu, const T_scale &sigma) |
template<class RNG > | |
double | normal_rng (const double mu, const double sigma, RNG &rng) |
template<typename T_y , typename T_scale , typename T_shape > | |
return_type< T_y, T_scale, T_shape >::type | pareto_ccdf_log (const T_y &y, const T_scale &y_min, const T_shape &alpha) |
template<typename T_y , typename T_scale , typename T_shape > | |
return_type< T_y, T_scale, T_shape >::type | pareto_cdf (const T_y &y, const T_scale &y_min, const T_shape &alpha) |
template<typename T_y , typename T_scale , typename T_shape > | |
return_type< T_y, T_scale, T_shape >::type | pareto_cdf_log (const T_y &y, const T_scale &y_min, const T_shape &alpha) |
template<bool propto, typename T_y , typename T_scale , typename T_shape > | |
return_type< T_y, T_scale, T_shape >::type | pareto_log (const T_y &y, const T_scale &y_min, const T_shape &alpha) |
template<typename T_y , typename T_scale , typename T_shape > | |
return_type< T_y, T_scale, T_shape >::type | pareto_log (const T_y &y, const T_scale &y_min, const T_shape &alpha) |
template<class RNG > | |
double | pareto_rng (const double y_min, const double alpha, RNG &rng) |
template<typename T_y , typename T_loc , typename T_scale , typename T_shape > | |
return_type< T_y, T_loc, T_scale, T_shape >::type | pareto_type_2_ccdf_log (const T_y &y, const T_loc &mu, const T_scale &lambda, const T_shape &alpha) |
template<typename T_y , typename T_loc , typename T_scale , typename T_shape > | |
return_type< T_y, T_loc, T_scale, T_shape >::type | pareto_type_2_cdf (const T_y &y, const T_loc &mu, const T_scale &lambda, const T_shape &alpha) |
template<typename T_y , typename T_loc , typename T_scale , typename T_shape > | |
return_type< T_y, T_loc, T_scale, T_shape >::type | pareto_type_2_cdf_log (const T_y &y, const T_loc &mu, const T_scale &lambda, const T_shape &alpha) |
template<bool propto, typename T_y , typename T_loc , typename T_scale , typename T_shape > | |
return_type< T_y, T_loc, T_scale, T_shape >::type | pareto_type_2_log (const T_y &y, const T_loc &mu, const T_scale &lambda, const T_shape &alpha) |
template<typename T_y , typename T_loc , typename T_scale , typename T_shape > | |
return_type< T_y, T_loc, T_scale, T_shape >::type | pareto_type_2_log (const T_y &y, const T_loc &mu, const T_scale &lambda, const T_shape &alpha) |
template<class RNG > | |
double | pareto_type_2_rng (const double mu, const double lambda, const double alpha, RNG &rng) |
template<typename T_n , typename T_rate > | |
return_type< T_rate >::type | poisson_ccdf_log (const T_n &n, const T_rate &lambda) |
template<typename T_n , typename T_rate > | |
return_type< T_rate >::type | poisson_cdf (const T_n &n, const T_rate &lambda) |
template<typename T_n , typename T_rate > | |
return_type< T_rate >::type | poisson_cdf_log (const T_n &n, const T_rate &lambda) |
template<bool propto, typename T_n , typename T_rate > | |
return_type< T_rate >::type | poisson_log (const T_n &n, const T_rate &lambda) |
template<typename T_n , typename T_rate > | |
return_type< T_rate >::type | poisson_log (const T_n &n, const T_rate &lambda) |
template<bool propto, typename T_n , typename T_log_rate > | |
return_type< T_log_rate >::type | poisson_log_log (const T_n &n, const T_log_rate &alpha) |
template<typename T_n , typename T_log_rate > | |
return_type< T_log_rate >::type | poisson_log_log (const T_n &n, const T_log_rate &alpha) |
template<class RNG > | |
int | poisson_log_rng (const double alpha, RNG &rng) |
template<class RNG > | |
int | poisson_rng (const double lambda, RNG &rng) |
template<typename T_y , typename T_scale > | |
return_type< T_y, T_scale >::type | rayleigh_ccdf_log (const T_y &y, const T_scale &sigma) |
template<typename T_y , typename T_scale > | |
return_type< T_y, T_scale >::type | rayleigh_cdf (const T_y &y, const T_scale &sigma) |
template<typename T_y , typename T_scale > | |
return_type< T_y, T_scale >::type | rayleigh_cdf_log (const T_y &y, const T_scale &sigma) |
template<bool propto, typename T_y , typename T_scale > | |
return_type< T_y, T_scale >::type | rayleigh_log (const T_y &y, const T_scale &sigma) |
template<typename T_y , typename T_scale > | |
return_type< T_y, T_scale >::type | rayleigh_log (const T_y &y, const T_scale &sigma) |
template<class RNG > | |
double | rayleigh_rng (const double sigma, RNG &rng) |
template<typename T_y , typename T_dof , typename T_scale > | |
return_type< T_y, T_dof, T_scale >::type | scaled_inv_chi_square_ccdf_log (const T_y &y, const T_dof &nu, const T_scale &s) |
template<typename T_y , typename T_dof , typename T_scale > | |
return_type< T_y, T_dof, T_scale >::type | scaled_inv_chi_square_cdf (const T_y &y, const T_dof &nu, const T_scale &s) |
The CDF of a scaled inverse chi-squared density for y with the specified degrees of freedom parameter and scale parameter. More... | |
template<typename T_y , typename T_dof , typename T_scale > | |
return_type< T_y, T_dof, T_scale >::type | scaled_inv_chi_square_cdf_log (const T_y &y, const T_dof &nu, const T_scale &s) |
template<bool propto, typename T_y , typename T_dof , typename T_scale > | |
return_type< T_y, T_dof, T_scale >::type | scaled_inv_chi_square_log (const T_y &y, const T_dof &nu, const T_scale &s) |
The log of a scaled inverse chi-squared density for y with the specified degrees of freedom parameter and scale parameter. More... | |
template<typename T_y , typename T_dof , typename T_scale > | |
return_type< T_y, T_dof, T_scale >::type | scaled_inv_chi_square_log (const T_y &y, const T_dof &nu, const T_scale &s) |
template<class RNG > | |
double | scaled_inv_chi_square_rng (const double nu, const double s, RNG &rng) |
template<typename T_y , typename T_loc , typename T_scale , typename T_shape > | |
return_type< T_y, T_loc, T_scale, T_shape >::type | skew_normal_ccdf_log (const T_y &y, const T_loc &mu, const T_scale &sigma, const T_shape &alpha) |
template<typename T_y , typename T_loc , typename T_scale , typename T_shape > | |
return_type< T_y, T_loc, T_scale, T_shape >::type | skew_normal_cdf (const T_y &y, const T_loc &mu, const T_scale &sigma, const T_shape &alpha) |
template<typename T_y , typename T_loc , typename T_scale , typename T_shape > | |
return_type< T_y, T_loc, T_scale, T_shape >::type | skew_normal_cdf_log (const T_y &y, const T_loc &mu, const T_scale &sigma, const T_shape &alpha) |
template<bool propto, typename T_y , typename T_loc , typename T_scale , typename T_shape > | |
return_type< T_y, T_loc, T_scale, T_shape >::type | skew_normal_log (const T_y &y, const T_loc &mu, const T_scale &sigma, const T_shape &alpha) |
template<typename T_y , typename T_loc , typename T_scale , typename T_shape > | |
return_type< T_y, T_loc, T_scale, T_shape >::type | skew_normal_log (const T_y &y, const T_loc &mu, const T_scale &sigma, const T_shape &alpha) |
template<class RNG > | |
double | skew_normal_rng (const double mu, const double sigma, const double alpha, RNG &rng) |
template<typename T_y , typename T_dof , typename T_loc , typename T_scale > | |
return_type< T_y, T_dof, T_loc, T_scale >::type | student_t_ccdf_log (const T_y &y, const T_dof &nu, const T_loc &mu, const T_scale &sigma) |
template<typename T_y , typename T_dof , typename T_loc , typename T_scale > | |
return_type< T_y, T_dof, T_loc, T_scale >::type | student_t_cdf (const T_y &y, const T_dof &nu, const T_loc &mu, const T_scale &sigma) |
template<typename T_y , typename T_dof , typename T_loc , typename T_scale > | |
return_type< T_y, T_dof, T_loc, T_scale >::type | student_t_cdf_log (const T_y &y, const T_dof &nu, const T_loc &mu, const T_scale &sigma) |
template<bool propto, typename T_y , typename T_dof , typename T_loc , typename T_scale > | |
return_type< T_y, T_dof, T_loc, T_scale >::type | student_t_log (const T_y &y, const T_dof &nu, const T_loc &mu, const T_scale &sigma) |
The log of the Student-t density for the given y, nu, mean, and scale parameter. More... | |
template<typename T_y , typename T_dof , typename T_loc , typename T_scale > | |
return_type< T_y, T_dof, T_loc, T_scale >::type | student_t_log (const T_y &y, const T_dof &nu, const T_loc &mu, const T_scale &sigma) |
template<class RNG > | |
double | student_t_rng (const double nu, const double mu, const double sigma, RNG &rng) |
template<typename T_y , typename T_low , typename T_high > | |
return_type< T_y, T_low, T_high >::type | uniform_ccdf_log (const T_y &y, const T_low &alpha, const T_high &beta) |
template<typename T_y , typename T_low , typename T_high > | |
return_type< T_y, T_low, T_high >::type | uniform_cdf (const T_y &y, const T_low &alpha, const T_high &beta) |
template<typename T_y , typename T_low , typename T_high > | |
return_type< T_y, T_low, T_high >::type | uniform_cdf_log (const T_y &y, const T_low &alpha, const T_high &beta) |
template<bool propto, typename T_y , typename T_low , typename T_high > | |
return_type< T_y, T_low, T_high >::type | uniform_log (const T_y &y, const T_low &alpha, const T_high &beta) |
The log of a uniform density for the given y, lower, and upper bound. More... | |
template<typename T_y , typename T_low , typename T_high > | |
return_type< T_y, T_low, T_high >::type | uniform_log (const T_y &y, const T_low &alpha, const T_high &beta) |
template<class RNG > | |
double | uniform_rng (const double alpha, const double beta, RNG &rng) |
template<bool propto, typename T_y , typename T_loc , typename T_scale > | |
return_type< T_y, T_loc, T_scale >::type | von_mises_log (T_y const &y, T_loc const &mu, T_scale const &kappa) |
template<typename T_y , typename T_loc , typename T_scale > | |
return_type< T_y, T_loc, T_scale >::type | von_mises_log (T_y const &y, T_loc const &mu, T_scale const &kappa) |
template<class RNG > | |
double | von_mises_rng (const double mu, const double kappa, RNG &rng) |
template<typename T_y , typename T_shape , typename T_scale > | |
return_type< T_y, T_shape, T_scale >::type | weibull_ccdf_log (const T_y &y, const T_shape &alpha, const T_scale &sigma) |
template<typename T_y , typename T_shape , typename T_scale > | |
return_type< T_y, T_shape, T_scale >::type | weibull_cdf (const T_y &y, const T_shape &alpha, const T_scale &sigma) |
template<typename T_y , typename T_shape , typename T_scale > | |
return_type< T_y, T_shape, T_scale >::type | weibull_cdf_log (const T_y &y, const T_shape &alpha, const T_scale &sigma) |
template<bool propto, typename T_y , typename T_shape , typename T_scale > | |
return_type< T_y, T_shape, T_scale >::type | weibull_log (const T_y &y, const T_shape &alpha, const T_scale &sigma) |
template<typename T_y , typename T_shape , typename T_scale > | |
return_type< T_y, T_shape, T_scale >::type | weibull_log (const T_y &y, const T_shape &alpha, const T_scale &sigma) |
template<class RNG > | |
double | weibull_rng (const double alpha, const double sigma, RNG &rng) |
template<bool propto, typename T_y , typename T_alpha , typename T_tau , typename T_beta , typename T_delta > | |
return_type< T_y, T_alpha, T_tau, T_beta, T_delta >::type | wiener_log (const T_y &y, const T_alpha &alpha, const T_tau &tau, const T_beta &beta, const T_delta &delta) |
The log of the first passage time density function for a (Wiener) drift diffusion model for the given ![]() ![]() ![]() ![]() ![]() | |
template<typename T_y , typename T_alpha , typename T_tau , typename T_beta , typename T_delta > | |
return_type< T_y, T_alpha, T_tau, T_beta, T_delta >::type | wiener_log (const T_y &y, const T_alpha &alpha, const T_tau &tau, const T_beta &beta, const T_delta &delta) |
template<typename T_initial , typename T_param > | |
std::vector< std::vector< typename stan::return_type< T_initial, T_param >::type > > | decouple_ode_states (const std::vector< std::vector< double > > &y, const std::vector< T_initial > &y0, const std::vector< T_param > &theta) |
Takes sensitivity output from integrators and returns results in precomputed_gradients format. More... | |
template<> | |
std::vector< std::vector< double > > | decouple_ode_states (const std::vector< std::vector< double > > &y, const std::vector< double > &y0, const std::vector< double > &theta) |
The decouple ODE states operation for the case of no sensitivities is equal to the indentity operation. More... | |
var | log_sum_exp (const std::vector< var > &x) |
Returns the log sum of exponentials. More... | |
var | sum (const std::vector< var > &m) |
Returns the sum of the entries of the specified vector. More... | |
std::vector< var > | to_var (const std::vector< double > &v) |
Converts argument to an automatic differentiation variable. More... | |
std::vector< var > | to_var (const std::vector< var > &v) |
Converts argument to an automatic differentiation variable. More... | |
void | add_initial_values (const std::vector< stan::math::var > &y0, std::vector< std::vector< stan::math::var > > &y) |
Increment the state derived from the coupled system in the with the original initial state. More... | |
static bool | empty_nested () |
Return true if there is no nested autodiff being executed. More... | |
static void | grad (vari *vi) |
Compute the gradient for all variables starting from the specified root variable implementation. More... | |
static size_t | nested_size () |
var | operator+ (const var &a, const var &b) |
Addition operator for variables (C++). More... | |
var | operator+ (const var &a, const double b) |
Addition operator for variable and scalar (C++). More... | |
var | operator+ (const double a, const var &b) |
Addition operator for scalar and variable (C++). More... | |
var | operator/ (const var &a, const var &b) |
Division operator for two variables (C++). More... | |
var | operator/ (const var &a, const double b) |
Division operator for dividing a variable by a scalar (C++). More... | |
var | operator/ (const double a, const var &b) |
Division operator for dividing a scalar by a variable (C++). More... | |
bool | operator== (const var &a, const var &b) |
Equality operator comparing two variables' values (C++). More... | |
bool | operator== (const var &a, const double b) |
Equality operator comparing a variable's value and a double (C++). More... | |
bool | operator== (const double a, const var &b) |
Equality operator comparing a scalar and a variable's value (C++). More... | |
bool | operator> (const var &a, const var &b) |
Greater than operator comparing variables' values (C++). More... | |
bool | operator> (const var &a, const double b) |
Greater than operator comparing variable's value and double (C++). More... | |
bool | operator> (const double a, const var &b) |
Greater than operator comparing a double and a variable's value (C++). More... | |
bool | operator>= (const var &a, const var &b) |
Greater than or equal operator comparing two variables' values (C++). More... | |
bool | operator>= (const var &a, const double b) |
Greater than or equal operator comparing variable's value and double (C++). More... | |
bool | operator>= (const double a, const var &b) |
Greater than or equal operator comparing double and variable's value (C++). More... | |
bool | operator< (const var &a, const var &b) |
Less than operator comparing variables' values (C++). More... | |
bool | operator< (const var &a, const double b) |
Less than operator comparing variable's value and a double (C++). More... | |
bool | operator< (const double a, const var &b) |
Less than operator comparing a double and variable's value (C++). More... | |
bool | operator<= (const var &a, const var &b) |
Less than or equal operator comparing two variables' values (C++). More... | |
bool | operator<= (const var &a, const double b) |
Less than or equal operator comparing a variable's value and a scalar (C++). More... | |
bool | operator<= (const double a, const var &b) |
Less than or equal operator comparing a double and variable's value (C++). More... | |
var | operator* (const var &a, const var &b) |
Multiplication operator for two variables (C++). More... | |
var | operator* (const var &a, const double b) |
Multiplication operator for a variable and a scalar (C++). More... | |
var | operator* (const double a, const var &b) |
Multiplication operator for a scalar and a variable (C++). More... | |
bool | operator!= (const var &a, const var &b) |
Inequality operator comparing two variables' values (C++). More... | |
bool | operator!= (const var &a, const double b) |
Inequality operator comparing a variable's value and a double (C++). More... | |
bool | operator!= (const double a, const var &b) |
Inequality operator comparing a double and a variable's value (C++). More... | |
var | operator- (const var &a, const var &b) |
Subtraction operator for variables (C++). More... | |
var | operator- (const var &a, const double b) |
Subtraction operator for variable and scalar (C++). More... | |
var | operator- (const double a, const var &b) |
Subtraction operator for scalar and variable (C++). More... | |
var & | operator-- (var &a) |
Prefix decrement operator for variables (C++). More... | |
var | operator-- (var &a, int) |
Postfix decrement operator for variables (C++). More... | |
var & | operator++ (var &a) |
Prefix increment operator for variables (C++). More... | |
var | operator++ (var &a, int) |
Postfix increment operator for variables (C++). More... | |
var | operator- (const var &a) |
Unary negation operator for variables (C++). More... | |
bool | operator! (const var &a) |
Prefix logical negation for the value of variables (C++). More... | |
var | operator+ (const var &a) |
Unary plus operator for variables (C++). More... | |
var | precomputed_gradients (const double value, const std::vector< var > &operands, const std::vector< double > &gradients) |
This function returns a var for an expression that has the specified value, vector of operands, and vector of partial derivatives of value with respect to the operands. More... | |
void | print_stack (std::ostream &o) |
Prints the auto-dif variable stack. More... | |
static void | recover_memory () |
Recover memory used for all variables for reuse. More... | |
static void | recover_memory_nested () |
Recover only the memory used for the top nested call. More... | |
static void | set_zero_all_adjoints () |
Reset all adjoint values in the stack to zero. More... | |
static void | set_zero_all_adjoints_nested () |
Reset all adjoint values in the top nested portion of the stack to zero. More... | |
static void | start_nested () |
Record the current position so that recover_memory_nested() can find it. More... | |
static void | grad (vari *vi) |
Eigen::Matrix< var,-1,-1 > | cholesky_decompose (const Eigen::Matrix< var,-1,-1 > &A) |
template<typename T1 , int R1, int C1, typename T2 , int R2, int C2> | |
boost::enable_if_c< boost::is_same< T1, var >::value||boost::is_same< T2, var >::value, Eigen::Matrix< var, 1, C1 > >::type | columns_dot_product (const Eigen::Matrix< T1, R1, C1 > &v1, const Eigen::Matrix< T2, R2, C2 > &v2) |
template<int R, int C> | |
Eigen::Matrix< var, 1, C > | columns_dot_self (const Eigen::Matrix< var, R, C > &x) |
Returns the dot product of each column of a matrix with itself. More... | |
matrix_v | crossprod (const matrix_v &M) |
Returns the result of pre-multiplying a matrix by its own transpose. More... | |
template<int R, int C> | |
var | determinant (const Eigen::Matrix< var, R, C > &m) |
template<typename T1 , typename T2 , int R, int C> | |
Eigen::Matrix< var, R, C > | divide (const Eigen::Matrix< T1, R, C > &v, const T2 &c) |
Return the division of the specified column vector by the specified scalar. More... | |
template<typename T1 , int R1, int C1, typename T2 , int R2, int C2> | |
boost::enable_if_c< boost::is_same< T1, var >::value||boost::is_same< T2, var >::value, var >::type | dot_product (const Eigen::Matrix< T1, R1, C1 > &v1, const Eigen::Matrix< T2, R2, C2 > &v2) |
Returns the dot product. More... | |
template<typename T1 , typename T2 > | |
boost::enable_if_c< boost::is_same< T1, var >::value||boost::is_same< T2, var >::value, var >::type | dot_product (const T1 *v1, const T2 *v2, size_t length) |
Returns the dot product. More... | |
template<typename T1 , typename T2 > | |
boost::enable_if_c< boost::is_same< T1, var >::value||boost::is_same< T2, var >::value, var >::type | dot_product (const std::vector< T1 > &v1, const std::vector< T2 > &v2) |
Returns the dot product. More... | |
template<int R, int C> | |
var | dot_self (const Eigen::Matrix< var, R, C > &v) |
Returns the dot product of a vector with itself. More... | |
void | grad (var &v, Eigen::Matrix< var, Eigen::Dynamic, 1 > &x, Eigen::VectorXd &g) |
Propagate chain rule to calculate gradients starting from the specified variable. More... | |
void | initialize_variable (var &variable, const var &value) |
Initialize variable to value. More... | |
template<int R, int C> | |
void | initialize_variable (Eigen::Matrix< var, R, C > &matrix, const var &value) |
Initialize every cell in the matrix to the specified value. More... | |
template<typename T > | |
void | initialize_variable (std::vector< T > &variables, const var &value) |
Initialize the variables in the standard vector recursively. More... | |
template<int R, int C> | |
var | log_determinant (const Eigen::Matrix< var, R, C > &m) |
template<int R, int C> | |
var | log_determinant_ldlt (stan::math::LDLT_factor< var, R, C > &A) |
template<int R, int C> | |
var | log_determinant_spd (const Eigen::Matrix< var, R, C > &m) |
Eigen::Matrix< var, Eigen::Dynamic, 1 > | log_softmax (const Eigen::Matrix< var, Eigen::Dynamic, 1 > &alpha) |
Return the softmax of the specified Eigen vector. More... | |
template<int R, int C> | |
var | log_sum_exp (const Eigen::Matrix< var, R, C > &x) |
Returns the log sum of exponentials. More... | |
template<int R1, int C1, int R2, int C2> | |
Eigen::Matrix< var, R1, C2 > | mdivide_left (const Eigen::Matrix< var, R1, C1 > &A, const Eigen::Matrix< var, R2, C2 > &b) |
template<int R1, int C1, int R2, int C2> | |
Eigen::Matrix< var, R1, C2 > | mdivide_left (const Eigen::Matrix< var, R1, C1 > &A, const Eigen::Matrix< double, R2, C2 > &b) |
template<int R1, int C1, int R2, int C2> | |
Eigen::Matrix< var, R1, C2 > | mdivide_left (const Eigen::Matrix< double, R1, C1 > &A, const Eigen::Matrix< var, R2, C2 > &b) |
template<int R1, int C1, int R2, int C2> | |
Eigen::Matrix< var, R1, C2 > | mdivide_left_ldlt (const stan::math::LDLT_factor< var, R1, C1 > &A, const Eigen::Matrix< var, R2, C2 > &b) |
Returns the solution of the system Ax=b given an LDLT_factor of A. More... | |
template<int R1, int C1, int R2, int C2> | |
Eigen::Matrix< var, R1, C2 > | mdivide_left_ldlt (const stan::math::LDLT_factor< var, R1, C1 > &A, const Eigen::Matrix< double, R2, C2 > &b) |
Returns the solution of the system Ax=b given an LDLT_factor of A. More... | |
template<int R1, int C1, int R2, int C2> | |
Eigen::Matrix< var, R1, C2 > | mdivide_left_ldlt (const stan::math::LDLT_factor< double, R1, C1 > &A, const Eigen::Matrix< var, R2, C2 > &b) |
Returns the solution of the system Ax=b given an LDLT_factor of A. More... | |
template<int R1, int C1, int R2, int C2> | |
Eigen::Matrix< var, R1, C2 > | mdivide_left_spd (const Eigen::Matrix< var, R1, C1 > &A, const Eigen::Matrix< var, R2, C2 > &b) |
template<int R1, int C1, int R2, int C2> | |
Eigen::Matrix< var, R1, C2 > | mdivide_left_spd (const Eigen::Matrix< var, R1, C1 > &A, const Eigen::Matrix< double, R2, C2 > &b) |
template<int R1, int C1, int R2, int C2> | |
Eigen::Matrix< var, R1, C2 > | mdivide_left_spd (const Eigen::Matrix< double, R1, C1 > &A, const Eigen::Matrix< var, R2, C2 > &b) |
template<int TriView, int R1, int C1, int R2, int C2> | |
Eigen::Matrix< var, R1, C2 > | mdivide_left_tri (const Eigen::Matrix< var, R1, C1 > &A, const Eigen::Matrix< var, R2, C2 > &b) |
template<int TriView, int R1, int C1, int R2, int C2> | |
Eigen::Matrix< var, R1, C2 > | mdivide_left_tri (const Eigen::Matrix< double, R1, C1 > &A, const Eigen::Matrix< var, R2, C2 > &b) |
template<int TriView, int R1, int C1, int R2, int C2> | |
Eigen::Matrix< var, R1, C2 > | mdivide_left_tri (const Eigen::Matrix< var, R1, C1 > &A, const Eigen::Matrix< double, R2, C2 > &b) |
template<typename T1 , typename T2 > | |
boost::enable_if_c< (boost::is_scalar< T1 >::value||boost::is_same< T1, var >::value)&&(boost::is_scalar< T2 >::value||boost::is_same< T2, var >::value), typename boost::math::tools::promote_args< T1, T2 >::type >::type | multiply (const T1 &v, const T2 &c) |
Return the product of two scalars. More... | |
template<typename T1 , typename T2 , int R2, int C2> | |
Eigen::Matrix< var, R2, C2 > | multiply (const T1 &c, const Eigen::Matrix< T2, R2, C2 > &m) |
Return the product of scalar and matrix. More... | |
template<typename T1 , int R1, int C1, typename T2 > | |
Eigen::Matrix< var, R1, C1 > | multiply (const Eigen::Matrix< T1, R1, C1 > &m, const T2 &c) |
Return the product of scalar and matrix. More... | |
template<typename T1 , int R1, int C1, typename T2 , int R2, int C2> | |
boost::enable_if_c< boost::is_same< T1, var >::value||boost::is_same< T2, var >::value, Eigen::Matrix< var, R1, C2 > >::type | multiply (const Eigen::Matrix< T1, R1, C1 > &m1, const Eigen::Matrix< T2, R2, C2 > &m2) |
Return the product of the specified matrices. More... | |
template<typename T1 , int C1, typename T2 , int R2> | |
boost::enable_if_c< boost::is_same< T1, var >::value||boost::is_same< T2, var >::value, var >::type | multiply (const Eigen::Matrix< T1, 1, C1 > &rv, const Eigen::Matrix< T2, R2, 1 > &v) |
Return the scalar product of the specified row vector and specified column vector. More... | |
matrix_v | multiply_lower_tri_self_transpose (const matrix_v &L) |
template<typename TA , int RA, int CA, typename TB , int RB, int CB> | |
boost::enable_if_c< boost::is_same< TA, var >::value||boost::is_same< TB, var >::value, Eigen::Matrix< var, CB, CB > >::type | quad_form (const Eigen::Matrix< TA, RA, CA > &A, const Eigen::Matrix< TB, RB, CB > &B) |
template<typename TA , int RA, int CA, typename TB , int RB> | |
boost::enable_if_c< boost::is_same< TA, var >::value||boost::is_same< TB, var >::value, var >::type | quad_form (const Eigen::Matrix< TA, RA, CA > &A, const Eigen::Matrix< TB, RB, 1 > &B) |
template<typename TA , int RA, int CA, typename TB , int RB, int CB> | |
boost::enable_if_c< boost::is_same< TA, var >::value||boost::is_same< TB, var >::value, Eigen::Matrix< var, CB, CB > >::type | quad_form_sym (const Eigen::Matrix< TA, RA, CA > &A, const Eigen::Matrix< TB, RB, CB > &B) |
template<typename TA , int RA, int CA, typename TB , int RB> | |
boost::enable_if_c< boost::is_same< TA, var >::value||boost::is_same< TB, var >::value, var >::type | quad_form_sym (const Eigen::Matrix< TA, RA, CA > &A, const Eigen::Matrix< TB, RB, 1 > &B) |
template<typename T1 , int R1, int C1, typename T2 , int R2, int C2> | |
boost::enable_if_c< boost::is_same< T1, var >::value||boost::is_same< T2, var >::value, Eigen::Matrix< var, R1, 1 > >::type | rows_dot_product (const Eigen::Matrix< T1, R1, C1 > &v1, const Eigen::Matrix< T2, R2, C2 > &v2) |
var | sd (const std::vector< var > &v) |
Return the sample standard deviation of the specified standard vector. More... | |
template<int R, int C> | |
var | sd (const Eigen::Matrix< var, R, C > &m) |
Eigen::Matrix< var, Eigen::Dynamic, 1 > | softmax (const Eigen::Matrix< var, Eigen::Dynamic, 1 > &alpha) |
Return the softmax of the specified Eigen vector. More... | |
std::vector< var > | sort_asc (std::vector< var > xs) |
Return the specified standard vector in ascending order with gradients kept. More... | |
template<int R, int C> | |
Eigen::Matrix< var, R, C > | sort_asc (Eigen::Matrix< var, R, C > xs) |
Return the specified eigen vector in ascending order with gradients kept. More... | |
std::vector< var > | sort_desc (std::vector< var > xs) |
Return the specified standard vector in descending order with gradients kept. More... | |
template<int R, int C> | |
Eigen::Matrix< var, R, C > | sort_desc (Eigen::Matrix< var, R, C > xs) |
Return the specified eigen vector in descending order with gradients kept. More... | |
template<int R1, int C1, int R2, int C2> | |
var | squared_distance (const Eigen::Matrix< var, R1, C1 > &v1, const Eigen::Matrix< var, R2, C2 > &v2) |
template<int R1, int C1, int R2, int C2> | |
var | squared_distance (const Eigen::Matrix< var, R1, C1 > &v1, const Eigen::Matrix< double, R2, C2 > &v2) |
template<int R1, int C1, int R2, int C2> | |
var | squared_distance (const Eigen::Matrix< double, R1, C1 > &v1, const Eigen::Matrix< var, R2, C2 > &v2) |
void | stan_print (std::ostream *o, const var &x) |
template<int R, int C> | |
var | sum (const Eigen::Matrix< var, R, C > &m) |
Returns the sum of the coefficients of the specified matrix, column vector or row vector. More... | |
matrix_v | tcrossprod (const matrix_v &M) |
Returns the result of post-multiplying a matrix by its own transpose. More... | |
matrix_v | to_var (const stan::math::matrix_d &m) |
Converts argument to an automatic differentiation variable. More... | |
matrix_v | to_var (const matrix_v &m) |
Converts argument to an automatic differentiation variable. More... | |
vector_v | to_var (const stan::math::vector_d &v) |
Converts argument to an automatic differentiation variable. More... | |
vector_v | to_var (const vector_v &v) |
Converts argument to an automatic differentiation variable. More... | |
row_vector_v | to_var (const stan::math::row_vector_d &rv) |
Converts argument to an automatic differentiation variable. More... | |
row_vector_v | to_var (const row_vector_v &rv) |
Converts argument to an automatic differentiation variable. More... | |
template<typename T1 , int R1, int C1, typename T2 , int R2, int C2, typename T3 , int R3, int C3> | |
boost::enable_if_c< stan::is_var< T1 >::value||stan::is_var< T2 >::value||stan::is_var< T3 >::value, var >::type | trace_gen_inv_quad_form_ldlt (const Eigen::Matrix< T1, R1, C1 > &D, const stan::math::LDLT_factor< T2, R2, C2 > &A, const Eigen::Matrix< T3, R3, C3 > &B) |
Compute the trace of an inverse quadratic form. More... | |
template<typename TD , int RD, int CD, typename TA , int RA, int CA, typename TB , int RB, int CB> | |
boost::enable_if_c< boost::is_same< TD, var >::value||boost::is_same< TA, var >::value||boost::is_same< TB, var >::value, var >::type | trace_gen_quad_form (const Eigen::Matrix< TD, RD, CD > &D, const Eigen::Matrix< TA, RA, CA > &A, const Eigen::Matrix< TB, RB, CB > &B) |
template<typename T2 , int R2, int C2, typename T3 , int R3, int C3> | |
boost::enable_if_c< stan::is_var< T2 >::value||stan::is_var< T3 >::value, var >::type | trace_inv_quad_form_ldlt (const stan::math::LDLT_factor< T2, R2, C2 > &A, const Eigen::Matrix< T3, R3, C3 > &B) |
Compute the trace of an inverse quadratic form. More... | |
template<typename TA , int RA, int CA, typename TB , int RB, int CB> | |
boost::enable_if_c< boost::is_same< TA, var >::value||boost::is_same< TB, var >::value, var >::type | trace_quad_form (const Eigen::Matrix< TA, RA, CA > &A, const Eigen::Matrix< TB, RB, CB > &B) |
template<int R, int C> | |
Eigen::Matrix< var, R, C > | unit_vector_constrain (const Eigen::Matrix< var, R, C > &y) |
Return the unit length vector corresponding to the free vector y. More... | |
template<int R, int C> | |
Eigen::Matrix< var, R, C > | unit_vector_constrain (const Eigen::Matrix< var, R, C > &y, var &lp) |
Return the unit length vector corresponding to the free vector y. More... | |
var | variance (const std::vector< var > &v) |
Return the sample variance of the specified standard vector. More... | |
template<int R, int C> | |
var | variance (const Eigen::Matrix< var, R, C > &m) |
void | cvodes_silent_err_handler (int error_code, const char *module, const char *function, char *msg, void *eh_data) |
void | cvodes_check_flag (int flag, const std::string &func_name) |
void | cvodes_set_options (void *cvodes_mem, double rel_tol, double abs_tol, long int max_num_steps) |
template<typename F > | |
void | gradient (const F &f, const Eigen::Matrix< double, Eigen::Dynamic, 1 > &x, double &fx, Eigen::Matrix< double, Eigen::Dynamic, 1 > &grad_fx) |
Calculate the value and the gradient of the specified function at the specified argument. More... | |
void | free_cvodes_memory (N_Vector &cvodes_state, N_Vector *cvodes_state_sens, void *cvodes_mem, size_t S) |
Free memory allocated for CVODES state, sensitivity, and general memory. More... | |
template<typename F , typename T_initial , typename T_param > | |
std::vector< std::vector< typename stan::return_type< T_initial, T_param >::type > > | integrate_ode_bdf (const F &f, const std::vector< T_initial > &y0, const double t0, const std::vector< double > &ts, const std::vector< T_param > &theta, const std::vector< double > &x, const std::vector< int > &x_int, std::ostream *msgs=0, double relative_tolerance=1e-10, double absolute_tolerance=1e-10, long int max_num_steps=1e8) |
Return the solutions for the specified system of ordinary differential equations given the specified initial state, initial times, times of desired solution, and parameters and data, writing error and warning messages to the specified stream. More... | |
template<typename F > | |
void | jacobian (const F &f, const Eigen::Matrix< double, Eigen::Dynamic, 1 > &x, Eigen::Matrix< double, Eigen::Dynamic, 1 > &fx, Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > &J) |
var | abs (const var &a) |
Return the absolute value of the variable (std). More... | |
var | acos (const var &a) |
Return the principal value of the arc cosine of a variable, in radians (cmath). More... | |
var | acosh (const var &a) |
The inverse hyperbolic cosine function for variables (C99). More... | |
int | as_bool (const var &v) |
Return 1 if the argument is unequal to zero and 0 otherwise. More... | |
var | asin (const var &a) |
Return the principal value of the arc sine, in radians, of the specified variable (cmath). More... | |
var | asinh (const var &a) |
The inverse hyperbolic sine function for variables (C99). More... | |
var | atan (const var &a) |
Return the principal value of the arc tangent, in radians, of the specified variable (cmath). More... | |
var | atan2 (const var &a, const var &b) |
Return the principal value of the arc tangent, in radians, of the first variable divided by the second (cmath). More... | |
var | atan2 (const var &a, const double b) |
Return the principal value of the arc tangent, in radians, of the first variable divided by the second scalar (cmath). More... | |
var | atan2 (const double a, const var &b) |
Return the principal value of the arc tangent, in radians, of the first scalar divided by the second variable (cmath). More... | |
var | atanh (const var &a) |
The inverse hyperbolic tangent function for variables (C99). More... | |
var | bessel_first_kind (const int &v, const var &a) |
var | bessel_second_kind (const int &v, const var &a) |
var | binary_log_loss (const int y, const stan::math::var &y_hat) |
The log loss function for variables (stan). More... | |
double | calculate_chain (const double &x, const double &val) |
var | cbrt (const var &a) |
Returns the cube root of the specified variable (C99). More... | |
var | ceil (const var &a) |
Return the ceiling of the specified variable (cmath). More... | |
var | cos (const var &a) |
Return the cosine of a radian-scaled variable (cmath). More... | |
var | cosh (const var &a) |
Return the hyperbolic cosine of the specified variable (cmath). More... | |
var | digamma (const stan::math::var &a) |
var | erf (const var &a) |
The error function for variables (C99). More... | |
var | erfc (const var &a) |
The complementary error function for variables (C99). More... | |
var | exp (const var &a) |
Return the exponentiation of the specified variable (cmath). More... | |
var | exp2 (const var &a) |
Exponentiation base 2 function for variables (C99). More... | |
var | expm1 (const stan::math::var &a) |
The exponentiation of the specified variable minus 1 (C99). More... | |
var | fabs (const var &a) |
Return the absolute value of the variable (cmath). More... | |
var | falling_factorial (const var &a, const double &b) |
var | falling_factorial (const var &a, const var &b) |
var | falling_factorial (const double &a, const var &b) |
var | fdim (const stan::math::var &a, const stan::math::var &b) |
Return the positive difference between the first variable's the value and the second's (C99). More... | |
var | fdim (const double &a, const stan::math::var &b) |
Return the positive difference between the first value and the value of the second variable (C99). More... | |
var | fdim (const stan::math::var &a, const double &b) |
Return the positive difference between the first variable's value and the second value (C99). More... | |
var | floor (const var &a) |
Return the floor of the specified variable (cmath). More... | |
var | fma (const stan::math::var &a, const stan::math::var &b, const stan::math::var &c) |
The fused multiply-add function for three variables (C99). More... | |
var | fma (const stan::math::var &a, const stan::math::var &b, const double &c) |
The fused multiply-add function for two variables and a value (C99). More... | |
var | fma (const stan::math::var &a, const double &b, const stan::math::var &c) |
The fused multiply-add function for a variable, value, and variable (C99). More... | |
var | fma (const stan::math::var &a, const double &b, const double &c) |
The fused multiply-add function for a variable and two values (C99). More... | |
var | fma (const double &a, const stan::math::var &b, const double &c) |
The fused multiply-add function for a value, variable, and value (C99). More... | |
var | fma (const double &a, const double &b, const stan::math::var &c) |
The fused multiply-add function for two values and a variable, and value (C99). More... | |
var | fma (const double &a, const stan::math::var &b, const stan::math::var &c) |
The fused multiply-add function for a value and two variables (C99). More... | |
var | fmax (const stan::math::var &a, const stan::math::var &b) |
Returns the maximum of the two variable arguments (C99). More... | |
var | fmax (const stan::math::var &a, const double &b) |
Returns the maximum of the variable and scalar, promoting the scalar to a variable if it is larger (C99). More... | |
var | fmax (const double &a, const stan::math::var &b) |
Returns the maximum of a scalar and variable, promoting the scalar to a variable if it is larger (C99). More... | |
var | fmin (const stan::math::var &a, const stan::math::var &b) |
Returns the minimum of the two variable arguments (C99). More... | |
var | fmin (const stan::math::var &a, double b) |
Returns the minimum of the variable and scalar, promoting the scalar to a variable if it is larger (C99). More... | |
var | fmin (double a, const stan::math::var &b) |
Returns the minimum of a scalar and variable, promoting the scalar to a variable if it is larger (C99). More... | |
var | fmod (const var &a, const var &b) |
Return the floating point remainder after dividing the first variable by the second (cmath). More... | |
var | fmod (const var &a, const double b) |
Return the floating point remainder after dividing the the first variable by the second scalar (cmath). More... | |
var | fmod (const double a, const var &b) |
Return the floating point remainder after dividing the first scalar by the second variable (cmath). More... | |
var | gamma_p (const stan::math::var &a, const stan::math::var &b) |
var | gamma_p (const stan::math::var &a, const double &b) |
var | gamma_p (const double &a, const stan::math::var &b) |
var | gamma_q (const stan::math::var &a, const stan::math::var &b) |
var | gamma_q (const stan::math::var &a, const double &b) |
var | gamma_q (const double &a, const stan::math::var &b) |
void | grad_inc_beta (var &g1, var &g2, const var &a, const var &b, const var &z) |
var | hypot (const var &a, const var &b) |
Returns the length of the hypoteneuse of a right triangle with sides of the specified lengths (C99). More... | |
var | hypot (const var &a, double b) |
Returns the length of the hypoteneuse of a right triangle with sides of the specified lengths (C99). More... | |
var | hypot (double a, const var &b) |
Returns the length of the hypoteneuse of a right triangle with sides of the specified lengths (C99). More... | |
var | ibeta (const var &a, const var &b, const var &x) |
The normalized incomplete beta function of a, b, and x. More... | |
var | if_else (bool c, const var &y_true, const var &y_false) |
If the specified condition is true, return the first variable, otherwise return the second variable. More... | |
var | if_else (bool c, double y_true, const var &y_false) |
If the specified condition is true, return a new variable constructed from the first scalar, otherwise return the second variable. More... | |
var | if_else (bool c, const var &y_true, const double y_false) |
If the specified condition is true, return the first variable, otherwise return a new variable constructed from the second scalar. More... | |
var | inc_beta (const stan::math::var &a, const stan::math::var &b, const stan::math::var &c) |
var | inv (const var &a) |
| |
var | inv_cloglog (const stan::math::var &a) |
Return the inverse complementary log-log function applied specified variable (stan). More... | |
var | inv_logit (const stan::math::var &a) |
The inverse logit function for variables (stan). More... | |
var | inv_Phi (const stan::math::var &p) |
The inverse of unit normal cumulative density function. More... | |
var | inv_sqrt (const var &a) |
| |
var | inv_square (const var &a) |
| |
int | is_inf (const var &v) |
Returns 1 if the input's value is infinite and 0 otherwise. More... | |
bool | is_nan (const var &v) |
Returns 1 if the input's value is NaN and 0 otherwise. More... | |
bool | is_uninitialized (var x) |
Returns true if the specified variable is uninitialized. More... | |
var | lgamma (const stan::math::var &a) |
The log gamma function for variables (C99). More... | |
var | lmgamma (int a, const stan::math::var &b) |
var | log (const var &a) |
Return the natural log of the specified variable (cmath). More... | |
var | log10 (const var &a) |
Return the base 10 log of the specified variable (cmath). More... | |
var | log1m (const stan::math::var &a) |
The log (1 - x) function for variables. More... | |
var | log1m_exp (const stan::math::var &a) |
Return the log of 1 minus the exponential of the specified variable. More... | |
var | log1p (const stan::math::var &a) |
The log (1 + x) function for variables (C99). More... | |
var | log1p_exp (const stan::math::var &a) |
Return the log of 1 plus the exponential of the specified variable. More... | |
var | log2 (const stan::math::var &a) |
Returns the base 2 logarithm of the specified variable (C99). More... | |
var | log_diff_exp (const stan::math::var &a, const stan::math::var &b) |
Returns the log sum of exponentials. More... | |
var | log_diff_exp (const stan::math::var &a, const double &b) |
Returns the log sum of exponentials. More... | |
var | log_diff_exp (const double &a, const stan::math::var &b) |
Returns the log sum of exponentials. More... | |
var | log_falling_factorial (const var &a, const double &b) |
var | log_falling_factorial (const var &a, const var &b) |
var | log_falling_factorial (const double &a, const var &b) |
void | log_mix_partial_helper (const double &theta_val, const double &lambda1_val, const double &lambda2_val, double &one_m_exp_lam2_m_lam1, double &one_m_t_prod_exp_lam2_m_lam1, double &one_d_t_plus_one_m_t_prod_exp_lam2_m_lam1) |
template<typename T_theta , typename T_lambda1 , typename T_lambda2 > | |
return_type< T_theta, T_lambda1, T_lambda2 >::type | log_mix (const T_theta &theta, const T_lambda1 &lambda1, const T_lambda2 &lambda2) |
Return the log mixture density with specified mixing proportion and log densities and its derivative at each. More... | |
var | log_rising_factorial (const var &a, const double &b) |
var | log_rising_factorial (const var &a, const var &b) |
var | log_rising_factorial (const double &a, const var &b) |
var | log_sum_exp (const stan::math::var &a, const stan::math::var &b) |
Returns the log sum of exponentials. More... | |
var | log_sum_exp (const stan::math::var &a, const double &b) |
Returns the log sum of exponentials. More... | |
var | log_sum_exp (const double &a, const stan::math::var &b) |
Returns the log sum of exponentials. More... | |
var | modified_bessel_first_kind (const int &v, const var &a) |
var | modified_bessel_second_kind (const int &v, const var &a) |
var | multiply_log (const var &a, const var &b) |
Return the value of a*log(b). More... | |
var | multiply_log (const var &a, const double b) |
Return the value of a*log(b). More... | |
var | multiply_log (const double a, const var &b) |
Return the value of a*log(b). More... | |
var | owens_t (const var &h, const var &a) |
The Owen's T function of h and a. More... | |
var | owens_t (const var &h, double a) |
The Owen's T function of h and a. More... | |
var | owens_t (double h, const var &a) |
The Owen's T function of h and a. More... | |
var | Phi (const stan::math::var &a) |
The unit normal cumulative density function for variables (stan). More... | |
var | Phi_approx (const stan::math::var &a) |
Approximation of the unit normal CDF for variables (stan). More... | |
var | pow (const var &base, const var &exponent) |
Return the base raised to the power of the exponent (cmath). More... | |
var | pow (const var &base, const double exponent) |
Return the base variable raised to the power of the exponent scalar (cmath). More... | |
var | pow (const double base, const var &exponent) |
Return the base scalar raised to the power of the exponent variable (cmath). More... | |
double | primitive_value (const var &v) |
Return the primitive double value for the specified auto-diff variable. More... | |
var | rising_factorial (const var &a, const double &b) |
var | rising_factorial (const var &a, const var &b) |
var | rising_factorial (const double &a, const var &b) |
var | round (const var &a) |
Returns the rounded form of the specified variable (C99). More... | |
var | sin (const var &a) |
Return the sine of a radian-scaled variable (cmath). More... | |
var | sinh (const var &a) |
Return the hyperbolic sine of the specified variable (cmath). More... | |
var | sqrt (const var &a) |
Return the square root of the specified variable (cmath). More... | |
var | square (const var &x) |
Return the square of the input variable. More... | |
var | squared_distance (const stan::math::var &a, const stan::math::var &b) |
Returns the log sum of exponentials. More... | |
var | squared_distance (const stan::math::var &a, const double &b) |
Returns the log sum of exponentials. More... | |
var | squared_distance (const double &a, const stan::math::var &b) |
Returns the log sum of exponentials. More... | |
var | step (const stan::math::var &a) |
Return the step, or heaviside, function applied to the specified variable (stan). More... | |
var | tan (const var &a) |
Return the tangent of a radian-scaled variable (cmath). More... | |
var | tanh (const var &a) |
Return the hyperbolic tangent of the specified variable (cmath). More... | |
var | tgamma (const stan::math::var &a) |
Return the Gamma function applied to the specified variable (C99). More... | |
var | to_var (const double &x) |
Converts argument to an automatic differentiation variable. More... | |
var | to_var (const var &x) |
Converts argument to an automatic differentiation variable. More... | |
var | trunc (const var &a) |
Returns the truncatation of the specified variable (C99). More... | |
double | value_of (const var &v) |
Return the value of the specified variable. More... | |
double | value_of_rec (const var &v) |
Return the value of the specified variable. More... | |
Variables | |
const double | CONSTRAINT_TOLERANCE = 1E-8 |
The tolerance for checking arithmetic bounds In rank and in simplexes. More... | |
const double | E = boost::math::constants::e<double>() |
The base of the natural logarithm, ![]() | |
const double | SQRT_2 = std::sqrt(2.0) |
The value of the square root of 2, ![]() | |
const double | INV_SQRT_2 = 1.0 / SQRT_2 |
The value of 1 over the square root of 2, ![]() | |
const double | LOG_2 = std::log(2.0) |
The natural logarithm of 2, ![]() | |
const double | LOG_10 = std::log(10.0) |
The natural logarithm of 10, ![]() | |
const double | INFTY = std::numeric_limits<double>::infinity() |
Positive infinity. More... | |
const double | NEGATIVE_INFTY = - std::numeric_limits<double>::infinity() |
Negative infinity. More... | |
const double | NOT_A_NUMBER = std::numeric_limits<double>::quiet_NaN() |
(Quiet) not-a-number value. More... | |
const double | EPSILON = std::numeric_limits<double>::epsilon() |
Smallest positive value. More... | |
const double | NEGATIVE_EPSILON = - std::numeric_limits<double>::epsilon() |
Largest negative value (i.e., smallest absolute value). More... | |
const double | POISSON_MAX_RATE = std::pow(2.0, 30) |
Largest rate parameter allowed in Poisson RNG. More... | |
const double | LOG_PI_OVER_FOUR = std::log(boost::math::constants::pi<double>()) / 4.0 |
Log pi divided by 4 ![]() | |
const double | SQRT_PI = std::sqrt(boost::math::constants::pi<double>()) |
const double | SQRT_2_TIMES_SQRT_PI = SQRT_2 * SQRT_PI |
const double | TWO_OVER_SQRT_PI = 2.0 / SQRT_PI |
const double | NEG_TWO_OVER_SQRT_PI = -TWO_OVER_SQRT_PI |
const double | INV_SQRT_TWO_PI = 1.0 / std::sqrt(2.0 * boost::math::constants::pi<double>()) |
const double | LOG_PI = std::log(boost::math::constants::pi<double>()) |
const double | LOG_SQRT_PI = std::log(SQRT_PI) |
const double | LOG_ZERO = std::log(0.0) |
const double | LOG_TWO = std::log(2.0) |
const double | LOG_HALF = std::log(0.5) |
const double | NEG_LOG_TWO = - LOG_TWO |
const double | NEG_LOG_SQRT_TWO_PI = - std::log(std::sqrt(2.0 * boost::math::constants::pi<double>())) |
const double | NEG_LOG_PI = - LOG_PI |
const double | NEG_LOG_SQRT_PI = -std::log(std::sqrt(boost::math::constants::pi<double>())) |
const double | NEG_LOG_TWO_OVER_TWO = - LOG_TWO / 2.0 |
const double | LOG_TWO_PI = LOG_TWO + LOG_PI |
const double | NEG_LOG_TWO_PI = - LOG_TWO_PI |
const std::string | MAJOR_VERSION = STAN_STRING(STAN_MATH_MAJOR) |
Major version number for Stan math library. More... | |
const std::string | MINOR_VERSION = STAN_STRING(STAN_MATH_MINOR) |
Minor version number for Stan math library. More... | |
const std::string | PATCH_VERSION = STAN_STRING(STAN_MATH_PATCH) |
Patch version for Stan math library. More... | |
Matrices and templated mathematical functions.
Templated probability distributions. All paramaterizations are based on Bayesian Data Analysis. Function gradients via reverse-mode automatic differentiation.
Definition at line 10 of file chainablestack.hpp.
typedef Eigen::Matrix<double, Eigen::Dynamic, Eigen::Dynamic> stan::math::matrix_d |
Type for matrix of double values.
Definition at line 23 of file typedefs.hpp.
typedef Eigen::Matrix<fvar<double>, Eigen::Dynamic, Eigen::Dynamic> stan::math::matrix_fd |
Definition at line 17 of file typedefs.hpp.
typedef Eigen::Matrix<fvar<fvar<double> >, Eigen::Dynamic, Eigen::Dynamic> stan::math::matrix_ffd |
Definition at line 21 of file typedefs.hpp.
typedef Eigen::Matrix<fvar<fvar<var> >, Eigen::Dynamic, Eigen::Dynamic> stan::math::matrix_ffv |
Definition at line 18 of file typedefs.hpp.
typedef Eigen::Matrix<fvar<var>, Eigen::Dynamic, Eigen::Dynamic> stan::math::matrix_fv |
Definition at line 14 of file typedefs.hpp.
typedef Eigen::Matrix<var, Eigen::Dynamic, Eigen::Dynamic> stan::math::matrix_v |
The type of a matrix holding stan::math::var
values.
Definition at line 21 of file typedefs.hpp.
typedef Eigen::Matrix<double, 1, Eigen::Dynamic> stan::math::row_vector_d |
Type for (row) vector of double values.
Definition at line 37 of file typedefs.hpp.
typedef Eigen::Matrix<fvar<double>, 1, Eigen::Dynamic> stan::math::row_vector_fd |
Definition at line 33 of file typedefs.hpp.
typedef Eigen::Matrix<fvar<fvar<double> >, 1, Eigen::Dynamic> stan::math::row_vector_ffd |
Definition at line 37 of file typedefs.hpp.
typedef Eigen::Matrix<fvar<fvar<var> >, 1, Eigen::Dynamic> stan::math::row_vector_ffv |
Definition at line 34 of file typedefs.hpp.
typedef Eigen::Matrix<fvar<var>, 1, Eigen::Dynamic> stan::math::row_vector_fv |
Definition at line 30 of file typedefs.hpp.
typedef Eigen::Matrix<var, 1, Eigen::Dynamic> stan::math::row_vector_v |
The type of a row vector holding stan::math::var
values.
Definition at line 37 of file typedefs.hpp.
typedef Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic >::Index stan::math::size_type |
Type for sizes and indexes in an Eigen matrix with double e.
Definition at line 13 of file typedefs.hpp.
typedef Eigen::Matrix<double, Eigen::Dynamic, 1> stan::math::vector_d |
Type for (column) vector of double values.
Definition at line 30 of file typedefs.hpp.
typedef Eigen::Matrix<fvar<double>, Eigen::Dynamic, 1> stan::math::vector_fd |
Definition at line 25 of file typedefs.hpp.
typedef Eigen::Matrix<fvar<fvar<double> >, Eigen::Dynamic, 1> stan::math::vector_ffd |
Definition at line 29 of file typedefs.hpp.
typedef Eigen::Matrix<fvar<fvar<var> >, Eigen::Dynamic, 1> stan::math::vector_ffv |
Definition at line 26 of file typedefs.hpp.
typedef Eigen::Matrix<fvar<var>, Eigen::Dynamic, 1> stan::math::vector_fv |
Definition at line 22 of file typedefs.hpp.
typedef Eigen::Matrix<var, Eigen::Dynamic, 1> stan::math::vector_v |
The type of a (column) vector holding stan::math::var
values.
Definition at line 29 of file typedefs.hpp.
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Return the sum of the specified matrices.
The two matrices must have the same dimensions.
T1 | Scalar type of first matrix. |
T2 | Scalar type of second matrix. |
R | Row type of matrices. |
C | Column type of matrices. |
m1 | First matrix. |
m2 | Second matrix. |
std::invalid_argument | if m1 and m2 do not have the same dimensions. |
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Increment the state derived from the coupled system in the with the original initial state.
This is necessary because the coupled system subtracts out the initial state in its representation when the initial state is unknown.
[in] | y0 | original initial values to add back into the coupled system. |
[in,out] | y | state of the coupled system on input, incremented with initial values on output. |
Definition at line 34 of file coupled_ode_system.hpp.
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Return the result of appending the second argument matrix after the first argument matrix, that is, putting them side by side, with the first matrix followed by the second matrix.
The inputs can be (matrix, matrix), (matrix, vector), (vector, matrix), or (vector, vector) and the output is always a matrix.
T1 | Scalar type of first matrix. |
T2 | Scalar type of second matrix. |
R1 | Row specification of first matrix. |
C1 | Column specification of first matrix. |
R2 | Row specification of second matrix. |
C2 | Column specification of second matrix. |
A | First matrix. |
B | Second matrix. |
Definition at line 39 of file append_col.hpp.
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Return the result of concatenaing the first row vector followed by the second row vector side by side, with the result being a row vector.
This function applies to (row_vector, row_vector) and returns a row_vector.
T1 | Scalar type of first row vector. |
T2 | Scalar type of second row vector. |
C1 | Column specification of first row vector. |
C2 | Column specification of second row vector. |
A | First vector. |
B | Second vector |
Definition at line 85 of file append_col.hpp.
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Return the result of appending the second argument matrix after the first argument matrix, that is, putting them side by side, with the first matrix followed by the second matrix.
This is an overloaded template function for the case when both matrices have the same type.
The inputs can be (matrix, matrix), (matrix, vector), (vector, matrix), or (vector, vector), and the output is always a matrix.
T | Scalar type of both matrices. |
R1 | Row specification of first matrix. |
C1 | Column specification of first matrix. |
R2 | Row specification of second matrix. |
C2 | Column specification of second matrix. |
A | First matrix. |
B | Second matrix. |
Definition at line 128 of file append_col.hpp.
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Return the result of concatenaing the first row vector followed by the second row vector side by side, with the result being a row vector.
This function applies to (row_vector, row_vector) and returns a row_vector.
T | Scalar type of both vectors. |
C1 | Column specification of first row vector. |
C2 | Column specification of second row vector. |
A | First vector. |
B | Second vector |
Definition at line 160 of file append_col.hpp.
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Return the result of stacking an scalar on top of the a row vector, with the result being a row vector.
This function applies to (scalar, row vector) and returns a row vector.
T1 | Scalar type of the scalar |
T2 | Scalar type of the row vector. |
R | Row specification of the row vector. |
A | scalar. |
B | row vector. |
Definition at line 188 of file append_col.hpp.
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Return the result of stacking a row vector on top of the an scalar, with the result being a row vector.
This function applies to (row vector, scalar) and returns a row vector.
T1 | Scalar type of the row vector. |
T2 | Scalar type of the scalar |
R | Row specification of the row vector. |
A | row vector. |
B | scalar. |
Definition at line 218 of file append_col.hpp.
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Return the result of stacking the rows of the first argument matrix on top of the second argument matrix.
The inputs can be (matrix, matrix), (matrix, row_vector), (row_vector, matrix), or (row_vector, row_vector), and the output is always a matrix.
T1 | Scalar type of first matrix. |
T2 | Scalar type of second matrix. |
R1 | Row specification of first matrix. |
C1 | Column specification of first matrix. |
R2 | Row specification of second matrix. |
C2 | Column specification of second matrix. |
A | First matrix. |
B | Second matrix. |
Definition at line 37 of file append_row.hpp.
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Return the result of stacking the first vector on top of the second vector, with the result being a vector.
This function applies to (vector, vector) and returns a vector.
T1 | Scalar type of first vector. |
T2 | Scalar type of second vector. |
R1 | Row specification of first vector. |
R2 | Row specification of second vector. |
A | First vector. |
B | Second vector. |
Definition at line 80 of file append_row.hpp.
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Return the result of stacking the rows of the first argument matrix on top of the second argument matrix.
This is an overload for the case when the scalar types of the two input matrix are the same.
The inputs can be (matrix, matrix), (matrix, row_vector), (row_vector, matrix), or (row_vector, row_vector), and the output is always a matrix.
T | Scalar type of both matrices. |
R1 | Row specification of first matrix. |
C1 | Column specification of first matrix. |
R2 | Row specification of second matrix. |
C2 | Column specification of second matrix. |
A | First matrix. |
B | Second matrix. |
Definition at line 121 of file append_row.hpp.
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Return the result of stacking the first vector on top of the second vector, with the result being a vector.
This is an overloaded template function for the case where both inputs have the same scalar type.
This function applies to (vector, vector) and returns a vector.
T | Scalar type of both vectors. |
R1 | Row specification of first vector. |
R2 | Row specification of second vector. |
A | First vector. |
B | Second vector. |
Definition at line 155 of file append_row.hpp.
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Return the result of stacking an scalar on top of the a vector, with the result being a vector.
This function applies to (scalar, vector) and returns a vector.
T1 | Scalar type of the scalar |
T2 | Scalar type of the vector. |
R | Row specification of the vector. |
A | scalar. |
B | vector. |
Definition at line 182 of file append_row.hpp.
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Return the result of stacking a vector on top of the an scalar, with the result being a vector.
This function applies to (vector, scalar) and returns a vector.
T1 | Scalar type of the vector. |
T2 | Scalar type of the scalar |
R | Row specification of the vector. |
A | vector. |
B | scalar. |
Definition at line 211 of file append_row.hpp.
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Return 1 if the argument is unequal to zero and 0 otherwise.
x | Value. |
Definition at line 14 of file as_bool.hpp.
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Return 1 if the argument is unequal to zero and 0 otherwise.
v | Value. |
Definition at line 15 of file as_bool.hpp.
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Copy the right-hand side's value to the left-hand side variable.
The assign()
function is overloaded. This instance will match arguments where the right-hand side is assignable to the left and they are not both std::vector
or Eigen::Matrix
types.
LHS | Type of left-hand side. |
RHS | Type of right-hand side. |
lhs | Left-hand side. |
rhs | Right-hand side. |
Definition at line 51 of file assign.hpp.
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Copy the right-hand side's value to the left-hand side variable.
The assign()
function is overloaded. This instance will be called for arguments that are both Eigen::Matrix
types, but whose shapes are not compatible. The shapes are specified in the row and column template parameters.
LHS | Type of left-hand side matrix elements. |
RHS | Type of right-hand side matrix elements. |
R1 | Row shape of left-hand side matrix. |
C1 | Column shape of left-hand side matrix. |
R2 | Row shape of right-hand side matrix. |
C2 | Column shape of right-hand side matrix. |
x | Left-hand side matrix. |
y | Right-hand side matrix. |
std::invalid_argument |
Definition at line 77 of file assign.hpp.
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Copy the right-hand side's value to the left-hand side variable.
The assign()
function is overloaded. This instance will be called for arguments that are both Eigen::Matrix
types and whose shapes match. The shapes are specified in the row and column template parameters.
LHS | Type of left-hand side matrix elements. |
RHS | Type of right-hand side matrix elements. |
R | Row shape of both matrices. |
C | Column shape of both mtarices. |
x | Left-hand side matrix. |
y | Right-hand side matrix. |
std::invalid_argument | if sizes do not match. |
Definition at line 113 of file assign.hpp.
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Copy the right-hand side's value to the left-hand side variable.
The assign()
function is overloaded. This instance will be called for arguments that are both Eigen::Matrix
types and whose shapes match. The shape of the right-hand side matrix is specified in the row and column shape template parameters.
LHS | Type of matrix block elements. |
RHS | Type of right-hand side matrix elements. |
R | Row shape for right-hand side matrix. |
C | Column shape for right-hand side matrix. |
x | Left-hand side block view of matrix. |
y | Right-hand side matrix. |
std::invalid_argument | if sizes do not match. |
Definition at line 142 of file assign.hpp.
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Copy the right-hand side's value to the left-hand side variable.
The assign()
function is overloaded. This instance will be called for arguments that are both std::vector
, and will call assign()
element-by element.
For example, a std::vector<int>
can be assigned to a std::vector<double>
using this function.
LHS | Type of left-hand side vector elements. |
RHS | Type of right-hand side vector elements. |
x | Left-hand side vector. |
y | Right-hand side vector. |
std::invalid_argument | if sizes do not match. |
Definition at line 177 of file assign.hpp.
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Return the principal value of the arc tangent, in radians, of the first variable divided by the second (cmath).
The partial derivatives are defined by
, and
.
a | Numerator variable. |
b | Denominator variable. |
Return the principal value of the arc tangent, in radians, of the first variable divided by the second scalar (cmath).
The derivative with respect to the variable is
.
a | Numerator variable. |
b | Denominator scalar. |
Return the principal value of the arc tangent, in radians, of the first scalar divided by the second variable (cmath).
The derivative with respect to the variable is
.
a | Numerator scalar. |
b | Denominator variable. |
void stan::math::autocorrelation | ( | const std::vector< T > & | y, |
std::vector< T > & | ac, | ||
Eigen::FFT< T > & | fft | ||
) |
Write autocorrelation estimates for every lag for the specified input sequence into the specified result using the specified FFT engine.
The return vector be resized to the same length as the input sequence with lags given by array index.
The implementation involves a fast Fourier transform, followed by a normalization, followed by an inverse transform.
An FFT engine can be created for reuse for type double with:
Eigen::FFT<double> fft;
T | Scalar type. |
y | Input sequence. |
ac | Autocorrelations. |
fft | FFT engine instance. |
Definition at line 54 of file autocorrelation.hpp.
void stan::math::autocorrelation | ( | const std::vector< T > & | y, |
std::vector< T > & | ac | ||
) |
Write autocorrelation estimates for every lag for the specified input sequence into the specified result.
The return vector be resized to the same length as the input sequence with lags given by array index.
The implementation involves a fast Fourier transform, followed by a normalization, followed by an inverse transform.
This method is just a light wrapper around the three-argument autocorrelation function
T | Scalar type. |
y | Input sequence. |
ac | Autocorrelations. |
Definition at line 123 of file autocorrelation.hpp.
void stan::math::autocovariance | ( | const std::vector< T > & | y, |
std::vector< T > & | acov, | ||
Eigen::FFT< T > & | fft | ||
) |
Write autocovariance estimates for every lag for the specified input sequence into the specified result using the specified FFT engine.
The return vector be resized to the same length as the input sequence with lags given by array index.
The implementation involves a fast Fourier transform, followed by a normalization, followed by an inverse transform.
An FFT engine can be created for reuse for type double with:
Eigen::FFT<double> fft;
T | Scalar type. |
y | Input sequence. |
acov | Autocovariance. |
fft | FFT engine instance. |
Definition at line 34 of file autocovariance.hpp.
void stan::math::autocovariance | ( | const std::vector< T > & | y, |
std::vector< T > & | acov | ||
) |
Write autocovariance estimates for every lag for the specified input sequence into the specified result.
The return vector be resized to the same length as the input sequence with lags given by array index.
The implementation involves a fast Fourier transform, followed by a normalization, followed by an inverse transform.
This method is just a light wrapper around the three-argument autocovariance function
T | Scalar type. |
y | Input sequence. |
acov | Autocovariances. |
Definition at line 62 of file autocovariance.hpp.
return_type<T_prob>::type stan::math::bernoulli_ccdf_log | ( | const T_n & | n, |
const T_prob & | theta | ||
) |
Definition at line 26 of file bernoulli_ccdf_log.hpp.
return_type<T_prob>::type stan::math::bernoulli_cdf | ( | const T_n & | n, |
const T_prob & | theta | ||
) |
Definition at line 26 of file bernoulli_cdf.hpp.
return_type<T_prob>::type stan::math::bernoulli_cdf_log | ( | const T_n & | n, |
const T_prob & | theta | ||
) |
Definition at line 26 of file bernoulli_cdf_log.hpp.
return_type<T_prob>::type stan::math::bernoulli_log | ( | const T_n & | n, |
const T_prob & | theta | ||
) |
Definition at line 28 of file bernoulli_log.hpp.
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Definition at line 122 of file bernoulli_log.hpp.
return_type<T_prob>::type stan::math::bernoulli_logit_log | ( | const T_n & | n, |
const T_prob & | theta | ||
) |
Definition at line 28 of file bernoulli_logit_log.hpp.
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Definition at line 106 of file bernoulli_logit_log.hpp.
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Definition at line 22 of file bernoulli_rng.hpp.
Definition at line 15 of file bessel_first_kind.hpp.
Definition at line 27 of file bessel_first_kind.hpp.
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Definition at line 15 of file bessel_second_kind.hpp.
Definition at line 27 of file bessel_second_kind.hpp.
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return_type<T_size1, T_size2>::type stan::math::beta_binomial_ccdf_log | ( | const T_n & | n, |
const T_N & | N, | ||
const T_size1 & | alpha, | ||
const T_size2 & | beta | ||
) |
Definition at line 30 of file beta_binomial_ccdf_log.hpp.
return_type<T_size1, T_size2>::type stan::math::beta_binomial_cdf | ( | const T_n & | n, |
const T_N & | N, | ||
const T_size1 & | alpha, | ||
const T_size2 & | beta | ||
) |
Definition at line 31 of file beta_binomial_cdf.hpp.
return_type<T_size1, T_size2>::type stan::math::beta_binomial_cdf_log | ( | const T_n & | n, |
const T_N & | N, | ||
const T_size1 & | alpha, | ||
const T_size2 & | beta | ||
) |
Definition at line 30 of file beta_binomial_cdf_log.hpp.
return_type<T_size1, T_size2>::type stan::math::beta_binomial_log | ( | const T_n & | n, |
const T_N & | N, | ||
const T_size1 & | alpha, | ||
const T_size2 & | beta | ||
) |
Definition at line 32 of file beta_binomial_log.hpp.
return_type<T_size1, T_size2>::type stan::math::beta_binomial_log | ( | const T_n & | n, |
const T_N & | N, | ||
const T_size1 & | alpha, | ||
const T_size2 & | beta | ||
) |
Definition at line 177 of file beta_binomial_log.hpp.
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Definition at line 25 of file beta_binomial_rng.hpp.
return_type<T_y, T_scale_succ, T_scale_fail>::type stan::math::beta_ccdf_log | ( | const T_y & | y, |
const T_scale_succ & | alpha, | ||
const T_scale_fail & | beta | ||
) |
Definition at line 36 of file beta_ccdf_log.hpp.
return_type<T_y, T_scale_succ, T_scale_fail>::type stan::math::beta_cdf | ( | const T_y & | y, |
const T_scale_succ & | alpha, | ||
const T_scale_fail & | beta | ||
) |
Calculates the beta cumulative distribution function for the given variate and scale variables.
y | A scalar variate. |
alpha | Prior sample size. |
beta | Prior sample size. |
T_y | Type of y. |
T_scale_succ | Type of alpha. |
T_scale_fail | Type of beta. |
Definition at line 49 of file beta_cdf.hpp.
return_type<T_y, T_scale_succ, T_scale_fail>::type stan::math::beta_cdf_log | ( | const T_y & | y, |
const T_scale_succ & | alpha, | ||
const T_scale_fail & | beta | ||
) |
Definition at line 35 of file beta_cdf_log.hpp.
return_type<T_y, T_scale_succ, T_scale_fail>::type stan::math::beta_log | ( | const T_y & | y, |
const T_scale_succ & | alpha, | ||
const T_scale_fail & | beta | ||
) |
The log of the beta density for the specified scalar(s) given the specified sample size(s).
y, alpha, or beta can each either be scalar or a vector. Any vector inputs must be the same length.
The result log probability is defined to be the sum of the log probabilities for each observation/alpha/beta triple.
Prior sample sizes, alpha and beta, must be greater than 0.
y | (Sequence of) scalar(s). |
alpha | (Sequence of) prior sample size(s). |
beta | (Sequence of) prior sample size(s). |
T_y | Type of scalar outcome. |
T_scale_succ | Type of prior scale for successes. |
T_scale_fail | Type of prior scale for failures. |
Definition at line 54 of file beta_log.hpp.
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Definition at line 211 of file beta_log.hpp.
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Definition at line 29 of file beta_rng.hpp.
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Definition at line 15 of file binary_log_loss.hpp.
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Returns the log loss function for binary classification with specified reference and response values.
The log loss function for prediction given outcome
is
, and
.
y | Reference value in { 0 , 1 }. |
y_hat | Response value in [0, 1]. |
Definition at line 26 of file binary_log_loss.hpp.
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The log loss function for variables (stan).
See stan::math::binary_log_loss() for the double-based version.
The derivative with respect to the variable is
, and
.
y | Reference value. |
y_hat | Response variable. |
Definition at line 68 of file binary_log_loss.hpp.
return_type<T_prob>::type stan::math::binomial_ccdf_log | ( | const T_n & | n, |
const T_N & | N, | ||
const T_prob & | theta | ||
) |
Definition at line 33 of file binomial_ccdf_log.hpp.
return_type<T_prob>::type stan::math::binomial_cdf | ( | const T_n & | n, |
const T_N & | N, | ||
const T_prob & | theta | ||
) |
Definition at line 34 of file binomial_cdf.hpp.
return_type<T_prob>::type stan::math::binomial_cdf_log | ( | const T_n & | n, |
const T_N & | N, | ||
const T_prob & | theta | ||
) |
Definition at line 33 of file binomial_cdf_log.hpp.
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Definition at line 16 of file binomial_coefficient_log.hpp.
|
inline |
Definition at line 46 of file binomial_coefficient_log.hpp.
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Return the log of the binomial coefficient for the specified arguments.
The binomial coefficient, , read "N choose n", is defined for
by
.
This function uses Gamma functions to define the log and generalize the arguments to continuous N and n.
.
N | total number of objects. |
n | number of objects chosen. |
Definition at line 62 of file binomial_coefficient_log.hpp.
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Definition at line 70 of file binomial_coefficient_log.hpp.
return_type<T_prob>::type stan::math::binomial_log | ( | const T_n & | n, |
const T_N & | N, | ||
const T_prob & | theta | ||
) |
Definition at line 38 of file binomial_log.hpp.
|
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Definition at line 129 of file binomial_log.hpp.
return_type<T_prob>::type stan::math::binomial_logit_log | ( | const T_n & | n, |
const T_N & | N, | ||
const T_prob & | alpha | ||
) |
Definition at line 39 of file binomial_logit_log.hpp.
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Definition at line 133 of file binomial_logit_log.hpp.
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Definition at line 30 of file binomial_rng.hpp.
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Definition at line 8 of file calculate_chain.hpp.
boost::math::tools::promote_args<T_prob>::type stan::math::categorical_log | ( | int | n, |
const Eigen::Matrix< T_prob, Eigen::Dynamic, 1 > & | theta | ||
) |
Definition at line 25 of file categorical_log.hpp.
|
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Definition at line 56 of file categorical_log.hpp.
boost::math::tools::promote_args<T_prob>::type stan::math::categorical_log | ( | const std::vector< int > & | ns, |
const Eigen::Matrix< T_prob, Eigen::Dynamic, 1 > & | theta | ||
) |
Definition at line 68 of file categorical_log.hpp.
|
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Definition at line 116 of file categorical_log.hpp.
boost::math::tools::promote_args<T_prob>::type stan::math::categorical_logit_log | ( | int | n, |
const Eigen::Matrix< T_prob, Eigen::Dynamic, 1 > & | beta | ||
) |
Definition at line 22 of file categorical_logit_log.hpp.
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Definition at line 45 of file categorical_logit_log.hpp.
boost::math::tools::promote_args<T_prob>::type stan::math::categorical_logit_log | ( | const std::vector< int > & | ns, |
const Eigen::Matrix< T_prob, Eigen::Dynamic, 1 > & | beta | ||
) |
Definition at line 54 of file categorical_logit_log.hpp.
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Definition at line 89 of file categorical_logit_log.hpp.
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Definition at line 20 of file categorical_rng.hpp.
return_type<T_y, T_loc, T_scale>::type stan::math::cauchy_ccdf_log | ( | const T_y & | y, |
const T_loc & | mu, | ||
const T_scale & | sigma | ||
) |
Definition at line 26 of file cauchy_ccdf_log.hpp.
return_type<T_y, T_loc, T_scale>::type stan::math::cauchy_cdf | ( | const T_y & | y, |
const T_loc & | mu, | ||
const T_scale & | sigma | ||
) |
Calculates the cauchy cumulative distribution function for the given variate, location, and scale.
y | A scalar variate. |
mu | The location parameter. |
sigma | The scale parameter. |
Definition at line 38 of file cauchy_cdf.hpp.
return_type<T_y, T_loc, T_scale>::type stan::math::cauchy_cdf_log | ( | const T_y & | y, |
const T_loc & | mu, | ||
const T_scale & | sigma | ||
) |
Definition at line 26 of file cauchy_cdf_log.hpp.
return_type<T_y, T_loc, T_scale>::type stan::math::cauchy_log | ( | const T_y & | y, |
const T_loc & | mu, | ||
const T_scale & | sigma | ||
) |
The log of the Cauchy density for the specified scalar(s) given the specified location parameter(s) and scale parameter(s).
y, mu, or sigma can each either be scalar a vector. Any vector inputs must be the same length.
The result log probability is defined to be the sum of the log probabilities for each observation/mu/sigma triple.
y | (Sequence of) scalar(s). |
mu | (Sequence of) location(s). |
sigma | (Sequence of) scale(s). |
T_y | Type of scalar outcome. |
T_loc | Type of location. |
T_scale | Type of scale. |
Definition at line 45 of file cauchy_log.hpp.
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Definition at line 147 of file cauchy_log.hpp.
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Definition at line 22 of file cauchy_rng.hpp.
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Return the ceiling of the specified variable (cmath).
The derivative of the ceiling function is defined and zero everywhere but at integers, and we set them to zero for convenience,
.
The ceiling function rounds up. For double values, this is the smallest integral value that is not less than the specified value. Although this function is not differentiable because it is discontinuous at integral values, its gradient is returned as zero everywhere.
a | Input variable. |
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Return true
if the value is between the low and high values, inclusively.
T_y | Type of value |
T_low | Type of low value |
T_high | Type of high value |
function | Function name (for error messages) |
name | Variable name (for error messages) |
y | Value to check |
low | Low bound |
high | High bound |
true
if the value is between low and high, inclusively. <code>std::domain_error</code> | otherwise. This also throws if any of the arguments are NaN. |
Definition at line 95 of file check_bounded.hpp.
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Return true
if the specified matrix is a valid Cholesky factor.
A Cholesky factor is a lower triangular matrix whose diagonal elements are all positive. Note that Cholesky factors need not be square, but require at least as many rows M as columns N (i.e., M >= N).
T_y | Type of elements of Cholesky factor |
function | Function name (for error messages) |
name | Variable name (for error messages) |
y | Matrix to test |
true
if the matrix is a valid Cholesky factor <code>std::domain_error</code> | if y is not a valid Choleksy factor, if number of rows is less than the number of columns, if there are 0 columns, or if any element in matrix is NaN |
Definition at line 35 of file check_cholesky_factor.hpp.
bool stan::math::check_cholesky_factor_corr | ( | const char * | function, |
const char * | name, | ||
const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > & | y | ||
) |
Return true
if the specified matrix is a valid Cholesky factor of a correlation matrix.
A Cholesky factor is a lower triangular matrix whose diagonal elements are all positive. Note that Cholesky factors need not be square, but require at least as many rows M as columns N (i.e., M >= N).
Tolerance is specified by math::CONSTRAINT_TOLERANCE
.
T_y | Type of elements of Cholesky factor |
function | Function name (for error messages) |
name | Variable name (for error messages) |
y | Matrix to test |
true
if the matrix is a valid Cholesky factor of a correlation matrix <code>std::domain_error</code> | if y is not a valid Choleksy factor, if number of rows is less than the number of columns, if there are 0 columns, or if any element in matrix is NaN |
Definition at line 39 of file check_cholesky_factor_corr.hpp.
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Return true
if the specified index is a valid column of the matrix.
By default, this is a 1-indexed check (as opposed to 0-indexed). Behavior can be changed by setting stan::error_index::value
. This function will throw an std::out_of_range
exception if the index is out of bounds.
T_y | Type of scalar. |
R | Number of rows of the matrix |
C | Number of columns of the matrix |
function | Function name (for error messages) |
name | Variable name (for error messages) |
y | Matrix |
i | Index to check |
true
if the index is a valid column index of the matrix. std::out_of_range | if index is an invalid column index |
Definition at line 37 of file check_column_index.hpp.
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Return true
if the dimension of x is consistent, which is defined to be expected_size
if x is a vector or 1 if x is not a vector.
T | Type of value |
function | Function name (for error messages) |
name | Variable name (for error messages) |
x | Variable to check for consistent size |
expected_size | Expected size if x is a vector |
true
if x is scalar or if x is vector-like and has size of expected_size
<code>invalid_argument</code> | if the size is inconsistent |
Definition at line 29 of file check_consistent_size.hpp.
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Return true
if the dimension of x1 is consistent with x2.
Consistent size is defined as having the same size if vector-like or being a scalar.
T1 | Type of x1 |
T2 | Type of x2 |
function | Function name (for error messages) |
name1 | Variable name (for error messages) |
x1 | Variable to check for consistent size |
name2 | Variable name (for error messages) |
x2 | Variable to check for consistent size |
true
if x1 and x2 have consistent sizes <code>invalid_argument</code> | if sizes are inconsistent |
Definition at line 31 of file check_consistent_sizes.hpp.
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Return true
if the dimension of x1, x2, and x3 are consistent.
Consistent size is defined as having the same size if vector-like or being a scalar.
T1 | Type of x1 |
T2 | Type of x2 |
T3 | Type of x3 |
function | Function name (for error messages) |
name1 | Variable name (for error messages) |
x1 | Variable to check for consistent size |
name2 | Variable name (for error messages) |
x2 | Variable to check for consistent size |
name3 | Variable name (for error messages) |
x3 | Variable to check for consistent size |
true
if x1, x2, and x3 have consistent sizes <code>invalid_argument</code> | if sizes are inconsistent |
Definition at line 66 of file check_consistent_sizes.hpp.
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Return true
if the dimension of x1, x2, x3, and x4 are consistent.
Consistent size is defined as having the same size if vector-like or being a scalar.
T1 | Type of x1 |
T2 | Type of x2 |
T3 | Type of x3 |
T4 | Type of x4 |
function | Function name (for error messages) |
name1 | Variable name (for error messages) |
x1 | Variable to check for consistent size |
name2 | Variable name (for error messages) |
x2 | Variable to check for consistent size |
name3 | Variable name (for error messages) |
x3 | Variable to check for consistent size |
name4 | Variable name (for error messages) |
x4 | Variable to check for consistent size |
true
if x1, x2, x3, and x4 have consistent sizes <code>invalid_argument</code> | if sizes are inconsistent |
Definition at line 107 of file check_consistent_sizes.hpp.
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Definition at line 128 of file check_consistent_sizes.hpp.
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Return true
if the specified matrix is a valid correlation matrix.
A valid correlation matrix is symmetric, has a unit diagonal (all 1 values), and has all values between -1 and 1 (inclusive).
This function throws exceptions if the variable is not a valid correlation matrix.
T_y | Type of scalar |
function | Name of the function this was called from |
name | Name of the variable |
y | Matrix to test |
true
if the specified matrix is a valid correlation matrix <code>std::invalid_argument</code> | if the matrix is not square or if the matrix is 0x0 |
<code>std::domain_error</code> | if the matrix is non-symmetric, diagonals not near 1, not positive definite, or any of the elements nan. |
Definition at line 45 of file check_corr_matrix.hpp.
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Return true
if the specified matrix is a valid covariance matrix.
A valid covariance matrix is a square, symmetric matrix that is positive definite.
T | Type of scalar. |
function | Function name (for error messages) |
name | Variable name (for error messages) |
y | Matrix to test |
true
if the matrix is a valid covariance matrix <code>std::invalid_argument</code> | if the matrix is not square or if the matrix is 0x0 |
<code>std::domain_error</code> | if the matrix is not symmetric, if the matrix is not positive definite, or if any element of the matrix is nan |
Definition at line 31 of file check_cov_matrix.hpp.
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Return true
if y
is equal to eq
.
This function is vectorized over both y
and eq
. If both y
and eq
are scalar or vector-like, then each element is compared in order. If one of y
or eq
are vector and the other is scalar, then the scalar is broadcast to the size of the vector.
T_y | Type of variable |
T_eq | Type of comparison |
function | Function name (for error messages) |
name | Variable name (for error messages) |
y | Variable to check equality |
eq | Expected value for y |
true
if y is equal to eq <code>std::domain_error</code> | if y is unequal to eq or if any element of y or eq is NaN. |
Definition at line 90 of file check_equal.hpp.
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Return true
if y
is finite.
This function is vectorized and will check each element of y
.
T_y | Type of y |
function | Function name (for error messages) |
name | Variable name (for error messages) |
y | Variable to check |
true
if y is finite. <code>domain_error</code> | if y is infinity, -infinity, or NaN. |
Definition at line 62 of file check_finite.hpp.
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Return true
if y
is strictly greater than low
.
This function is vectorized and will check each element of y
against each element of low
.
T_y | Type of y |
T_low | Type of lower bound |
function | Function name (for error messages) |
name | Variable name (for error messages) |
y | Variable to check |
low | Lower bound |
true
if y is strictly greater than low. <code>domain_error</code> | if y is not greater than low or if any element of y or low is NaN. |
Definition at line 84 of file check_greater.hpp.
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Return true
if y
is greater or equal than low
.
This function is vectorized and will check each element of y
against each element of low
.
T_y | Type of y |
T_low | Type of lower bound |
function | Function name (for error messages) |
name | Variable name (for error messages) |
y | Variable to check |
low | Lower bound |
true
if y is greater or equal than low. <code>domain_error</code> | if y is not greater or equal to low or if any element of y or low is NaN. |
Definition at line 84 of file check_greater_or_equal.hpp.
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Return true
if the argument is a valid stan::math::LDLT_factor
.
LDLT_factor
can be constructed in an invalid state, so it must be checked. A invalid LDLT_factor
is constructed from a non positive definite matrix.
T | Type of scalar |
R | Rows of the matrix |
C | Columns of the matrix |
function | Function name (for error messages) |
name | Variable name (for error messages) |
A | stan::math::LDLT_factor to check for validity. |
true
if the matrix is positive definite. std::domain_error
the LDLT_factor was created improperly (A.success() == false) Definition at line 34 of file check_ldlt_factor.hpp.
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Return true
if y
is strictly less than high
.
This function is vectorized and will check each element of y
against each element of high
.
T_y | Type of y |
T_high | Type of upper bound |
function | Function name (for error messages) |
name | Variable name (for error messages) |
y | Variable to check |
high | Upper bound |
true
if y is strictly less than low. <code>domain_error</code> | if y is not less than low or if any element of y or high is NaN. |
Definition at line 81 of file check_less.hpp.
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Return true
if y
is less or equal to high
.
This function is vectorized and will check each element of y
against each element of high
.
T_y | Type of y |
T_high | Type of upper bound |
function | Function name (for error messages) |
name | Variable name (for error messages) |
y | Variable to check |
high | Upper bound |
true
if y is less than or equal to low. <code>std::domain_error</code> | if y is not less than or equal to low or if any element of y or high is NaN. |
Definition at line 81 of file check_less_or_equal.hpp.
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Return true
if the specified matrix is lower triangular.
A matrix x is not lower triangular if there is a non-zero entry x[m, n] with m < n. This function only inspects the upper triangular portion of the matrix, not including the diagonal.
T | Type of scalar of the matrix |
function | Function name (for error messages) |
name | Variable name (for error messages) |
y | Matrix to test |
true
if the matrix is lower triangular. <code>std::domain_error</code> | if the matrix is not lower triangular or if any element in the upper triangular portion is NaN |
Definition at line 34 of file check_lower_triangular.hpp.
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Return true
if the two matrices are of the same size.
This function checks not only the runtime sizes, but the static sizes as well. For example, a 4x1 matrix is not the same as a vector with 4 elements.
T1 | Scalar type of the first matrix |
T2 | Scalar type of the second matrix |
R1 | Rows specified at compile time of the first matrix |
C1 | Columns specified at compile time of the first matrix |
R2 | Rows specified at compile time of the second matrix |
C2 | Columns specified at compile time of the second matrix |
function | Function name (for error messages) |
name1 | Variable name for the first matrix (for error messages) |
y1 | First matrix |
name2 | Variable name for the second matrix (for error messages) |
y2 | Second matrix |
true
if the dimensions of the two matrices match <code>std::invalid_argument</code> | if the dimensions of the matrices do not match |
Definition at line 37 of file check_matching_dims.hpp.
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Return true
if two structures at the same size.
This function only checks the runtime sizes for variables that implement a size()
method.
T_y1 | Type of the first variable |
T_y2 | Type of the second variable |
function | Function name (for error messages) |
name1 | First variable name (for error messages) |
y1 | First variable |
name2 | Second variable name (for error messages) |
y2 | Second variable |
true
if the sizes match <code>std::invalid_argument</code> | if the sizes do not match |
Definition at line 29 of file check_matching_sizes.hpp.
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Return true
if the matrices can be multiplied.
This checks the runtime sizes to determine whether the two matrices are multiplicable. This allows Eigen matrices, vectors, and row vectors to be checked.
T1 | Type of first matrix |
T2 | Type of second matrix |
function | Function name (for error messages) |
name1 | Variable name for the first matrix (for error messages) |
y1 | First matrix |
name2 | Variable name for the second matrix (for error messages) |
y2 | Second matrix |
true
if the two matrices are multiplicable <code>std::invalid_argument</code> | if the matrices are not multiplicable or if either matrix is size 0 for either rows or columns |
Definition at line 33 of file check_multiplicable.hpp.
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Return true
if y
is non-negative.
This function is vectorized and will check each element of y
.
T_y | Type of y |
function | Function name (for error messages) |
name | Variable name (for error messages) |
y | Variable to check |
true
if y is greater than or equal to 0. <code>domain_error</code> | if y is negative or if any element of y is NaN. |
Definition at line 66 of file check_nonnegative.hpp.
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Return true
if the specified matrix/vector is of non-zero size.
Throws a std:invalid_argument otherwise. The message will indicate that the variable name "has size 0".
T_y | Type of container |
function | Function name (for error messages) |
name | Variable name (for error messages) |
y | Container to test. This will accept matrices and vectors |
true
if the the specified matrix/vector is of non-zero size <code>std::invalid_argument</code> | if the specified matrix/vector has zero size |
Definition at line 30 of file check_nonzero_size.hpp.
|
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Return true
if y
is not NaN
.
This function is vectorized and will check each element of y
. If any element is NaN
, this function will throw an exception.
T_y | Type of y |
function | Function name (for error messages) |
name | Variable name (for error messages) |
y | Variable to check |
true
if y is not NaN. <code>domain_error</code> | if any element of y is NaN. |
Definition at line 63 of file check_not_nan.hpp.
bool stan::math::check_ordered | ( | const char * | function, |
const char * | name, | ||
const std::vector< T_y > & | y | ||
) |
Return true
if the specified vector is sorted into strictly increasing order.
T_y | Type of scalar |
function | Function name (for error messages) |
name | Variable name (for error messages) |
y | std::vector to test |
true
if the vector is ordered <code>std::domain_error</code> | if the vector elements are not ordered, if there are duplicated values, or if any element is NaN . |
Definition at line 30 of file check_ordered.hpp.
bool stan::math::check_ordered | ( | const char * | function, |
const char * | name, | ||
const Eigen::Matrix< T_y, Eigen::Dynamic, 1 > & | y | ||
) |
Return true
if the specified vector is sorted into strictly increasing order.
T_y | Type of scalar |
function | Function name (for error messages) |
name | Variable name (for error messages) |
y | Vector to test |
true
if the vector is ordered <code>std::domain_error</code> | if the vector elements are not ordered, if there are duplicated values, or if any element is NaN . |
Definition at line 31 of file check_ordered.hpp.
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Return true
if the specified square, symmetric matrix is positive definite.
T_y | Type of scalar of the matrix |
function | Function name (for error messages) |
name | Variable name (for error messages) |
y | Matrix to test |
true
if the matrix is positive definite <code>std::invalid_argument</code> | if the matrix is not square or if the matrix has 0 size. |
<code>std::domain_error</code> | if the matrix is not symmetric, if it is not positive definite, or if any element is NaN . |
Definition at line 37 of file check_pos_definite.hpp.
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Return true
if the specified LDLT transform of a matrix is positive definite.
Derived | Derived type of the Eigen::LDLT transform. |
function | Function name (for error messages) |
name | Variable name (for error messages) |
cholesky | Eigen::LDLT to test, whose progenitor must not have any NaN elements |
true
if the matrix is positive definite <code>std::domain_error</code> | if the matrix is not positive definite. |
Definition at line 77 of file check_pos_definite.hpp.
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Return true
if the specified LLT transform of a matrix is positive definite.
Derived | Derived type of the Eigen::LLT transform. |
function | Function name (for error messages) |
name | Variable name (for error messages) |
cholesky | Eigen::LLT to test, whose progenitor must not have any NaN elements |
true
if the matrix is positive definite <code>std::domain_error</code> | if the diagonal of the L matrix is not positive. |
Definition at line 103 of file check_pos_definite.hpp.
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Return true
if the specified matrix is positive definite.
T_y | scalar type of the matrix |
function | Function name (for error messages) |
name | Variable name (for error messages) |
y | Matrix to test |
true
if the matrix is positive semi-definite. <code>std::invalid_argument</code> | if the matrix is not square or if the matrix has 0 size. |
<code>std::domain_error</code> | if the matrix is not symmetric, or if it is not positive semi-definite, or if any element of the matrix is NaN . |
Definition at line 35 of file check_pos_semidefinite.hpp.
|
inline |
Return true
if y
is positive.
This function is vectorized and will check each element of y
.
T_y | Type of y |
function | Function name (for error messages) |
name | Variable name (for error messages) |
y | Variable to check |
true
if y is greater than 0. <code>domain_error</code> | if y is negative or zero or if any element of y is NaN. |
Definition at line 68 of file check_positive.hpp.
|
inline |
Return true
if y
is positive and finite.
This function is vectorized and will check each element of y
.
T_y | Type of y |
function | Function name (for error messages) |
name | Variable name (for error messages) |
y | Variable to check |
true
if every element of y is greater than 0 and y is not infinite. <code>domain_error</code> | if any element of y is not positive or if any element of y is NaN. |
Definition at line 28 of file check_positive_finite.hpp.
bool stan::math::check_positive_ordered | ( | const char * | function, |
const char * | name, | ||
const Eigen::Matrix< T_y, Eigen::Dynamic, 1 > & | y | ||
) |
Return true
if the specified vector contains non-negative values and is sorted into strictly increasing order.
function | Function name (for error messages) |
name | Variable name (for error messages) |
y | Vector to test |
true
if the vector is positive, ordered <code>std::domain_error</code> | if the vector contains non-positive values, if the values are not ordered, if there are duplicated values, or if any element is NaN . |
Definition at line 32 of file check_positive_ordered.hpp.
|
inline |
Return true
if size
is positive.
function | Function name (for error messages) |
name | Variable name (for error messages) |
expr | Expression for the dimension size (for error messages) |
size | Size value to check |
true
if size
is greater than 0. <code>std::invalid_argument</code> | if size is zero or negative. |
Definition at line 23 of file check_positive_size.hpp.
|
inline |
Return true
if specified index is within range.
This check is 1-indexed by default. This behavior can be changed by setting stan::error_index::value
.
function | Function name (for error messages) |
name | Variable name (for error messages) |
max | Maximum size of the variable |
index | Index to check |
nested_level | Nested level (for error messages) |
error_msg | Additional error message (for error messages) |
true
if the index is within range <code>std::out_of_range</code> | if the index is not in range |
Definition at line 29 of file check_range.hpp.
|
inline |
Return true
if specified index is within range.
This check is 1-indexed by default. This behavior can be changed by setting stan::error_index::value
.
function | Function name (for error messages) |
name | Variable name (for error messages) |
max | Maximum size of the variable |
index | Index to check |
error_msg | Additional error message (for error messages) |
true
if the index is within range <code>std::out_of_range</code> | if the index is not in range |
Definition at line 62 of file check_range.hpp.
|
inline |
Return true
if specified index is within range.
This check is 1-indexed by default. This behavior can be changed by setting stan::error_index::value
.
function | Function name (for error messages) |
name | Variable name (for error messages) |
max | Maximum size of the variable |
index | Index to check |
true
if the index is within range <code>std::out_of_range</code> | if the index is not in range |
Definition at line 89 of file check_range.hpp.
|
inline |
Return true
if the specified index is a valid row of the matrix.
This check is 1-indexed by default. This behavior can be changed by setting stan::error_index::value
.
T | Scalar type |
R | Compile time rows |
C | Compile time columns |
function | Function name (for error messages) |
name | Variable name (for error messages) |
y | Matrix to test |
i | is index |
true
if the index is a valid row index in the matrix <code>std::out_of_range</code> | if the index is out of range. |
Definition at line 32 of file check_row_index.hpp.
bool stan::math::check_simplex | ( | const char * | function, |
const char * | name, | ||
const Eigen::Matrix< T_prob, Eigen::Dynamic, 1 > & | theta | ||
) |
Return true
if the specified vector is simplex.
To be a simplex, all values must be greater than or equal to 0 and the values must sum to 1.
A valid simplex is one where the sum of hte elements is equal to 1. This function tests that the sum is within the tolerance specified by CONSTRAINT_TOLERANCE
. This function only accepts Eigen vectors, statically typed vectors, not general matrices with 1 column.
T_prob | Scalar type of the vector |
function | Function name (for error messages) |
name | Variable name (for error messages) |
theta | Vector to test. |
true
if the vector is a simplex <code>std::invalid_argument</code> | if theta is a 0-vector. |
<code>std::domain_error</code> | if the vector is not a simplex or if any element is NaN . |
Definition at line 41 of file check_simplex.hpp.
|
inline |
Return true
if the provided sizes match.
T_size1 | Type of size 1 |
T_size2 | Type of size 2 |
function | Function name (for error messages) |
name_i | Variable name 1 (for error messages) |
i | Size 1 |
name_j | Variable name 2 (for error messages) |
j | Size 2 |
true
if the sizes match <code>std::invalid_argument</code> | if the sizes do not match |
Definition at line 30 of file check_size_match.hpp.
|
inline |
Return true
if the provided sizes match.
T_size1 | Type of size 1 |
T_size2 | Type of size 2 |
function | Function name (for error messages) |
expr_i | Expression for variable name 1 (for error messages) |
name_i | Variable name 1 (for error messages) |
i | Size 1 |
expr_j | Expression for variable name 2 (for error messages) |
name_j | Variable name 2 (for error messages) |
j | Size 2 |
true
if the sizes match <code>std::invalid_argument</code> | if the sizes do not match |
Definition at line 67 of file check_size_match.hpp.
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Return true
if the specified matrix is a square, symmetric, and positive semi-definite.
T | Scalar type of the matrix |
function | Function name (for error messages) |
name | Variable name (for error messages) |
y | Matrix to test |
true
if the matrix is a square, symmetric, and positive semi-definite. <code>std::invalid_argument</code> | if the matrix is not square or if the matrix is 0x0 |
<code>std::domain_error</code> | if the matrix is not symmetric or if the matrix is not positive semi-definite |
Definition at line 31 of file check_spsd_matrix.hpp.
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Return true
if the specified matrix is square.
This check allows 0x0 matrices.
T | Type of scalar. |
function | Function name (for error messages) |
name | Variable name (for error messages) |
y | Matrix to test |
true
if the matrix is a square matrix. <code>std::invalid_argument</code> | if the matrix is not square |
Definition at line 28 of file check_square.hpp.
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Return true
if the specified index is valid in std vector.
This check is 1-indexed by default. This behavior can be changed by setting stan::error_index::value
.
T | Scalar type |
function | Function name (for error messages) |
name | Variable name (for error messages) |
y | std::vector to test |
i | Index |
true
if the index is a valid in std vector. <code>std::out_of_range</code> | if the index is out of range. |
Definition at line 30 of file check_std_vector_index.hpp.
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Return true
if the specified matrix is symmetric.
The error message is either 0 or 1 indexed, specified by stan::error_index::value
.
T_y | Type of scalar. |
function | Function name (for error messages) |
name | Variable name (for error messages) |
y | Matrix to test |
true
if the matrix is symmetric <code>std::invalid_argument</code> | if the matrix is not square. |
<code>std::domain_error</code> | if any element not on the main diagonal is NaN |
Definition at line 37 of file check_symmetric.hpp.
bool stan::math::check_unit_vector | ( | const char * | function, |
const char * | name, | ||
const Eigen::Matrix< T_prob, Eigen::Dynamic, 1 > & | theta | ||
) |
Return true
if the specified vector is unit vector.
A valid unit vector is one where the square of the elements summed is equal to 1. This function tests that the sum is within the tolerance specified by CONSTRAINT_TOLERANCE
. This function only accepts Eigen vectors, statically typed vectors, not general matrices with 1 column.
T_prob | Scalar type of the vector |
function | Function name (for error messages) |
name | Variable name (for error messages) |
theta | Vector to test. |
true
if the vector is a unit vector. <code>std::invalid_argument</code> | if theta is a 0-vector. |
<code>std::domain_error</code> | if the vector is not a unit vector or if any element is NaN . |
Definition at line 36 of file check_unit_vector.hpp.
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Return true
if the matrix is either a row vector or column vector.
This function checks the runtime size of the matrix to check whether it is a row or column vector.
T | Scalar type of the matrix |
R | Compile time rows of the matrix |
C | Compile time columns of the matrix |
function | Function name (for error messages) |
name | Variable name (for error messages) |
x | Matrix |
true
if x either has 1 columns or 1 rows <code>std::invalid_argument</code> | if x is not a row or column vector. |
Definition at line 34 of file check_vector.hpp.
return_type<T_y, T_dof>::type stan::math::chi_square_ccdf_log | ( | const T_y & | y, |
const T_dof & | nu | ||
) |
Definition at line 30 of file chi_square_ccdf_log.hpp.
return_type<T_y, T_dof>::type stan::math::chi_square_cdf | ( | const T_y & | y, |
const T_dof & | nu | ||
) |
Calculates the chi square cumulative distribution function for the given variate and degrees of freedom.
y A scalar variate. nu Degrees of freedom.
Definition at line 39 of file chi_square_cdf.hpp.
return_type<T_y, T_dof>::type stan::math::chi_square_cdf_log | ( | const T_y & | y, |
const T_dof & | nu | ||
) |
Definition at line 30 of file chi_square_cdf_log.hpp.
return_type<T_y, T_dof>::type stan::math::chi_square_log | ( | const T_y & | y, |
const T_dof & | nu | ||
) |
The log of a chi-squared density for y with the specified degrees of freedom parameter.
The degrees of freedom prarameter must be greater than 0. y must be greater than or equal to 0.
y | A scalar variable. |
nu | Degrees of freedom. |
std::domain_error | if nu is not greater than or equal to 0 |
std::domain_error | if y is not greater than or equal to 0. |
T_y | Type of scalar. |
T_dof | Type of degrees of freedom. |
Definition at line 49 of file chi_square_log.hpp.
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Definition at line 146 of file chi_square_log.hpp.
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Definition at line 24 of file chi_square_rng.hpp.
Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic> stan::math::cholesky_corr_constrain | ( | const Eigen::Matrix< T, Eigen::Dynamic, 1 > & | y, |
int | K | ||
) |
Definition at line 20 of file cholesky_corr_constrain.hpp.
Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic> stan::math::cholesky_corr_constrain | ( | const Eigen::Matrix< T, Eigen::Dynamic, 1 > & | y, |
int | K, | ||
T & | lp | ||
) |
Definition at line 58 of file cholesky_corr_constrain.hpp.
Eigen::Matrix<T, Eigen::Dynamic, 1> stan::math::cholesky_corr_free | ( | const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > & | x | ) |
Definition at line 18 of file cholesky_corr_free.hpp.
Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic> stan::math::cholesky_decompose | ( | const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > & | m | ) |
Return the lower-triangular Cholesky factor (i.e., matrix square root) of the specified square, symmetric matrix.
The return value will be a lower-traingular matrix such that the original matrix
is given by
.
m | Symmetrix matrix. |
std::domain_error | if m is not a symmetric matrix or if m is not positive definite (if m has more than 0 elements) |
Definition at line 25 of file cholesky_decompose.hpp.
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Definition at line 131 of file cholesky_decompose.hpp.
Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic> stan::math::cholesky_factor_constrain | ( | const Eigen::Matrix< T, Eigen::Dynamic, 1 > & | x, |
int | M, | ||
int | N | ||
) |
Return the Cholesky factor of the specified size read from the specified vector.
A total of (N choose 2) + N + (M - N) * N elements are required to read an M by N Cholesky factor.
T | Type of scalars in matrix |
x | Vector of unconstrained values |
M | Number of rows |
N | Number of columns |
Definition at line 29 of file cholesky_factor_constrain.hpp.
Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic> stan::math::cholesky_factor_constrain | ( | const Eigen::Matrix< T, Eigen::Dynamic, 1 > & | x, |
int | M, | ||
int | N, | ||
T & | lp | ||
) |
Return the Cholesky factor of the specified size read from the specified vector and increment the specified log probability reference with the log Jacobian adjustment of the transform.
A total of (N choose 2) + N + N * (M - N) free parameters are required to read an M by N Cholesky factor.
T | Type of scalars in matrix |
x | Vector of unconstrained values |
M | Number of rows |
N | Number of columns |
lp | Log probability that is incremented with the log Jacobian |
Definition at line 73 of file cholesky_factor_constrain.hpp.
Eigen::Matrix<T, Eigen::Dynamic, 1> stan::math::cholesky_factor_free | ( | const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > & | y | ) |
Return the unconstrained vector of parameters correspdonding to the specified Cholesky factor.
A Cholesky factor must be lower triangular and have positive diagonal elements.
y | Cholesky factor. |
std::domain_error | If the matrix is not a Cholesky factor. |
Definition at line 24 of file cholesky_factor_free.hpp.
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Return the specified column of the specified matrix using start-at-1 indexing.
This is equivalent to calling m.col(i - 1)
and assigning the resulting template expression to a column vector.
m | Matrix. |
j | Column index (count from 1). |
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Definition at line 18 of file columns_dot_product.hpp.
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Returns the dot product of the specified vectors.
v1 | First vector. |
v2 | Second vector. |
std::domain_error | If the vectors are not the same size or if they are both not vector dimensioned. |
Definition at line 22 of file columns_dot_product.hpp.
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Definition at line 25 of file columns_dot_product.hpp.
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Definition at line 35 of file columns_dot_product.hpp.
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Definition at line 52 of file columns_dot_product.hpp.
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Definition at line 15 of file columns_dot_self.hpp.
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Returns the dot product of each column of a matrix with itself.
x | Matrix. |
T | scalar type |
Definition at line 16 of file columns_dot_self.hpp.
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Returns the dot product of each column of a matrix with itself.
x | Matrix. |
T | scalar type |
Definition at line 22 of file columns_dot_self.hpp.
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Return the result of transforming the specified scalar to have a valid correlation value between -1 and 1 (inclusive).
The transform used is the hyperbolic tangent function,
.
x | Scalar input. |
T | Type of scalar. |
Definition at line 25 of file corr_constrain.hpp.
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Return the result of transforming the specified scalar to have a valid correlation value between -1 and 1 (inclusive).
The transform used is as specified for corr_constrain(T)
. The log absolute Jacobian determinant is
.
T | Type of scalar. |
Definition at line 43 of file corr_constrain.hpp.
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Return the unconstrained scalar that when transformed to a valid correlation produces the specified value.
This function inverts the transform defined for corr_constrain(T)
, which is the inverse hyperbolic tangent,
.
y | Correlation scalar input. |
T | Type of scalar. |
Definition at line 29 of file corr_free.hpp.
Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic> stan::math::corr_matrix_constrain | ( | const Eigen::Matrix< T, Eigen::Dynamic, 1 > & | x, |
typename math::index_type< Eigen::Matrix< T, Eigen::Dynamic, 1 > >::type | k | ||
) |
Return the correlation matrix of the specified dimensionality derived from the specified vector of unconstrained values.
The input vector must be of length . The values in the input vector represent unconstrained (partial) correlations among the dimensions.
The transform based on partial correlations is as specified in
The free vector entries are first constrained to be valid correlation values using corr_constrain(T)
.
x | Vector of unconstrained partial correlations. |
k | Dimensionality of returned correlation matrix. |
T | Type of scalar. |
std::invalid_argument | if x is not a valid correlation matrix. |
Definition at line 40 of file corr_matrix_constrain.hpp.
Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic> stan::math::corr_matrix_constrain | ( | const Eigen::Matrix< T, Eigen::Dynamic, 1 > & | x, |
typename math::index_type< Eigen::Matrix< T, Eigen::Dynamic, 1 > >::type | k, | ||
T & | lp | ||
) |
Return the correlation matrix of the specified dimensionality derived from the specified vector of unconstrained values.
The input vector must be of length . The values in the input vector represent unconstrained (partial) correlations among the dimensions.
The transform is as specified for corr_matrix_constrain(Matrix, size_t)
; the paper it cites also defines the Jacobians for correlation inputs, which are composed with the correlation constrained Jacobians defined in corr_constrain(T, double)
for this function.
x | Vector of unconstrained partial correlations. |
k | Dimensionality of returned correlation matrix. |
lp | Log probability reference to increment. |
T | Type of scalar. |
Definition at line 78 of file corr_matrix_constrain.hpp.
Eigen::Matrix<T, Eigen::Dynamic, 1> stan::math::corr_matrix_free | ( | const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > & | y | ) |
Return the vector of unconstrained partial correlations that define the specified correlation matrix when transformed.
The constraining transform is defined as for corr_matrix_constrain(Matrix, size_t)
. The inverse transform in this function is simpler in that it only needs to compute the partial correlations and then free those.
y | The correlation matrix to free. |
T | Type of scalar. |
std::domain_error | if the correlation matrix has no elements or is not a square matrix. |
std::runtime_error | if the correlation matrix cannot be factorized by factor_cov_matrix() or if the sds returned by factor_cov_matrix() on log scale are unconstrained. |
Definition at line 39 of file corr_matrix_free.hpp.
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Returns a squared exponential kernel.
T_x | type of std::vector of elements |
T_sigma | type of sigma |
T_l | type of length scale |
x | std::vector of elements that can be used in square distance. This function assumes each element of x is the same size. |
sigma | standard deviation |
l | length scale |
std::domain_error | if sigma <= 0, l <= 0, or x is nan or infinite |
Definition at line 35 of file cov_exp_quad.hpp.
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Returns a squared exponential kernel.
T_x1 | type of first std::vector of elements |
T_x2 | type of second std::vector of elements |
T_sigma | type of sigma |
T_l | type of length scale |
x1 | std::vector of elements that can be used in square distance |
x2 | std::vector of elements that can be used in square distance |
sigma | standard deviation |
l | length scale |
std::domain_error | if sigma <= 0, l <= 0, or x is nan or infinite |
Definition at line 85 of file cov_exp_quad.hpp.
Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic> stan::math::cov_matrix_constrain | ( | const Eigen::Matrix< T, Eigen::Dynamic, 1 > & | x, |
typename math::index_type< Eigen::Matrix< T, Eigen::Dynamic, 1 > >::type | K | ||
) |
Return the symmetric, positive-definite matrix of dimensions K by K resulting from transforming the specified finite vector of size K plus (K choose 2).
See cov_matrix_free()
for the inverse transform.
x | The vector to convert to a covariance matrix. |
K | The number of rows and columns of the resulting covariance matrix. |
std::domain_error | if (x.size() != K + (K choose 2)). |
Definition at line 31 of file cov_matrix_constrain.hpp.
Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic> stan::math::cov_matrix_constrain | ( | const Eigen::Matrix< T, Eigen::Dynamic, 1 > & | x, |
typename math::index_type< Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > >::type | K, | ||
T & | lp | ||
) |
Return the symmetric, positive-definite matrix of dimensions K by K resulting from transforming the specified finite vector of size K plus (K choose 2).
See cov_matrix_free()
for the inverse transform.
x | The vector to convert to a covariance matrix. |
K | The dimensions of the resulting covariance matrix. |
lp | Reference |
std::domain_error | if (x.size() != K + (K choose 2)). |
Definition at line 71 of file cov_matrix_constrain.hpp.
Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic> stan::math::cov_matrix_constrain_lkj | ( | const Eigen::Matrix< T, Eigen::Dynamic, 1 > & | x, |
size_t | k | ||
) |
Return the covariance matrix of the specified dimensionality derived from constraining the specified vector of unconstrained values.
The input vector must be of length . The first
values in the input represent unconstrained (partial) correlations and the last
are unconstrained standard deviations of the dimensions.
The transform scales the correlation matrix transform defined in corr_matrix_constrain(Matrix, size_t)
with the constrained deviations.
x | Input vector of unconstrained partial correlations and standard deviations. |
k | Dimensionality of returned covariance matrix. |
T | Type of scalar. |
Definition at line 34 of file cov_matrix_constrain_lkj.hpp.
Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic> stan::math::cov_matrix_constrain_lkj | ( | const Eigen::Matrix< T, Eigen::Dynamic, 1 > & | x, |
size_t | k, | ||
T & | lp | ||
) |
Return the covariance matrix of the specified dimensionality derived from constraining the specified vector of unconstrained values and increment the specified log probability reference with the log absolute Jacobian determinant.
The transform is defined as for cov_matrix_constrain(Matrix, size_t)
.
The log absolute Jacobian determinant is derived by composing the log absolute Jacobian determinant for the underlying correlation matrix as defined in cov_matrix_constrain(Matrix, size_t, T&)
with the Jacobian of the transfrom of the correlation matrix into a covariance matrix by scaling by standard deviations.
x | Input vector of unconstrained partial correlations and standard deviations. |
k | Dimensionality of returned covariance matrix. |
lp | Log probability reference to increment. |
T | Type of scalar. |
Definition at line 73 of file cov_matrix_constrain_lkj.hpp.
Eigen::Matrix<T, Eigen::Dynamic, 1> stan::math::cov_matrix_free | ( | const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > & | y | ) |
The covariance matrix derived from the symmetric view of the lower-triangular view of the K by K specified matrix is freed to return a vector of size K + (K choose 2).
This is the inverse of the cov_matrix_constrain()
function so that for any finite vector x
of size K
x == cov_matrix_free(cov_matrix_constrain(x, K))
.
In order for this round-trip to work (and really for this function to work), the symmetric view of its lower-triangular view must be positive definite.
y | Matrix of dimensions K by K such that he symmetric view of the lower-triangular view is positive definite. |
std::domain_error | if y is not square, has zero dimensionality, or has a non-positive diagonal element. |
Definition at line 37 of file cov_matrix_free.hpp.
Eigen::Matrix<T, Eigen::Dynamic, 1> stan::math::cov_matrix_free_lkj | ( | const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > & | y | ) |
Return the vector of unconstrained partial correlations and deviations that transform to the specified covariance matrix.
The constraining transform is defined as for cov_matrix_constrain(Matrix, size_t)
. The inverse first factors out the deviations, then applies the freeing transfrom of corr_matrix_free(Matrix&)
.
y | Covariance matrix to free. |
T | Type of scalar. |
std::domain_error | if the correlation matrix has no elements or is not a square matrix. |
std::runtime_error | if the correlation matrix cannot be factorized by factor_cov_matrix() |
Definition at line 32 of file cov_matrix_free_lkj.hpp.
Returns the result of pre-multiplying a matrix by its own transpose.
M | Matrix to multiply. |
Definition at line 17 of file crossprod.hpp.
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Definition at line 17 of file crossprod.hpp.
Returns the result of pre-multiplying a matrix by its own transpose.
M | Matrix to multiply. |
Definition at line 17 of file crossprod.hpp.
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Definition at line 79 of file csr_matrix_times_vector.hpp.
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Return the cumulative sum of the specified vector.
The cumulative sum of a vector of values
T | Scalar type of vector. |
x | Vector of values. |
Definition at line 23 of file cumulative_sum.hpp.
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Return the cumulative sum of the specified matrix.
The cumulative sum is of the same type as the input and has values defined by
T | Scalar type of matrix. |
R | Row type of matrix. |
C | Column type of matrix. |
m | Matrix of values. |
Definition at line 49 of file cumulative_sum.hpp.
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Definition at line 23 of file cvodes_utils.hpp.
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Definition at line 31 of file cvodes_utils.hpp.
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Definition at line 18 of file cvodes_utils.hpp.
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Takes sensitivity output from integrators and returns results in precomputed_gradients format.
Solution input vector size depends on requested sensitivities, which can be enabled for initials and parameters. For each sensitivity N states are computed. The input vector is expected to be ordered by states, i.e. first the N states, then optionally the N sensitivities for the initials (first the N states for the first initial and so on), finally the sensitivities for the M parameters follow optionally.
T1_initial | type of scalars for initial values. |
T2_param | type of scalars for parameters. |
[in] | y | output from integrator in column-major format as a coupled system output |
[in] | y0 | initial state. |
[in] | theta | parameters |
Definition at line 38 of file decouple_ode_states.hpp.
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The decouple ODE states operation for the case of no sensitivities is equal to the indentity operation.
[in] | y | output from integrator |
[in] | y0 | initial state. |
[in] | theta | parameters |
Definition at line 89 of file decouple_ode_states.hpp.
void stan::math::derivative | ( | const F & | f, |
const T & | x, | ||
T & | fx, | ||
T & | dfx_dx | ||
) |
Return the derivative of the specified univariate function at the specified argument.
T | Argument type |
F | Function type |
[in] | f | Function |
[in] | x | Argument |
[out] | fx | Value of function applied to argument |
[out] | dfx_dx | Value of derivative |
Definition at line 26 of file derivative.hpp.
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Returns the determinant of the specified square matrix.
m | Specified matrix. |
std::domain_error | if matrix is not square. |
Definition at line 18 of file determinant.hpp.
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Definition at line 21 of file determinant.hpp.
Definition at line 66 of file determinant.hpp.
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Return a square diagonal matrix with the specified vector of coefficients as the diagonal values.
[in] | v | Specified vector. |
Definition at line 18 of file diag_matrix.hpp.
Eigen::Matrix<typename boost::math::tools::promote_args<T1, T2>::type, R1, C1> stan::math::diag_post_multiply | ( | const Eigen::Matrix< T1, R1, C1 > & | m1, |
const Eigen::Matrix< T2, R2, C2 > & | m2 | ||
) |
Definition at line 14 of file diag_post_multiply.hpp.
Eigen::Matrix<typename boost::math::tools::promote_args<T1, T2>::type, R2, C2> stan::math::diag_pre_multiply | ( | const Eigen::Matrix< T1, R1, C1 > & | m1, |
const Eigen::Matrix< T2, R2, C2 > & | m2 | ||
) |
Definition at line 14 of file diag_pre_multiply.hpp.
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Return a column vector of the diagonal elements of the specified matrix.
The matrix is not required to be square.
m | Specified matrix. |
Definition at line 18 of file diagonal.hpp.
Definition at line 16 of file digamma.hpp.
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Definition at line 24 of file digamma.hpp.
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Vectorized version of digamma().
x | Container. |
T | Container type. |
std::domain_error | if any value is a negative integer or 0 |
Definition at line 34 of file digamma.hpp.
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boost::math::tools::promote_args<T_prob, T_prior_sample_size>::type stan::math::dirichlet_log | ( | const Eigen::Matrix< T_prob, Eigen::Dynamic, 1 > & | theta, |
const Eigen::Matrix< T_prior_sample_size, Eigen::Dynamic, 1 > & | alpha | ||
) |
The log of the Dirichlet density for the given theta and a vector of prior sample sizes, alpha.
Each element of alpha must be greater than 0. Each element of theta must be greater than or 0. Theta sums to 1.
theta | A scalar vector. |
alpha | Prior sample sizes. |
std::domain_error | if any element of alpha is less than or equal to 0. |
std::domain_error | if any element of theta is less than 0. |
std::domain_error | if the sum of theta is not 1. |
T_prob | Type of scalar. |
T_prior_sample_size | Type of prior sample sizes. |
Definition at line 46 of file dirichlet_log.hpp.
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Definition at line 79 of file dirichlet_log.hpp.
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Return a draw from a Dirichlet distribution with specified parameters and pseudo-random number generator.
For prior counts greater than zero, the usual algorithm that draws gamma variates and normalizes is used.
For prior counts less than zero (i.e., parameters with value less than one), a log-scale version of the following algorithm is used to deal with underflow:
G. Marsaglia and W. Tsang. A simple method for generating gamma variables. ACM Transactions on Mathematical Software. 26(3):363–372, 2000.
RNG | Type of pseudo-random number generator. |
alpha | Prior count (plus 1) parameter for Dirichlet. |
rng | Pseudo-random number generator. |
Definition at line 46 of file dirichlet_rng.hpp.
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Returns the distance between the specified vectors.
v1 | First vector. |
v2 | Second vector. |
std::domain_error | If the vectors are not the same size or if they are both not vector dimensioned. |
Definition at line 24 of file distance.hpp.
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Definition at line 16 of file divide.hpp.
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Return the division of the first scalar by the second scalar.
[in] | x | Specified vector. |
[in] | y | Specified scalar. |
Definition at line 22 of file divide.hpp.
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Return the division of the specified column vector by the specified scalar.
[in] | v | Specified vector. |
[in] | c | Specified scalar. |
Definition at line 23 of file divide.hpp.
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Return specified matrix divided by specified scalar.
R | Row type for matrix. |
C | Column type for matrix. |
m | Matrix. |
c | Scalar. |
Definition at line 23 of file divide.hpp.
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Definition at line 26 of file divide.hpp.
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Definition at line 27 of file divide.hpp.
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Definition at line 39 of file divide.hpp.
T_shape stan::math::do_lkj_constant | ( | const T_shape & | eta, |
const unsigned int & | K | ||
) |
Definition at line 53 of file lkj_corr_log.hpp.
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Throw a domain error with a consistently formatted message.
This is an abstraction for all Stan functions to use when throwing domain errors. This will allow us to change the behavior for all functions at once. (We've already changed behavior mulitple times up to Stan v2.5.0.)
The message is: "<function>: <name> <msg1><y><msg2>"
T | Type of variable |
function | Name of the function |
name | Name of the variable |
y | Variable |
msg1 | Message to print before the variable |
msg2 | Message to print after the variable |
std::domain_error |
Definition at line 32 of file domain_error.hpp.
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Throw a domain error with a consistently formatted message.
This is an abstraction for all Stan functions to use when throwing domain errors. This will allow us to change the behavior for all functions at once. (We've already changed behavior mulitple times up to Stan v2.5.0.)
The message is: "<function>: <name> <msg1><y>"
T | Type of variable |
function | Name of the function |
name | Name of the variable |
y | Variable |
msg1 | Message to print before the variable |
std::domain_error |
Definition at line 67 of file domain_error.hpp.
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Throw a domain error with a consistently formatted message.
This is an abstraction for all Stan functions to use when throwing domain errors. This will allow us to change the behavior for all functions at once. (We've already changed behavior mulitple times up to Stan v2.5.0.)
The message is: "<function>: <name>[<i+error_index>] <msg1><y>" where error_index is the value of stan::error_index::value which indicates whether the message should be 0 or 1 indexed.
T | Type of variable |
function | Name of the function |
name | Name of the variable |
y | Variable |
i | Index |
msg1 | Message to print before the variable |
msg2 | Message to print after the variable |
std::domain_error |
Definition at line 38 of file domain_error_vec.hpp.
|
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Throw a domain error with a consistently formatted message.
This is an abstraction for all Stan functions to use when throwing domain errors. This will allow us to change the behavior for all functions at once. (We've already changed behavior mulitple times up to Stan v2.5.0.)
The message is: "<function>: <name>[<i+error_index>] <msg1><y>" where error_index is the value of stan::error_index::value which indicates whether the message should be 0 or 1 indexed.
T | Type of variable |
function | Name of the function |
name | Name of the variable |
y | Variable |
i | Index |
msg | Message to print before the variable |
std::domain_error |
Definition at line 73 of file domain_error_vec.hpp.
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|
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Definition at line 20 of file dot_product.hpp.
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Returns the dot product of the specified vectors.
v1 | First vector. |
v2 | Second vector. |
std::domain_error | If the vectors are not the same size or if they are both not vector dimensioned. |
Definition at line 22 of file dot_product.hpp.
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Definition at line 37 of file dot_product.hpp.
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Returns the dot product of the specified arrays of doubles.
v1 | First array. |
v2 | Second array. |
length | Length of both arrays. |
Definition at line 37 of file dot_product.hpp.
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Returns the dot product of the specified arrays of doubles.
v1 | First array. |
v2 | Second array. |
std::domain_error | if the vectors are not the same size. |
Definition at line 50 of file dot_product.hpp.
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Definition at line 54 of file dot_product.hpp.
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Definition at line 71 of file dot_product.hpp.
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Definition at line 86 of file dot_product.hpp.
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Definition at line 101 of file dot_product.hpp.
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Definition at line 116 of file dot_product.hpp.
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Definition at line 130 of file dot_product.hpp.
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Definition at line 144 of file dot_product.hpp.
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Definition at line 158 of file dot_product.hpp.
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Definition at line 170 of file dot_product.hpp.
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Definition at line 182 of file dot_product.hpp.
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Returns the dot product.
[in] | v1 | First column vector. |
[in] | v2 | Second column vector. |
std::domain_error | if length of v1 is not equal to length of v2. |
Definition at line 212 of file dot_product.hpp.
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Returns the dot product.
[in] | v1 | First array. |
[in] | v2 | Second array. |
[in] | length | Length of both arrays. |
Definition at line 233 of file dot_product.hpp.
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Returns the dot product.
[in] | v1 | First vector. |
[in] | v2 | Second vector. |
std::domain_error | if sizes of v1 and v2 do not match. |
Definition at line 249 of file dot_product.hpp.
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Definition at line 11 of file dot_self.hpp.
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Definition at line 16 of file dot_self.hpp.
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Returns the dot product of the specified vector with itself.
v | Vector. |
R | number of rows or Eigen::Dynamic for dynamic |
C | number of rows or Eigen::Dyanmic for dynamic |
std::domain_error | If v is not vector dimensioned. |
Definition at line 18 of file dot_self.hpp.
Returns the dot product of a vector with itself.
[in] | v | Vector. |
R | number of rows or Eigen::Dynamic for dynamic; one of R or C must be 1 |
C | number of rows or Eigen::Dyanmic for dynamic; one of R or C must be 1 |
Definition at line 80 of file dot_self.hpp.
return_type<T_y, T_loc, T_scale>::type stan::math::double_exponential_ccdf_log | ( | const T_y & | y, |
const T_loc & | mu, | ||
const T_scale & | sigma | ||
) |
Definition at line 26 of file double_exponential_ccdf_log.hpp.
return_type<T_y, T_loc, T_scale>::type stan::math::double_exponential_cdf | ( | const T_y & | y, |
const T_loc & | mu, | ||
const T_scale & | sigma | ||
) |
Calculates the double exponential cumulative density function.
y | A scalar variate. |
mu | The location parameter. |
sigma | The scale parameter. |
Definition at line 40 of file double_exponential_cdf.hpp.
return_type<T_y, T_loc, T_scale>::type stan::math::double_exponential_cdf_log | ( | const T_y & | y, |
const T_loc & | mu, | ||
const T_scale & | sigma | ||
) |
Definition at line 26 of file double_exponential_cdf_log.hpp.
return_type<T_y, T_loc, T_scale>::type stan::math::double_exponential_log | ( | const T_y & | y, |
const T_loc & | mu, | ||
const T_scale & | sigma | ||
) |
Definition at line 31 of file double_exponential_log.hpp.
return_type<T_y, T_loc, T_scale>::type stan::math::double_exponential_log | ( | const T_y & | y, |
const T_loc & | mu, | ||
const T_scale & | sigma | ||
) |
Definition at line 130 of file double_exponential_log.hpp.
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Definition at line 23 of file double_exponential_rng.hpp.
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Return the base of the natural logarithm.
Definition at line 95 of file constants.hpp.
Eigen::Matrix<T, Eigen::Dynamic, 1> stan::math::eigenvalues_sym | ( | const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > & | m | ) |
Return the eigenvalues of the specified symmetric matrix in descending order of magnitude.
This function is more efficient than the general eigenvalues function for symmetric matrices.
See eigen_decompose()
for more information.
m | Specified matrix. |
Definition at line 22 of file eigenvalues_sym.hpp.
Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic> stan::math::eigenvectors_sym | ( | const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > & | m | ) |
Definition at line 13 of file eigenvectors_sym.hpp.
Eigen::Matrix<typename boost::math::tools::promote_args<T1, T2>::type, R, C> stan::math::elt_divide | ( | const Eigen::Matrix< T1, R, C > & | m1, |
const Eigen::Matrix< T2, R, C > & | m2 | ||
) |
Return the elementwise division of the specified matrices.
T1 | Type of scalars in first matrix. |
T2 | Type of scalars in second matrix. |
R | Row type of both matrices. |
C | Column type of both matrices. |
m1 | First matrix |
m2 | Second matrix |
Definition at line 25 of file elt_divide.hpp.
Eigen::Matrix<typename boost::math::tools::promote_args<T1, T2>::type, R, C> stan::math::elt_divide | ( | const Eigen::Matrix< T1, R, C > & | m, |
T2 | s | ||
) |
Return the elementwise division of the specified matrix by the specified scalar.
T1 | Type of scalars in the matrix. |
T2 | Type of the scalar. |
R | Row type of the matrix. |
C | Column type of the matrix. |
m | matrix |
s | scalar |
Definition at line 51 of file elt_divide.hpp.
Eigen::Matrix<typename boost::math::tools::promote_args<T1, T2>::type, R, C> stan::math::elt_divide | ( | T1 | s, |
const Eigen::Matrix< T2, R, C > & | m | ||
) |
Return the elementwise division of the specified scalar by the specified matrix.
T1 | Type of the scalar. |
T2 | Type of scalars in the matrix. |
R | Row type of the matrix. |
C | Column type of the matrix. |
s | scalar |
m | matrix |
Definition at line 69 of file elt_divide.hpp.
Eigen::Matrix<typename boost::math::tools::promote_args<T1, T2>::type, R, C> stan::math::elt_multiply | ( | const Eigen::Matrix< T1, R, C > & | m1, |
const Eigen::Matrix< T2, R, C > & | m2 | ||
) |
Return the elementwise multiplication of the specified matrices.
T1 | Type of scalars in first matrix. |
T2 | Type of scalars in second matrix. |
R | Row type of both matrices. |
C | Column type of both matrices. |
m1 | First matrix |
m2 | Second matrix |
Definition at line 25 of file elt_multiply.hpp.
|
inlinestatic |
Return true if there is no nested autodiff being executed.
Definition at line 12 of file empty_nested.hpp.
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Exponentiation base 2 function for variables (C99).
For non-variable function, see boost::math::exp2().
The derivatie is
.
a | The variable. |
return_type<T_y, T_loc, T_scale, T_inv_scale>::type stan::math::exp_mod_normal_ccdf_log | ( | const T_y & | y, |
const T_loc & | mu, | ||
const T_scale & | sigma, | ||
const T_inv_scale & | lambda | ||
) |
Definition at line 26 of file exp_mod_normal_ccdf_log.hpp.
return_type<T_y, T_loc, T_scale, T_inv_scale>::type stan::math::exp_mod_normal_cdf | ( | const T_y & | y, |
const T_loc & | mu, | ||
const T_scale & | sigma, | ||
const T_inv_scale & | lambda | ||
) |
Definition at line 26 of file exp_mod_normal_cdf.hpp.
return_type<T_y, T_loc, T_scale, T_inv_scale>::type stan::math::exp_mod_normal_cdf_log | ( | const T_y & | y, |
const T_loc & | mu, | ||
const T_scale & | sigma, | ||
const T_inv_scale & | lambda | ||
) |
Definition at line 26 of file exp_mod_normal_cdf_log.hpp.
return_type<T_y, T_loc, T_scale, T_inv_scale>::type stan::math::exp_mod_normal_log | ( | const T_y & | y, |
const T_loc & | mu, | ||
const T_scale & | sigma, | ||
const T_inv_scale & | lambda | ||
) |
Definition at line 27 of file exp_mod_normal_log.hpp.
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Definition at line 141 of file exp_mod_normal_log.hpp.
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Definition at line 26 of file exp_mod_normal_rng.hpp.
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return_type<T_y, T_inv_scale>::type stan::math::exponential_ccdf_log | ( | const T_y & | y, |
const T_inv_scale & | beta | ||
) |
Definition at line 27 of file exponential_ccdf_log.hpp.
return_type<T_y, T_inv_scale>::type stan::math::exponential_cdf | ( | const T_y & | y, |
const T_inv_scale & | beta | ||
) |
Calculates the exponential cumulative distribution function for the given y and beta.
Inverse scale parameter must be greater than 0. y must be greater than or equal to 0.
y | A scalar variable. |
beta | Inverse scale parameter. |
T_y | Type of scalar. |
T_inv_scale | Type of inverse scale. |
Definition at line 40 of file exponential_cdf.hpp.
return_type<T_y, T_inv_scale>::type stan::math::exponential_cdf_log | ( | const T_y & | y, |
const T_inv_scale & | beta | ||
) |
Definition at line 28 of file exponential_cdf_log.hpp.
return_type<T_y, T_inv_scale>::type stan::math::exponential_log | ( | const T_y & | y, |
const T_inv_scale & | beta | ||
) |
The log of an exponential density for y with the specified inverse scale parameter.
Inverse scale parameter must be greater than 0. y must be greater than or equal to 0.
y | A scalar variable. |
beta | Inverse scale parameter. |
std::domain_error | if beta is not greater than 0. |
std::domain_error | if y is not greater than or equal to 0. |
T_y | Type of scalar. |
T_inv_scale | Type of inverse scale. |
Definition at line 54 of file exponential_log.hpp.
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Definition at line 111 of file exponential_log.hpp.
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Definition at line 24 of file exponential_rng.hpp.
T stan::math::F32 | ( | T | a, |
T | b, | ||
T | c, | ||
T | d, | ||
T | e, | ||
T | z, | ||
T | precision = 1e-6 |
||
) |
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Return the absolute value of the variable (cmath).
Choosing an arbitrary value at the non-differentiable point 0,
.
where is the signum function, taking values -1 if
, 0 if
, and 1 if
.
The function abs()
provides the same behavior, with abs()
defined in stdlib.h and fabs()
defined in cmath
. The derivative is 0 if the input is 0.
Returns std::numeric_limits<double>::quiet_NaN() for NaN inputs.
a | Input variable. |
bool stan::math::factor_cov_matrix | ( | const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > & | Sigma, |
Eigen::Array< T, Eigen::Dynamic, 1 > & | CPCs, | ||
Eigen::Array< T, Eigen::Dynamic, 1 > & | sds | ||
) |
This function is intended to make starting values, given a covariance matrix Sigma.
The transformations are hard coded as log for standard deviations and Fisher transformations (atanh()) of CPCs
[in] | Sigma | covariance matrix |
[out] | CPCs | fill this unbounded (does not resize) |
[out] | sds | fill this unbounded (does not resize) |
Definition at line 27 of file factor_cov_matrix.hpp.
void stan::math::factor_U | ( | const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > & | U, |
Eigen::Array< T, Eigen::Dynamic, 1 > & | CPCs | ||
) |
This function is intended to make starting values, given a unit upper-triangular matrix U such that U'DU is a correlation matrix.
U | Sigma matrix |
CPCs | fill this unbounded |
Definition at line 29 of file factor_U.hpp.
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Definition at line 15 of file falling_factorial.hpp.
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Definition at line 30 of file falling_factorial.hpp.
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Definition at line 43 of file falling_factorial.hpp.
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Definition at line 56 of file falling_factorial.hpp.
Definition at line 61 of file falling_factorial.hpp.
Definition at line 66 of file falling_factorial.hpp.
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Return the positive difference between the first variable's the value and the second's (C99).
See stan::math::fdim() for the double-based version.
The partial derivative with respect to the first argument is
if
, and
if
.
With respect to the second argument, the partial is
if
, and
if
.
a | First variable. |
b | Second variable. |
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Return the positive difference between the first value and the value of the second variable (C99).
See fdim(var, var) for definitions of values and derivatives.
The derivative with respect to the variable is
if
, and
if
.
a | First value. |
b | Second variable. |
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Return the positive difference between the first variable's value and the second value (C99).
See fdim(var, var) for definitions of values and derivatives.
The derivative with respect to the variable is
if
, and
if
.
a | First value. |
b | Second variable. |
void stan::math::fill | ( | T & | x, |
const S & | y | ||
) |
void stan::math::fill | ( | std::vector< T > & | x, |
const S & | y | ||
) |
void stan::math::fill | ( | Eigen::Matrix< T, R, C > & | x, |
const S & | y | ||
) |
void stan::math::finite_diff_grad_hessian | ( | const F & | f, |
const Eigen::Matrix< double,-1, 1 > & | x, | ||
double & | fx, | ||
Eigen::Matrix< double,-1,-1 > & | hess, | ||
std::vector< Eigen::Matrix< double,-1,-1 > > & | grad_hess_fx, | ||
const double | epsilon = 1e-04 |
||
) |
Calculate the value and the gradient of the hessian of the specified function at the specified argument using second-order autodiff and first-order finite difference.
The functor must implement
double operator()(const Eigen::Matrix<double, Eigen::Dynamic, 1>&)
Reference:
De Levie: An improved numerical approximation for the first derivative, page 3
4 calls to the function, f.
F | Type of function |
[in] | f | Function |
[in] | x | Argument to function |
[out] | fx | Function applied to argument |
[out] | hess | Hessian matrix |
[out] | grad_hess_fx | gradient of Hessian of function at argument |
[in] | epsilon | perturbation size |
Definition at line 43 of file finite_diff_grad_hessian.hpp.
void stan::math::finite_diff_gradient | ( | const F & | f, |
const Eigen::Matrix< double,-1, 1 > & | x, | ||
double & | fx, | ||
Eigen::Matrix< double,-1, 1 > & | grad_fx, | ||
const double | epsilon = 1e-03 |
||
) |
Calculate the value and the gradient of the specified function at the specified argument using finite difference.
The functor must implement
double operator()(const Eigen::Matrix<double, Eigen::Dynamic, 1>&)
Error should be on order of epsilon ^ 6. The reference for this algorithm is:
De Levie: An improved numerical approximation for the first derivative, page 3
This function involves 6 calls to f.
F | Type of function |
[in] | f | Function |
[in] | x | Argument to function |
[out] | fx | Function applied to argument |
[out] | grad_fx | Gradient of function at argument |
[in] | epsilon | perturbation size |
Definition at line 39 of file finite_diff_gradient.hpp.
double stan::math::finite_diff_hess_helper | ( | const F & | f, |
const Eigen::Matrix< double, Eigen::Dynamic, 1 > & | x, | ||
const int | lambda, | ||
const double | epsilon = 1e-03 |
||
) |
Definition at line 13 of file finite_diff_hessian.hpp.
void stan::math::finite_diff_hessian | ( | const F & | f, |
const Eigen::Matrix< double,-1, 1 > & | x, | ||
double & | fx, | ||
Eigen::Matrix< double,-1, 1 > & | grad_fx, | ||
Eigen::Matrix< double,-1,-1 > & | hess_fx, | ||
const double | epsilon = 1e-03 |
||
) |
Calculate the value and the Hessian of the specified function at the specified argument using second-order finite difference.
The functor must implement
double operator()(const Eigen::Matrix<double, Eigen::Dynamic, 1>&)
Error should be on order of epsilon ^ 4, with 4 calls to the function f.
Reference: Eberly: Derivative Approximation by Finite Differences Page 6
F | Type of function |
[in] | f | Function |
[in] | x | Argument to function |
[out] | fx | Function applied to argument |
[out] | grad_fx | Gradient of function at argument |
[out] | hess_fx | Hessian of function at argument |
[in] | epsilon | perturbation size |
Definition at line 67 of file finite_diff_hessian.hpp.
|
inline |
Return the floor of the specified variable (cmath).
The derivative of the floor function is defined and zero everywhere but at integers, so we set these derivatives to zero for convenience,
.
The floor function rounds down. For double values, this is the largest integral value that is not greater than the specified value. Although this function is not differentiable because it is discontinuous at integral values, its gradient is returned as zero everywhere.
a | Input variable. |
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The fused multiply-add function for three variables (C99).
This function returns the product of the first two arguments plus the third argument.
The double-based version ::fma(double, double, double)
is defined in <cmath>
.
The partial derivatives are
, and
, and
.
a | First multiplicand. |
b | Second multiplicand. |
c | Summand. |
|
inline |
The fused multiply-add function for two variables and a value (C99).
This function returns the product of the first two arguments plus the third argument.
The double-based version ::fma(double, double, double)
is defined in <cmath>
.
The partial derivatives are
, and
.
a | First multiplicand. |
b | Second multiplicand. |
c | Summand. |
|
inline |
The fused multiply-add function for a variable, value, and variable (C99).
This function returns the product of the first two arguments plus the third argument.
The double-based version ::fma(double, double, double)
is defined in <cmath>
.
The partial derivatives are
, and
.
a | First multiplicand. |
b | Second multiplicand. |
c | Summand. |
|
inline |
The fused multiply-add function for a variable and two values (C99).
This function returns the product of the first two arguments plus the third argument.
The double-based version ::fma(double, double, double)
is defined in <cmath>
.
The derivative is
.
a | First multiplicand. |
b | Second multiplicand. |
c | Summand. |
|
inline |
The fused multiply-add function for a value, variable, and value (C99).
This function returns the product of the first two arguments plus the third argument.
The double-based version ::fma(double, double, double)
is defined in <cmath>
.
The derivative is
, and
a | First multiplicand. |
b | Second multiplicand. |
c | Summand. |
|
inline |
The fused multiply-add function for two values and a variable, and value (C99).
This function returns the product of the first two arguments plus the third argument.
The double-based version ::fma(double, double, double)
is defined in <cmath>
.
The derivative is
.
a | First multiplicand. |
b | Second multiplicand. |
c | Summand. |
|
inline |
The fused multiply-add function for a value and two variables (C99).
This function returns the product of the first two arguments plus the third argument.
The double-based version ::fma(double, double, double)
is defined in <cmath>
.
The partial derivaties are
, and
.
a | First multiplicand. |
b | Second multiplicand. |
c | Summand. |
|
inline |
Returns the maximum of the two variable arguments (C99).
No new variable implementations are created, with this function defined as if by
fmax(a, b) = a
if a's value is greater than b's, and .
fmax(a, b) = b
if b's value is greater than or equal to a's.
a | First variable. |
b | Second variable. |
|
inline |
Returns the maximum of the variable and scalar, promoting the scalar to a variable if it is larger (C99).
For fmax(a, b)
, if a's value is greater than b, then a is returned, otherwise a fesh variable implementation wrapping the value b is returned.
a | First variable. |
b | Second value |
|
inline |
Returns the maximum of a scalar and variable, promoting the scalar to a variable if it is larger (C99).
For fmax(a, b)
, if a is greater than b's value, then a fresh variable implementation wrapping a is returned, otherwise b is returned.
a | First value. |
b | Second variable. |
|
inline |
Returns the minimum of the two variable arguments (C99).
For fmin(a, b)
, if a's value is less than b's, then a is returned, otherwise b is returned.
a | First variable. |
b | Second variable. |
|
inline |
Returns the minimum of the variable and scalar, promoting the scalar to a variable if it is larger (C99).
For fmin(a, b)
, if a's value is less than or equal to b, then a is returned, otherwise a fresh variable wrapping b is returned.
a | First variable. |
b | Second value |
|
inline |
Returns the minimum of a scalar and variable, promoting the scalar to a variable if it is larger (C99).
For fmin(a, b)
, if a is less than b's value, then a fresh variable implementation wrapping a is returned, otherwise b is returned.
a | First value. |
b | Second variable. |
Return the floating point remainder after dividing the first variable by the second (cmath).
The partial derivatives with respect to the variables are defined everywhere but where , but we set these to match other values, with
, and
.
a | First variable. |
b | Second variable. |
Return the floating point remainder after dividing the the first variable by the second scalar (cmath).
The derivative with respect to the variable is
.
a | First variable. |
b | Second scalar. |
Return the floating point remainder after dividing the first scalar by the second variable (cmath).
The derivative with respect to the variable is
.
a | First scalar. |
b | Second variable. |
return_type<T_y, T_shape, T_scale>::type stan::math::frechet_ccdf_log | ( | const T_y & | y, |
const T_shape & | alpha, | ||
const T_scale & | sigma | ||
) |
Definition at line 31 of file frechet_ccdf_log.hpp.
return_type<T_y, T_shape, T_scale>::type stan::math::frechet_cdf | ( | const T_y & | y, |
const T_shape & | alpha, | ||
const T_scale & | sigma | ||
) |
Definition at line 31 of file frechet_cdf.hpp.
return_type<T_y, T_shape, T_scale>::type stan::math::frechet_cdf_log | ( | const T_y & | y, |
const T_shape & | alpha, | ||
const T_scale & | sigma | ||
) |
Definition at line 31 of file frechet_cdf_log.hpp.
return_type<T_y, T_shape, T_scale>::type stan::math::frechet_log | ( | const T_y & | y, |
const T_shape & | alpha, | ||
const T_scale & | sigma | ||
) |
Definition at line 34 of file frechet_log.hpp.
|
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Definition at line 140 of file frechet_log.hpp.
|
inline |
Definition at line 27 of file frechet_rng.hpp.
|
inline |
Free memory allocated for CVODES state, sensitivity, and general memory.
[in] | cvodes_state | State vector. |
[in] | cvodes_state_sens | Sensivity vector. |
[in] | cvodes_mem | Memory held for CVODES. |
[in] | S | Number of sensitivities being calculated. |
Definition at line 34 of file integrate_ode_bdf.hpp.
return_type<T_y, T_shape, T_inv_scale>::type stan::math::gamma_ccdf_log | ( | const T_y & | y, |
const T_shape & | alpha, | ||
const T_inv_scale & | beta | ||
) |
Definition at line 35 of file gamma_ccdf_log.hpp.
return_type<T_y, T_shape, T_inv_scale>::type stan::math::gamma_cdf | ( | const T_y & | y, |
const T_shape & | alpha, | ||
const T_inv_scale & | beta | ||
) |
The cumulative density function for a gamma distribution for y with the specified shape and inverse scale parameters.
y | A scalar variable. |
alpha | Shape parameter. |
beta | Inverse scale parameter. |
std::domain_error | if alpha is not greater than 0. |
std::domain_error | if beta is not greater than 0. |
std::domain_error | if y is not greater than or equal to 0. |
T_y | Type of scalar. |
T_shape | Type of shape. |
T_inv_scale | Type of inverse scale. |
Definition at line 49 of file gamma_cdf.hpp.
return_type<T_y, T_shape, T_inv_scale>::type stan::math::gamma_cdf_log | ( | const T_y & | y, |
const T_shape & | alpha, | ||
const T_inv_scale & | beta | ||
) |
Definition at line 35 of file gamma_cdf_log.hpp.
return_type<T_y, T_shape, T_inv_scale>::type stan::math::gamma_log | ( | const T_y & | y, |
const T_shape & | alpha, | ||
const T_inv_scale & | beta | ||
) |
The log of a gamma density for y with the specified shape and inverse scale parameters.
Shape and inverse scale parameters must be greater than 0. y must be greater than or equal to 0.
y | A scalar variable. |
alpha | Shape parameter. |
beta | Inverse scale parameter. |
std::domain_error | if alpha is not greater than 0. |
std::domain_error | if beta is not greater than 0. |
std::domain_error | if y is not greater than or equal to 0. |
T_y | Type of scalar. |
T_shape | Type of shape. |
T_inv_scale | Type of inverse scale. |
Definition at line 54 of file gamma_log.hpp.
|
inline |
Definition at line 166 of file gamma_log.hpp.
|
inline |
Definition at line 15 of file gamma_p.hpp.
Definition at line 51 of file gamma_p.hpp.
|
inline |
Definition at line 86 of file gamma_p.hpp.
|
inline |
Definition at line 104 of file gamma_p.hpp.
|
inline |
Definition at line 109 of file gamma_p.hpp.
|
inline |
Definition at line 114 of file gamma_p.hpp.
|
inline |
Definition at line 15 of file gamma_q.hpp.
Definition at line 51 of file gamma_q.hpp.
|
inline |
|
inline |
Definition at line 58 of file gamma_q.hpp.
|
inline |
Definition at line 63 of file gamma_q.hpp.
|
inline |
Definition at line 68 of file gamma_q.hpp.
Definition at line 86 of file gamma_q.hpp.
|
inline |
Definition at line 30 of file gamma_rng.hpp.
return_type< T_y, typename return_type<T_F, T_G, T_V, T_W, T_m0, T_C0>::type >::type stan::math::gaussian_dlm_obs_log | ( | const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > & | y, |
const Eigen::Matrix< T_F, Eigen::Dynamic, Eigen::Dynamic > & | F, | ||
const Eigen::Matrix< T_G, Eigen::Dynamic, Eigen::Dynamic > & | G, | ||
const Eigen::Matrix< T_V, Eigen::Dynamic, Eigen::Dynamic > & | V, | ||
const Eigen::Matrix< T_W, Eigen::Dynamic, Eigen::Dynamic > & | W, | ||
const Eigen::Matrix< T_m0, Eigen::Dynamic, 1 > & | m0, | ||
const Eigen::Matrix< T_C0, Eigen::Dynamic, Eigen::Dynamic > & | C0 | ||
) |
The log of a Gaussian dynamic linear model (GDLM).
This distribution is equivalent to, for ,
If V is a vector, then the Kalman filter is applied sequentially.
y | A r x T matrix of observations. Rows are variables, columns are observations. |
F | A n x r matrix. The design matrix. |
G | A n x n matrix. The transition matrix. |
V | A r x r matrix. The observation covariance matrix. |
W | A n x n matrix. The state covariance matrix. |
m0 | A n x 1 matrix. The mean vector of the distribution of the initial state. |
C0 | A n x n matrix. The covariance matrix of the distribution of the initial state. |
std::domain_error | if a matrix in the Kalman filter is not positive semi-definite. |
T_y | Type of scalar. |
T_F | Type of design matrix. |
T_G | Type of transition matrix. |
T_V | Type of observation covariance matrix. |
T_W | Type of state covariance matrix. |
T_m0 | Type of initial state mean vector. |
T_C0 | Type of initial state covariance matrix. |
Definition at line 79 of file gaussian_dlm_obs_log.hpp.
|
inline |
Definition at line 225 of file gaussian_dlm_obs_log.hpp.
return_type< T_y, typename return_type<T_F, T_G, T_V, T_W, T_m0, T_C0>::type >::type stan::math::gaussian_dlm_obs_log | ( | const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > & | y, |
const Eigen::Matrix< T_F, Eigen::Dynamic, Eigen::Dynamic > & | F, | ||
const Eigen::Matrix< T_G, Eigen::Dynamic, Eigen::Dynamic > & | G, | ||
const Eigen::Matrix< T_V, Eigen::Dynamic, 1 > & | V, | ||
const Eigen::Matrix< T_W, Eigen::Dynamic, Eigen::Dynamic > & | W, | ||
const Eigen::Matrix< T_m0, Eigen::Dynamic, 1 > & | m0, | ||
const Eigen::Matrix< T_C0, Eigen::Dynamic, Eigen::Dynamic > & | C0 | ||
) |
The log of a Gaussian dynamic linear model (GDLM) with uncorrelated observation disturbances.
This distribution is equivalent to, for ,
If V is a vector, then the Kalman filter is applied sequentially.
y | A r x T matrix of observations. Rows are variables, columns are observations. |
F | A n x r matrix. The design matrix. |
G | A n x n matrix. The transition matrix. |
V | A size r vector. The diagonal of the observation covariance matrix. |
W | A n x n matrix. The state covariance matrix. |
m0 | A n x 1 matrix. The mean vector of the distribution of the initial state. |
C0 | A n x n matrix. The covariance matrix of the distribution of the initial state. |
std::domain_error | if a matrix in the Kalman filter is not semi-positive definite. |
T_y | Type of scalar. |
T_F | Type of design matrix. |
T_G | Type of transition matrix. |
T_V | Type of observation variances |
T_W | Type of state covariance matrix. |
T_m0 | Type of initial state mean vector. |
T_C0 | Type of initial state covariance matrix. |
Definition at line 285 of file gaussian_dlm_obs_log.hpp.
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inline |
Definition at line 442 of file gaussian_dlm_obs_log.hpp.
|
inline |
Return a reference to the value of the specified vector at the specified base-one index.
If the index is out of range, throw a std::out_of_range
exception with the specified error message and index indicated.
x | Vector from which to get a value. |
i | Index into vector plus 1. |
error_msg | Error message if the index is out of range. |
idx | Nested index level to report in error message if the index is out of range. |
i - 1
T | type of value. |
Definition at line 27 of file get_base1.hpp.
|
inline |
Return a reference to the value of the specified vector at the specified base-one indexes.
If an index is out of range, throw a std::out_of_range
exception with the specified error message and index indicated.
x | Vector from which to get a value. |
i1 | First index plus 1. |
i2 | Second index plus 1. |
error_msg | Error message if an index is out of range. |
idx | Nested index level to report in error message if the index is out of range. |
T | type of value. |
Definition at line 53 of file get_base1.hpp.
|
inline |
Return a reference to the value of the specified vector at the specified base-one indexes.
If an index is out of range, throw a std::out_of_range
exception with the specified error message and index indicated.
x | Vector from which to get a value. |
i1 | First index plus 1. |
i2 | Second index plus 1. |
i3 | Third index plus 1. |
error_msg | Error message if an index is out of range. |
idx | Nested index level to report in error message if the index is out of range. |
T | type of value. |
Definition at line 81 of file get_base1.hpp.
|
inline |
Return a reference to the value of the specified vector at the specified base-one indexes.
If an index is out of range, throw a std::out_of_range
exception with the specified error message and index indicated.
x | Vector from which to get a value. |
i1 | First index plus 1. |
i2 | Second index plus 1. |
i3 | Third index plus 1. |
i4 | Fourth index plus 1. |
error_msg | Error message if an index is out of range. |
idx | Nested index level to report in error message if the index is out of range. |
T | type of value. |
Definition at line 111 of file get_base1.hpp.
|
inline |
Return a reference to the value of the specified vector at the specified base-one indexes.
If an index is out of range, throw a std::out_of_range
exception with the specified error message and index indicated.
x | Vector from which to get a value. |
i1 | First index plus 1. |
i2 | Second index plus 1. |
i3 | Third index plus 1. |
i4 | Fourth index plus 1. |
i5 | Fifth index plus 1. |
error_msg | Error message if an index is out of range. |
idx | Nested index level to report in error message if the index is out of range. |
T | type of value. |
Definition at line 143 of file get_base1.hpp.
|
inline |
Return a reference to the value of the specified vector at the specified base-one indexes.
If an index is out of range, throw a std::out_of_range
exception with the specified error message and index indicated.
x | Vector from which to get a value. |
i1 | First index plus 1. |
i2 | Second index plus 1. |
i3 | Third index plus 1. |
i4 | Fourth index plus 1. |
i5 | Fifth index plus 1. |
i6 | Sixth index plus 1. |
error_msg | Error message if an index is out of range. |
idx | Nested index level to report in error message if the index is out of range. |
T | type of value. |
Definition at line 178 of file get_base1.hpp.
|
inline |
Return a reference to the value of the specified vector at the specified base-one indexes.
If an index is out of range, throw a std::out_of_range
exception with the specified error message and index indicated.
x | Vector from which to get a value. |
i1 | First index plus 1. |
i2 | Second index plus 1. |
i3 | Third index plus 1. |
i4 | Fourth index plus 1. |
i5 | Fifth index plus 1. |
i6 | Sixth index plus 1. |
i7 | Seventh index plus 1. |
error_msg | Error message if an index is out of range. |
idx | Nested index level to report in error message if the index is out of range. |
T | type of value. |
Definition at line 216 of file get_base1.hpp.
|
inline |
Return a reference to the value of the specified vector at the specified base-one indexes.
If an index is out of range, throw a std::out_of_range
exception with the specified error message and index indicated.
x | Vector from which to get a value. |
i1 | First index plus 1. |
i2 | Second index plus 1. |
i3 | Third index plus 1. |
i4 | Fourth index plus 1. |
i5 | Fifth index plus 1. |
i6 | Sixth index plus 1. |
i7 | Seventh index plus 1. |
i8 | Eigth index plus 1. |
error_msg | Error message if an index is out of range. |
idx | Nested index level to report in error message if the index is out of range. |
T | type of value. |
Definition at line 256 of file get_base1.hpp.
|
inline |
Return a copy of the row of the specified vector at the specified base-one row index.
If the index is out of range, throw a std::out_of_range
exception with the specified error message and index indicated.
Warning: Because a copy is involved, it is inefficient to access element of matrices by first using this method to get a row then using a second call to get the value at a specified column.
x | Matrix from which to get a row |
m | Index into matrix plus 1. |
error_msg | Error message if the index is out of range. |
idx | Nested index level to report in error message if the index is out of range. |
i - 1
. T | type of value. |
Definition at line 297 of file get_base1.hpp.
|
inline |
Return a reference to the value of the specified matrix at the specified base-one row and column indexes.
If either index is out of range, throw a std::out_of_range
exception with the specified error message and index indicated.
x | Matrix from which to get a row |
m | Row index plus 1. |
n | Column index plus 1. |
error_msg | Error message if either index is out of range. |
idx | Nested index level to report in error message if either index is out of range. |
m - 1
and column n - 1
. T | type of value. |
Definition at line 324 of file get_base1.hpp.
|
inline |
Return a reference to the value of the specified column vector at the specified base-one index.
If the index is out of range, throw a std::out_of_range
exception with the specified error message and index indicated.
x | Column vector from which to get a value. |
m | Row index plus 1. |
error_msg | Error message if the index is out of range. |
idx | Nested index level to report in error message if the index is out of range. |
m - 1
. T | type of value. |
Definition at line 351 of file get_base1.hpp.
|
inline |
Return a reference to the value of the specified row vector at the specified base-one index.
If the index is out of range, throw a std::out_of_range
exception with the specified error message and index indicated.
x | Row vector from which to get a value. |
n | Column index plus 1. |
error_msg | Error message if the index is out of range. |
idx | Nested index level to report in error message if the index is out of range. |
n - 1
. T | type of value. |
Definition at line 376 of file get_base1.hpp.
|
inline |
Return a reference to the value of the specified vector at the specified base-one index.
If the index is out of range, throw a std::out_of_range
exception with the specified error message and index indicated.
x | Vector from which to get a value. |
i | Index into vector plus 1. |
error_msg | Error message if the index is out of range. |
idx | Nested index level to report in error message if the index is out of range. |
i - 1
T | type of value. |
Definition at line 27 of file get_base1_lhs.hpp.
|
inline |
Return a reference to the value of the specified vector at the specified base-one indexes.
If an index is out of range, throw a std::out_of_range
exception with the specified error message and index indicated.
x | Vector from which to get a value. |
i1 | First index plus 1. |
i2 | Second index plus 1. |
error_msg | Error message if an index is out of range. |
idx | Nested index level to report in error message if the index is out of range. |
T | type of value. |
Definition at line 53 of file get_base1_lhs.hpp.
|
inline |
Return a reference to the value of the specified vector at the specified base-one indexes.
If an index is out of range, throw a std::out_of_range
exception with the specified error message and index indicated.
x | Vector from which to get a value. |
i1 | First index plus 1. |
i2 | Second index plus 1. |
i3 | Third index plus 1. |
error_msg | Error message if an index is out of range. |
idx | Nested index level to report in error message if the index is out of range. |
T | type of value. |
Definition at line 81 of file get_base1_lhs.hpp.
|
inline |
Return a reference to the value of the specified vector at the specified base-one indexes.
If an index is out of range, throw a std::out_of_range
exception with the specified error message and index indicated.
x | Vector from which to get a value. |
i1 | First index plus 1. |
i2 | Second index plus 1. |
i3 | Third index plus 1. |
i4 | Fourth index plus 1. |
error_msg | Error message if an index is out of range. |
idx | Nested index level to report in error message if the index is out of range. |
T | type of value. |
Definition at line 111 of file get_base1_lhs.hpp.
|
inline |
Return a reference to the value of the specified vector at the specified base-one indexes.
If an index is out of range, throw a std::out_of_range
exception with the specified error message and index indicated.
x | Vector from which to get a value. |
i1 | First index plus 1. |
i2 | Second index plus 1. |
i3 | Third index plus 1. |
i4 | Fourth index plus 1. |
i5 | Fifth index plus 1. |
error_msg | Error message if an index is out of range. |
idx | Nested index level to report in error message if the index is out of range. |
T | type of value. |
Definition at line 144 of file get_base1_lhs.hpp.
|
inline |
Return a reference to the value of the specified vector at the specified base-one indexes.
If an index is out of range, throw a std::out_of_range
exception with the specified error message and index indicated.
x | Vector from which to get a value. |
i1 | First index plus 1. |
i2 | Second index plus 1. |
i3 | Third index plus 1. |
i4 | Fourth index plus 1. |
i5 | Fifth index plus 1. |
i6 | Sixth index plus 1. |
error_msg | Error message if an index is out of range. |
idx | Nested index level to report in error message if the index is out of range. |
T | type of value. |
Definition at line 179 of file get_base1_lhs.hpp.
|
inline |
Return a reference to the value of the specified vector at the specified base-one indexes.
If an index is out of range, throw a std::out_of_range
exception with the specified error message and index indicated.
x | Vector from which to get a value. |
i1 | First index plus 1. |
i2 | Second index plus 1. |
i3 | Third index plus 1. |
i4 | Fourth index plus 1. |
i5 | Fifth index plus 1. |
i6 | Sixth index plus 1. |
i7 | Seventh index plus 1. |
error_msg | Error message if an index is out of range. |
idx | Nested index level to report in error message if the index is out of range. |
T | type of value. |
Definition at line 217 of file get_base1_lhs.hpp.
|
inline |
Return a reference to the value of the specified vector at the specified base-one indexes.
If an index is out of range, throw a std::out_of_range
exception with the specified error message and index indicated.
x | Vector from which to get a value. |
i1 | First index plus 1. |
i2 | Second index plus 1. |
i3 | Third index plus 1. |
i4 | Fourth index plus 1. |
i5 | Fifth index plus 1. |
i6 | Sixth index plus 1. |
i7 | Seventh index plus 1. |
i8 | Eigth index plus 1. |
error_msg | Error message if an index is out of range. |
idx | Nested index level to report in error message if the index is out of range. |
T | type of value. |
Definition at line 258 of file get_base1_lhs.hpp.
|
inline |
Return a copy of the row of the specified vector at the specified base-one row index.
If the index is out of range, throw a std::out_of_range
exception with the specified error message and index indicated.
Warning: Because a copy is involved, it is inefficient to access element of matrices by first using this method to get a row then using a second call to get the value at a specified column.
x | Matrix from which to get a row |
m | Index into matrix plus 1. |
error_msg | Error message if the index is out of range. |
idx | Nested index level to report in error message if the index is out of range. |
i - 1
. T | type of value. |
Definition at line 301 of file get_base1_lhs.hpp.
|
inline |
Return a reference to the value of the specified matrix at the specified base-one row and column indexes.
If either index is out of range, throw a std::out_of_range
exception with the specified error message and index indicated.
x | Matrix from which to get a row |
m | Row index plus 1. |
n | Column index plus 1. |
error_msg | Error message if either index is out of range. |
idx | Nested index level to report in error message if either index is out of range. |
m - 1
and column n - 1
. T | type of value. |
Definition at line 328 of file get_base1_lhs.hpp.
|
inline |
Return a reference to the value of the specified column vector at the specified base-one index.
If the index is out of range, throw a std::out_of_range
exception with the specified error message and index indicated.
x | Column vector from which to get a value. |
m | Row index plus 1. |
error_msg | Error message if the index is out of range. |
idx | Nested index level to report in error message if the index is out of range. |
m - 1
. T | type of value. |
Definition at line 355 of file get_base1_lhs.hpp.
|
inline |
Return a reference to the value of the specified row vector at the specified base-one index.
If the index is out of range, throw a std::out_of_range
exception with the specified error message and index indicated.
x | Row vector from which to get a value. |
n | Column index plus 1. |
error_msg | Error message if the index is out of range. |
idx | Nested index level to report in error message if the index is out of range. |
n - 1
. T | type of value. |
Definition at line 380 of file get_base1_lhs.hpp.
|
inline |
Definition at line 14 of file get_lp.hpp.
|
static |
|
inline |
Propagate chain rule to calculate gradients starting from the specified variable.
Resizes the input vector to be the correct size.
The grad() function does not itself recover any memory. use recover_memory()
or recover_memory_nested()
to recover memory.
[in] | v | Value of function being differentiated |
[in] | x | Variables being differentiated with respect to |
[out] | g | Gradient, d/dx v, evaluated at x. |
|
static |
Compute the gradient for all variables starting from the specified root variable implementation.
Does not recover memory. This chainable variable's adjoint is initialized using the method init_dependent()
and then the chain rule is applied working down the stack from this vari and calling each vari's chain()
method in turn.
This function computes a nested gradient only going back as far as the last nesting.
This function does not recover any memory from the computation.
vi | Variable implementation for root of partial derivative propagation. |
void stan::math::grad_2F1 | ( | T & | gradA, |
T & | gradC, | ||
T | a, | ||
T | b, | ||
T | c, | ||
T | z, | ||
T | precision = 1e-6 |
||
) |
Definition at line 13 of file grad_2F1.hpp.
void stan::math::grad_F32 | ( | T * | g, |
T | a, | ||
T | b, | ||
T | c, | ||
T | d, | ||
T | e, | ||
T | z, | ||
T | precision = 1e-6 |
||
) |
Definition at line 11 of file grad_F32.hpp.
void stan::math::grad_hessian | ( | const F & | f, |
const Eigen::Matrix< double, Eigen::Dynamic, 1 > & | x, | ||
double & | fx, | ||
Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > & | H, | ||
std::vector< Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > > & | grad_H | ||
) |
Calculate the value, the Hessian, and the gradient of the Hessian of the specified function at the specified argument.
The functor must implement
stan::math::fvar<stan::math::fvar<stan::math::var> > operator()(const Eigen::Matrix<stan::math::fvar<stan::math::fvar<stan::math::var> >, Eigen::Dynamic, 1>&)
using only operations that are defined for stan::math::fvar
and stan::math::var
.
This latter constraint usually requires the functions to be defined in terms of the libraries defined in Stan or in terms of functions with appropriately general namespace imports that eventually depend on functions defined in Stan.
F | Type of function |
[in] | f | Function |
[in] | x | Argument to function |
[out] | fx | Function applied to argument |
[out] | H | Hessian of function at argument |
[out] | grad_H | Gradient of the Hessian of function at argument |
Definition at line 45 of file grad_hessian.hpp.
|
inline |
Definition at line 17 of file grad_inc_beta.hpp.
|
inline |
Definition at line 24 of file grad_inc_beta.hpp.
void stan::math::grad_inc_beta | ( | stan::math::fvar< T > & | g1, |
stan::math::fvar< T > & | g2, | ||
stan::math::fvar< T > | a, | ||
stan::math::fvar< T > | b, | ||
stan::math::fvar< T > | z | ||
) |
Definition at line 24 of file grad_inc_beta.hpp.
void stan::math::grad_reg_inc_beta | ( | T & | g1, |
T & | g2, | ||
T | a, | ||
T | b, | ||
T | z, | ||
T | digammaA, | ||
T | digammaB, | ||
T | digammaSum, | ||
T | betaAB | ||
) |
Definition at line 14 of file grad_reg_inc_beta.hpp.
T stan::math::grad_reg_inc_gamma | ( | T | a, |
T | z, | ||
T | g, | ||
T | dig, | ||
T | precision = 1e-6 |
||
) |
Definition at line 16 of file grad_reg_inc_gamma.hpp.
void stan::math::grad_tr_mat_times_hessian | ( | const F & | f, |
const Eigen::Matrix< double, Eigen::Dynamic, 1 > & | x, | ||
const Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > & | M, | ||
Eigen::Matrix< double, Eigen::Dynamic, 1 > & | grad_tr_MH | ||
) |
Definition at line 20 of file grad_tr_mat_times_hessian.hpp.
void stan::math::gradient | ( | const F & | f, |
const Eigen::Matrix< T, Eigen::Dynamic, 1 > & | x, | ||
T & | fx, | ||
Eigen::Matrix< T, Eigen::Dynamic, 1 > & | grad_fx | ||
) |
Calculate the value and the gradient of the specified function at the specified argument.
The functor must implement
stan::math::fvar<T> operator()(const Eigen::Matrix<T, Eigen::Dynamic, 1>&)
using only operations that are defined for stan::math::fvar
. This latter constraint usually requires the functions to be defined in terms of the libraries defined in Stan or in terms of functions with appropriately general namespace imports that eventually depend on functions defined in Stan.
Time and memory usage is on the order of the size of the fully unfolded expression for the function applied to the argument, independently of dimension.
F | Type of function |
[in] | f | Function |
[in] | x | Argument to function |
[out] | fx | Function applied to argument |
[out] | grad_fx | Gradient of function at argument |
Definition at line 41 of file gradient.hpp.
void stan::math::gradient | ( | const F & | f, |
const Eigen::Matrix< double, Eigen::Dynamic, 1 > & | x, | ||
double & | fx, | ||
Eigen::Matrix< double, Eigen::Dynamic, 1 > & | grad_fx | ||
) |
Calculate the value and the gradient of the specified function at the specified argument.
The functor must implement
stan::math::var operator()(const Eigen::Matrix<stan::math::var, Eigen::Dynamic, 1>&)
using only operations that are defined for stan::math::var
. This latter constraint usually requires the functions to be defined in terms of the libraries defined in Stan or in terms of functions with appropriately general namespace imports that eventually depend on functions defined in Stan.
Time and memory usage is on the order of the size of the fully unfolded expression for the function applied to the argument, independently of dimension.
F | Type of function |
[in] | f | Function |
[in] | x | Argument to function |
[out] | fx | Function applied to argument |
[out] | grad_fx | Gradient of function at argument |
Definition at line 43 of file gradient.hpp.
void stan::math::gradient_dot_vector | ( | const F & | f, |
const Eigen::Matrix< T1, Eigen::Dynamic, 1 > & | x, | ||
const Eigen::Matrix< T2, Eigen::Dynamic, 1 > & | v, | ||
T1 & | fx, | ||
T1 & | grad_fx_dot_v | ||
) |
Definition at line 17 of file gradient_dot_vector.hpp.
return_type<T_y, T_loc, T_scale>::type stan::math::gumbel_ccdf_log | ( | const T_y & | y, |
const T_loc & | mu, | ||
const T_scale & | beta | ||
) |
Definition at line 28 of file gumbel_ccdf_log.hpp.
return_type<T_y, T_loc, T_scale>::type stan::math::gumbel_cdf | ( | const T_y & | y, |
const T_loc & | mu, | ||
const T_scale & | beta | ||
) |
Definition at line 28 of file gumbel_cdf.hpp.
return_type<T_y, T_loc, T_scale>::type stan::math::gumbel_cdf_log | ( | const T_y & | y, |
const T_loc & | mu, | ||
const T_scale & | beta | ||
) |
Definition at line 28 of file gumbel_cdf_log.hpp.
return_type<T_y, T_loc, T_scale>::type stan::math::gumbel_log | ( | const T_y & | y, |
const T_loc & | mu, | ||
const T_scale & | beta | ||
) |
Definition at line 28 of file gumbel_log.hpp.
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Definition at line 118 of file gumbel_log.hpp.
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Definition at line 24 of file gumbel_rng.hpp.
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std::vector<T> stan::math::head | ( | const std::vector< T > & | sv, |
size_t | n | ||
) |
void stan::math::hessian | ( | const F & | f, |
const Eigen::Matrix< double, Eigen::Dynamic, 1 > & | x, | ||
double & | fx, | ||
Eigen::Matrix< double, Eigen::Dynamic, 1 > & | grad, | ||
Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > & | H | ||
) |
Calculate the value, the gradient, and the Hessian, of the specified function at the specified argument in O(N^2) time and O(N^2) space.
The functor must implement
stan::math::fvar<stan::math::var> operator()(const Eigen::Matrix<stan::math::fvar<stan::math::var>, Eigen::Dynamic, 1>&)
using only operations that are defined for stan::math::fvar
and stan::math::var
.
This latter constraint usually requires the functions to be defined in terms of the libraries defined in Stan or in terms of functions with appropriately general namespace imports that eventually depend on functions defined in Stan.
F | Type of function |
[in] | f | Function |
[in] | x | Argument to function |
[out] | fx | Function applied to argument |
[out] | grad | gradient of function at argument |
[out] | H | Hessian of function at argument |
Definition at line 45 of file hessian.hpp.
void stan::math::hessian | ( | const F & | f, |
const Eigen::Matrix< T, Eigen::Dynamic, 1 > & | x, | ||
T & | fx, | ||
Eigen::Matrix< T, Eigen::Dynamic, 1 > & | grad, | ||
Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > & | H | ||
) |
Definition at line 74 of file hessian.hpp.
void stan::math::hessian_times_vector | ( | const F & | f, |
const Eigen::Matrix< double, Eigen::Dynamic, 1 > & | x, | ||
const Eigen::Matrix< double, Eigen::Dynamic, 1 > & | v, | ||
double & | fx, | ||
Eigen::Matrix< double, Eigen::Dynamic, 1 > & | Hv | ||
) |
Definition at line 16 of file hessian_times_vector.hpp.
void stan::math::hessian_times_vector | ( | const F & | f, |
const Eigen::Matrix< T, Eigen::Dynamic, 1 > & | x, | ||
const Eigen::Matrix< T, Eigen::Dynamic, 1 > & | v, | ||
T & | fx, | ||
Eigen::Matrix< T, Eigen::Dynamic, 1 > & | Hv | ||
) |
Definition at line 45 of file hessian_times_vector.hpp.
double stan::math::hypergeometric_log | ( | const T_n & | n, |
const T_N & | N, | ||
const T_a & | a, | ||
const T_b & | b | ||
) |
Definition at line 29 of file hypergeometric_log.hpp.
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Definition at line 86 of file hypergeometric_log.hpp.
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Definition at line 16 of file hypergeometric_rng.hpp.
Returns the length of the hypoteneuse of a right triangle with sides of the specified lengths (C99).
See hypot() for double-based function.
The partial derivatives are given by
, and
.
a | Length of first side. |
b | Length of second side. |
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The normalized incomplete beta function of a, b, and x.
Used to compute the cumulative density function for the beta distribution.
a | Shape parameter a <= 0; a and b can't both be 0 |
b | Shape parameter b <= 0 |
x | Random variate. 0 <= x <= 1 |
if | constraints are violated or if any argument is NaN |
The normalized incomplete beta function of a, b, and x.
Used to compute the cumulative density function for the beta distribution.
Partial derivatives are those specified by wolfram alpha. The values were checked using both finite differences and by independent code for calculating the derivatives found in JSS (paper by Boik and Robison-Cox).
a | Shape parameter. |
b | Shape parameter. |
x | Random variate. |
if | any argument is NaN. |
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Returns the result of applying the identity constraint transform to the input.
This method is effectively a no-op and is mainly useful as a placeholder in auto-generated code.
x | Free scalar. |
T | Type of scalar. |
Definition at line 22 of file identity_constrain.hpp.
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Returns the result of applying the identity constraint transform to the input and increments the log probability reference with the log absolute Jacobian determinant.
This method is effectively a no-op and mainly useful as a placeholder in auto-generated code.
x | Free scalar. lp Reference to log probability. |
T | Type of scalar. |
Definition at line 41 of file identity_constrain.hpp.
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Returns the result of applying the inverse of the identity constraint transform to the input.
This method is effectively a no-op and mainly useful as a placeholder in auto-generated code.
y | Constrained scalar. |
T | Type of scalar. |
Definition at line 21 of file identity_free.hpp.
If the specified condition is true, return the first variable, otherwise return the second variable.
c | Boolean condition. |
y_true | Variable to return if condition is true. |
y_false | Variable to return if condition is false. |
Definition at line 17 of file if_else.hpp.
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Return the second argument if the first argument is true and otherwise return the second argument.
This is just a convenience method to provide a function with the same behavior as the built-in ternary operator. In general, this function behaves as if defined by
if_else(c, y1, y0) = c ? y1 : y0
.
c | Boolean condition value. |
y_true | Value to return if condition is true. |
y_false | Value to return if condition is false. |
Definition at line 25 of file if_else.hpp.
If the specified condition is true, return a new variable constructed from the first scalar, otherwise return the second variable.
c | Boolean condition. |
y_true | Value to promote to variable and return if condition is true. |
y_false | Variable to return if condition is false. |
Definition at line 29 of file if_else.hpp.
If the specified condition is true, return the first variable, otherwise return a new variable constructed from the second scalar.
c | Boolean condition. |
y_true | Variable to return if condition is true. |
y_false | Value to promote to variable and return if condition is false. |
Definition at line 44 of file if_else.hpp.
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Definition at line 10 of file inc_beta.hpp.
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Definition at line 20 of file inc_beta.hpp.
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Definition at line 45 of file inc_beta.hpp.
T stan::math::inc_beta_dda | ( | T | a, |
T | b, | ||
T | z, | ||
T | digamma_a, | ||
T | digamma_ab | ||
) |
Returns the partial derivative of the regularized incomplete beta function, I_{z}(a, b) with respect to a.
The power series used to compute the deriative tends to converge slowly when a and b are large, especially if z approaches 1. The implementation will throw an exception if the series have not converged within 100,000 iterations. The current implementation has been tested for values of a and b up to 12500 and z = 0.999.
T | scalar types of arguments |
a | a |
b | b |
z | upper bound of the integral |
digamma_a | value of digamma(a) |
digamma_ab | value of digamma(b) |
Definition at line 39 of file inc_beta_dda.hpp.
T stan::math::inc_beta_ddb | ( | T | a, |
T | b, | ||
T | z, | ||
T | digamma_b, | ||
T | digamma_ab | ||
) |
Returns the partial derivative of the regularized incomplete beta function, I_{z}(a, b) with respect to b.
The power series used to compute the deriative tends to converge slowly when a and b are large, especailly if z approaches 1. The implementation will throw an exception if the series have not converged within 100,000 iterations. The current implementation has been tested for values of a and b up to 12500 and z = 0.999.
T | scalar types of arguments |
a | a |
b | b |
z | upper bound of the integral |
digamma_b | value of digamma(b) |
digamma_ab | value of digamma(b) |
Definition at line 39 of file inc_beta_ddb.hpp.
T stan::math::inc_beta_ddz | ( | T | a, |
T | b, | ||
T | z | ||
) |
Returns the partial derivative of the regularized incomplete beta function, I_{z}(a, b) with respect to z.
T | scalar types of arguments |
a | a |
b | b |
z | upper bound of the integral |
Definition at line 27 of file inc_beta_ddz.hpp.
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Definition at line 35 of file inc_beta_ddz.hpp.
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Definition at line 17 of file initialize.hpp.
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Definition at line 23 of file initialize.hpp.
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Definition at line 27 of file initialize.hpp.
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Definition at line 32 of file initialize.hpp.
Initialize variable to value.
(Function may look pointless, but its needed to bottom out recursion.)
Definition at line 15 of file initialize_variable.hpp.
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Initialize every cell in the matrix to the specified value.
Definition at line 24 of file initialize_variable.hpp.
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Initialize the variables in the standard vector recursively.
Definition at line 34 of file initialize_variable.hpp.
unsigned int stan::math::int_step | ( | const T | y | ) |
The integer step, or Heaviside, function.
For double NaN input, int_step(NaN) returns 0.
y | Value to test. |
T | Scalar argument type. |
Definition at line 25 of file int_step.hpp.
std::vector<std::vector<typename stan::return_type<T_initial, T_param>::type> > stan::math::integrate_ode_bdf | ( | const F & | f, |
const std::vector< T_initial > & | y0, | ||
const double | t0, | ||
const std::vector< double > & | ts, | ||
const std::vector< T_param > & | theta, | ||
const std::vector< double > & | x, | ||
const std::vector< int > & | x_int, | ||
std::ostream * | msgs = 0 , |
||
double | relative_tolerance = 1e-10 , |
||
double | absolute_tolerance = 1e-10 , |
||
long int | max_num_steps = 1e8 |
||
) |
Return the solutions for the specified system of ordinary differential equations given the specified initial state, initial times, times of desired solution, and parameters and data, writing error and warning messages to the specified stream.
This function is templated to allow the initial times to be either data or autodiff variables and the parameters to be data or autodiff variables. The autodiff-based implementation for reverse-mode are defined in namespace stan::math
and may be invoked via argument-dependent lookup by including their headers.
The solver used is based on the backward differentiation formula which is an implicit numerical integration scheme appropiate for stiff ODE systems.
F | type of ODE system function. |
T_initial | type of scalars for initial values. |
T_param | type of scalars for parameters. |
[in] | f | functor for the base ordinary differential equation. |
[in] | y0 | initial state. |
[in] | t0 | initial time. |
[in] | ts | times of the desired solutions, in strictly increasing order, all greater than the initial time. |
[in] | theta | parameter vector for the ODE. |
[in] | x | continuous data vector for the ODE. |
[in] | x_int | integer data vector for the ODE. |
[in,out] | msgs | the print stream for warning messages. |
[in] | relative_tolerance | relative tolerance passed to CVODE. |
[in] | absolute_tolerance | absolute tolerance passed to CVODE. |
[in] | max_num_steps | maximal number of admissable steps between time-points |
Definition at line 83 of file integrate_ode_bdf.hpp.
std::vector<std::vector<typename stan::return_type<T1, T2>::type> > stan::math::integrate_ode_rk45 | ( | const F & | f, |
const std::vector< T1 > | y0, | ||
const double | t0, | ||
const std::vector< double > & | ts, | ||
const std::vector< T2 > & | theta, | ||
const std::vector< double > & | x, | ||
const std::vector< int > & | x_int, | ||
std::ostream * | msgs = 0 , |
||
double | relative_tolerance = 1e-6 , |
||
double | absolute_tolerance = 1e-6 , |
||
int | max_num_steps = 1E6 |
||
) |
Return the solutions for the specified system of ordinary differential equations given the specified initial state, initial times, times of desired solution, and parameters and data, writing error and warning messages to the specified stream.
Warning: If the system of equations is stiff, roughly defined by having varying time scales across dimensions, then this solver is likely to be slow.
This function is templated to allow the initial times to be either data or autodiff variables and the parameters to be data or autodiff variables. The autodiff-based implementation for reverse-mode are defined in namespace stan::math
and may be invoked via argument-dependent lookup by including their headers.
This function uses the Dormand-Prince method as implemented in Boost's boost::numeric::odeint::runge_kutta_dopri5
integrator.
F | type of ODE system function. |
T1 | type of scalars for initial values. |
T2 | type of scalars for parameters. |
[in] | f | functor for the base ordinary differential equation. |
[in] | y0 | initial state. |
[in] | t0 | initial time. |
[in] | ts | times of the desired solutions, in strictly increasing order, all greater than the initial time. |
[in] | theta | parameter vector for the ODE. |
[in] | x | continuous data vector for the ODE. |
[in] | x_int | integer data vector for the ODE. |
[out] | msgs | the print stream for warning messages. |
[in] | relative_tolerance | relative tolerance parameter for Boost's ode solver. Defaults to 1e-6. |
[in] | absolute_tolerance | absolute tolerance parameter for Boost's ode solver. Defaults to 1e-6. |
[in] | max_num_steps | maximum number of steps to take within the Boost ode solver. |
Definition at line 67 of file integrate_ode_rk45.hpp.
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return_type<T_y, T_dof>::type stan::math::inv_chi_square_ccdf_log | ( | const T_y & | y, |
const T_dof & | nu | ||
) |
Definition at line 33 of file inv_chi_square_ccdf_log.hpp.
return_type<T_y, T_dof>::type stan::math::inv_chi_square_cdf | ( | const T_y & | y, |
const T_dof & | nu | ||
) |
Definition at line 33 of file inv_chi_square_cdf.hpp.
return_type<T_y, T_dof>::type stan::math::inv_chi_square_cdf_log | ( | const T_y & | y, |
const T_dof & | nu | ||
) |
Definition at line 33 of file inv_chi_square_cdf_log.hpp.
return_type<T_y, T_dof>::type stan::math::inv_chi_square_log | ( | const T_y & | y, |
const T_dof & | nu | ||
) |
The log of an inverse chi-squared density for y with the specified degrees of freedom parameter.
The degrees of freedom prarameter must be greater than 0. y must be greater than 0.
y | A scalar variable. |
nu | Degrees of freedom. |
std::domain_error | if nu is not greater than or equal to 0 |
std::domain_error | if y is not greater than or equal to 0. |
T_y | Type of scalar. |
T_dof | Type of degrees of freedom. |
Definition at line 52 of file inv_chi_square_log.hpp.
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Definition at line 142 of file inv_chi_square_log.hpp.
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Definition at line 28 of file inv_chi_square_rng.hpp.
Definition at line 15 of file inv_cloglog.hpp.
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Vectorized version of inv_cloglog().
x | Container. |
T | Container type. |
Definition at line 32 of file inv_cloglog.hpp.
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Return the inverse complementary log-log function applied specified variable (stan).
See stan::math::inv_cloglog() for the double-based version.
The derivative is given by
.
a | Variable argument. |
Definition at line 36 of file inv_cloglog.hpp.
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The inverse complementary log-log function.
The function is defined by
inv_cloglog(x) = 1 - exp(-exp(x))
.
This function can be used to implement the inverse link function for complementary-log-log regression.
x | Argument. |
Definition at line 47 of file inv_cloglog.hpp.
return_type<T_y, T_shape, T_scale>::type stan::math::inv_gamma_ccdf_log | ( | const T_y & | y, |
const T_shape & | alpha, | ||
const T_scale & | beta | ||
) |
Definition at line 35 of file inv_gamma_ccdf_log.hpp.
return_type<T_y, T_shape, T_scale>::type stan::math::inv_gamma_cdf | ( | const T_y & | y, |
const T_shape & | alpha, | ||
const T_scale & | beta | ||
) |
The CDF of an inverse gamma density for y with the specified shape and scale parameters.
y, shape, and scale parameters must be greater than 0.
y | A scalar variable. |
alpha | Shape parameter. |
beta | Scale parameter. |
std::domain_error | if alpha is not greater than 0. |
std::domain_error | if beta is not greater than 0. |
std::domain_error | if y is not greater than 0. |
T_y | Type of scalar. |
T_shape | Type of shape. |
T_scale | Type of scale. |
Definition at line 51 of file inv_gamma_cdf.hpp.
return_type<T_y, T_shape, T_scale>::type stan::math::inv_gamma_cdf_log | ( | const T_y & | y, |
const T_shape & | alpha, | ||
const T_scale & | beta | ||
) |
Definition at line 35 of file inv_gamma_cdf_log.hpp.
return_type<T_y, T_shape, T_scale>::type stan::math::inv_gamma_log | ( | const T_y & | y, |
const T_shape & | alpha, | ||
const T_scale & | beta | ||
) |
The log of an inverse gamma density for y with the specified shape and scale parameters.
Shape and scale parameters must be greater than 0. y must be greater than 0.
y | A scalar variable. |
alpha | Shape parameter. |
beta | Scale parameter. |
std::domain_error | if alpha is not greater than 0. |
std::domain_error | if beta is not greater than 0. |
std::domain_error | if y is not greater than 0. |
T_y | Type of scalar. |
T_shape | Type of shape. |
T_scale | Type of scale. |
Definition at line 51 of file inv_gamma_log.hpp.
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Definition at line 163 of file inv_gamma_log.hpp.
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Definition at line 30 of file inv_gamma_rng.hpp.
Definition at line 15 of file inv_logit.hpp.
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Vectorized version of inv_logit().
x | Container. |
T | Container type. |
Definition at line 32 of file inv_logit.hpp.
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The inverse logit function for variables (stan).
See stan::math::inv_logit() for the double-based version.
The derivative of inverse logit is
.
a | Argument variable. |
Definition at line 34 of file inv_logit.hpp.
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Returns the inverse logit function applied to the argument.
The inverse logit function is defined by
.
This function can be used to implement the inverse link function for logistic regression.
The inverse to this function is stan::math::logit
.
a | Argument. |
Definition at line 50 of file inv_logit.hpp.
Definition at line 15 of file inv_Phi.hpp.
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The inverse of the unit normal cumulative distribution function.
The return value for a specified input probability, $p$, is the unit normal variate, $x$, such that
Algorithm first derived in 2003 by Peter Jon Aklam at http://home.online.no/~pjacklam/notes/invnorm/
p | Argument between 0 and 1. |
Definition at line 26 of file inv_Phi.hpp.
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Vectorized version of inv_Phi().
x | Container of variables in range [0, 1]. |
T | Container type. |
std::domain_error | if any value is not between 0 and 1. |
Definition at line 34 of file inv_Phi.hpp.
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The inverse of unit normal cumulative density function.
See stan::math::inv_Phi() for the double-based version.
The derivative is the reciprocal of unit normal density function,
p | Probability |
Definition at line 37 of file inv_Phi.hpp.
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Definition at line 9 of file inv_sqrt.hpp.
Definition at line 15 of file inv_sqrt.hpp.
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Vectorized version of inv_sqrt().
x | Container. |
T | Container type. |
Definition at line 32 of file inv_sqrt.hpp.
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Definition at line 7 of file inv_square.hpp.
Definition at line 15 of file inv_square.hpp.
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Vectorized version of inv_square().
x | Container. |
T | Container type. |
Definition at line 32 of file inv_square.hpp.
boost::math::tools::promote_args<T_y, T_dof, T_scale>::type stan::math::inv_wishart_log | ( | const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > & | W, |
const T_dof & | nu, | ||
const Eigen::Matrix< T_scale, Eigen::Dynamic, Eigen::Dynamic > & | S | ||
) |
The log of the Inverse-Wishart density for the given W, degrees of freedom, and scale matrix.
The scale matrix, S, must be k x k, symmetric, and semi-positive definite.
W | A scalar matrix |
nu | Degrees of freedom |
S | The scale matrix |
std::domain_error | if nu is not greater than k-1 |
std::domain_error | if S is not square, not symmetric, or not semi-positive definite. |
T_y | Type of scalar. |
T_dof | Type of degrees of freedom. |
T_scale | Type of scale. |
Definition at line 52 of file inv_wishart_log.hpp.
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Definition at line 125 of file inv_wishart_log.hpp.
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Definition at line 21 of file inv_wishart_rng.hpp.
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Throw an invalid_argument exception with a consistently formatted message.
This is an abstraction for all Stan functions to use when throwing invalid argument. This will allow us to change the behavior for all functions at once.
The message is: "<function>: <name> <msg1><y><msg2>"
T | Type of variable |
function | Name of the function |
name | Name of the variable |
y | Variable |
msg1 | Message to print before the variable |
msg2 | Message to print after the variable |
std::invalid_argument |
Definition at line 31 of file invalid_argument.hpp.
|
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Throw an invalid_argument exception with a consistently formatted message.
This is an abstraction for all Stan functions to use when throwing invalid argument. This will allow us to change the behavior for all functions at once. (We've already changed behavior mulitple times up to Stan v2.5.0.)
The message is: "<function>: <name> <msg1><y>"
T | Type of variable |
function | Name of the function |
name | Name of the variable |
y | Variable |
msg1 | Message to print before the variable |
std::invalid_argument |
Definition at line 66 of file invalid_argument.hpp.
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Throw an invalid argument exception with a consistently formatted message.
This is an abstraction for all Stan functions to use when throwing invalid arguments. This will allow us to change the behavior for all functions at once. (We've already changed behavior mulitple times up to Stan v2.5.0.)
The message is: "<function>: <name>[<i+error_index>] <msg1><y>" where error_index is the value of stan::error_index::value which indicates whether the message should be 0 or 1 indexed.
T | Type of variable |
function | Name of the function |
name | Name of the variable |
y | Variable |
i | Index |
msg1 | Message to print before the variable |
msg2 | Message to print after the variable |
std::invalid_argument |
Definition at line 38 of file invalid_argument_vec.hpp.
|
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Throw an invalid argument exception with a consistently formatted message.
This is an abstraction for all Stan functions to use when throwing invalid arguments. This will allow us to change the behavior for all functions at once. (We've already changed behavior mulitple times up to Stan v2.5.0.)
The message is: "<function>: <name>[<i+error_index>] <msg1><y>" where error_index is the value of stan::error_index::value which indicates whether the message should be 0 or 1 indexed.
T | Type of variable |
function | Name of the function |
name | Name of the variable |
y | Variable |
i | Index |
msg | Message to print before the variable |
std::invalid_argument |
Definition at line 74 of file invalid_argument_vec.hpp.
|
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Returns the inverse of the specified matrix.
m | Specified matrix. |
Definition at line 18 of file inverse.hpp.
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Definition at line 20 of file inverse.hpp.
void stan::math::inverse_softmax | ( | const Vector & | simplex, |
Vector & | y | ||
) |
Writes the inverse softmax of the simplex argument into the second argument.
See stan::math::softmax
for the inverse function and a definition of the relation.
The inverse softmax function is defined by
.
This function defines the inverse of stan::math::softmax
up to a scaling factor.
Because of the definition, values of 0.0 in the simplex are converted to negative infinity, and values of 1.0 are converted to 0.0.
There is no check that the input vector is a valid simplex vector.
simplex | Simplex vector input. |
y | Vector into which the inverse softmax is written. |
std::invalid_argument | if size of the input and output vectors differ. |
Definition at line 34 of file inverse_softmax.hpp.
|
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Returns the inverse of the specified symmetric, pos/neg-definite matrix.
m | Specified matrix. |
Definition at line 20 of file inverse_spd.hpp.
bool stan::math::is_aligned | ( | T * | ptr, |
unsigned int | bytes_aligned | ||
) |
Return true
if the specified pointer is aligned on the number of bytes.
This doesn't really make sense other than for powers of 2.
ptr | Pointer to test. |
bytes_aligned | Number of bytes of alignment required. |
true
if pointer is aligned. Type | of object to which pointer points. |
Definition at line 30 of file stack_alloc.hpp.
|
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Returns 1 if the input is infinite and 0 otherwise.
Delegates to boost::math::isinf
.
x | Value to test. |
1
if the value is infinite. Definition at line 19 of file is_inf.hpp.
|
inline |
Returns 1 if the input's value is infinite and 0 otherwise.
Delegates to stan::math::is_inf
.
x | Value to test. |
1
if the value is infinite and 0
otherwise. Definition at line 22 of file is_inf.hpp.
|
inline |
Returns 1 if the input's value is infinite and 0 otherwise.
Delegates to stan::math::is_inf
.
v | Value to test. |
1
if the value is infinite and 0
otherwise. Definition at line 23 of file is_inf.hpp.
|
inline |
Returns 1 if the input is NaN and 0 otherwise.
Delegates to boost::math::isnan
.
x | Value to test. |
1
if the value is NaN. Definition at line 18 of file is_nan.hpp.
|
inline |
Returns 1 if the input's value is NaN and 0 otherwise.
Delegates to stan::math::is_nan(double)
.
v | Value to test. |
1
if the value is NaN and 0
otherwise. Definition at line 21 of file is_nan.hpp.
|
inline |
Returns 1 if the input's value is NaN and 0 otherwise.
Delegates to stan::math::is_nan
.
x | Value to test. |
1
if the value is NaN and 0
otherwise. Definition at line 22 of file is_nan.hpp.
|
inline |
Returns true
if the specified variable is uninitialized.
Arithmetic types are always initialized by definition (the value is not specified).
T | Type of object to test. |
x | Object to test. |
true
if the specified object is uninitialized. Definition at line 19 of file is_uninitialized.hpp.
|
inline |
Returns true
if the specified variable is uninitialized.
This overload of the stan::math::is_uninitialized()
function delegates the return to the is_uninitialized()
method on the specified variable.
x | Object to test. |
true
if the specified object is uninitialized. Definition at line 23 of file is_uninitialized.hpp.
void stan::math::jacobian | ( | const F & | f, |
const Eigen::Matrix< T, Eigen::Dynamic, 1 > & | x, | ||
Eigen::Matrix< T, Eigen::Dynamic, 1 > & | fx, | ||
Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > & | J | ||
) |
Definition at line 14 of file jacobian.hpp.
void stan::math::jacobian | ( | const F & | f, |
const Eigen::Matrix< double, Eigen::Dynamic, 1 > & | x, | ||
Eigen::Matrix< double, Eigen::Dynamic, 1 > & | fx, | ||
Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > & | J | ||
) |
Definition at line 15 of file jacobian.hpp.
|
inline |
Return the lower-bounded value for the specified unconstrained input and specified lower bound.
The transform applied is
where is the constant lower bound.
If the lower bound is negative infinity, this function reduces to identity_constrain(x)
.
x | Unconstrained scalar input. |
lb | Lower-bound on constrained ouptut. |
T | Type of scalar. |
TL | Type of lower bound. |
Definition at line 35 of file lb_constrain.hpp.
|
inline |
Return the lower-bounded value for the speicifed unconstrained input and specified lower bound, incrementing the specified reference with the log absolute Jacobian determinant of the transform.
If the lower bound is negative infinity, this function reduces to identity_constraint(x, lp)
.
x | Unconstrained scalar input. |
lb | Lower-bound on output. |
lp | Reference to log probability to increment. |
T | Type of scalar. |
TL | Type of lower bound. |
Definition at line 61 of file lb_constrain.hpp.
|
inline |
Return the unconstrained value that produces the specified lower-bound constrained value.
If the lower bound is negative infinity, it is ignored and the function reduces to identity_free(y)
.
y | Input scalar. |
lb | Lower bound. |
T | Type of scalar. |
TL | Type of lower bound. |
std::domain_error | if y is lower than the lower bound. |
Definition at line 32 of file lb_free.hpp.
|
inline |
Return the log of the beta function applied to the specified arguments.
The beta function is defined for and
by
.
This function returns its log,
.
See boost::math::lgamma() for the double-based and stan::math for the variable-based log Gamma function.
a | First value |
b | Second value |
T1 | Type of first value. |
T2 | Type of second value. |
Definition at line 15 of file lgamma.hpp.
|
inline |
|
inline |
The log gamma function for variables (C99).
The derivatie is the digamma function,
.
a | The variable. |
Definition at line 35 of file lgamma.hpp.
|
inline |
Vectorized version of lgamma().
x | Container. |
T | Container type. |
std::domain_error | if any value is a negative integer or 0. |
Definition at line 35 of file lgamma.hpp.
boost::math::tools::promote_args<T_covar, T_shape>::type stan::math::lkj_corr_cholesky_log | ( | const Eigen::Matrix< T_covar, Eigen::Dynamic, Eigen::Dynamic > & | L, |
const T_shape & | eta | ||
) |
Definition at line 56 of file lkj_corr_cholesky_log.hpp.
|
inline |
Definition at line 99 of file lkj_corr_cholesky_log.hpp.
|
inline |
Definition at line 52 of file lkj_corr_cholesky_rng.hpp.
boost::math::tools::promote_args<T_y, T_shape>::type stan::math::lkj_corr_log | ( | const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > & | y, |
const T_shape & | eta | ||
) |
Definition at line 86 of file lkj_corr_log.hpp.
|
inline |
Definition at line 122 of file lkj_corr_log.hpp.
|
inline |
Definition at line 52 of file lkj_corr_rng.hpp.
boost::math::tools::promote_args<T_y, T_loc, T_scale, T_shape>::type stan::math::lkj_cov_log | ( | const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > & | y, |
const Eigen::Matrix< T_loc, Eigen::Dynamic, 1 > & | mu, | ||
const Eigen::Matrix< T_scale, Eigen::Dynamic, 1 > & | sigma, | ||
const T_shape & | eta | ||
) |
Definition at line 24 of file lkj_cov_log.hpp.
|
inline |
Definition at line 74 of file lkj_cov_log.hpp.
boost::math::tools::promote_args<T_y, T_loc, T_scale, T_shape>::type stan::math::lkj_cov_log | ( | const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > & | y, |
const T_loc & | mu, | ||
const T_scale & | sigma, | ||
const T_shape & | eta | ||
) |
Definition at line 87 of file lkj_cov_log.hpp.
|
inline |
Definition at line 124 of file lkj_cov_log.hpp.
|
inline |
Definition at line 16 of file lmgamma.hpp.
|
inline |
Definition at line 28 of file lmgamma.hpp.
|
inline |
Return the natural logarithm of the multivariate gamma function with the speciifed dimensions and argument.
The multivariate gamma function for dimensionality
and argument
is defined by
,
where is the gamma function.
k | Number of dimensions. |
x | Function argument. |
T | Type of scalar. |
Definition at line 57 of file lmgamma.hpp.
|
inline |
|
inline |
|
inline |
Return natural logarithm of ten.
Definition at line 114 of file constants.hpp.
|
inline |
|
inline |
|
inline |
Definition at line 16 of file log1m_exp.hpp.
|
inline |
Vectorized version of log1m_exp().
x | Container. |
T | Container type. |
Definition at line 32 of file log1m_exp.hpp.
|
inline |
Return the log of 1 minus the exponential of the specified variable.
Definition at line 38 of file log1m_exp.hpp.
|
inline |
Calculates the log of 1 minus the exponential of the specified value without overflow log1m_exp(x) = log(1-exp(x)).
This function is only defined for x<0
Definition at line 38 of file log1m_exp.hpp.
Definition at line 15 of file log1m_inv_logit.hpp.
|
inline |
Returns the natural logarithm of 1 minus the inverse logit of the specified argument.
T | Scalar type |
u | Input. |
Definition at line 36 of file log1m_inv_logit.hpp.
|
inline |
|
inline |
Definition at line 13 of file log1p_exp.hpp.
|
inline |
Return the log of 1 plus the exponential of the specified variable.
Definition at line 28 of file log1p_exp.hpp.
|
inline |
Vectorized version of log1m_exp().
x | Container. |
T | Container type. |
Definition at line 32 of file log1p_exp.hpp.
|
inline |
Calculates the log of 1 plus the exponential of the specified value without overflow.
This function is related to other special functions by:
log1p_exp(x)
= log1p(exp(a))
= log(1 + exp(x))
= log_sum_exp(0, x)
.
Definition at line 42 of file log1p_exp.hpp.
|
inline |
|
inline |
|
inline |
Returns the base 2 logarithm of the specified variable (C99).
See stan::math::log2() for the double-based version.
The derivative is
.
a | Specified variable. |
|
inline |
Definition at line 13 of file log_determinant.hpp.
|
inline |
Returns the log absolute determinant of the specified square matrix.
m | Specified matrix. |
std::domain_error | if matrix is not square. |
Definition at line 18 of file log_determinant.hpp.
|
inline |
Definition at line 20 of file log_determinant.hpp.
|
inline |
Definition at line 12 of file log_determinant_ldlt.hpp.
var stan::math::log_determinant_ldlt | ( | stan::math::LDLT_factor< var, R, C > & | A | ) |
Definition at line 48 of file log_determinant_ldlt.hpp.
|
inline |
Definition at line 15 of file log_determinant_spd.hpp.
|
inline |
Returns the log absolute determinant of the specified square matrix.
m | Specified matrix. |
std::domain_error | if matrix is not square. |
Definition at line 19 of file log_determinant_spd.hpp.
|
inline |
Definition at line 14 of file log_diff_exp.hpp.
|
inline |
Definition at line 26 of file log_diff_exp.hpp.
|
inline |
Definition at line 37 of file log_diff_exp.hpp.
|
inline |
The natural logarithm of the difference of the natural exponentiation of x1 and the natural exponentiation of x2.
This function is only defined for x<0
Definition at line 50 of file log_diff_exp.hpp.
|
inline |
Returns the log sum of exponentials.
Definition at line 54 of file log_diff_exp.hpp.
|
inline |
Returns the log sum of exponentials.
Definition at line 61 of file log_diff_exp.hpp.
|
inline |
Returns the log sum of exponentials.
Definition at line 68 of file log_diff_exp.hpp.
|
inline |
Definition at line 15 of file log_falling_factorial.hpp.
|
inline |
Definition at line 27 of file log_falling_factorial.hpp.
|
inline |
Definition at line 37 of file log_falling_factorial.hpp.
|
inline |
Definition at line 68 of file log_falling_factorial.hpp.
Definition at line 73 of file log_falling_factorial.hpp.
Definition at line 78 of file log_falling_factorial.hpp.
Definition at line 15 of file log_inv_logit.hpp.
|
inline |
Returns the natural logarithm of the inverse logit of the specified argument.
T | Scalar type |
u | Input. |
Definition at line 36 of file log_inv_logit.hpp.
|
inline |
Definition at line 26 of file ordered_logistic_log.hpp.
|
inline |
Return the log mixture density with specified mixing proportion and log densities.
[in] | theta | mixing proportion in [0, 1]. |
lambda1 | first log density. | |
lambda2 | second log density. |
Definition at line 46 of file log_mix.hpp.
|
inline |
Return the log mixture density with specified mixing proportion and log densities and its derivative at each.
T_theta | theta scalar type. |
T_lambda1 | lambda1 scalar type. |
T_lambda2 | lambda2 scalar type. |
[in] | theta | mixing proportion in [0, 1]. |
[in] | lambda1 | first log density. |
[in] | lambda2 | second log density. |
Definition at line 88 of file log_mix.hpp.
|
inline |
Return the log mixture density with specified mixing proportion and log densities and its derivative at each.
T | scalar type. |
[in] | theta | mixing proportion in [0, 1]. |
[in] | lambda1 | first log density. |
[in] | lambda2 | second log density. |
Definition at line 117 of file log_mix.hpp.
|
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Definition at line 143 of file log_mix.hpp.
|
inline |
Definition at line 168 of file log_mix.hpp.
|
inline |
Definition at line 193 of file log_mix.hpp.
|
inline |
Definition at line 217 of file log_mix.hpp.
|
inline |
Definition at line 238 of file log_mix.hpp.
|
inline |
Definition at line 259 of file log_mix.hpp.
|
inline |
Definition at line 28 of file log_mix.hpp.
|
inline |
Definition at line 29 of file log_mix.hpp.
|
inline |
Definition at line 16 of file log_rising_factorial.hpp.
|
inline |
Definition at line 28 of file log_rising_factorial.hpp.
|
inline |
Definition at line 39 of file log_rising_factorial.hpp.
|
inline |
Definition at line 49 of file log_rising_factorial.hpp.
Definition at line 54 of file log_rising_factorial.hpp.
Definition at line 59 of file log_rising_factorial.hpp.
|
inline |
Definition at line 16 of file log_softmax.hpp.
|
inline |
Return the natural logarithm of the softmax of the specified vector.
For the log softmax function, the entries in the Jacobian are
T | Scalar type of values in vector. |
[in] | v | Vector to transform. |
Definition at line 44 of file log_softmax.hpp.
|
inline |
Return the softmax of the specified Eigen vector.
Softmax is guaranteed to return a simplex.
The gradient calculations are unfolded.
alpha | Unconstrained input vector. |
std::domain_error | If the input vector is size 0. |
Definition at line 61 of file log_softmax.hpp.
Definition at line 14 of file log_sum_exp.hpp.
|
inline |
Definition at line 15 of file log_sum_exp.hpp.
fvar<T> stan::math::log_sum_exp | ( | const Eigen::Matrix< fvar< T >, R, C > & | v | ) |
Definition at line 19 of file log_sum_exp.hpp.
|
inline |
Return the log of the sum of the exponentiated values of the specified sequence of values.
The function is defined as follows to prevent overflow in exponential calculations.
.
[in] | x | array of specified values |
Definition at line 24 of file log_sum_exp.hpp.
|
inline |
Definition at line 26 of file log_sum_exp.hpp.
double stan::math::log_sum_exp | ( | const Eigen::Matrix< double, R, C > & | x | ) |
Return the log of the sum of the exponentiated values of the specified matrix of values.
The matrix may be a full matrix, a vector, or a row vector.
The function is defined as follows to prevent overflow in exponential calculations.
.
[in] | x | Matrix of specified values |
Definition at line 28 of file log_sum_exp.hpp.
|
inline |
Definition at line 36 of file log_sum_exp.hpp.
Returns the log sum of exponentials.
Definition at line 45 of file log_sum_exp.hpp.
|
inline |
Calculates the log sum of exponetials without overflow.
,
where .
a | the first variable |
b | the second variable |
Definition at line 48 of file log_sum_exp.hpp.
|
inline |
Returns the log sum of exponentials.
Definition at line 50 of file log_sum_exp.hpp.
Returns the log sum of exponentials.
x | matrix |
Definition at line 54 of file log_sum_exp.hpp.
|
inline |
Returns the log sum of exponentials.
Definition at line 57 of file log_sum_exp.hpp.
|
inline |
Returns the log sum of exponentials.
Definition at line 64 of file log_sum_exp.hpp.
|
inline |
The logical and function which returns 1 if both arguments are unequal to zero and 0 otherwise.
Equivalent to x1 != 0 && x2 != 0
.
T1 | Type of first argument. |
T2 | Type of second argument. |
x1 | First argument |
x2 | Second argument |
true
if both x1 and x2 are not equal to 0. Definition at line 30 of file logical_and.hpp.
|
inline |
Return 1 if the first argument is equal to the second.
Equivalent to x1 == x2
.
T1 | Type of first argument. |
T2 | Type of second argument. |
x1 | First argument |
x2 | Second argument |
true
iff x1 == x2
Definition at line 19 of file logical_eq.hpp.
|
inline |
Return 1 if the first argument is strictly greater than the second.
Equivalent to x1 < x2
.
T1 | Type of first argument. |
T2 | Type of second argument. |
x1 | First argument |
x2 | Second argument |
true
iff x1 > x2
Definition at line 19 of file logical_gt.hpp.
|
inline |
Return 1 if the first argument is greater than or equal to the second.
Equivalent to x1 >= x2
.
T1 | Type of first argument. |
T2 | Type of second argument. |
x1 | First argument |
x2 | Second argument |
true
iff x1 >= x2
Definition at line 19 of file logical_gte.hpp.
|
inline |
Return 1 if the first argument is strictly less than the second.
Equivalent to x1 < x2
.
T1 | Type of first argument. |
T2 | Type of second argument. |
x1 | First argument |
x2 | Second argument |
true
iff x1 < x2
Definition at line 20 of file logical_lt.hpp.
|
inline |
Return 1 if the first argument is less than or equal to the second.
Equivalent to x1 <= x2
.
T1 | Type of first argument. |
T2 | Type of second argument. |
x1 | First argument |
x2 | Second argument |
true
iff x1 <= x2
Definition at line 19 of file logical_lte.hpp.
|
inline |
The logical negation function which returns 1 if the input is equal to zero and 0 otherwise.
T | Type to compare to zero. |
x | Value to compare to zero. |
Definition at line 17 of file logical_negation.hpp.
|
inline |
Return 1 if the first argument is unequal to the second.
Equivalent to x1 != x2
.
T1 | Type of first argument. |
T2 | Type of second argument. |
x1 | First argument |
x2 | Second argument |
true
iff x1 != x2
Definition at line 19 of file logical_neq.hpp.
|
inline |
The logical or function which returns 1 if either argument is unequal to zero and 0 otherwise.
Equivalent to x1 != 0 || x2 != 0
.
T1 | Type of first argument. |
T2 | Type of second argument. |
x1 | First argument |
x2 | Second argument |
true
if either x1 or x2 is not equal to 0. Definition at line 29 of file logical_or.hpp.
return_type<T_y, T_loc, T_scale>::type stan::math::logistic_ccdf_log | ( | const T_y & | y, |
const T_loc & | mu, | ||
const T_scale & | sigma | ||
) |
Definition at line 31 of file logistic_ccdf_log.hpp.
return_type<T_y, T_loc, T_scale>::type stan::math::logistic_cdf | ( | const T_y & | y, |
const T_loc & | mu, | ||
const T_scale & | sigma | ||
) |
Definition at line 31 of file logistic_cdf.hpp.
return_type<T_y, T_loc, T_scale>::type stan::math::logistic_cdf_log | ( | const T_y & | y, |
const T_loc & | mu, | ||
const T_scale & | sigma | ||
) |
Definition at line 30 of file logistic_cdf_log.hpp.
return_type<T_y, T_loc, T_scale>::type stan::math::logistic_log | ( | const T_y & | y, |
const T_loc & | mu, | ||
const T_scale & | sigma | ||
) |
Definition at line 32 of file logistic_log.hpp.
|
inline |
Definition at line 142 of file logistic_log.hpp.
|
inline |
Definition at line 24 of file logistic_rng.hpp.
|
inline |
Returns the logit function applied to the argument.
The logit function is defined as for by returning the log odds of
treated as a probability,
.
The inverse to this function is stan::math::inv_logit
.
a | Argument. |
return_type<T_y, T_loc, T_scale>::type stan::math::lognormal_ccdf_log | ( | const T_y & | y, |
const T_loc & | mu, | ||
const T_scale & | sigma | ||
) |
Definition at line 25 of file lognormal_ccdf_log.hpp.
return_type<T_y, T_loc, T_scale>::type stan::math::lognormal_cdf | ( | const T_y & | y, |
const T_loc & | mu, | ||
const T_scale & | sigma | ||
) |
Definition at line 25 of file lognormal_cdf.hpp.
return_type<T_y, T_loc, T_scale>::type stan::math::lognormal_cdf_log | ( | const T_y & | y, |
const T_loc & | mu, | ||
const T_scale & | sigma | ||
) |
Definition at line 25 of file lognormal_cdf_log.hpp.
return_type<T_y, T_loc, T_scale>::type stan::math::lognormal_log | ( | const T_y & | y, |
const T_loc & | mu, | ||
const T_scale & | sigma | ||
) |
Definition at line 33 of file lognormal_log.hpp.
|
inline |
Definition at line 158 of file lognormal_log.hpp.
|
inline |
Definition at line 21 of file lognormal_rng.hpp.
|
inline |
Return the lower- and upper-bounded scalar derived by transforming the specified free scalar given the specified lower and upper bounds.
The transform is the transformed and scaled inverse logit,
If the lower bound is negative infinity and upper bound finite, this function reduces to ub_constrain(x, ub)
. If the upper bound is positive infinity and the lower bound finite, this function reduces to lb_constrain(x, lb)
. If the upper bound is positive infinity and the lower bound negative infinity, this function reduces to identity_constrain(x)
.
x | Free scalar to transform. |
lb | Lower bound. |
ub | Upper bound. |
T | Type of scalar. |
TL | Type of lower bound. |
TU | Type of upper bound. |
std::domain_error | if ub <= lb |
Definition at line 45 of file lub_constrain.hpp.
boost::math::tools::promote_args<T, TL, TU>::type stan::math::lub_constrain | ( | const T | x, |
const TL | lb, | ||
const TU | ub, | ||
T & | lp | ||
) |
Return the lower- and upper-bounded scalar derived by transforming the specified free scalar given the specified lower and upper bounds and increment the specified log probability with the log absolute Jacobian determinant.
The transform is as defined in lub_constrain(T, double, double)
. The log absolute Jacobian determinant is given by
If the lower bound is negative infinity and upper bound finite, this function reduces to ub_constrain(x, ub, lp)
. If the upper bound is positive infinity and the lower bound finite, this function reduces to lb_constrain(x, lb, lp)
. If the upper bound is positive infinity and the lower bound negative infinity, this function reduces to identity_constrain(x, lp)
.
x | Free scalar to transform. |
lb | Lower bound. |
ub | Upper bound. |
lp | Log probability scalar reference. |
T | Type of scalar. |
TL | Type of lower bound. |
TU | Type of upper bound. |
std::domain_error | if ub <= lb |
Definition at line 115 of file lub_constrain.hpp.
|
inline |
Return the unconstrained scalar that transforms to the specified lower- and upper-bounded scalar given the specified bounds.
The transfrom in lub_constrain(T, double, double)
, is reversed by a transformed and scaled logit,
where and
are the lower and upper bounds.
If the lower bound is negative infinity and upper bound finite, this function reduces to ub_free(y, ub)
. If the upper bound is positive infinity and the lower bound finite, this function reduces to lb_free(x, lb)
. If the upper bound is positive infinity and the lower bound negative infinity, this function reduces to identity_free(y)
.
T | Type of scalar. |
y | Scalar input. |
lb | Lower bound. |
ub | Upper bound. |
std::invalid_argument | if the lower bound is greater than the upper bound, y is less than the lower bound, or y is greater than the upper bound |
Definition at line 47 of file lub_free.hpp.
|
inline |
Returns the difference between 1.0 and the next value representable.
Definition at line 151 of file constants.hpp.
const Eigen::Array<T, Eigen::Dynamic, 1> stan::math::make_nu | ( | const T | eta, |
const size_t | K | ||
) |
This function calculates the degrees of freedom for the t distribution that corresponds to the shape parameter in the Lewandowski et.
al. distribution
eta | hyperparameter on (0, inf), eta = 1 <-> correlation matrix is uniform |
K | number of variables in covariance matrix |
Definition at line 22 of file make_nu.hpp.
boost::math::tools::promote_args<T_y, T_Mu, T_Sigma, T_D>::type stan::math::matrix_normal_prec_log | ( | const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > & | y, |
const Eigen::Matrix< T_Mu, Eigen::Dynamic, Eigen::Dynamic > & | Mu, | ||
const Eigen::Matrix< T_Sigma, Eigen::Dynamic, Eigen::Dynamic > & | Sigma, | ||
const Eigen::Matrix< T_D, Eigen::Dynamic, Eigen::Dynamic > & | D | ||
) |
The log of the matrix normal density for the given y, mu, Sigma and D where Sigma and D are given as precision matrices, not covariance matrices.
y | An mxn matrix. |
Mu | The mean matrix. |
Sigma | The mxm inverse covariance matrix (i.e., the precision matrix) of the rows of y. |
D | The nxn inverse covariance matrix (i.e., the precision matrix) of the columns of y. |
std::domain_error | if Sigma or D are not square, not symmetric, or not semi-positive definite. |
T_y | Type of scalar. |
T_Mu | Type of location. |
T_Sigma | Type of Sigma. |
T_D | Type of D. |
Definition at line 43 of file matrix_normal_prec_log.hpp.
boost::math::tools::promote_args<T_y, T_Mu, T_Sigma, T_D>::type stan::math::matrix_normal_prec_log | ( | const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > & | y, |
const Eigen::Matrix< T_Mu, Eigen::Dynamic, Eigen::Dynamic > & | Mu, | ||
const Eigen::Matrix< T_Sigma, Eigen::Dynamic, Eigen::Dynamic > & | Sigma, | ||
const Eigen::Matrix< T_D, Eigen::Dynamic, Eigen::Dynamic > & | D | ||
) |
Definition at line 112 of file matrix_normal_prec_log.hpp.
|
inline |
Returns the maximum coefficient in the specified column vector.
x | Specified vector. |
Type | of values being compared and returned |
std::domain_error | If the size of the vector is zero. |
|
inline |
|
inline |
|
inline |
Definition at line 24 of file mdivide_left.hpp.
|
inline |
Returns the solution of the system Ax=b.
A | Matrix. |
b | Right hand side matrix or vector. |
std::domain_error | if A is not square or the rows of b don't match the size of A. |
Definition at line 25 of file mdivide_left.hpp.
|
inline |
Definition at line 68 of file mdivide_left.hpp.
|
inline |
Definition at line 94 of file mdivide_left.hpp.
|
inline |
Definition at line 274 of file mdivide_left.hpp.
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Definition at line 301 of file mdivide_left.hpp.
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Definition at line 328 of file mdivide_left.hpp.
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Returns the solution of the system Ax=b given an LDLT_factor of A.
A | LDLT_factor |
b | Right hand side matrix or vector. |
std::domain_error | if rows of b don't match the size of A. |
Definition at line 25 of file mdivide_left_ldlt.hpp.
|
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Returns the solution of the system Ax=b given an LDLT_factor of A.
A | LDLT_factor |
b | Right hand side matrix or vector. |
std::domain_error | if rows of b don't match the size of A. |
Definition at line 26 of file mdivide_left_ldlt.hpp.
|
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Returns the solution of the system Ax=b given an LDLT_factor of A.
A | LDLT_factor |
b | Right hand side matrix or vector. |
std::domain_error | if rows of b don't match the size of A. |
Definition at line 246 of file mdivide_left_ldlt.hpp.
|
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Returns the solution of the system Ax=b given an LDLT_factor of A.
A | LDLT_factor |
b | Right hand side matrix or vector. |
std::domain_error | if rows of b don't match the size of A. |
Definition at line 274 of file mdivide_left_ldlt.hpp.
|
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Returns the solution of the system Ax=b given an LDLT_factor of A.
A | LDLT_factor |
b | Right hand side matrix or vector. |
std::domain_error | if rows of b don't match the size of A. |
Definition at line 302 of file mdivide_left_ldlt.hpp.
|
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Returns the solution of the system Ax=b where A is symmetric positive definite.
A | Matrix. |
b | Right hand side matrix or vector. |
std::domain_error | if A is not square or the rows of b don't match the size of A. |
Definition at line 28 of file mdivide_left_spd.hpp.
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Definition at line 248 of file mdivide_left_spd.hpp.
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Definition at line 275 of file mdivide_left_spd.hpp.
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Definition at line 302 of file mdivide_left_spd.hpp.
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Returns the solution of the system Ax=b when A is triangular.
A | Triangular matrix. Specify upper or lower with TriView being Eigen::Upper or Eigen::Lower. |
b | Right hand side matrix or vector. |
std::domain_error | if A is not square or the rows of b don't match the size of A. |
Definition at line 27 of file mdivide_left_tri.hpp.
|
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Returns the solution of the system Ax=b when A is triangular and b=I.
A | Triangular matrix. Specify upper or lower with TriView being Eigen::Upper or Eigen::Lower. |
std::domain_error | if A is not square |
Definition at line 50 of file mdivide_left_tri.hpp.
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Definition at line 304 of file mdivide_left_tri.hpp.
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Definition at line 330 of file mdivide_left_tri.hpp.
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Definition at line 356 of file mdivide_left_tri.hpp.
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Definition at line 16 of file mdivide_left_tri_low.hpp.
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Definition at line 22 of file mdivide_left_tri_low.hpp.
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Definition at line 32 of file mdivide_left_tri_low.hpp.
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Definition at line 68 of file mdivide_left_tri_low.hpp.
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Definition at line 109 of file mdivide_left_tri_low.hpp.
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Definition at line 24 of file mdivide_right.hpp.
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Returns the solution of the system Ax=b.
A | Matrix. |
b | Right hand side matrix or vector. |
std::domain_error | if A is not square or the rows of b don't match the size of A. |
Definition at line 26 of file mdivide_right.hpp.
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Definition at line 68 of file mdivide_right.hpp.
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Definition at line 95 of file mdivide_right.hpp.
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Returns the solution of the system xA=b given an LDLT_factor of A.
A | LDLT_factor |
b | Right hand side matrix or vector. |
std::domain_error | if rows of b don't match the size of A. |
Definition at line 26 of file mdivide_right_ldlt.hpp.
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Definition at line 38 of file mdivide_right_ldlt.hpp.
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Returns the solution of the system Ax=b where A is symmetric positive definite.
A | Matrix. |
b | Right hand side matrix or vector. |
std::domain_error | if A is not square or the rows of b don't match the size of A. |
Definition at line 29 of file mdivide_right_spd.hpp.
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Returns the solution of the system Ax=b when A is triangular.
A | Triangular matrix. Specify upper or lower with TriView being Eigen::Upper or Eigen::Lower. |
b | Right hand side matrix or vector. |
std::domain_error | if A is not square or the rows of b don't match the size of A. |
Definition at line 29 of file mdivide_right_tri.hpp.
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Definition at line 22 of file mdivide_right_tri_low.hpp.
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Returns the solution of the system tri(A)x=b when tri(A) is a lower triangular view of the matrix A.
A | Matrix. |
b | Right hand side matrix or vector. |
std::domain_error | if A is not square or the rows of b don't match the size of A. |
Definition at line 25 of file mdivide_right_tri_low.hpp.
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Definition at line 68 of file mdivide_right_tri_low.hpp.
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Definition at line 103 of file mdivide_right_tri_low.hpp.
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|
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|
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Definition at line 15 of file modified_bessel_first_kind.hpp.
Definition at line 27 of file modified_bessel_first_kind.hpp.
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|
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Definition at line 15 of file modified_bessel_second_kind.hpp.
Definition at line 27 of file modified_bessel_second_kind.hpp.
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|
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Definition at line 10 of file modulus.hpp.
boost::math::tools::promote_args<T_y, T_covar, T_w>::type stan::math::multi_gp_cholesky_log | ( | const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > & | y, |
const Eigen::Matrix< T_covar, Eigen::Dynamic, Eigen::Dynamic > & | L, | ||
const Eigen::Matrix< T_w, Eigen::Dynamic, 1 > & | w | ||
) |
The log of a multivariate Gaussian Process for the given y, w, and a Cholesky factor L of the kernel matrix Sigma.
Sigma = LL', a square, semi-positive definite matrix.. y is a dxN matrix, where each column is a different observation and each row is a different output dimension. The Gaussian Process is assumed to have a scaled kernel matrix with a different scale for each output dimension. This distribution is equivalent to: for (i in 1:d) row(y, i) ~ multi_normal(0, (1/w[i])*LL').
y | A dxN matrix |
L | The Cholesky decomposition of a kernel matrix |
w | A d-dimensional vector of positve inverse scale parameters for each output. |
std::domain_error | if Sigma is not square, not symmetric, or not semi-positive definite. |
T_y | Type of scalar. |
T_covar | Type of kernel. |
T_w | Type of weight. |
Definition at line 43 of file multi_gp_cholesky_log.hpp.
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Definition at line 106 of file multi_gp_cholesky_log.hpp.
boost::math::tools::promote_args<T_y, T_covar, T_w>::type stan::math::multi_gp_log | ( | const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > & | y, |
const Eigen::Matrix< T_covar, Eigen::Dynamic, Eigen::Dynamic > & | Sigma, | ||
const Eigen::Matrix< T_w, Eigen::Dynamic, 1 > & | w | ||
) |
The log of a multivariate Gaussian Process for the given y, Sigma, and w.
y is a dxN matrix, where each column is a different observation and each row is a different output dimension. The Gaussian Process is assumed to have a scaled kernel matrix with a different scale for each output dimension. This distribution is equivalent to: for (i in 1:d) row(y, i) ~ multi_normal(0, (1/w[i])*Sigma).
y | A dxN matrix |
Sigma | The NxN kernel matrix |
w | A d-dimensional vector of positve inverse scale parameters for each output. |
std::domain_error | if Sigma is not square, not symmetric, or not semi-positive definite. |
T_y | Type of scalar. |
T_covar | Type of kernel. |
T_w | Type of weight. |
Definition at line 45 of file multi_gp_log.hpp.
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Definition at line 112 of file multi_gp_log.hpp.
return_type<T_y, T_loc, T_covar>::type stan::math::multi_normal_cholesky_log | ( | const T_y & | y, |
const T_loc & | mu, | ||
const T_covar & | L | ||
) |
The log of the multivariate normal density for the given y, mu, and a Cholesky factor L of the variance matrix.
Sigma = LL', a square, semi-positive definite matrix.
y | A scalar vector |
mu | The mean vector of the multivariate normal distribution. |
L | The Cholesky decomposition of a variance matrix of the multivariate normal distribution |
std::domain_error | if LL' is not square, not symmetric, or not semi-positive definite. |
T_y | Type of scalar. |
T_loc | Type of location. |
T_covar | Type of scale. |
Definition at line 47 of file multi_normal_cholesky_log.hpp.
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Definition at line 153 of file multi_normal_cholesky_log.hpp.
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Definition at line 29 of file multi_normal_cholesky_rng.hpp.
return_type<T_y, T_loc, T_covar>::type stan::math::multi_normal_log | ( | const T_y & | y, |
const T_loc & | mu, | ||
const T_covar & | Sigma | ||
) |
Definition at line 27 of file multi_normal_log.hpp.
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Definition at line 128 of file multi_normal_log.hpp.
return_type<T_y, T_loc, T_covar>::type stan::math::multi_normal_prec_log | ( | const T_y & | y, |
const T_loc & | mu, | ||
const T_covar & | Sigma | ||
) |
Definition at line 35 of file multi_normal_prec_log.hpp.
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Definition at line 143 of file multi_normal_prec_log.hpp.
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Definition at line 24 of file multi_normal_rng.hpp.
return_type<T_y, T_dof, T_loc, T_scale>::type stan::math::multi_student_t_log | ( | const T_y & | y, |
const T_dof & | nu, | ||
const T_loc & | mu, | ||
const T_scale & | Sigma | ||
) |
Return the log of the multivariate Student t distribution at the specified arguments.
propto | Carry out calculations up to a proportion |
Definition at line 35 of file multi_student_t_log.hpp.
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Definition at line 170 of file multi_student_t_log.hpp.
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Definition at line 29 of file multi_student_t_rng.hpp.
boost::math::tools::promote_args<T_prob>::type stan::math::multinomial_log | ( | const std::vector< int > & | ns, |
const Eigen::Matrix< T_prob, Eigen::Dynamic, 1 > & | theta | ||
) |
Definition at line 24 of file multinomial_log.hpp.
boost::math::tools::promote_args<T_prob>::type stan::math::multinomial_log | ( | const std::vector< int > & | ns, |
const Eigen::Matrix< T_prob, Eigen::Dynamic, 1 > & | theta | ||
) |
Definition at line 59 of file multinomial_log.hpp.
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Definition at line 23 of file multinomial_rng.hpp.
|
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Definition at line 21 of file multiply.hpp.
|
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Return specified matrix multiplied by specified scalar.
R | Row type for matrix. |
C | Column type for matrix. |
m | Matrix. |
c | Scalar. |
Definition at line 26 of file multiply.hpp.
|
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Return the product of two scalars.
[in] | v | First scalar. |
[in] | c | Specified scalar. |
Definition at line 32 of file multiply.hpp.
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Definition at line 33 of file multiply.hpp.
|
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Return the product of scalar and matrix.
[in] | c | Specified scalar. |
[in] | m | Matrix. |
Definition at line 44 of file multiply.hpp.
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Definition at line 45 of file multiply.hpp.
|
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Return specified scalar multiplied by specified matrix.
R | Row type for matrix. |
C | Column type for matrix. |
c | Scalar. |
m | Matrix. |
Definition at line 46 of file multiply.hpp.
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Definition at line 57 of file multiply.hpp.
|
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Return the product of scalar and matrix.
[in] | m | Matrix. |
[in] | c | Specified scalar. |
Definition at line 58 of file multiply.hpp.
|
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Return the product of the specified matrices.
The number of columns in the first matrix must be the same as the number of rows in the second matrix.
m1 | First matrix. |
m2 | Second matrix. |
std::domain_error | if the number of columns of m1 does not match the number of rows of m2. |
Definition at line 63 of file multiply.hpp.
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Definition at line 64 of file multiply.hpp.
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Definition at line 71 of file multiply.hpp.
|
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Return the product of the specified matrices.
The number of columns in the first matrix must be the same as the number of rows in the second matrix.
[in] | m1 | First matrix. |
[in] | m2 | Second matrix. |
std::domain_error | if the number of columns of m1 does not match the number of rows of m2. |
Definition at line 77 of file multiply.hpp.
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Definition at line 78 of file multiply.hpp.
|
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Return the scalar product of the specified row vector and specified column vector.
The return is the same as the dot product. The two vectors must be the same size.
rv | Row vector. |
v | Column vector. |
std::domain_error | if rv and v are not the same size. |
Definition at line 81 of file multiply.hpp.
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Definition at line 97 of file multiply.hpp.
|
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Definition at line 116 of file multiply.hpp.
|
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Return the scalar product of the specified row vector and specified column vector.
The return is the same as the dot product. The two vectors must be the same size.
[in] | rv | Row vector. |
[in] | v | Column vector. |
std::domain_error | if rv and v are not the same size |
Definition at line 129 of file multiply.hpp.
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Definition at line 135 of file multiply.hpp.
|
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Definition at line 146 of file multiply.hpp.
|
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Definition at line 157 of file multiply.hpp.
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Definition at line 15 of file multiply_log.hpp.
|
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Definition at line 25 of file multiply_log.hpp.
|
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Definition at line 35 of file multiply_log.hpp.
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Calculated the value of the first argument times log of the second argument while behaving properly with 0 inputs.
.
a | the first variable |
b | the second variable |
Definition at line 51 of file multiply_log.hpp.
Return the value of a*log(b).
When both a and b are 0, the value returned is 0. The partial deriviative with respect to a is log(b). The partial deriviative with respect to b is a/b. When a and b are both 0, this is set to Inf.
a | First variable. |
b | Second variable. |
Definition at line 74 of file multiply_log.hpp.
Return the value of a*log(b).
When both a and b are 0, the value returned is 0. The partial deriviative with respect to a is log(b).
a | First variable. |
b | Second scalar. |
Definition at line 87 of file multiply_log.hpp.
Return the value of a*log(b).
When both a and b are 0, the value returned is 0. The partial deriviative with respect to b is a/b. When a and b are both 0, this is set to Inf.
a | First scalar. |
b | Second variable. |
Definition at line 101 of file multiply_log.hpp.
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Definition at line 17 of file multiply_lower_tri_self_transpose.hpp.
Returns the result of multiplying the lower triangular portion of the input matrix by its own transpose.
L | Matrix to multiply. |
std::domain_error | If the input matrix is not square. |
Definition at line 18 of file multiply_lower_tri_self_transpose.hpp.
Definition at line 19 of file multiply_lower_tri_self_transpose.hpp.
return_type<T_location, T_precision>::type stan::math::neg_binomial_2_ccdf_log | ( | const T_n & | n, |
const T_location & | mu, | ||
const T_precision & | phi | ||
) |
Definition at line 18 of file neg_binomial_2_ccdf_log.hpp.
return_type<T_location, T_precision>::type stan::math::neg_binomial_2_cdf | ( | const T_n & | n, |
const T_location & | mu, | ||
const T_precision & | phi | ||
) |
Definition at line 26 of file neg_binomial_2_cdf.hpp.
return_type<T_location, T_precision>::type stan::math::neg_binomial_2_cdf_log | ( | const T_n & | n, |
const T_location & | mu, | ||
const T_precision & | phi | ||
) |
Definition at line 19 of file neg_binomial_2_cdf_log.hpp.
return_type<T_location, T_precision>::type stan::math::neg_binomial_2_log | ( | const T_n & | n, |
const T_location & | mu, | ||
const T_precision & | phi | ||
) |
Definition at line 37 of file neg_binomial_2_log.hpp.
|
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Definition at line 141 of file neg_binomial_2_log.hpp.
return_type<T_log_location, T_precision>::type stan::math::neg_binomial_2_log_log | ( | const T_n & | n, |
const T_log_location & | eta, | ||
const T_precision & | phi | ||
) |
Definition at line 35 of file neg_binomial_2_log_log.hpp.
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Definition at line 142 of file neg_binomial_2_log_log.hpp.
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Definition at line 28 of file neg_binomial_2_log_rng.hpp.
|
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Definition at line 28 of file neg_binomial_2_rng.hpp.
return_type<T_shape, T_inv_scale>::type stan::math::neg_binomial_ccdf_log | ( | const T_n & | n, |
const T_shape & | alpha, | ||
const T_inv_scale & | beta | ||
) |
Definition at line 34 of file neg_binomial_ccdf_log.hpp.
return_type<T_shape, T_inv_scale>::type stan::math::neg_binomial_cdf | ( | const T_n & | n, |
const T_shape & | alpha, | ||
const T_inv_scale & | beta | ||
) |
Definition at line 29 of file neg_binomial_cdf.hpp.
return_type<T_shape, T_inv_scale>::type stan::math::neg_binomial_cdf_log | ( | const T_n & | n, |
const T_shape & | alpha, | ||
const T_inv_scale & | beta | ||
) |
Definition at line 34 of file neg_binomial_cdf_log.hpp.
return_type<T_shape, T_inv_scale>::type stan::math::neg_binomial_log | ( | const T_n & | n, |
const T_shape & | alpha, | ||
const T_inv_scale & | beta | ||
) |
Definition at line 39 of file neg_binomial_log.hpp.
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Definition at line 183 of file neg_binomial_log.hpp.
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Definition at line 29 of file neg_binomial_rng.hpp.
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|
inlinestatic |
Definition at line 10 of file nested_size.hpp.
return_type<T_y, T_loc, T_scale>::type stan::math::normal_ccdf_log | ( | const T_y & | y, |
const T_loc & | mu, | ||
const T_scale & | sigma | ||
) |
Definition at line 26 of file normal_ccdf_log.hpp.
return_type<T_y, T_loc, T_scale>::type stan::math::normal_cdf | ( | const T_y & | y, |
const T_loc & | mu, | ||
const T_scale & | sigma | ||
) |
Calculates the normal cumulative distribution function for the given variate, location, and scale.
.
y | A scalar variate. |
mu | The location of the normal distribution. |
sigma | The scale of the normal distriubtion |
T_y | Type of y. |
T_loc | Type of mean parameter. |
T_scale | Type of standard deviation paramater. |
Definition at line 40 of file normal_cdf.hpp.
return_type<T_y, T_loc, T_scale>::type stan::math::normal_cdf_log | ( | const T_y & | y, |
const T_loc & | mu, | ||
const T_scale & | sigma | ||
) |
Definition at line 26 of file normal_cdf_log.hpp.
return_type<T_y, T_loc, T_scale>::type stan::math::normal_log | ( | const T_y & | y, |
const T_loc & | mu, | ||
const T_scale & | sigma | ||
) |
The log of the normal density for the specified scalar(s) given the specified mean(s) and deviation(s).
y, mu, or sigma can each be either a scalar or a vector. Any vector inputs must be the same length.
The result log probability is defined to be the sum of the log probabilities for each observation/mean/deviation triple.
y | (Sequence of) scalar(s). |
mu | (Sequence of) location parameter(s) for the normal distribution. |
sigma | (Sequence of) scale parameters for the normal distribution. |
std::domain_error | if the scale is not positive. |
T_y | Underlying type of scalar in sequence. |
T_loc | Type of location parameter. |
Definition at line 45 of file normal_log.hpp.
|
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Definition at line 138 of file normal_log.hpp.
|
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Definition at line 19 of file normal_rng.hpp.
|
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Return (quiet) not-a-number.
Definition at line 141 of file constants.hpp.
|
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Returns 1, the number of elements in a primitive type.
x | Argument of primitive type. |
Definition at line 19 of file num_elements.hpp.
|
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Returns the size of the specified matrix.
m | argument matrix |
Definition at line 31 of file num_elements.hpp.
|
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Returns the number of elements in the specified vector.
This assumes it is not ragged and that each of its contained elements has the same number of elements.
v | argument vector |
Definition at line 45 of file num_elements.hpp.
|
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Prefix logical negation for the value of variables (C++).
The expression (!a) is equivalent to negating the scalar value of the variable a.
Note that this is the only logical operator defined for variables. Overridden logical conjunction (&&) and disjunction (||) operators do not apply the same "short circuit" rules as the built-in logical operators.
a | Variable to negate. |
Definition at line 31 of file operator_unary_not.hpp.
|
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Definition at line 14 of file operator_not_equal.hpp.
|
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Definition at line 21 of file operator_not_equal.hpp.
|
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Inequality operator comparing two variables' values (C++).
a | First variable. |
b | Second variable. |
Definition at line 26 of file operator_not_equal.hpp.
|
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Definition at line 28 of file operator_not_equal.hpp.
|
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Inequality operator comparing a variable's value and a double (C++).
a | First variable. |
b | Second value. |
Definition at line 39 of file operator_not_equal.hpp.
|
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Inequality operator comparing a double and a variable's value (C++).
a | First value. |
b | Second variable. |
Definition at line 52 of file operator_not_equal.hpp.
|
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Definition at line 14 of file operator_multiplication.hpp.
Definition at line 22 of file operator_multiplication.hpp.
Definition at line 29 of file operator_multiplication.hpp.
Multiplication operator for two variables (C++).
The partial derivatives are
, and
.
a | First variable operand. |
b | Second variable operand. |
Definition at line 83 of file operator_multiplication.hpp.
Multiplication operator for a variable and a scalar (C++).
The partial derivative for the variable is
, and
a | Variable operand. |
b | Scalar operand. |
Definition at line 98 of file operator_multiplication.hpp.
Multiplication operator for a scalar and a variable (C++).
The partial derivative for the variable is
.
a | Scalar operand. |
b | Variable operand. |
Definition at line 115 of file operator_multiplication.hpp.
|
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Definition at line 13 of file operator_addition.hpp.
|
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Definition at line 20 of file operator_addition.hpp.
|
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Definition at line 27 of file operator_addition.hpp.
Unary plus operator for variables (C++).
The function simply returns its input, because
.
The effect of unary plus on a built-in C++ scalar type is integer promotion. Because variables are all double-precision floating point already, promotion is not necessary.
a | Argument variable. |
Definition at line 43 of file operator_unary_plus.hpp.
Addition operator for variables (C++).
The partial derivatives are defined by
, and
.
a | First variable operand. |
b | Second variable operand. |
Definition at line 84 of file operator_addition.hpp.
Addition operator for variable and scalar (C++).
The derivative with respect to the variable is
.
a | First variable operand. |
b | Second scalar operand. |
Definition at line 99 of file operator_addition.hpp.
Addition operator for scalar and variable (C++).
The derivative with respect to the variable is
.
a | First scalar operand. |
b | Second variable operand. |
Definition at line 116 of file operator_addition.hpp.
Prefix increment operator for variables (C++).
Following C++, (++a) is defined to behave exactly as (a = a + 1.0) does, but is faster and uses less memory. In particular, the result is an assignable lvalue.
a | Variable to increment. |
Definition at line 36 of file operator_unary_increment.hpp.
Postfix increment operator for variables (C++).
Following C++, the expression (a++)
is defined to behave like the sequence of operations
var temp = a; a = a + 1.0; return temp;
a | Variable to increment. |
Definition at line 52 of file operator_unary_increment.hpp.
|
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Definition at line 14 of file operator_subtraction.hpp.
Definition at line 14 of file operator_unary_minus.hpp.
|
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Definition at line 21 of file operator_subtraction.hpp.
|
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Definition at line 28 of file operator_subtraction.hpp.
Unary negation operator for variables (C++).
.
a | Argument variable. |
Definition at line 51 of file operator_unary_negative.hpp.
Subtraction operator for variables (C++).
The partial derivatives are defined by
, and
.
a | First variable operand. |
b | Second variable operand. |
Definition at line 99 of file operator_subtraction.hpp.
Subtraction operator for variable and scalar (C++).
The derivative for the variable is
, and
a | First variable operand. |
b | Second scalar operand. |
Definition at line 114 of file operator_subtraction.hpp.
Subtraction operator for scalar and variable (C++).
The derivative for the variable is
, and
a | First scalar operand. |
b | Second variable operand. |
Definition at line 131 of file operator_subtraction.hpp.
Prefix decrement operator for variables (C++).
Following C++, (–a)
is defined to behave exactly as
a = a - 1.0)
does, but is faster and uses less memory. In particular, the result is an assignable lvalue.
a | Variable to decrement. |
Definition at line 40 of file operator_unary_decrement.hpp.
Postfix decrement operator for variables (C++).
Following C++, the expression (a–)
is defined to behave like the sequence of operations
var temp = a; a = a - 1.0; return temp;
a | Variable to decrement. |
Definition at line 56 of file operator_unary_decrement.hpp.
|
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Definition at line 14 of file operator_division.hpp.
|
inline |
Definition at line 22 of file operator_division.hpp.
|
inline |
Definition at line 30 of file operator_division.hpp.
|
inline |
Definition at line 51 of file divide.hpp.
|
inline |
Definition at line 57 of file divide.hpp.
|
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Definition at line 63 of file divide.hpp.
Division operator for two variables (C++).
The partial derivatives for the variables are
, and
.
a | First variable operand. |
b | Second variable operand. |
Definition at line 96 of file operator_division.hpp.
Division operator for dividing a variable by a scalar (C++).
The derivative with respect to the variable is
.
a | Variable operand. |
b | Scalar operand. |
Definition at line 111 of file operator_division.hpp.
Division operator for dividing a scalar by a variable (C++).
The derivative with respect to the variable is
.
a | Scalar operand. |
b | Variable operand. |
Definition at line 128 of file operator_division.hpp.
|
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Definition at line 12 of file operator_less_than.hpp.
|
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Definition at line 18 of file operator_less_than.hpp.
|
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Definition at line 24 of file operator_less_than.hpp.
Less than operator comparing variables' values (C++).
a | First variable. |
b | Second variable. |
Definition at line 24 of file operator_less_than.hpp.
|
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Less than operator comparing variable's value and a double (C++).
a | First variable. |
b | Second value. |
Definition at line 36 of file operator_less_than.hpp.
|
inline |
Less than operator comparing a double and variable's value (C++).
a | First value. |
b | Second variable. |
Definition at line 48 of file operator_less_than.hpp.
|
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Definition at line 14 of file operator_less_than_or_equal.hpp.
|
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Definition at line 21 of file operator_less_than_or_equal.hpp.
Less than or equal operator comparing two variables' values (C++).
a | First variable. |
b | Second variable. |
Definition at line 26 of file operator_less_than_or_equal.hpp.
|
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Definition at line 28 of file operator_less_than_or_equal.hpp.
|
inline |
Less than or equal operator comparing a variable's value and a scalar (C++).
a | First variable. |
b | Second value. |
Definition at line 39 of file operator_less_than_or_equal.hpp.
|
inline |
Less than or equal operator comparing a double and variable's value (C++).
a | First value. |
b | Second variable. |
Definition at line 52 of file operator_less_than_or_equal.hpp.
|
inline |
Definition at line 14 of file operator_equal.hpp.
|
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Definition at line 21 of file operator_equal.hpp.
Equality operator comparing two variables' values (C++).
a | First variable. |
b | Second variable. |
Definition at line 26 of file operator_equal.hpp.
|
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Definition at line 28 of file operator_equal.hpp.
|
inline |
Equality operator comparing a variable's value and a double (C++).
a | First variable. |
b | Second value. |
Definition at line 39 of file operator_equal.hpp.
|
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Equality operator comparing a scalar and a variable's value (C++).
a | First scalar. |
b | Second variable. |
Definition at line 51 of file operator_equal.hpp.
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Definition at line 14 of file operator_greater_than.hpp.
|
inline |
Definition at line 21 of file operator_greater_than.hpp.
Greater than operator comparing variables' values (C++).
a | First variable. |
b | Second variable. |
Definition at line 25 of file operator_greater_than.hpp.
|
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Definition at line 28 of file operator_greater_than.hpp.
|
inline |
Greater than operator comparing variable's value and double (C++).
a | First variable. |
b | Second value. |
Definition at line 37 of file operator_greater_than.hpp.
|
inline |
Greater than operator comparing a double and a variable's value (C++).
a | First value. |
b | Second variable. |
Definition at line 49 of file operator_greater_than.hpp.
|
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Definition at line 14 of file operator_greater_than_or_equal.hpp.
|
inline |
Definition at line 21 of file operator_greater_than_or_equal.hpp.
Greater than or equal operator comparing two variables' values (C++).
a | First variable. |
b | Second variable. |
Definition at line 27 of file operator_greater_than_or_equal.hpp.
|
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Definition at line 28 of file operator_greater_than_or_equal.hpp.
|
inline |
Greater than or equal operator comparing variable's value and double (C++).
a | First variable. |
b | Second value. |
Definition at line 40 of file operator_greater_than_or_equal.hpp.
|
inline |
Greater than or equal operator comparing double and variable's value (C++).
a | First value. |
b | Second variable. |
Definition at line 53 of file operator_greater_than_or_equal.hpp.
Eigen::Matrix<T, Eigen::Dynamic, 1> stan::math::ordered_constrain | ( | const Eigen::Matrix< T, Eigen::Dynamic, 1 > & | x | ) |
Return an increasing ordered vector derived from the specified free vector.
The returned constrained vector will have the same dimensionality as the specified free vector.
x | Free vector of scalars. |
T | Type of scalar. |
Definition at line 23 of file ordered_constrain.hpp.
|
inline |
Return a positive valued, increasing ordered vector derived from the specified free vector and increment the specified log probability reference with the log absolute Jacobian determinant of the transform.
The returned constrained vector will have the same dimensionality as the specified free vector.
x | Free vector of scalars. |
lp | Log probability reference. |
T | Type of scalar. |
Definition at line 56 of file ordered_constrain.hpp.
Eigen::Matrix<T, Eigen::Dynamic, 1> stan::math::ordered_free | ( | const Eigen::Matrix< T, Eigen::Dynamic, 1 > & | y | ) |
Return the vector of unconstrained scalars that transform to the specified positive ordered vector.
This function inverts the constraining operation defined in ordered_constrain(Matrix)
,
y | Vector of positive, ordered scalars. |
T | Type of scalar. |
std::domain_error | if y is not a vector of positive, ordered scalars. |
Definition at line 26 of file ordered_free.hpp.
boost::math::tools::promote_args<T_lambda, T_cut>::type stan::math::ordered_logistic_log | ( | int | y, |
const T_lambda & | lambda, | ||
const Eigen::Matrix< T_cut, Eigen::Dynamic, 1 > & | c | ||
) |
Returns the (natural) log probability of the specified integer outcome given the continuous location and specified cutpoints in an ordered logistic model.
Typically the continous location will be the dot product of a vector of regression coefficients and a vector of predictors for the outcome.
propto | True if calculating up to a proportion. |
T_loc | Location type. |
T_cut | Cut-point type. |
y | Outcome. |
lambda | Location. |
c | Positive increasing vector of cutpoints. |
std::domain_error | If the outcome is not between 1 and the number of cutpoints plus 2; if the cutpoint vector is empty; if the cutpoint vector contains a non-positive, non-finite value; or if the cutpoint vector is not sorted in ascending order. |
Definition at line 61 of file ordered_logistic_log.hpp.
boost::math::tools::promote_args<T_lambda, T_cut>::type stan::math::ordered_logistic_log | ( | int | y, |
const T_lambda & | lambda, | ||
const Eigen::Matrix< T_cut, Eigen::Dynamic, 1 > & | c | ||
) |
Definition at line 107 of file ordered_logistic_log.hpp.
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Definition at line 24 of file ordered_logistic_rng.hpp.
|
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Throw an out_of_range exception with a consistently formatted message.
This is an abstraction for all Stan functions to use when throwing out of range. This will allow us to change the behavior for all functions at once.
The message is: "<function>: index <index> out of range; expecting index to be between " "1 and <max><msg1><msg2>"
function | Name of the function |
max | Max |
index | Index |
msg1 | Message to print. Default is "". |
msg2 | Message to print. Default is "". |
Definition at line 30 of file out_of_range.hpp.
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Definition at line 14 of file owens_t.hpp.
Definition at line 34 of file owens_t.hpp.
Definition at line 48 of file owens_t.hpp.
|
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The Owen's T function of h and a.
Used to compute the cumulative density function for the skew normal distribution.
T1 | Type of first argument. |
T2 | Type of second argument. |
h | First argument |
a | Second argument |
Definition at line 62 of file owens_t.hpp.
The Owen's T function of h and a.
Used to compute the cumulative density function for the skew normal distribution.
h | var parameter. |
a | var parameter. |
Definition at line 71 of file owens_t.hpp.
The Owen's T function of h and a.
Used to compute the cumulative density function for the skew normal distribution.
h | var parameter. |
a | double parameter. |
Definition at line 85 of file owens_t.hpp.
The Owen's T function of h and a.
Used to compute the cumulative density function for the skew normal distribution.
h | double parameter. |
a | var parameter. |
Definition at line 99 of file owens_t.hpp.
return_type<T_y, T_scale, T_shape>::type stan::math::pareto_ccdf_log | ( | const T_y & | y, |
const T_scale & | y_min, | ||
const T_shape & | alpha | ||
) |
Definition at line 25 of file pareto_ccdf_log.hpp.
return_type<T_y, T_scale, T_shape>::type stan::math::pareto_cdf | ( | const T_y & | y, |
const T_scale & | y_min, | ||
const T_shape & | alpha | ||
) |
Definition at line 26 of file pareto_cdf.hpp.
return_type<T_y, T_scale, T_shape>::type stan::math::pareto_cdf_log | ( | const T_y & | y, |
const T_scale & | y_min, | ||
const T_shape & | alpha | ||
) |
Definition at line 25 of file pareto_cdf_log.hpp.
return_type<T_y, T_scale, T_shape>::type stan::math::pareto_log | ( | const T_y & | y, |
const T_scale & | y_min, | ||
const T_shape & | alpha | ||
) |
Definition at line 29 of file pareto_log.hpp.
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Definition at line 132 of file pareto_log.hpp.
|
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Definition at line 21 of file pareto_rng.hpp.
return_type<T_y, T_loc, T_scale, T_shape>::type stan::math::pareto_type_2_ccdf_log | ( | const T_y & | y, |
const T_loc & | mu, | ||
const T_scale & | lambda, | ||
const T_shape & | alpha | ||
) |
Definition at line 26 of file pareto_type_2_ccdf_log.hpp.
return_type<T_y, T_loc, T_scale, T_shape>::type stan::math::pareto_type_2_cdf | ( | const T_y & | y, |
const T_loc & | mu, | ||
const T_scale & | lambda, | ||
const T_shape & | alpha | ||
) |
Definition at line 27 of file pareto_type_2_cdf.hpp.
return_type<T_y, T_loc, T_scale, T_shape>::type stan::math::pareto_type_2_cdf_log | ( | const T_y & | y, |
const T_loc & | mu, | ||
const T_scale & | lambda, | ||
const T_shape & | alpha | ||
) |
Definition at line 27 of file pareto_type_2_cdf_log.hpp.
return_type<T_y, T_loc, T_scale, T_shape>::type stan::math::pareto_type_2_log | ( | const T_y & | y, |
const T_loc & | mu, | ||
const T_scale & | lambda, | ||
const T_shape & | alpha | ||
) |
Definition at line 30 of file pareto_type_2_log.hpp.
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Definition at line 149 of file pareto_type_2_log.hpp.
|
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Definition at line 22 of file pareto_type_2_rng.hpp.
void stan::math::partial_derivative | ( | const F & | f, |
const Eigen::Matrix< T, Eigen::Dynamic, 1 > & | x, | ||
int | n, | ||
T & | fx, | ||
T & | dfx_dxn | ||
) |
Return the partial derivative of the specified multiivariate function at the specified argument.
T | Argument type |
F | Function type |
f | Function | |
[in] | x | Argument vector |
[in] | n | Index of argument with which to take derivative |
[out] | fx | Value of function applied to argument |
[out] | dfx_dxn | Value of partial derivative |
Definition at line 27 of file partial_derivative.hpp.
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The unit normal cumulative distribution function.
The return value for a specified input is the probability that a random unit normal variate is less than or equal to the specified value, defined by
This function can be used to implement the inverse link function for probit regression.
Phi will underflow to 0 below -37.5 and overflow to 1 above 8
x | Argument. |
|
inline |
|
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The unit normal cumulative density function for variables (stan).
See stan::math::Phi() for the double-based version.
The derivative is the unit normal density function,
.
a | Variable argument. |
|
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Approximation of the unit normal CDF.
http://www.jiem.org/index.php/jiem/article/download/60/27
This function can be used to implement the inverse link function for probit regression.
x | Argument. |
Definition at line 23 of file Phi_approx.hpp.
|
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Approximation of the unit normal CDF for variables (stan).
http://www.jiem.org/index.php/jiem/article/download/60/27
a | Variable argument. |
Definition at line 47 of file Phi_approx.hpp.
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return_type<T_rate>::type stan::math::poisson_ccdf_log | ( | const T_n & | n, |
const T_rate & | lambda | ||
) |
Definition at line 27 of file poisson_ccdf_log.hpp.
return_type<T_rate>::type stan::math::poisson_cdf | ( | const T_n & | n, |
const T_rate & | lambda | ||
) |
Definition at line 28 of file poisson_cdf.hpp.
return_type<T_rate>::type stan::math::poisson_cdf_log | ( | const T_n & | n, |
const T_rate & | lambda | ||
) |
Definition at line 27 of file poisson_cdf_log.hpp.
return_type<T_rate>::type stan::math::poisson_log | ( | const T_n & | n, |
const T_rate & | lambda | ||
) |
Definition at line 29 of file poisson_log.hpp.
|
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Definition at line 101 of file poisson_log.hpp.
return_type<T_log_rate>::type stan::math::poisson_log_log | ( | const T_n & | n, |
const T_log_rate & | alpha | ||
) |
Definition at line 32 of file poisson_log_log.hpp.
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Definition at line 112 of file poisson_log_log.hpp.
|
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Definition at line 23 of file poisson_log_rng.hpp.
|
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Definition at line 24 of file poisson_rng.hpp.
|
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Return the positive value for the specified unconstrained input.
The transform applied is
.
x | Arbitrary input scalar. |
Definition at line 22 of file positive_constrain.hpp.
|
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Return the positive value for the specified unconstrained input, incrementing the scalar reference with the log absolute Jacobian determinant.
See positive_constrain(T)
for details of the transform. The log absolute Jacobian determinant is
.
x | Arbitrary input scalar. |
lp | Log probability reference. |
T | Type of scalar. |
Definition at line 44 of file positive_constrain.hpp.
|
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Return the unconstrained value corresponding to the specified positive-constrained value.
The transform is the inverse of the transform applied by
positive_constrain(T)
, namely
.
The input is validated using stan::math::check_positive()
.
y | Input scalar. |
T | Type of scalar. |
std::domain_error | if the variable is negative. |
Definition at line 29 of file positive_free.hpp.
|
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Eigen::Matrix<T, Eigen::Dynamic, 1> stan::math::positive_ordered_constrain | ( | const Eigen::Matrix< T, Eigen::Dynamic, 1 > & | x | ) |
Return an increasing positive ordered vector derived from the specified free vector.
The returned constrained vector will have the same dimensionality as the specified free vector.
x | Free vector of scalars. |
T | Type of scalar. |
Definition at line 23 of file positive_ordered_constrain.hpp.
|
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Return a positive valued, increasing positive ordered vector derived from the specified free vector and increment the specified log probability reference with the log absolute Jacobian determinant of the transform.
The returned constrained vector will have the same dimensionality as the specified free vector.
x | Free vector of scalars. |
lp | Log probability reference. |
T | Type of scalar. |
Definition at line 55 of file positive_ordered_constrain.hpp.
Eigen::Matrix<T, Eigen::Dynamic, 1> stan::math::positive_ordered_free | ( | const Eigen::Matrix< T, Eigen::Dynamic, 1 > & | y | ) |
Return the vector of unconstrained scalars that transform to the specified positive ordered vector.
This function inverts the constraining operation defined in positive_ordered_constrain(Matrix)
,
y | Vector of positive, ordered scalars. |
T | Type of scalar. |
std::domain_error | if y is not a vector of positive, ordered scalars. |
Definition at line 26 of file positive_ordered_free.hpp.
|
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This function returns a var for an expression that has the specified value, vector of operands, and vector of partial derivatives of value with respect to the operands.
[in] | value | The value of the resulting dependent variable. |
[in] | operands | operands. |
[in] | gradients | vector of partial derivatives of result with respect to operands. |
Definition at line 98 of file precomputed_gradients.hpp.
|
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Return the primitive double value for the specified auto-diff variable.
v | input variable. |
Definition at line 17 of file primitive_value.hpp.
|
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Return the primitive value of the specified forward-mode autodiff variable.
This function applies recursively to higher-order autodiff types to return a primitive double value.
T | scalar type for autodiff variable. |
v | input variable. |
Definition at line 22 of file primitive_value.hpp.
|
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Return the value of the specified arithmetic argument unmodified with its own declared type.
This template function can only be instantiated with arithmetic types as defined by Boost's is_arithmetic
trait metaprogram.
This function differs from stan::math::value_of
in that it does not cast all return types to double
.
T | type of arithmetic input. |
x | input. |
Definition at line 30 of file primitive_value.hpp.
|
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Return the primitive value of the specified argument.
This implementation only applies to non-arithmetic types as defined by Boost's is_arithmetic
trait metaprogram.
T | type of non-arithmetic input. |
x | input. |
Definition at line 47 of file primitive_value.hpp.
|
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Helper function to return the matrix size as either "dynamic" or "1".
n | Eigen matrix size specification. |
o | Output stream. |
Definition at line 26 of file assign.hpp.
|
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Prints the auto-dif variable stack.
This function is used for debugging purposes.
Only works if all members of stack are vari* as it casts to vari*.
o | ostream to modify |
Definition at line 20 of file print_stack.hpp.
|
inline |
Return a probability value constrained to fall between 0 and 1 (inclusive) for the specified free scalar.
The transform is the inverse logit,
.
x | Free scalar. |
T | Type of scalar. |
Definition at line 27 of file prob_constrain.hpp.
|
inline |
Return a probability value constrained to fall between 0 and 1 (inclusive) for the specified free scalar and increment the specified log probability reference with the log absolute Jacobian determinant of the transform.
The transform is as defined for prob_constrain(T)
. The log absolute Jacobian determinant is
The log absolute Jacobian determinant is
.
x | Free scalar. |
lp | Log probability reference. |
T | Type of scalar. |
Definition at line 55 of file prob_constrain.hpp.
|
inline |
Return the free scalar that when transformed to a probability produces the specified scalar.
The function that reverses the constraining transform specified in prob_constrain(T)
is the logit function,
.
y | Scalar input. |
T | Type of scalar. |
std::domain_error | if y is less than 0 or greater than 1. |
Definition at line 27 of file prob_free.hpp.
|
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|
inline |
|
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Definition at line 14 of file promote_common.hpp.
promote_scalar_type<T, S>::type stan::math::promote_scalar | ( | const S & | x | ) |
This is the top-level function to call to promote the scalar types of an input of type S to type T.
T | scalar type of output. |
S | input type. |
x | input vector. |
Definition at line 67 of file promote_scalar.hpp.
Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic> stan::math::qr_Q | ( | const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > & | m | ) |
Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic> stan::math::qr_R | ( | const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > & | m | ) |
|
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Compute B^T A B.
Definition at line 21 of file quad_form.hpp.
|
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Definition at line 33 of file quad_form.hpp.
|
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Definition at line 124 of file quad_form.hpp.
|
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Definition at line 141 of file quad_form.hpp.
|
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Definition at line 17 of file quad_form_diag.hpp.
|
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Definition at line 14 of file quad_form_sym.hpp.
|
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Definition at line 19 of file quad_form_sym.hpp.
|
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Definition at line 25 of file quad_form_sym.hpp.
|
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Definition at line 28 of file quad_form_sym.hpp.
|
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Definition at line 34 of file quad_form_sym.hpp.
|
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Definition at line 39 of file quad_form_sym.hpp.
|
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Definition at line 43 of file quad_form_sym.hpp.
|
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Definition at line 53 of file quad_form_sym.hpp.
|
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|
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return_type<T_y, T_scale>::type stan::math::rayleigh_ccdf_log | ( | const T_y & | y, |
const T_scale & | sigma | ||
) |
Definition at line 27 of file rayleigh_ccdf_log.hpp.
return_type<T_y, T_scale>::type stan::math::rayleigh_cdf | ( | const T_y & | y, |
const T_scale & | sigma | ||
) |
Definition at line 28 of file rayleigh_cdf.hpp.
return_type<T_y, T_scale>::type stan::math::rayleigh_cdf_log | ( | const T_y & | y, |
const T_scale & | sigma | ||
) |
Definition at line 28 of file rayleigh_cdf_log.hpp.
return_type<T_y, T_scale>::type stan::math::rayleigh_log | ( | const T_y & | y, |
const T_scale & | sigma | ||
) |
Definition at line 29 of file rayleigh_log.hpp.
|
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Definition at line 109 of file rayleigh_log.hpp.
|
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Definition at line 24 of file rayleigh_rng.hpp.
Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic> stan::math::read_corr_L | ( | const Eigen::Array< T, Eigen::Dynamic, 1 > & | CPCs, |
const size_t | K | ||
) |
Return the Cholesky factor of the correlation matrix of the specified dimensionality corresponding to the specified canonical partial correlations.
It is generally better to work with the Cholesky factor rather than the correlation matrix itself when the determinant, inverse, etc. of the correlation matrix is needed for some statistical calculation.
See read_corr_matrix(Array, size_t, T)
for more information.
CPCs | The (K choose 2) canonical partial correlations in (-1, 1). |
K | Dimensionality of correlation matrix. |
T | Type of underlying scalar. |
Definition at line 41 of file read_corr_L.hpp.
Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic> stan::math::read_corr_L | ( | const Eigen::Array< T, Eigen::Dynamic, 1 > & | CPCs, |
const size_t | K, | ||
T & | log_prob | ||
) |
Return the Cholesky factor of the correlation matrix of the specified dimensionality corresponding to the specified canonical partial correlations, incrementing the specified scalar reference with the log absolute determinant of the Jacobian of the transformation.
The implementation is Ben Goodrich's Cholesky factor-based approach to the C-vine method of:
CPCs | The (K choose 2) canonical partial correlations in (-1, 1). |
K | Dimensionality of correlation matrix. |
log_prob | Reference to variable to increment with the log Jacobian determinant. |
T | Type of underlying scalar. |
Definition at line 95 of file read_corr_L.hpp.
Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic> stan::math::read_corr_matrix | ( | const Eigen::Array< T, Eigen::Dynamic, 1 > & | CPCs, |
const size_t | K | ||
) |
Return the correlation matrix of the specified dimensionality corresponding to the specified canonical partial correlations.
See read_corr_matrix(Array, size_t, T)
for more information.
CPCs | The (K choose 2) canonical partial correlations in (-1, 1). |
K | Dimensionality of correlation matrix. |
T | Type of underlying scalar. |
Definition at line 28 of file read_corr_matrix.hpp.
Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic> stan::math::read_corr_matrix | ( | const Eigen::Array< T, Eigen::Dynamic, 1 > & | CPCs, |
const size_t | K, | ||
T & | log_prob | ||
) |
Return the correlation matrix of the specified dimensionality corresponding to the specified canonical partial correlations, incrementing the specified scalar reference with the log absolute determinant of the Jacobian of the transformation.
It is usually preferable to utilize the version that returns the Cholesky factor of the correlation matrix rather than the correlation matrix itself in statistical calculations.
CPCs | The (K choose 2) canonical partial correlations in (-1, 1). |
K | Dimensionality of correlation matrix. |
log_prob | Reference to variable to increment with the log Jacobian determinant. |
T | Type of underlying scalar. |
Definition at line 56 of file read_corr_matrix.hpp.
Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic> stan::math::read_cov_L | ( | const Eigen::Array< T, Eigen::Dynamic, 1 > & | CPCs, |
const Eigen::Array< T, Eigen::Dynamic, 1 > & | sds, | ||
T & | log_prob | ||
) |
This is the function that should be called prior to evaluating the density of any elliptical distribution.
CPCs | on (-1, 1) |
sds | on (0, inf) |
log_prob | the log probability value to increment with the Jacobian |
Definition at line 23 of file read_cov_L.hpp.
Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic> stan::math::read_cov_matrix | ( | const Eigen::Array< T, Eigen::Dynamic, 1 > & | CPCs, |
const Eigen::Array< T, Eigen::Dynamic, 1 > & | sds, | ||
T & | log_prob | ||
) |
A generally worse alternative to call prior to evaluating the density of an elliptical distribution.
CPCs | on (-1, 1) |
sds | on (0, inf) |
log_prob | the log probability value to increment with the Jacobian |
Definition at line 23 of file read_cov_matrix.hpp.
Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic> stan::math::read_cov_matrix | ( | const Eigen::Array< T, Eigen::Dynamic, 1 > & | CPCs, |
const Eigen::Array< T, Eigen::Dynamic, 1 > & | sds | ||
) |
Builds a covariance matrix from CPCs and standard deviations.
CPCs | in (-1, 1) |
sds | in (0, inf) |
Definition at line 41 of file read_cov_matrix.hpp.
|
inlinestatic |
Recover memory used for all variables for reuse.
std::logic_error | if empty_nested() returns false |
Definition at line 18 of file recover_memory.hpp.
|
inlinestatic |
Recover only the memory used for the top nested call.
If there is nothing on the nested stack, then a std::logic_error
exception is thrown.
std::logic_error | if empty_nested() returns true |
Definition at line 20 of file recover_memory_nested.hpp.
|
inline |
Definition at line 13 of file rep_array.hpp.
|
inline |
Definition at line 21 of file rep_array.hpp.
|
inline |
Definition at line 31 of file rep_array.hpp.
|
inline |
Definition at line 16 of file rep_matrix.hpp.
|
inline |
Definition at line 26 of file rep_matrix.hpp.
|
inline |
Definition at line 36 of file rep_matrix.hpp.
|
inline |
Definition at line 15 of file rep_row_vector.hpp.
|
inline |
Definition at line 16 of file rep_vector.hpp.
|
inline |
Recursively resize the specified vector of vectors, which must bottom out at scalar values, Eigen vectors or Eigen matrices.
x | Array-like object to resize. |
dims | New dimensions. |
T | Type of object being resized. |
Definition at line 63 of file resize.hpp.
|
inline |
Definition at line 16 of file rising_factorial.hpp.
|
inline |
Definition at line 28 of file rising_factorial.hpp.
|
inline |
Definition at line 41 of file rising_factorial.hpp.
|
inline |
Definition at line 54 of file rising_factorial.hpp.
Definition at line 59 of file rising_factorial.hpp.
Definition at line 64 of file rising_factorial.hpp.
|
inline |
Returns the rounded form of the specified variable (C99).
See round() for the double-based version.
The derivative is zero everywhere but numbers half way between whole numbers, so for convenience the derivative is defined to be everywhere zero,
.
a | Specified variable. |
|
inline |
Return the specified row of the specified matrix, using start-at-1 indexing.
This is equivalent to calling m.row(i - 1)
and assigning the resulting template expression to a row vector.
T | Scalar value type for matrix. |
m | Matrix. |
i | Row index (count from 1). |
|
inline |
|
inline |
Definition at line 18 of file rows_dot_product.hpp.
|
inline |
Returns the dot product of the specified vectors.
v1 | First vector. |
v2 | Second vector. |
std::domain_error | If the vectors are not the same size or if they are both not vector dimensioned. |
Definition at line 22 of file rows_dot_product.hpp.
|
inline |
Definition at line 25 of file rows_dot_product.hpp.
|
inline |
Definition at line 35 of file rows_dot_product.hpp.
|
inline |
Definition at line 52 of file rows_dot_product.hpp.
|
inline |
Definition at line 15 of file rows_dot_self.hpp.
|
inline |
Returns the dot product of each row of a matrix with itself.
x | Matrix. |
T | scalar type |
Definition at line 16 of file rows_dot_self.hpp.
|
inline |
Definition at line 11 of file scaled_add.hpp.
return_type<T_y, T_dof, T_scale>::type stan::math::scaled_inv_chi_square_ccdf_log | ( | const T_y & | y, |
const T_dof & | nu, | ||
const T_scale & | s | ||
) |
Definition at line 33 of file scaled_inv_chi_square_ccdf_log.hpp.
return_type<T_y, T_dof, T_scale>::type stan::math::scaled_inv_chi_square_cdf | ( | const T_y & | y, |
const T_dof & | nu, | ||
const T_scale & | s | ||
) |
The CDF of a scaled inverse chi-squared density for y with the specified degrees of freedom parameter and scale parameter.
y | A scalar variable. |
nu | Degrees of freedom. |
s | Scale parameter. |
std::domain_error | if nu is not greater than 0 |
std::domain_error | if s is not greater than 0. |
std::domain_error | if y is not greater than 0. |
T_y | Type of scalar. |
T_dof | Type of degrees of freedom. |
Definition at line 48 of file scaled_inv_chi_square_cdf.hpp.
return_type<T_y, T_dof, T_scale>::type stan::math::scaled_inv_chi_square_cdf_log | ( | const T_y & | y, |
const T_dof & | nu, | ||
const T_scale & | s | ||
) |
Definition at line 34 of file scaled_inv_chi_square_cdf_log.hpp.
return_type<T_y, T_dof, T_scale>::type stan::math::scaled_inv_chi_square_log | ( | const T_y & | y, |
const T_dof & | nu, | ||
const T_scale & | s | ||
) |
The log of a scaled inverse chi-squared density for y with the specified degrees of freedom parameter and scale parameter.
y | A scalar variable. |
nu | Degrees of freedom. |
s | Scale parameter. |
std::domain_error | if nu is not greater than 0 |
std::domain_error | if s is not greater than 0. |
std::domain_error | if y is not greater than 0. |
T_y | Type of scalar. |
T_dof | Type of degrees of freedom. |
Definition at line 53 of file scaled_inv_chi_square_log.hpp.
|
inline |
Definition at line 175 of file scaled_inv_chi_square_log.hpp.
|
inline |
Definition at line 28 of file scaled_inv_chi_square_rng.hpp.
|
inline |
|
inline |
|
inline |
Return the specified number of elements as a vector starting from the specified element - 1 of the specified vector.
Definition at line 19 of file segment.hpp.
|
inline |
Definition at line 35 of file segment.hpp.
std::vector<T> stan::math::segment | ( | const std::vector< T > & | sv, |
size_t | i, | ||
size_t | n | ||
) |
Definition at line 52 of file segment.hpp.
|
static |
Reset all adjoint values in the stack to zero.
Definition at line 14 of file set_zero_all_adjoints.hpp.
|
static |
Reset all adjoint values in the top nested portion of the stack to zero.
Definition at line 17 of file set_zero_all_adjoints_nested.hpp.
|
inline |
Eigen::Matrix<T, Eigen::Dynamic, 1> stan::math::simplex_constrain | ( | const Eigen::Matrix< T, Eigen::Dynamic, 1 > & | y | ) |
Return the simplex corresponding to the specified free vector.
A simplex is a vector containing values greater than or equal to 0 that sum to 1. A vector with (K-1) unconstrained values will produce a simplex of size K.
The transform is based on a centered stick-breaking process.
y | Free vector input of dimensionality K - 1. |
T | Type of scalar. |
Definition at line 30 of file simplex_constrain.hpp.
Eigen::Matrix<T, Eigen::Dynamic, 1> stan::math::simplex_constrain | ( | const Eigen::Matrix< T, Eigen::Dynamic, 1 > & | y, |
T & | lp | ||
) |
Return the simplex corresponding to the specified free vector and increment the specified log probability reference with the log absolute Jacobian determinant of the transform.
The simplex transform is defined through a centered stick-breaking process.
y | Free vector input of dimensionality K - 1. |
lp | Log probability reference to increment. |
T | Type of scalar. |
Definition at line 69 of file simplex_constrain.hpp.
Eigen::Matrix<T, Eigen::Dynamic, 1> stan::math::simplex_free | ( | const Eigen::Matrix< T, Eigen::Dynamic, 1 > & | x | ) |
Return an unconstrained vector that when transformed produces the specified simplex.
It applies to a simplex of dimensionality K and produces an unconstrained vector of dimensionality (K-1).
The simplex transform is defined through a centered stick-breaking process.
x | Simplex of dimensionality K. |
T | Type of scalar. |
std::domain_error | if x is not a valid simplex |
Definition at line 30 of file simplex_free.hpp.
|
inline |
Eigen::Matrix<T, Eigen::Dynamic, 1> stan::math::singular_values | ( | const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > & | m | ) |
Return the vector of the singular values of the specified matrix in decreasing order of magnitude.
See the documentation for svd()
for information on the signular values.
m | Specified matrix. |
Definition at line 21 of file singular_values.hpp.
|
inline |
|
inline |
return_type<T_y, T_loc, T_scale, T_shape>::type stan::math::skew_normal_ccdf_log | ( | const T_y & | y, |
const T_loc & | mu, | ||
const T_scale & | sigma, | ||
const T_shape & | alpha | ||
) |
Definition at line 27 of file skew_normal_ccdf_log.hpp.
return_type<T_y, T_loc, T_scale, T_shape>::type stan::math::skew_normal_cdf | ( | const T_y & | y, |
const T_loc & | mu, | ||
const T_scale & | sigma, | ||
const T_shape & | alpha | ||
) |
Definition at line 27 of file skew_normal_cdf.hpp.
return_type<T_y, T_loc, T_scale, T_shape>::type stan::math::skew_normal_cdf_log | ( | const T_y & | y, |
const T_loc & | mu, | ||
const T_scale & | sigma, | ||
const T_shape & | alpha | ||
) |
Definition at line 27 of file skew_normal_cdf_log.hpp.
return_type<T_y, T_loc, T_scale, T_shape>::type stan::math::skew_normal_log | ( | const T_y & | y, |
const T_loc & | mu, | ||
const T_scale & | sigma, | ||
const T_shape & | alpha | ||
) |
Definition at line 28 of file skew_normal_log.hpp.
|
inline |
Definition at line 147 of file skew_normal_log.hpp.
|
inline |
Definition at line 22 of file skew_normal_rng.hpp.
|
inline |
Definition at line 14 of file softmax.hpp.
|
inline |
Return the softmax of the specified vector.
The entries in the Jacobian of the softmax function are given by
T | Scalar type of values in vector. |
[in] | v | Vector to transform. |
Definition at line 46 of file softmax.hpp.
|
inline |
Return the softmax of the specified Eigen vector.
Softmax is guaranteed to return a simplex.
The gradient calculations are unfolded.
alpha | Unconstrained input vector. |
std::domain_error | If the input vector is size 0. |
Definition at line 59 of file softmax.hpp.
|
inline |
Definition at line 17 of file sort_asc.hpp.
|
inline |
Return the specified standard vector in ascending order with gradients kept.
xs | Standard vector to order. |
T | Type of elements of the vector. |
Definition at line 21 of file sort_asc.hpp.
|
inline |
Definition at line 25 of file sort_asc.hpp.
|
inline |
Return the specified eigen vector in ascending order with gradients kept.
xs | Eigen vector to order. |
T | Type of elements of the vector. |
Definition at line 35 of file sort_asc.hpp.
|
inline |
|
inline |
Definition at line 17 of file sort_desc.hpp.
Return the specified standard vector in descending order with gradients kept.
xs | Standard vector to order. |
T | Type of elements of the vector. |
Definition at line 21 of file sort_desc.hpp.
|
inline |
Definition at line 25 of file sort_desc.hpp.
|
inline |
|
inline |
Return the specified eigen vector in descending order with gradients kept.
xs | Eigen vector to order. |
T | Type of elements of the vector. |
Definition at line 35 of file sort_desc.hpp.
|
inline |
std::vector<int> stan::math::sort_indices_asc | ( | const C & | xs | ) |
Return a sorted copy of the argument container in ascending order.
C | type of container |
xs | Container to sort |
Definition at line 23 of file sort_indices_asc.hpp.
std::vector<int> stan::math::sort_indices_desc | ( | const C & | xs | ) |
Return a sorted copy of the argument container in ascending order.
C | type of container |
xs | Container to sort |
Definition at line 23 of file sort_indices_desc.hpp.
|
inline |
|
inline |
Return the square root of two.
Definition at line 104 of file constants.hpp.
Definition at line 15 of file square.hpp.
|
inline |
Return the square of the specified argument.
.
The implementation of square(x)
is just x * x
. Given this, this method is mainly useful in cases where x
is not a simple primitive type, particularly when it is an auto-dif type.
x | Input to square. |
Definition at line 20 of file square.hpp.
|
inline |
Vectorized version of square().
x | Container. |
T | Container type. |
Definition at line 32 of file square.hpp.
Return the square of the input variable.
Using square(x)
is more efficient than using x * x
.
x | Variable to square. |
Definition at line 46 of file square.hpp.
|
inline |
Returns the squared distance.
x1 | First vector. |
x2 | Second vector. |
std::domain_error | If the vectors are not the same size or if they are both not vector dimensioned. |
Definition at line 21 of file squared_distance.hpp.
|
inline |
Returns the squared distance between the specified vectors of the same dimensions.
R | Rows at compile time of vector inputs |
C | columns at compile time of vector inputs |
v1 | First vector. |
v2 | Second vector. |
std::domain_error | If the vectors are not the same size or if they are both not vector dimensioned. |
Definition at line 26 of file squared_distance.hpp.
|
inline |
Returns the squared distance between the specified vectors of the same dimensions.
R | Rows at compile time of vector inputs |
C | columns at compile time of vector inputs |
T | Child scalar type of fvar vector input |
v1 | First vector. |
v2 | Second vector. |
std::domain_error | If the vectors are not the same size or if they are both not vector dimensioned. |
Definition at line 30 of file squared_distance.hpp.
|
inline |
Returns the log sum of exponentials.
Definition at line 46 of file squared_distance.hpp.
|
inline |
Returns the squared distance between the specified vectors of the same dimensions.
R1 | Rows at compile time of first vector input |
C1 | Columns at compile time of first vector input |
R2 | Rows at compile time of second vector input |
C2 | Columns at compile time of second vector input |
v1 | First vector. |
v2 | Second vector. |
std::domain_error | If the vectors are not the same size or if they are both not vector dimensioned. |
Definition at line 52 of file squared_distance.hpp.
|
inline |
Returns the log sum of exponentials.
Definition at line 53 of file squared_distance.hpp.
|
inline |
Returns the squared distance between the specified vectors of the same dimensions.
R1 | Rows at compile time of first vector input |
C1 | Columns at compile time of first vector input |
R2 | Rows at compile time of second vector input |
C2 | Columns at compile time of second vector input |
T | Child scalar type of fvar vector input |
v1 | First vector. |
v2 | Second vector. |
std::domain_error | If the vectors are not the same size or if they are both not vector dimensioned. |
Definition at line 59 of file squared_distance.hpp.
|
inline |
Returns the log sum of exponentials.
Definition at line 60 of file squared_distance.hpp.
|
inline |
Returns the squared distance between the specified vectors of the same dimensions.
R | Rows at compile time of vector inputs |
C | columns at compile time of vector inputs |
T | Child scalar type of fvar vector input |
v1 | First vector. |
v2 | Second vector. |
std::domain_error | If the vectors are not the same size or if they are both not vector dimensioned. |
Definition at line 87 of file squared_distance.hpp.
|
inline |
Definition at line 112 of file squared_distance.hpp.
|
inline |
Returns the squared distance between the specified vectors of the same dimensions.
R1 | Rows at compile time of first vector input |
C1 | Columns at compile time of first vector input |
R2 | Rows at compile time of second vector input |
C2 | Columns at compile time of second vector input |
T | Child scalar type of fvar vector input |
v1 | First vector. |
v2 | Second vector. |
std::domain_error | If the vectors are not the same size or if they are both not vector dimensioned. |
Definition at line 116 of file squared_distance.hpp.
|
inline |
Definition at line 122 of file squared_distance.hpp.
|
inline |
Definition at line 132 of file squared_distance.hpp.
|
inline |
Returns the squared distance between the specified vectors of the same dimensions.
R | Rows at compile time of vector inputs |
C | columns at compile time of vector inputs |
T | Child scalar type of fvar vector input |
v1 | First vector. |
v2 | Second vector. |
std::domain_error | If the vectors are not the same size or if they are both not vector dimensioned. |
Definition at line 143 of file squared_distance.hpp.
|
inline |
Returns the squared distance between the specified vectors of the same dimensions.
R1 | Rows at compile time of first vector input |
C1 | Columns at compile time of first vector input |
R2 | Rows at compile time of second vector input |
C2 | Columns at compile time of second vector input |
T | Child scalar type of fvar vector input |
v1 | First vector. |
v2 | Second vector. |
std::domain_error | If the vectors are not the same size or if they are both not vector dimensioned. |
Definition at line 172 of file squared_distance.hpp.
|
inline |
Definition at line 10 of file stan_print.hpp.
void stan::math::stan_print | ( | std::ostream * | o, |
const T & | x | ||
) |
Definition at line 12 of file stan_print.hpp.
void stan::math::stan_print | ( | std::ostream * | o, |
const std::vector< T > & | x | ||
) |
Definition at line 17 of file stan_print.hpp.
void stan::math::stan_print | ( | std::ostream * | o, |
const Eigen::Matrix< T, Eigen::Dynamic, 1 > & | x | ||
) |
Definition at line 27 of file stan_print.hpp.
void stan::math::stan_print | ( | std::ostream * | o, |
const Eigen::Matrix< T, 1, Eigen::Dynamic > & | x | ||
) |
Definition at line 38 of file stan_print.hpp.
void stan::math::stan_print | ( | std::ostream * | o, |
const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > & | x | ||
) |
Definition at line 49 of file stan_print.hpp.
|
inlinestatic |
Record the current position so that recover_memory_nested()
can find it.
Definition at line 13 of file start_nested.hpp.
|
inline |
Return the step, or heaviside, function applied to the specified variable (stan).
See stan::math::step() for the double-based version.
The derivative of the step function is zero everywhere but at 0, so for convenience, it is taken to be everywhere zero,
.
a | Variable argument. |
|
inline |
return_type<T_y, T_dof, T_loc, T_scale>::type stan::math::student_t_ccdf_log | ( | const T_y & | y, |
const T_dof & | nu, | ||
const T_loc & | mu, | ||
const T_scale & | sigma | ||
) |
Definition at line 33 of file student_t_ccdf_log.hpp.
return_type<T_y, T_dof, T_loc, T_scale>::type stan::math::student_t_cdf | ( | const T_y & | y, |
const T_dof & | nu, | ||
const T_loc & | mu, | ||
const T_scale & | sigma | ||
) |
Definition at line 33 of file student_t_cdf.hpp.
return_type<T_y, T_dof, T_loc, T_scale>::type stan::math::student_t_cdf_log | ( | const T_y & | y, |
const T_dof & | nu, | ||
const T_loc & | mu, | ||
const T_scale & | sigma | ||
) |
Definition at line 33 of file student_t_cdf_log.hpp.
return_type<T_y, T_dof, T_loc, T_scale>::type stan::math::student_t_log | ( | const T_y & | y, |
const T_dof & | nu, | ||
const T_loc & | mu, | ||
const T_scale & | sigma | ||
) |
The log of the Student-t density for the given y, nu, mean, and scale parameter.
The scale parameter must be greater than 0.
y | A scalar variable. |
nu | Degrees of freedom. |
mu | The mean of the Student-t distribution. |
sigma | The scale parameter of the Student-t distribution. |
std::domain_error | if sigma is not greater than 0. |
std::domain_error | if nu is not greater than 0. |
T_y | Type of scalar. |
T_dof | Type of degrees of freedom. |
T_loc | Type of location. |
T_scale | Type of scale. |
Definition at line 58 of file student_t_log.hpp.
|
inline |
Definition at line 222 of file student_t_log.hpp.
|
inline |
Definition at line 28 of file student_t_rng.hpp.
|
inline |
|
inline |
Return a nrows x 1 subcolumn starting at (i-1, j-1).
m | Matrix |
i | Starting row + 1 |
j | Starting column + 1 |
nrows | Number of rows in block |
Definition at line 22 of file sub_col.hpp.
|
inline |
Return a 1 x nrows subrow starting at (i-1, j-1).
m | Matrix |
i | Starting row + 1 |
j | Starting column + 1 |
ncols | Number of columns in block |
Definition at line 23 of file sub_row.hpp.
|
inline |
Return the result of subtracting the second specified matrix from the first specified matrix.
The return scalar type is the promotion of the input types.
T1 | Scalar type of first matrix. |
T2 | Scalar type of second matrix. |
R | Row type of matrices. |
C | Column type of matrices. |
m1 | First matrix. |
m2 | Second matrix. |
Definition at line 27 of file subtract.hpp.
|
inline |
Definition at line 43 of file subtract.hpp.
|
inline |
Definition at line 56 of file subtract.hpp.
|
inline |
|
inline |
|
inline |
|
inline |
std::vector<T> stan::math::tail | ( | const std::vector< T > & | sv, |
size_t | n | ||
) |
|
inline |
|
inline |
|
inline |
Definition at line 17 of file tcrossprod.hpp.
Returns the result of post-multiplying a matrix by its own transpose.
M | Matrix to multiply. |
Definition at line 17 of file tcrossprod.hpp.
Returns the result of post-multiplying a matrix by its own transpose.
M | Matrix to multiply. |
Definition at line 25 of file tcrossprod.hpp.
Definition at line 15 of file tgamma.hpp.
|
inline |
Vectorized version of tgamma().
x | Container. |
T | Container type. |
std::domain_error | if any value is 0 or a negative integer |
Definition at line 34 of file tgamma.hpp.
|
inline |
Return the Gamma function applied to the specified variable (C99).
See boost::math::tgamma() for the double-based version.
The derivative with respect to the argument is
where is the digamma function.
See boost::math::digamma() for the double-based version.
a | Argument to function. |
Definition at line 65 of file tgamma.hpp.
|
inline |
Definition at line 15 of file to_array_1d.hpp.
|
inline |
Definition at line 29 of file to_array_1d.hpp.
|
inline |
Definition at line 36 of file to_array_1d.hpp.
|
inline |
Definition at line 13 of file to_array_2d.hpp.
|
inline |
Definition at line 12 of file to_fvar.hpp.
|
inline |
Definition at line 14 of file to_fvar.hpp.
|
inline |
Definition at line 16 of file to_fvar.hpp.
Definition at line 19 of file to_fvar.hpp.
|
inline |
Definition at line 23 of file to_fvar.hpp.
|
inline |
Definition at line 24 of file to_fvar.hpp.
|
inline |
Definition at line 33 of file to_fvar.hpp.
|
inline |
Definition at line 34 of file to_fvar.hpp.
|
inline |
Definition at line 16 of file to_matrix.hpp.
|
inline |
Definition at line 23 of file to_matrix.hpp.
|
inline |
Definition at line 40 of file to_matrix.hpp.
|
inline |
Definition at line 16 of file to_row_vector.hpp.
|
inline |
Definition at line 24 of file to_row_vector.hpp.
|
inline |
Definition at line 30 of file to_row_vector.hpp.
|
inline |
Converts argument to an automatic differentiation variable.
Returns a stan::math::var variable with the input value.
[in] | x | A scalar value |
Definition at line 17 of file to_var.hpp.
|
inline |
Converts argument to an automatic differentiation variable.
Returns a stan::math::var variable with the input value.
[in] | v | A std::vector<double> |
Definition at line 20 of file to_var.hpp.
|
inline |
Converts argument to an automatic differentiation variable.
Returns a stan::math::var variable with the input value.
[in] | m | A Matrix with scalars |
Definition at line 21 of file to_var.hpp.
Converts argument to an automatic differentiation variable.
Returns a stan::math::var variable with the input value.
[in] | x | An automatic differentiation variable. |
Definition at line 29 of file to_var.hpp.
Converts argument to an automatic differentiation variable.
Returns a stan::math::var variable with the input value.
[in] | v | A std::vector<var> |
Definition at line 35 of file to_var.hpp.
Converts argument to an automatic differentiation variable.
Returns a stan::math::var variable with the input value.
[in] | m | A Matrix with automatic differentiation variables. |
Definition at line 36 of file to_var.hpp.
|
inline |
Converts argument to an automatic differentiation variable.
Returns a stan::math::var variable with the input value.
[in] | v | A Vector of scalars |
Definition at line 48 of file to_var.hpp.
Converts argument to an automatic differentiation variable.
Returns a stan::math::var variable with the input value.
[in] | v | A Vector of automatic differentiation variables |
Definition at line 63 of file to_var.hpp.
|
inline |
Converts argument to an automatic differentiation variable.
Returns a stan::math::var variable with the input value.
[in] | rv | A row vector of scalars |
Definition at line 75 of file to_var.hpp.
|
inline |
Converts argument to an automatic differentiation variable.
Returns a stan::math::var variable with the input value.
[in] | rv | A row vector with automatic differentiation variables |
Definition at line 90 of file to_var.hpp.
|
inline |
Definition at line 16 of file to_vector.hpp.
|
inline |
Definition at line 24 of file to_vector.hpp.
|
inline |
Definition at line 30 of file to_vector.hpp.
|
inline |
|
inline |
|
inline |
Compute the trace of an inverse quadratic form.
I.E., this computes trace(D B^T A^-1 B) where D is a square matrix and the LDLT_factor of A is provided.
Definition at line 27 of file trace_gen_inv_quad_form_ldlt.hpp.
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Definition at line 30 of file trace_gen_inv_quad_form_ldlt.hpp.
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Definition at line 15 of file trace_gen_quad_form.hpp.
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Compute trace(D B^T A B).
Definition at line 17 of file trace_gen_quad_form.hpp.
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Definition at line 116 of file trace_gen_quad_form.hpp.
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Definition at line 27 of file trace_inv_quad_form_ldlt.hpp.
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Compute the trace of an inverse quadratic form.
I.E., this computes trace(B^T A^-1 B) where the LDLT_factor of A is provided.
Definition at line 177 of file trace_inv_quad_form_ldlt.hpp.
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Compute trace(B^T A B).
Definition at line 17 of file trace_quad_form.hpp.
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Definition at line 18 of file trace_quad_form.hpp.
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Definition at line 30 of file trace_quad_form.hpp.
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Definition at line 42 of file trace_quad_form.hpp.
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Definition at line 98 of file trace_quad_form.hpp.
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Definition at line 12 of file transpose.hpp.
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Returns the truncatation of the specified variable (C99).
See trunc() for the double-based version.
The derivative is zero everywhere but at integer values, so for convenience the derivative is defined to be everywhere zero,
.
a | Specified variable. |
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Return the upper-bounded value for the specified unconstrained scalar and upper bound.
The transform is
where is the upper bound.
If the upper bound is positive infinity, this function reduces to identity_constrain(x)
.
x | Free scalar. |
ub | Upper bound. |
T | Type of scalar. |
TU | Type of upper bound. |
Definition at line 37 of file ub_constrain.hpp.
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Return the upper-bounded value for the specified unconstrained scalar and upper bound and increment the specified log probability reference with the log absolute Jacobian determinant of the transform.
The transform is as specified for ub_constrain(T, double)
. The log absolute Jacobian determinant is
.
If the upper bound is positive infinity, this function reduces to identity_constrain(x, lp)
.
x | Free scalar. |
ub | Upper bound. |
lp | Log probability reference. |
T | Type of scalar. |
TU | Type of upper bound. |
Definition at line 70 of file ub_constrain.hpp.
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Return the free scalar that corresponds to the specified upper-bounded value with respect to the specified upper bound.
The transform is the reverse of the ub_constrain(T, double)
transform,
where is the upper bound.
If the upper bound is positive infinity, this function reduces to identity_free(y)
.
y | Upper-bounded scalar. |
ub | Upper bound. |
T | Type of scalar. |
TU | Type of upper bound. |
std::invalid_argument | if y is greater than the upper bound. |
Definition at line 39 of file ub_free.hpp.
return_type<T_y, T_low, T_high>::type stan::math::uniform_ccdf_log | ( | const T_y & | y, |
const T_low & | alpha, | ||
const T_high & | beta | ||
) |
Definition at line 25 of file uniform_ccdf_log.hpp.
return_type<T_y, T_low, T_high>::type stan::math::uniform_cdf | ( | const T_y & | y, |
const T_low & | alpha, | ||
const T_high & | beta | ||
) |
Definition at line 24 of file uniform_cdf.hpp.
return_type<T_y, T_low, T_high>::type stan::math::uniform_cdf_log | ( | const T_y & | y, |
const T_low & | alpha, | ||
const T_high & | beta | ||
) |
Definition at line 25 of file uniform_cdf_log.hpp.
return_type<T_y, T_low, T_high>::type stan::math::uniform_log | ( | const T_y & | y, |
const T_low & | alpha, | ||
const T_high & | beta | ||
) |
The log of a uniform density for the given y, lower, and upper bound.
y | A scalar variable. |
alpha | Lower bound. |
beta | Upper bound. |
std::invalid_argument | if the lower bound is greater than or equal to the lower bound |
T_y | Type of scalar. |
T_low | Type of lower bound. |
T_high | Type of upper bound. |
Definition at line 48 of file uniform_log.hpp.
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Definition at line 126 of file uniform_log.hpp.
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Definition at line 21 of file uniform_rng.hpp.
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Definition at line 20 of file unit_vector_constrain.hpp.
Eigen::Matrix<T, R, C> stan::math::unit_vector_constrain | ( | const Eigen::Matrix< T, R, C > & | y | ) |
Return the unit length vector corresponding to the free vector y.
See https://en.wikipedia.org/wiki/N-sphere#Generating_random_points
y | vector of K unrestricted variables |
T | Scalar type. |
Definition at line 25 of file unit_vector_constrain.hpp.
Eigen::Matrix<T, R, C> stan::math::unit_vector_constrain | ( | const Eigen::Matrix< T, R, C > & | y, |
T & | lp | ||
) |
Return the unit length vector corresponding to the free vector y.
See https://en.wikipedia.org/wiki/N-sphere#Generating_random_points
y | vector of K unrestricted variables |
lp | Log probability reference to increment. |
T | Scalar type. |
Definition at line 45 of file unit_vector_constrain.hpp.
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Definition at line 54 of file unit_vector_constrain.hpp.
Eigen::Matrix<var, R, C> stan::math::unit_vector_constrain | ( | const Eigen::Matrix< var, R, C > & | y | ) |
Return the unit length vector corresponding to the free vector y.
See https://en.wikipedia.org/wiki/N-sphere#Generating_random_points
y | vector of K unrestricted variables |
T | Scalar type. |
Definition at line 64 of file unit_vector_constrain.hpp.
Eigen::Matrix<var, R, C> stan::math::unit_vector_constrain | ( | const Eigen::Matrix< var, R, C > & | y, |
var & | lp | ||
) |
Return the unit length vector corresponding to the free vector y.
See https://en.wikipedia.org/wiki/N-sphere#Generating_random_points
y | vector of K unrestricted variables |
lp | Log probability reference to increment. |
T | Scalar type. |
Definition at line 112 of file unit_vector_constrain.hpp.
Eigen::Matrix<T, Eigen::Dynamic, 1> stan::math::unit_vector_free | ( | const Eigen::Matrix< T, Eigen::Dynamic, 1 > & | x | ) |
Transformation of a unit length vector to a "free" vector However, we are just fixing the unidentified radius to 1.
Thus, the transformation is just the identity
x | unit vector of dimension K |
T | Scalar type. |
Definition at line 24 of file unit_vector_free.hpp.
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Definition at line 12 of file validate_non_negative_index.hpp.
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Return the value of the specified variable.
v | Variable. |
Definition at line 16 of file value_of.hpp.
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Convert a std::vector of type T to a std::vector of child_type<T>::type.
T | Scalar type in std::vector |
[in] | x | std::vector to be converted |
Definition at line 22 of file value_of.hpp.
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Return the value of the specified variable.
This function is used internally by auto-dif functions along with stan::math::value_of(T x)
to extract the double
value of either a scalar or an auto-dif variable. This function will be called when the argument is a stan::math::var
even if the function is not referred to by namespace because of argument-dependent lookup.
v | Variable. |
Definition at line 22 of file value_of.hpp.
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Return the value of the specified scalar argument converted to a double value.
See the stan::math::primitive_value
function to extract values without casting to double
.
This function is meant to cover the primitive types. For types requiring pass-by-reference, this template function should be specialized.
T | Type of scalar. |
x | Scalar to convert to double. |
Definition at line 24 of file value_of.hpp.
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Convert a matrix of type T to a matrix of doubles.
T must implement value_of. See test/math/fwd/mat/fun/value_of.cpp for fvar and var usage.
T | Scalar type in matrix |
R | Rows of matrix |
C | Columns of matrix |
[in] | M | Matrix to be converted |
Definition at line 25 of file value_of.hpp.
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Return the specified argument.
See value_of(T)
for a polymorphic implementation using static casts.
This inline pass-through no-op should be compiled away.
x | Specified std::vector. |
Definition at line 42 of file value_of.hpp.
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Return the specified argument.
See value_of(T)
for a polymorphic implementation using static casts.
This inline pass-through no-op should be compiled away.
x | Specified matrix. |
Definition at line 47 of file value_of.hpp.
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Return the specified argument.
See value_of(T)
for a polymorphic implementation using static casts.
This inline pass-through no-op should be compiled away.
x | Specified value. |
Definition at line 40 of file value_of.hpp.
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Return the value of the specified variable.
v | Variable. |
Definition at line 16 of file value_of_rec.hpp.
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Return the value of the specified variable.
T must implement value_of_rec.
T | Scalar type |
v | Variable. |
Definition at line 21 of file value_of_rec.hpp.
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Convert a std::vector of type T to a std::vector of doubles.
T must implement value_of_rec. See test/math/fwd/mat/fun/value_of_rec.cpp for fvar and var usage.
T | Scalar type in std::vector |
[in] | x | std::vector to be converted |
Definition at line 23 of file value_of_rec.hpp.
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Return the value of the specified scalar argument converted to a double value.
See the stan::math::primitive_value
function to extract values without casting to double
.
This function is meant to cover the primitive types. For types requiring pass-by-reference, this template function should be specialized.
T | Type of scalar. |
x | Scalar to convert to double. |
Definition at line 24 of file value_of_rec.hpp.
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Convert a matrix of type T to a matrix of doubles.
T must implement value_of_rec. See test/unit/math/fwd/mat/fun/value_of_test.cpp for fvar and var usage.
T | Scalar type in matrix |
R | Rows of matrix |
C | Columns of matrix |
[in] | M | Matrix to be converted |
Definition at line 24 of file value_of_rec.hpp.
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Return the specified argument.
See value_of_rec(T)
for a polymorphic implementation using static casts.
This inline pass-through no-op should be compiled away.
x | Specified std::vector. |
Definition at line 43 of file value_of_rec.hpp.
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Return the specified argument.
See value_of_rec(T)
for a polymorphic implementation using static casts.
This inline pass-through no-op should be compiled away.
x | Specified matrix. |
Definition at line 46 of file value_of_rec.hpp.
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Return the specified argument.
See value_of(T)
for a polymorphic implementation using static casts.
This inline pass-through no-op should be compiled away.
x | Specified value. |
Definition at line 40 of file value_of_rec.hpp.
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Returns the sample variance (divide by length - 1) of the coefficients in the specified standard vector.
v | Specified vector. |
std::domain_error | if the size of the vector is less than 1. |
Definition at line 24 of file variance.hpp.
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Returns the sample variance (divide by length - 1) of the coefficients in the specified column vector.
m | Specified vector. |
Definition at line 46 of file variance.hpp.
Return the sample variance of the specified standard vector.
Raise domain error if size is not greater than zero.
[in] | v | a vector |
Definition at line 52 of file variance.hpp.
Definition at line 69 of file variance.hpp.
return_type<T_y, T_loc, T_scale>::type stan::math::von_mises_log | ( | T_y const & | y, |
T_loc const & | mu, | ||
T_scale const & | kappa | ||
) |
Definition at line 27 of file von_mises_log.hpp.
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Definition at line 135 of file von_mises_log.hpp.
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Definition at line 31 of file von_mises_rng.hpp.
return_type<T_y, T_shape, T_scale>::type stan::math::weibull_ccdf_log | ( | const T_y & | y, |
const T_shape & | alpha, | ||
const T_scale & | sigma | ||
) |
Definition at line 29 of file weibull_ccdf_log.hpp.
return_type<T_y, T_shape, T_scale>::type stan::math::weibull_cdf | ( | const T_y & | y, |
const T_shape & | alpha, | ||
const T_scale & | sigma | ||
) |
Definition at line 29 of file weibull_cdf.hpp.
return_type<T_y, T_shape, T_scale>::type stan::math::weibull_cdf_log | ( | const T_y & | y, |
const T_shape & | alpha, | ||
const T_scale & | sigma | ||
) |
Definition at line 29 of file weibull_cdf_log.hpp.
return_type<T_y, T_shape, T_scale>::type stan::math::weibull_log | ( | const T_y & | y, |
const T_shape & | alpha, | ||
const T_scale & | sigma | ||
) |
Definition at line 32 of file weibull_log.hpp.
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Definition at line 143 of file weibull_log.hpp.
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Definition at line 23 of file weibull_rng.hpp.
return_type<T_y, T_alpha, T_tau, T_beta, T_delta>::type stan::math::wiener_log | ( | const T_y & | y, |
const T_alpha & | alpha, | ||
const T_tau & | tau, | ||
const T_beta & | beta, | ||
const T_delta & | delta | ||
) |
The log of the first passage time density function for a (Wiener) drift diffusion model for the given , boundary separation
, nondecision time
, relative bias
, and drift rate
.
and
must be greater than 0, and
must be between 0 and 1.
should contain reaction times in seconds (strictly positive) with upper-boundary responses.
y | A scalar variate. |
alpha | The boundary separation. |
tau | The nondecision time. |
beta | The relative bias. |
delta | The drift rate. |
Definition at line 72 of file wiener_log.hpp.
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Definition at line 225 of file wiener_log.hpp.
boost::math::tools::promote_args<T_y, T_dof, T_scale>::type stan::math::wishart_log | ( | const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > & | W, |
const T_dof & | nu, | ||
const Eigen::Matrix< T_scale, Eigen::Dynamic, Eigen::Dynamic > & | S | ||
) |
The log of the Wishart density for the given W, degrees of freedom, and scale matrix.
The scale matrix, S, must be k x k, symmetric, and semi-positive definite. Dimension, k, is implicit. nu must be greater than k-1
W | A scalar matrix |
nu | Degrees of freedom |
S | The scale matrix |
std::domain_error | if nu is not greater than k-1 |
std::domain_error | if S is not square, not symmetric, or not semi-positive definite. |
T_y | Type of scalar. |
T_dof | Type of degrees of freedom. |
T_scale | Type of scale. |
Definition at line 58 of file wishart_log.hpp.
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Definition at line 127 of file wishart_log.hpp.
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Definition at line 29 of file wishart_rng.hpp.
const double stan::math::CONSTRAINT_TOLERANCE = 1E-8 |
The tolerance for checking arithmetic bounds In rank and in simplexes.
The default value is 1E-8
.
Definition at line 11 of file constraint_tolerance.hpp.
const double stan::math::E = boost::math::constants::e<double>() |
The base of the natural logarithm, .
Definition at line 15 of file constants.hpp.
const double stan::math::EPSILON = std::numeric_limits<double>::epsilon() |
Smallest positive value.
Definition at line 61 of file constants.hpp.
const double stan::math::INFTY = std::numeric_limits<double>::infinity() |
Positive infinity.
Definition at line 44 of file constants.hpp.
const double stan::math::INV_SQRT_2 = 1.0 / SQRT_2 |
The value of 1 over the square root of 2, .
Definition at line 27 of file constants.hpp.
const double stan::math::INV_SQRT_TWO_PI = 1.0 / std::sqrt(2.0 * boost::math::constants::pi<double>()) |
Definition at line 166 of file constants.hpp.
const double stan::math::LOG_10 = std::log(10.0) |
The natural logarithm of 10, .
Definition at line 39 of file constants.hpp.
const double stan::math::LOG_2 = std::log(2.0) |
The natural logarithm of 2, .
Definition at line 33 of file constants.hpp.
const double stan::math::LOG_HALF = std::log(0.5) |
Definition at line 179 of file constants.hpp.
const double stan::math::LOG_PI = std::log(boost::math::constants::pi<double>()) |
Definition at line 170 of file constants.hpp.
const double stan::math::LOG_PI_OVER_FOUR = std::log(boost::math::constants::pi<double>()) / 4.0 |
Log pi divided by 4 .
Definition at line 79 of file constants.hpp.
const double stan::math::LOG_SQRT_PI = std::log(SQRT_PI) |
Definition at line 173 of file constants.hpp.
const double stan::math::LOG_TWO = std::log(2.0) |
Definition at line 177 of file constants.hpp.
Definition at line 193 of file constants.hpp.
const double stan::math::LOG_ZERO = std::log(0.0) |
Definition at line 175 of file constants.hpp.
const std::string stan::math::MAJOR_VERSION = STAN_STRING(STAN_MATH_MAJOR) |
Major version number for Stan math library.
Definition at line 22 of file version.hpp.
const std::string stan::math::MINOR_VERSION = STAN_STRING(STAN_MATH_MINOR) |
Minor version number for Stan math library.
Definition at line 25 of file version.hpp.
const double stan::math::NEG_LOG_PI = - LOG_PI |
Definition at line 186 of file constants.hpp.
const double stan::math::NEG_LOG_SQRT_PI = -std::log(std::sqrt(boost::math::constants::pi<double>())) |
Definition at line 189 of file constants.hpp.
const double stan::math::NEG_LOG_SQRT_TWO_PI = - std::log(std::sqrt(2.0 * boost::math::constants::pi<double>())) |
Definition at line 184 of file constants.hpp.
const double stan::math::NEG_LOG_TWO = - LOG_TWO |
Definition at line 181 of file constants.hpp.
const double stan::math::NEG_LOG_TWO_OVER_TWO = - LOG_TWO / 2.0 |
Definition at line 191 of file constants.hpp.
const double stan::math::NEG_LOG_TWO_PI = - LOG_TWO_PI |
Definition at line 195 of file constants.hpp.
const double stan::math::NEG_TWO_OVER_SQRT_PI = -TWO_OVER_SQRT_PI |
Definition at line 163 of file constants.hpp.
const double stan::math::NEGATIVE_EPSILON = - std::numeric_limits<double>::epsilon() |
Largest negative value (i.e., smallest absolute value).
Definition at line 67 of file constants.hpp.
const double stan::math::NEGATIVE_INFTY = - std::numeric_limits<double>::infinity() |
Negative infinity.
Definition at line 50 of file constants.hpp.
const double stan::math::NOT_A_NUMBER = std::numeric_limits<double>::quiet_NaN() |
(Quiet) not-a-number value.
Definition at line 56 of file constants.hpp.
const std::string stan::math::PATCH_VERSION = STAN_STRING(STAN_MATH_PATCH) |
Patch version for Stan math library.
Definition at line 28 of file version.hpp.
const double stan::math::POISSON_MAX_RATE = std::pow(2.0, 30) |
Largest rate parameter allowed in Poisson RNG.
Definition at line 72 of file constants.hpp.
const double stan::math::SQRT_2 = std::sqrt(2.0) |
The value of the square root of 2, .
Definition at line 21 of file constants.hpp.
Definition at line 158 of file constants.hpp.
const double stan::math::SQRT_PI = std::sqrt(boost::math::constants::pi<double>()) |
Definition at line 156 of file constants.hpp.
const double stan::math::TWO_OVER_SQRT_PI = 2.0 / SQRT_PI |
Definition at line 161 of file constants.hpp.