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1""" 

2Sparse linear algebra (:mod:`scipy.sparse.linalg`) 

3================================================== 

4 

5.. currentmodule:: scipy.sparse.linalg 

6 

7Abstract linear operators 

8------------------------- 

9 

10.. autosummary:: 

11 :toctree: generated/ 

12 

13 LinearOperator -- abstract representation of a linear operator 

14 aslinearoperator -- convert an object to an abstract linear operator 

15 

16Matrix Operations 

17----------------- 

18 

19.. autosummary:: 

20 :toctree: generated/ 

21 

22 inv -- compute the sparse matrix inverse 

23 expm -- compute the sparse matrix exponential 

24 expm_multiply -- compute the product of a matrix exponential and a matrix 

25 

26Matrix norms 

27------------ 

28 

29.. autosummary:: 

30 :toctree: generated/ 

31 

32 norm -- Norm of a sparse matrix 

33 onenormest -- Estimate the 1-norm of a sparse matrix 

34 

35Solving linear problems 

36----------------------- 

37 

38Direct methods for linear equation systems: 

39 

40.. autosummary:: 

41 :toctree: generated/ 

42 

43 spsolve -- Solve the sparse linear system Ax=b 

44 spsolve_triangular -- Solve the sparse linear system Ax=b for a triangular matrix 

45 factorized -- Pre-factorize matrix to a function solving a linear system 

46 MatrixRankWarning -- Warning on exactly singular matrices 

47 use_solver -- Select direct solver to use 

48 

49Iterative methods for linear equation systems: 

50 

51.. autosummary:: 

52 :toctree: generated/ 

53 

54 bicg -- Use BIConjugate Gradient iteration to solve A x = b 

55 bicgstab -- Use BIConjugate Gradient STABilized iteration to solve A x = b 

56 cg -- Use Conjugate Gradient iteration to solve A x = b 

57 cgs -- Use Conjugate Gradient Squared iteration to solve A x = b 

58 gmres -- Use Generalized Minimal RESidual iteration to solve A x = b 

59 lgmres -- Solve a matrix equation using the LGMRES algorithm 

60 minres -- Use MINimum RESidual iteration to solve Ax = b 

61 qmr -- Use Quasi-Minimal Residual iteration to solve A x = b 

62 gcrotmk -- Solve a matrix equation using the GCROT(m,k) algorithm 

63 

64Iterative methods for least-squares problems: 

65 

66.. autosummary:: 

67 :toctree: generated/ 

68 

69 lsqr -- Find the least-squares solution to a sparse linear equation system 

70 lsmr -- Find the least-squares solution to a sparse linear equation system 

71 

72Matrix factorizations 

73--------------------- 

74 

75Eigenvalue problems: 

76 

77.. autosummary:: 

78 :toctree: generated/ 

79 

80 eigs -- Find k eigenvalues and eigenvectors of the square matrix A 

81 eigsh -- Find k eigenvalues and eigenvectors of a symmetric matrix 

82 lobpcg -- Solve symmetric partial eigenproblems with optional preconditioning 

83 

84Singular values problems: 

85 

86.. autosummary:: 

87 :toctree: generated/ 

88 

89 svds -- Compute k singular values/vectors for a sparse matrix 

90 

91Complete or incomplete LU factorizations 

92 

93.. autosummary:: 

94 :toctree: generated/ 

95 

96 splu -- Compute a LU decomposition for a sparse matrix 

97 spilu -- Compute an incomplete LU decomposition for a sparse matrix 

98 SuperLU -- Object representing an LU factorization 

99 

100Exceptions 

101---------- 

102 

103.. autosummary:: 

104 :toctree: generated/ 

105 

106 ArpackNoConvergence 

107 ArpackError 

108 

109""" 

110 

111from .isolve import * 

112from .dsolve import * 

113from .interface import * 

114from .eigen import * 

115from .matfuncs import * 

116from ._onenormest import * 

117from ._norm import * 

118from ._expm_multiply import * 

119 

120__all__ = [s for s in dir() if not s.startswith('_')] 

121 

122from scipy._lib._testutils import PytestTester 

123test = PytestTester(__name__) 

124del PytestTester