Source code for lenstronomy.Util.derivative_util
"""
routines to compute derivatives of spherical functions
"""
import numpy as np
from lenstronomy.Util.package_util import exporter
export, __all__ = exporter()
[docs]@export
def d_r_dx(x, y):
"""
derivative of r with respect to x
:param x:
:param y:
:return:
"""
return x / np.sqrt(x**2 + y**2)
[docs]@export
def d_r_dy(x, y):
"""
differential dr/dy
:param x:
:param y:
:return:
"""
return y / np.sqrt(x**2 + y**2)
[docs]@export
def d_r_dxx(x, y):
"""
second derivative dr/dxdx
:param x:
:param y:
:return:
"""
return y**2 / (x**2 + y**2)**(3./2)
[docs]@export
def d_r_dyy(x, y):
"""
second derivative dr/dxdx
:param x:
:param y:
:return:
"""
return x**2 / (x**2 + y**2)**(3./2)
[docs]@export
def d_r_dxy(x, y):
"""
second derivative dr/dxdx
:param x:
:param y:
:return:
"""
return -x * y / (x ** 2 + y ** 2) ** (3 / 2.)
[docs]@export
def d_phi_dx(x, y):
"""
angular derivative in respect to x when phi = arctan2(y, x)
:param x:
:param y:
:return:
"""
return -y / (x**2 + y**2)
[docs]@export
def d_phi_dy(x, y):
"""
angular derivative in respect to y when phi = arctan2(y, x)
:param x:
:param y:
:return:
"""
return x / (x**2 + y**2)
[docs]@export
def d_phi_dxx(x, y):
"""
second derivative of the orientation angle
:param x:
:param y:
:return:
"""
return 2 * x * y / (x**2 + y**2)**2
[docs]@export
def d_phi_dyy(x, y):
"""
second derivative of the orientation angle in dydy
:param x:
:param y:
:return:
"""
return -2 * x * y / (x ** 2 + y ** 2) ** 2
[docs]@export
def d_phi_dxy(x, y):
"""
second derivative of the orientation angle in dxdy
:param x:
:param y:
:return:
"""
return (-x**2 + y**2) / (x ** 2 + y ** 2) ** 2
[docs]@export
def d_x_diffr_dx(x, y):
"""
derivative of d(x/r)/dx
equivalent to second order derivatives dr_dxx
:param x:
:param y:
:return:
"""
return y**2 / (x**2 + y**2)**(3/2.)
[docs]@export
def d_y_diffr_dy(x, y):
"""
derivative of d(y/r)/dy
equivalent to second order derivatives dr_dyy
:param x:
:param y:
:return:
"""
return x**2 / (x**2 + y**2)**(3/2.)
[docs]@export
def d_y_diffr_dx(x, y):
"""
derivative of d(y/r)/dx
equivalent to second order derivatives dr_dxy
:param x:
:param y:
:return:
"""
return -x*y / (x**2 + y**2)**(3/2.)
[docs]@export
def d_x_diffr_dy(x, y):
"""
derivative of d(x/r)/dy
equivalent to second order derivatives dr_dyx
:param x:
:param y:
:return:
"""
return -x*y / (x**2 + y**2)**(3/2.)