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.)