Source code for lenstronomy.LensModel.Profiles.hessian
__author__ = 'sibirrer'
from lenstronomy.LensModel.Profiles.base_profile import LensProfileBase
__all__ = ['Hessian']
[docs]class Hessian(LensProfileBase):
"""
class for constant Hessian distortion (second order)
The input is in the same convention as the LensModel.hessian() output.
"""
param_names = ['f_xx', 'f_yy', 'f_xy', 'f_yx', 'ra_0', 'dec_0']
lower_limit_default = {'f_xx': -100, 'f_yy': -100, 'f_xy': -100, 'f_yx': -100, 'ra_0': -100, 'dec_0': -100}
upper_limit_default = {'f_xx': 100, 'f_yy': 100, 'f_xy': 100, 'f_yx': 100, 'ra_0': 100, 'dec_0': 100}
[docs] def function(self, x, y, f_xx, f_yy, f_xy, f_yx, ra_0=0, dec_0=0):
"""
:param x: x-coordinate (angle)
:param y: y0-coordinate (angle)
:param f_xx: dalpha_x/dx
:param f_yy: dalpha_y/dy
:param f_xy: dalpha_x/dy
:param f_yx: dalpha_y/dx
:param ra_0: x/ra position where shear deflection is 0
:param dec_0: y/dec position where shear deflection is 0
:return: lensing potential
"""
x_ = x - ra_0
y_ = y - dec_0
f_ = 1/2. * (f_xx * x_ * x_ + (f_xy + f_yx) * x_ * y_ + f_yy * y_ * y_)
return f_
[docs] def derivatives(self, x, y, f_xx, f_yy, f_xy, f_yx, ra_0=0, dec_0=0):
"""
:param x: x-coordinate (angle)
:param y: y0-coordinate (angle)
:param f_xx: dalpha_x/dx
:param f_yy: dalpha_y/dy
:param f_xy: dalpha_x/dy
:param f_yx: dalpha_y/dx
:param ra_0: x/ra position where shear deflection is 0
:param dec_0: y/dec position where shear deflection is 0
:return: deflection angles
"""
x_ = x - ra_0
y_ = y - dec_0
f_x = f_xx * x_ + f_xy * y_
f_y = f_yx * x_ + f_yy * y_
return f_x, f_y
[docs] def hessian(self, x, y, f_xx, f_yy, f_xy, f_yx, ra_0=0, dec_0=0):
"""
Hessian. Attention: If f_xy != f_yx then this function is not accurate!
:param x: x-coordinate (angle)
:param y: y0-coordinate (angle)
:param f_xx: dalpha_x/dx
:param f_yy: dalpha_y/dy
:param f_xy: dalpha_x/dy
:param f_yx: dalpha_y/dx
:param ra_0: x/ra position where shear deflection is 0
:param dec_0: y/dec position where shear deflection is 0
:return: f_xx, f_yy, f_xy
"""
return f_xx, f_xy, f_yx, f_yy