Source code for lenstronomy.LensModel.Profiles.flexion

from lenstronomy.LensModel.Profiles.base_profile import LensProfileBase

__all__ = ["Flexion"]



[docs]
class Flexion(LensProfileBase):
    """Class for flexion."""

    param_names = ["g1", "g2", "g3", "g4", "ra_0", "dec_0"]
    lower_limit_default = {
        "g1": -0.1,
        "g2": -0.1,
        "g3": -0.1,
        "g4": -0.1,
        "ra_0": -100,
        "dec_0": -100,
    }
    upper_limit_default = {
        "g1": 0.1,
        "g2": 0.1,
        "g3": 0.1,
        "g4": 0.1,
        "ra_0": 100,
        "dec_0": 100,
    }


[docs]
    def function(self, x, y, g1, g2, g3, g4, ra_0=0, dec_0=0):
        x_ = x - ra_0
        y_ = y - dec_0
        f_ = (
            1.0
            / 6
            * (
                g1 * x_**3
                + 3 * g2 * x_**2 * y_
                + 3 * g3 * x_ * y_**2
                + g4 * y_**3
            )
        )
        return f_



[docs]
    def derivatives(self, x, y, g1, g2, g3, g4, ra_0=0, dec_0=0):
        x_ = x - ra_0
        y_ = y - dec_0
        f_x = 1.0 / 2.0 * g1 * x_**2 + g2 * x_ * y_ + 1.0 / 2.0 * g3 * y_**2
        f_y = 1.0 / 2.0 * g2 * x_**2 + g3 * x_ * y_ + 1.0 / 2.0 * g4 * y_**2
        return f_x, f_y



[docs]
    def hessian(self, x, y, g1, g2, g3, g4, ra_0=0, dec_0=0):
        x_ = x - ra_0
        y_ = y - dec_0
        f_xx = g1 * x_ + g2 * y_
        f_yy = g3 * x_ + g4 * y_
        f_xy = g2 * x_ + g3 * y_
        return f_xx, f_xy, f_xy, f_yy