IterativeGeneralizedGaussianWBackground.compute_jacobian

giant.point_spread_functions.gaussians:

IterativeGeneralizedGaussianWBackground.compute_jacobian(x, y, computed)

This method computes the Jacobian of the PSF with respect to a change in the state.

It returns a mx8 matrix defined as

\[\mathbf{J} = \left[\begin{array}{cccccccc} \frac{\partial f}{\partial x_0} & \frac{\partial f}{\partial y_0} & \frac{\partial f}{\partial \sigma_x} & \frac{\partial f}{\partial \sigma_y} & \frac{\partial f}{\partial A} & \frac{\partial f}{\partial B} & \frac{\partial f}{\partial C} & \frac{\partial f}{\partial D}\end{array}\right]=\left[\begin{array}{cccccccc} \frac{x-x_0}{\sigma_x^2}f(x, y) & \frac{y-y_0}{\sigma_y^2}f(x, y) & \frac{(x-x_0)^2}{\sigma_x^3}f(x, y) & \frac{(y-y_0)^2}{\sigma_y^3}f(x, y) & \frac{f(x, y)}{A} & x & y & 1\end{array}\right]\]

Parameters:

• x (ndarray) – The x values to evaluate the Jacobian at as a length m array

• y (ndarray) – The y values to evaluate the Jacobian at as a length m array

• computed (ndarray) – The PSF evaluated at x and y as a length m array

Returns:

The Jacobian matrix as a mx8 numpy array

Return type:

ndarray