IterativeGaussianWBackground.compute_jacobian

giant.point_spread_functions.gaussians:

IterativeGaussianWBackground.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