derivatives

class cosmicjellyfish.fishermatrix.derivatives.derivatives(observable, fiducial, special_deriv_function=None, derivatives_type=None, freeparams=None, observables_type=None, external_settings=<object object>, feed_lvl=None, *, configuration=None)

Bases: object

This class is the main derivative engine for the different observables. It gives access to different derivative methods. After the constructor is called, the resulting dictionary of derivatives is found in its result attribute.

der_3pt_stencil(fwd, bwd, step)

Helper function to compute the 3PT symmetrical finite step size derivative

Parameters:

• fwd (float, numpy.ndarray) – Observable computed at the forward step

• bwd (float, numpy.ndarray) – Observable computed at the backwards step

• step (float) – Absolute step size of the numerical derivative

Returns:

Numerical derivative using the a 3 point stencil

Return type:

float, numpy.ndarray

derivative_3pt()

One of the possible derivative methods. Computes the numerical derivative using a finite differences 3 point symmetrical derivative

Returns:

A dictionary containing the derivative of the observable for each varied parameter.

Return type:

dict

Note

Implements the following equation:

\[\frac{\mathrm{d} \mathcal{O}}{\mathrm{d} \theta} = \frac{\mathcal{O}(\theta+h)-\mathcal{O}(\theta-h)}{2\,h}\]

der_fwd_4pt(fwdi, step)

Helper function to compute the 4PT forward finite step size derivative

Parameters:

• fwdi (list, numpy.ndarray) – Observable computed at the fiducial and at equally spaced points in the forward direction

• step (float) – Absolute distance between the size of the numerical derivative

Returns:

Numerical derivative using the a 4 point forward stencil

Return type:

float, numpy.ndarray

derivative_forward_4pt()

Compute a one-sided, four-point forward finite-difference derivative.

The stencil is (-11 f(x) + 18 f(x + h) - 9 f(x + 2h) + 2 f(x + 3h)) / (6h). Its coefficients were obtained with the Finite Difference Coefficients Calculator.

Returns:

Derivative of the observable for each varied parameter.

Return type:

dict

derivative_stem()

One of the possible derivative methods. Computes the numerical derivative using the SteM derivative method

Returns:

A dictionary containing the derivative of the observable for each varied parameter.

Return type:

dict

derivative_poly()

One of the possible derivative methods. Computes the numerical derivative using a polynomial derivative method

Returns:

A dictionary containing the derivative of the observable for each varied parameter.

Return type:

dict