Tikhonov

class jwst.extract_1d.soss_extract.atoca_utils.Tikhonov(a_mat, b_vec, t_mat)

Bases: object

Use Tikhonov regularization to solve the ill-posed problem A.x = b.

The matrix A is accidentally singular or close to singularity. Tikhonov regularization adds a regularization term in the equation and aims to minimize the equation:

||A.x - b||^2 + ||gamma.x||^2

where gamma is the Tikhonov regularization matrix.

Parameters:

a_matndarray

Matrix A (2D) in the system to solve A.x = b

b_vecndarray

Vector b (1D) in the system to solve A.x = b

t_matndarray

Tikhonov regularization matrix (2D) to be applied on b_vec

Methods Summary

solve([factor])	Solve the Tikhonov regularization problem.
test_factors(factors)	Test multiple candidate Tikhonov factors.

Methods Documentation

solve(factor=1.0)

Solve the Tikhonov regularization problem.

Minimize the equation:

||A.x - b||^2 + ||gamma.x||^2

by solving:

(A_T.A + gamma_T.gamma).x = A_T.b

where gamma is the Tikhonov matrix multiplied by a scale factor.

Parameters:

factorfloat, optional

Multiplicative constant of the regularization matrix

Returns:

ndarray

Solution of the system (1D)

test_factors(factors)

Test multiple candidate Tikhonov factors.

Parameters:

factorsndarray

1D array of factors to test

Returns:

TikhoTests

Dictionary of test results