uf3.regression.regularize.get_penalty_matrix_3D

get_penalty_matrix_3D(L: int, M: int, N: int, ridge: float = 0.0, curvature: float = 1.0, periodic=(False, False, True)) → numpy.ndarray[source]
Generates additive regularization matrix for linear regression

using curvature penalty and/or L2 (ridge) penalty. Curvature penalty here applies to coefficients that are spatially related in three dimensions that may not be adjacent after flattening for linear least-squares

Parameters

  • L (int) – length of coefficient matrix before flattening.

  • M (int) – width of coefficient matrix before flattening.

  • N (int) – depth of coefficient matrix before flattening.

  • ridge (float) – L2 (ridge) regularization strength.

  • curvature (float) – Local curvature regularization strength.

  • periodic (list) – periodicity in regularization for three dimensions. Default (False, False, True) for periodicity in angular space.

Returns

square penalty matrix for linear

least-squares of shape (L*M*N , L*M*N).

Return type

matrix_3d (numpy.ndarray)