qmat.mathutils

Base module for math utility functions

Functions

numericalOrder(nSteps, err)	Compute numerical order from two vectors containing the error and the number of time-steps.
lduFactorization(A)	Perform LDU factorization on a square matrix A.
getExtrapolationMatrix(nodes, times[, pOrder])	Generate a polynomial based extrapolation matrix,

Module Contents

numericalOrder(nSteps, err)

Compute numerical order from two vectors containing the error and the number of time-steps.

Parameters:

• nSteps (np.1darray or list) – Different number of steps to compute the error.

• err (np.1darray) – Diffenrent error values associated to the number of steps.

Returns:

• beta (float) – Order coefficient computed through linear regression.

• rmse (float) – The root mean square error of the linear regression.

lduFactorization(A: numpy.ndarray)

Perform LDU factorization on a square matrix A.

Parameters:

A (np.2darray) – The square matrix to factorize (n x n).

Returns:

• L (np.2darray) – Lower triangular matrix with ones on the diagonal.

• D (np.2darray) – Diagonal matrix.

• U (np.2darray) – Upper triangular matrix with ones on the diagonal.

getExtrapolationMatrix(nodes, times, pOrder=None)

Generate a polynomial based extrapolation matrix, base on polynomial regression of a function represented on given nodes.

Parameters:

• nodes (np.1darray like, shape (M,)) – The nodes where function values are known.

• times (np.1darray like, shape (N,)) – The times where to extrapolate the polynomial.

• pOrder (int) – Order of the polynomial regression on the node values (default = len(nodes)-1).

Returns:

P – Extrapolation matrix, that can be used on any node values.

Return type:

np.2darray, shape (N, M)