helpers.ParaDiagHelper module

get_E_matrix(N, alpha=0)[source]

Get NxN matrix with -1 on the lower subdiagonal, -alpha in the top right and 0 elsewhere

Parameters:

  • N (int) – Size of the matrix

  • alpha (float) – Negative of value in the top right

Returns:

sparse E matrix

get_FFT_matrix(N)[source]

Get matrix for computing FFT of size N. Normalization is like “ortho” in numpy. Compute inverse FFT by multiplying by the complex conjugate (numpy.conjugate) of this matrix

Parameters:

N (int) – Size of the data to be transformed

Returns:

Dense square matrix to compute forward transform

Return type:

numpy.ndarray

get_G_inv_matrix(l, L, alpha, sweeper_params)[source]
get_H_matrix(N, sweeper_params)[source]

Get sparse matrix for computing the collocation update. Requires not to do a collocation update!

Parameters:

  • N (int) – Number of collocation nodes

  • sweeper_params (dict) – Parameters for the sweeper

Returns:

Sparse matrix for collocation update

get_J_inv_matrix(N, alpha)[source]

Get matrix for weights in the weighted FFT

Parameters:

  • N (int) – Size of the matrix

  • alpha (float) – alpha parameter in ParaDiag

Returns:

sparse J_inv matrix

get_J_matrix(N, alpha)[source]

Get matrix for weights in the weighted inverse FFT

Parameters:

  • N (int) – Size of the matrix

  • alpha (float) – alpha parameter in ParaDiag

Returns:

sparse J matrix

get_weighted_FFT_matrix(N, alpha)[source]

Get matrix for the weighted FFT

Parameters:

  • N (int) – Size of the matrix

  • alpha (float) – alpha parameter in ParaDiag

Returns:

Dense weighted FFT matrix

get_weighted_iFFT_matrix(N, alpha)[source]

Get matrix for the weighted inverse FFT

Parameters:

  • N (int) – Size of the matrix

  • alpha (float) – alpha parameter in ParaDiag

Returns:

Dense weighted FFT matrix