capytaine.matrices.block module

This module implements block matrices to be used in Hierarchical Toeplitz matrices.

It takes inspiration from the following works:

• openHmx module from Gypsilab by Matthieu Aussal (GPL licensed)

• HierarchicalMatrices by Markus Neumann (GPL licensed)

class capytaine.matrices.block.BlockMatrix(blocks, _stored_block_shapes=None, check=True)

Bases: object

A (2D) matrix, stored as a set of submatrices (or blocks).

Parameters:

• blocks (list of list of matrices) – The blocks of the block matrix.

• check (bool, optional) – Should the code perform sanity checks on the inputs? (default: True)

Variables:

• shape (pair of ints) – shape of the full matrix

• nb_blocks (pair of ints) –

  number of blocks in each directions. Example:

  AAAABB
  AAAABB  ->  nb_blocks = (1, 2)
  AAAABB
  

access_block_by_path(path)

Access a diagonal block in a block matrix from the path of the corresponding leaf

all() → bool

property all_blocks: ndarray

The matrix of matrices. For a full block matrix, all the blocks are stored in memory.

any() → bool

astype(dtype: dtype) → BlockMatrix

property block_shapes: Tuple[List[int], List[int]]

The shapes of the blocks composing the BlockMatrix.

Example:

AAAABB
AAAABB  ->  block_shapes = ([3], [4, 2])
AAAABB

property density

display_color = <itertools.cycle object>

property dtype

The type of data of all of the subblocks.

fft_of_list(*, check=True)

Compute the fft of a list of block matrices of the same type and shape. The output is a list of block matrices of the same shape as the input ones. The fft is computed element-wise, so the block structure does not cause any mathematical difficulty. Returns an array of BlockMatrices.

full_matrix(dtype=None) → ndarray

Flatten the block structure and return a full matrix.

matmat(other)

Matrix-matrix product.

matvec(other)

Matrix vector product. Named as such to be used as scipy LinearOperator.

max() → Number

min() → Number

ndim = 2

no_toeplitz()

Recursively replace the block toeplitz matrices by usual block matrices. WARNING: the block matrices may still contain several references to the same block.

plot_shape()

Plot the structure of the matrix using matplotlib.

rmatvec(other)

Vector matrix product. Named as such to be used as scipy LinearOperator.

property sparcity

property stored_data_size

Return the number of entries actually stored in memory.

property str_shape