dctkit.math namespace

Subpackages

Submodules

dctkit.math.permutation module

dctkit.math.permutation.compute_permutation_vectors(n: int) → Array[source]

Computes all permutation vectors of length n.

Parameters:

n – The number of elements to permute.

Returns:

a JAX array of shape (n!, n) containing all permutations of the integers from 0 to n-1.

dctkit.math.permutation.permutation_sign(p: Array) → Array[source]

Vectorized version of permutation_sign. Takes similar arguments as permutation_sign but with additional array axes over which permutation_sign is mapped.

Original documentation:

Computes the sign of a permutation.

The sign is +1 for even permutations and -1 for odd permutations. It is computed as the determinant of the corresponding permutation matrix.

Parameters:

p – A 1D array representing a permutation of integers.

Returns:

the sign of the permutations.

dctkit.math.shifted_list module

class dctkit.math.shifted_list.ShiftedList(iterable: Iterable, off: int)[source]

Bases: list

List with indices shifted by an offset.

Parameters:

  • iterable – iterable used to initialize the list.

  • off (int) – offset.

dctkit.math.spmm module

dctkit.math.spmm.spmm(A: Tuple[Array | ndarray[tuple[Any, ...], dtype[_ScalarT]], Array | ndarray[tuple[Any, ...], dtype[_ScalarT]], Array | ndarray[tuple[Any, ...], dtype[_ScalarT]]], v: Array | ndarray[tuple[Any, ...], dtype[_ScalarT]], transpose=False, shape=None) → Array[source]

Performs the matrix-matrix product between a sparse matrix in COO format and a dense matrix or column vector.

Parameters:

  • A – tuple (rows,cols,values) representing the sparse matrix in COO format.

  • v – matrix or column vector.

  • transpose – whether to transpose A before multiplication.

  • shape – the number of rows of the matrix A.

Returns:

the result of the matrix-matrix product.