hafnian_

Functions for Hafnian

Functions

count_unique_permutations(nums)	Count the number of unique permutations of a list of numbers.
get_submat_haf(a, z)	Get the sub-matrix for hafnian calculation.
hafnian(matrix[, loop])	Calculate the hafnian for symmetric matrix, using the eigenvalue-trace method.
hafnian_batch(matrix[, loop])	Calculate the batch hafnian.
integer_partition(remaining, max_num)	Generate all unique integer partitions of m using integers up to n.
poly_lambda(submat, int_partition, power[, loop])	Get the coefficient of the polynomial.

count_unique_permutations(nums: list | ndarray) → float64

Count the number of unique permutations of a list of numbers.

get_submat_haf(a: Tensor, z: Tensor) → Tensor

Get the sub-matrix for hafnian calculation.

See https://arxiv.org/abs/1805.12498 paragraph after Eq.(3.20)

hafnian(matrix: Tensor, loop: bool = False) → Tensor

Calculate the hafnian for symmetric matrix, using the eigenvalue-trace method.

See https://arxiv.org/abs/2108.01622 Eq.(B3)

hafnian_batch(matrix: Tensor, loop: bool = False) → Tensor

Calculate the batch hafnian.

integer_partition(remaining: int, max_num: int) → list

Generate all unique integer partitions of m using integers up to n.

poly_lambda(submat: Tensor, int_partition: list, power: int, loop: bool = False) → Tensor

Get the coefficient of the polynomial.

See https://arxiv.org/abs/1805.12498 Eq.(3.26) (noting that Eq.(3.26) contains a typo) and https://research-information.bris.ac.uk/ws/portalfiles/portal/329011096/thesis.pdf Eq.(3.80)