utils

Various utilities used by the rest of the library.

HT	Hermitian conjugate of the input array.
n_slice	Number of elements returned by a slice, assuming a very long array.
block_svd	Completes a block singular-value decomposition.
normalize_SV	Normalises the input array and prints the norm in the logs.

temfpy.utils.HT(M)

Hermitian conjugate of the input array.

Return type:

ndarray

temfpy.utils.n_slice(x)

Number of elements returned by a slice, assuming a very long array.

Return type:

int

temfpy.utils.block_svd(CLR, vL, vR, e, degeneracy_tol=1e-12, overwrite=True)

Completes a block singular-value decomposition.

Assuming the matrix \(v_L^\dagger C_{LR} v_R\) is block diagonal, performs the SVD of each block to obtain singular vectors of CLR.

Blocks are delineated by approximately-equal values of e.

Parameters:

• CLR (ndarray (N, M)) – The matrix whose SVD is sought.

• vL (ndarray (N, K)) – The left almost-singular vectors of CLR.

• vR (ndarray (M, K)) – The right almost-singular vectors of CLR.

• e (ndarray (K,)) – Eigenvalues used to delineate blocks.

• degeneracy_tol (float) –

  Threshold for considering consecutive entries of e equal.

  Rows/columns i and i+1 are assumed to be in different blocks if abs(e[i] - e[i+1]) > degeneracy_tol.

• overwrite (bool) – Overwrite vL and vR with the signular vectors (default: True).

Return type:

tuple[ndarray, ndarray]

Returns:

The singular vectors of CLR.

temfpy.utils.normalize_SV(λ, logger)

Normalises the input array and prints the norm in the logs.

Return type:

ndarray