MomentGauge.Utility#

Module Contents#

Functions#

generalized_eigh_cholesky(A, B)

Compute the generalilzed eignvalue problem \(A \mathbf{x} = \lambda B \mathbf{x}\) in which A and B are Hermite matrix

generalized_eigh(A, B)

Compute the generalilzed eignvalue problem \(A \mathbf{x} = \lambda B \mathbf{x}\) in which A and B are Hermite matrix
MomentGauge.Utility.generalized_eigh_cholesky(A, B)#

Compute the generalilzed eignvalue problem \(A \mathbf{x} = \lambda B \mathbf{x}\) in which A and B are Hermite matrix

Parameters:

  • A (array of shape (M,M)) – a Hermite matrix of the shape (M, M)

  • B (array of shape (M,M)) – a Hermite matrix of the shape (M, M)

Returns:

A tuple containing

w: array of shape (M) - The eigenvalues in ascending order, each repeated according to its multiplicity.

V: array of shape (M,M) - The matrix whose ith column V[:, i] is the normalized eigenvector corresponding to the ith eigenvalue.

Return type:

Tuple

MomentGauge.Utility.generalized_eigh(A, B)#

Compute the generalilzed eignvalue problem \(A \mathbf{x} = \lambda B \mathbf{x}\) in which A and B are Hermite matrix

Parameters:

  • A (array of shape (M,M)) – a Hermite matrix of the shape (M, M)

  • B (array of shape (M,M)) – a Hermite matrix of the shape (M, M)

Returns:

A tuple containing

w: array of shape (M) - The eigenvalues in ascending order, each repeated according to its multiplicity.

V: array of shape (M,M) - The matrix whose ith column V[:, i] is the normalized eigenvector corresponding to the ith eigenvalue.

Return type:

Tuple