gw_fm_utils Module Reference

Common full-matrix operations used by GW modules. More...

Data Types
interface	fm_contract_aba

Functions/Subroutines
subroutine, public	cfm_contract_aba (matrix_a, matrix_b, matrix_c)
	Computes A^H B A for complex full matrices.
subroutine, public	fm_invert (matrix_a, eigenvalue_threshold, unit_nr)
	Inverts a symmetric matrix. First, Cholesky decomposition is tried. If it fails, the matrix is diagonalized and inverted by taking inverse eigenvalues.
subroutine, public	fm_sqrt (matrix_a, matrix_b, eigenvalue_threshold, unit_nr)
	For input A, computes B such that B^T B=A. First, Cholesky decomposition is tried. If it fails, B is computed by diagonalizing A.
subroutine, public	fm_contract_aba (matrix_a, matrix_b, matrix_c)
	Computes A^T B A.

Detailed Description

Common full-matrix operations used by GW modules.

History

09.2026 created Jan Wilhelm

Function/Subroutine Documentation

cfm_contract_aba()

subroutine, public gw_fm_utils::cfm_contract_aba	(	type(cp_cfm_type), intent(in)	matrix_a,
		type(cp_cfm_type), intent(inout)	matrix_b,
		type(cp_cfm_type), intent(inout), optional	matrix_c )

Computes A^H B A for complex full matrices.

Parameters

matrix_A	left and right matrix A; H denotes its Hermitian transpose
matrix_B	input matrix B; overwritten by A^H B A if matrix_C is absent
matrix_C	optional output matrix C=A^H B A

Definition at line 52 of file gw_fm_utils.F.

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fm_invert()

subroutine, public gw_fm_utils::fm_invert	(	type(cp_fm_type), intent(inout)	matrix_a,
		real(kind=dp), intent(in), optional	eigenvalue_threshold,
		integer, intent(in), optional	unit_nr )

Inverts a symmetric matrix. First, Cholesky decomposition is tried. If it fails, the matrix is diagonalized and inverted by taking inverse eigenvalues.

Parameters

matrix_A	input A; output inverse or filtered pseudoinverse
eigenvalue_threshold	optional relative eigenvalue threshold
unit_nr	optional output unit for a failed Cholesky decomposition

Definition at line 89 of file gw_fm_utils.F.

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fm_sqrt()

subroutine, public gw_fm_utils::fm_sqrt	(	type(cp_fm_type), intent(in)	matrix_a,
		type(cp_fm_type), intent(inout)	matrix_b,
		real(kind=dp), intent(in), optional	eigenvalue_threshold,
		integer, intent(in), optional	unit_nr )

For input A, computes B such that B^T B=A. First, Cholesky decomposition is tried. If it fails, B is computed by diagonalizing A.

Parameters

matrix_A	symmetric input matrix A, retained unchanged
matrix_B	output matrix B
eigenvalue_threshold	optional relative eigenvalue threshold
unit_nr	optional output unit for a failed Cholesky decomposition

Definition at line 135 of file gw_fm_utils.F.

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fm_contract_aba()

subroutine, public gw_fm_utils::fm_contract_aba	(	type(cp_fm_type), intent(in)	matrix_a,
		type(cp_fm_type), intent(inout)	matrix_b,
		type(cp_fm_type), intent(inout), optional	matrix_c )

Computes A^T B A.

Parameters

matrix_A	left and right matrix A
matrix_B	input matrix B; overwritten by A^T B A if matrix_C is absent
matrix_C	optional output matrix C=A^T B A

Definition at line 187 of file gw_fm_utils.F.