smod_qr_cholesky – Legolas v. 2.2.1

Submodule containing the implementation of the QR-cholesky algorithm. Using LAPACKS's zpbtrf and BLAS's zgbtrs, the original problem is written as a standard eigenvalue problem as $U^{-H}\mathcal{A}U^{-1}\textbf{Y} = \omega\textbf{Y}\$ where $\mathcal{B} = U^HU$ is positive definite and $\textbf{Y}=U\textbf{X}$ . Eventually a call to LAPACK's zgeev routine is done to obtain all eigenvalues and eigenvectors.

Uses

- mod_transform_matrix
- mod_banded_matrix_hermitian
- Ancestors:
- mod_solvers

Module Procedures

module procedure /home/runner/work/legolas/legolas/docs/ford/module/smod_qr_cholesky.html qr_cholesky module subroutine qr_cholesky(matrix_A, matrix_B, settings, omega, vr)

Solves the eigenvalue problem by rewriting it to a standard form through splitting of the B-matrix.

Arguments

Type	Intent		Name
type(matrix_t),	intent(in)	::	matrix_A	matrix A
type(matrix_t),	intent(in)	::	matrix_B	matrix B
type(settings_t),	intent(in)	::	settings	settings object
complex(kind=dp),	intent(out)	::	omega(:)	array with eigenvalues
complex(kind=dp),	intent(out)	::	vr(:,:)	array with right eigenvectors

smod_qr_cholesky Submodule

Contents

Module Procedures

Uses

Ancestors:

Module Procedures

module procedure /home/runner/work/legolas/legolas/docs/ford/module/smod_qr_cholesky.html qr_cholesky module subroutine qr_cholesky(matrix_A, matrix_B, settings, omega, vr)

Arguments

smod_qr_cholesky Submodule

Contents

Module Procedures

Uses

Ancestors:

Module Procedures

module procedure /home/runner/work/legolas/legolas/docs/ford/module/smod_qr_cholesky.html qr_cholesky module subroutine qr_cholesky(matrix_A, matrix_B, settings, omega, vr) Interface →

Arguments

module procedure /home/runner/work/legolas/legolas/docs/ford/module/smod_qr_cholesky.html qr_cholesky module subroutine qr_cholesky(matrix_A, matrix_B, settings, omega, vr)