mod_linear_systems – Legolas v. 2.2.1

Module containing functions to solve linear systems $AX = B$ .

Uses

Functions

solve_linear_system_complex_banded solve_linear_system_complex_banded_LU

Subroutines

get_LU_factorisation_banded throw_info_nonzero_warning

Functions

public function solve_linear_system_complex_banded(bandmatrix, vector) result(xvector)

Calculates the solution $X$ to a system of linear equations $AX = B$ where $A$ is a complex banded matrix and $B$ is a complex vector.

Arguments

Type	Intent	Optional	Attributes		Name
type(banded_matrix_t),	intent(in)			::	bandmatrix	the banded $A$ -matrix on the left-hand side
complex(kind=dp),	intent(in)			::	vector(:)	the $B$ -vector on the right-hand side

Return Value complex(kind=dp)(size(vector))

the solution vector $X$

public function solve_linear_system_complex_banded_LU(bandmatrix, vector, LU, ipiv) result(xvector)

Calculates the solution $X$ to a system of linear equations $AX = B$ where $A$ is a complex banded matrix and $B$ is a complex vector. Uses the LU factorisation of $A$ and pivoting information from zgbtrf.

Arguments

Type	Intent		Name
type(banded_matrix_t),	intent(in)	::	bandmatrix	the banded $A$ -matrix on the left-hand side
complex(kind=dp),	intent(in)	::	vector(:)	the $B$ -vector on the right-hand side
complex(kind=dp),	intent(in)	::	LU(:,:)	the LU factorisation of $A$ , from zgbtrf
integer,	intent(in)	::	ipiv(:)	the pivoting information from zgbtrf

Return Value complex(kind=dp)(size(vector))

the solution vector $X$

Subroutines

public subroutine get_LU_factorisation_banded(bandmatrix, LU, ipiv)

Calculates the LU factorisation of a complex banded matrix $A$ . Uses the LAPACK routine zgbtrf.

Arguments

Type	Intent	Attributes		Name
type(banded_matrix_t),	intent(in)		::	bandmatrix	the banded $A$ -matrix on the left-hand side
complex(kind=dp),	intent(out),	allocatable	::	LU(:,:)	the LU factorisation of $A$
integer,	intent(out),	allocatable	::	ipiv(:)	the pivoting information after factorisation

private subroutine throw_info_nonzero_warning(info, routine_name)

Arguments

Type	Intent	Optional	Attributes		Name
integer,	intent(in)			::	info
character(len=*),	intent(in)			::	routine_name

mod_linear_systems Module

Contents

Functions

Subroutines

Uses

Contents

Functions

Subroutines

Functions

public function solve_linear_system_complex_banded(bandmatrix, vector) result(xvector)

Arguments

Return Value complex(kind=dp)(size(vector))

public function solve_linear_system_complex_banded_LU(bandmatrix, vector, LU, ipiv) result(xvector)

Arguments

Return Value complex(kind=dp)(size(vector))

Subroutines

public subroutine get_LU_factorisation_banded(bandmatrix, LU, ipiv)

Arguments

private subroutine throw_info_nonzero_warning(info, routine_name)

Arguments