Module with a Lanczos-based eigenvalue solver. More...

Functions/Subroutines
subroutine, public	felanczossolve (MsgA, structA, coeffA, factorA, MsgB, structB, coeffB, factorB, MPARB, MTREEB, MSIFB, valueB, diagB, TOL, EVL, EVC, MIP, MOP, N, NEVAL, NEVEC, MAXLAN, MSING, LPU, IPSW, INFO)
	Solves a generalized symmetric eigenvalue problem. More...

subroutine	felfac (INFO, LPU, KSA, KSB, KPD, N, NEVAL, EPS, NN, MSING, MsgA, structA, coeffA, factorA, MsgB, structB, coeffB, factorB, diagB, MPARB, MTREEB, MSIFB, valueB)
	Administers the matrix factorizations for the Lanczos eigensolver. More...

subroutine	fefindandfixzeropivots (struct, coeff, NZERO, MSING, INFO)
	Repairs isolated zero pivot elements in the matrix. More...

subroutine	fesmm (INFO, LPU, IFLAG, Ndim, AllInt, X, Y, MsgA, structA, factorA, structB, coeffB, factorB, diagB, MPARB, MTREEB, MSIFB, valueB)
	Performs some linear algebra operations for the Lanczos eigensolver. More...

Variables
real(wp), dimension(:,:), allocatable, save	work1
	Internal work array. More...

real(wp), dimension(:,:), allocatable, save	work2
	Internal work array. More...

Detailed Description

Module with a Lanczos-based eigenvalue solver.

This module contains subroutines implementing the Lanczos eigenvalue solver on top of the GSF linear equation solver.

Function/Subroutine Documentation

◆ fefindandfixzeropivots()

subroutine felanczosmodule::fefindandfixzeropivots	(	type(sam), pointer	struct,
		type(cam), pointer	coeff,
		integer, intent(inout)	NZERO,
		integer(ik), dimension(:), intent(inout)	MSING,
		type(error_flag), pointer	INFO
	)

Repairs isolated zero pivot elements in the matrix.

Parameters

	struct	Symbolic assembly data for the matrix
	coeff	Coefficient assembly data for the matrix
[out]	NZERO	Number of zero pivot elements in the matrix
[out]	MSING	Array of singular equations detected during factorization
[out]	INFO	Error handler object, nullified on success

Author: Knut Morten Okstad

Date: 20 Sep 2005

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◆ felanczossolve()

subroutine, public felanczosmodule::felanczossolve	(	type(messagelevel), pointer	MsgA,
		type(sam), pointer	structA,
		type(cam), pointer	coeffA,
		type(gsfcolsup), pointer	factorA,
		type(messagelevel), pointer	MsgB,
		type(sam), pointer	structB,
		type(cam), pointer	coeffB,
		type(gsfcolsup), pointer	factorB,
		integer(ik), dimension(:), intent(in), optional	MPARB,
		integer(ik), dimension(:), intent(in), optional	MTREEB,
		integer(ik), dimension(:), intent(in), optional	MSIFB,
		real(wp), dimension(:), intent(inout), optional	valueB,
		real(wp), dimension(:), intent(inout), optional	diagB,
		real(wp), dimension(3), intent(inout)	TOL,
		real(wp), dimension(:), intent(out)	EVL,
		real(wp), dimension(:,:), intent(out)	EVC,
		integer(ik), dimension(:), intent(in)	MIP,
		integer(ik), dimension(:), intent(out)	MOP,
		integer, intent(in)	N,
		integer, intent(in)	NEVAL,
		integer, intent(in)	NEVEC,
		integer, intent(in)	MAXLAN,
		integer(ik), dimension(:), intent(out)	MSING,
		integer, intent(in)	LPU,
		integer, intent(in)	IPSW,
		type(error_flag), pointer	INFO
	)

Solves a generalized symmetric eigenvalue problem.

Parameters

	MsgA	GSF information for matrix A
	MsgB	GSF information for matrix B
	structA	Symbolic assembly data for matrix A
	structB	Symbolic assembly data for matrix B
	coeffA	Coefficient assembly data for matrix A
	coeffB	Coefficient assembly data for matrix B
	factorA	Factorization data for matrix A
	factorB	Factorization data for matrix B
[in]	MPARB	Sparse PARameters for SPR-matrix B
[in]	MTREEB	Elimination assembly TREES for SPR-matrix B
[in]	MSIFB	Storage Information for SPR-matrix B
	valueB	Matrix values for SPR-matrix B
	diagB	The diagonal values for SPR-matrix B
	TOL	Tolerances
[out]	EVL	Computed eigenvalues
[out]	EVC	Computed eigenvectors
[in]	MIP	Input options
[in]	N	Dimension of the equation system
[in]	NEVAL	Number of eigenvalues to return
[in]	NEVEC	Number of eigenvectors to return
[in]	MAXLAN	Maximum number of Lanczos vectors
[in]	LPU	File unit number for res-file output
[in]	IPSW	Print switch for debug output
[out]	MOP	Output options
[out]	MSING	Array of singular equations detected during factorization
[out]	INFO	Error handler object, nullified on success

This subroutine determines the NEVAL smallest eigenvalues λ_i of the generalized, symmetric eigenproblem

(A - λ_i*B) * q_i = 0

The routine also returns NLV (=MOP(3)) ortogonal Lanczos vectors or, optionally, approximations to NEVEC eigenvectors (corresponding to the NEVEC first eigenvalues). The eigenvectors, which are B-orthonormal, are returned as the first NEVEC vectors in EVC.

A is a symmetric matrix stored in sparse (compressed) format. B is either a symmetric sparse (KSB=1) or a diagonal (KSB=2) matrix. For both A and B the original matrices or their appropriate factors are accepted as input (in coeffA/factorA and coeffB/factorB). A truncated Lanczos method is used to transform the problem to tridiagonal, special form. The reduced, tridiagonal eigenproblem is solved by implicit QL transformation. Various reorthogonalization schemes may be specified.

This is the GSF version of the SPRLAN subroutine of the SAM library. The matrix B may optionally be represented by an SPR data structure, when KSB = MIP(2) = 3.

Author: Knut Morten Okstad

Date: 12 May 2005

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◆ felfac()

subroutine felanczosmodule::felfac	(	type(error_flag), pointer	INFO,
		integer, intent(in)	LPU,
		integer(ik), intent(inout)	KSA,
		integer(ik), intent(inout)	KSB,
		integer, intent(in)	KPD,
		integer, intent(in)	N,
		integer, intent(in)	NEVAL,
		real(wp), intent(in)	EPS,
		integer(ik), intent(out)	NN,
		integer(ik), dimension(:), intent(out)	MSING,
		type(messagelevel), pointer	MsgA,
		type(sam), pointer	structA,
		type(cam), pointer	coeffA,
		type(gsfcolsup), pointer	factorA,
		type(messagelevel), pointer	MsgB,
		type(sam), pointer	structB,
		type(cam), pointer	coeffB,
		type(gsfcolsup), pointer	factorB,
		real(wp), dimension(:), intent(inout), optional	diagB,
		integer(ik), dimension(:), intent(in), optional	MPARB,
		integer(ik), dimension(:), intent(in), optional	MTREEB,
		integer(ik), dimension(:), intent(in), optional	MSIFB,
		real(wp), dimension(:), intent(inout), optional	valueB
	)

private

Administers the matrix factorizations for the Lanczos eigensolver.

Parameters

[out]	INFO	Error handler object, nullified on success
[in]	LPU	File unit number for res-file output
[in]	KSA	Factorization option for matrix A
[in]	KSB	Factorization option for matrix B
[in]	KPD	Factorization option
[in]	N	Dimension of the equation system
[in]	NEVAL	Number of eigenvalues to return
[in]	EPS	Singularity tolerance
[in]	NN	Number of singular equations when B is diagonal
[out]	MSING	Array of singular equations detected during factorization
	MsgA	GSF information for matrix A
	structA	Symbolic assembly data for matrix A
	coeffA	Coefficient assembly data for matrix A
	factorA	Factorization data for matrix A
	MsgB	GSF information for matrix B
	structB	Symbolic assembly data for matrix B
	coeffB	Coefficient assembly data for matrix B
	factorB	Factorization data for matrix B
	diagB	The diagonal values for SPR-matrix B
[in]	MPARB	Sparse PARameters for SPR-matrix B
[in]	MTREEB	Elimination assembly TREES for SPR-matrix B
[in]	MSIFB	Storage Information for SPR-matrix B
	valueB	Matrix values for SPR-matrix B

Author: Knut Morten Okstad

Date: 12 May 2005

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◆ fesmm()

subroutine felanczosmodule::fesmm	(	type(error_flag), pointer	INFO,
		integer, intent(in)	LPU,
		integer, intent(in)	IFLAG,
		integer, intent(in)	Ndim,
		character(len=1), intent(in)	AllInt,
		real(wp), dimension(:), intent(inout)	X,
		real(wp), dimension(:), intent(out)	Y,
		type(messagelevel), pointer	MsgA,
		type(sam), pointer	structA,
		type(gsfcolsup), pointer	factorA,
		type(sam), optional, pointer	structB,
		type(cam), optional, pointer	coeffB,
		type(gsfcolsup), optional, pointer	factorB,
		real(wp), dimension(:), intent(in), optional	diagB,
		integer(ik), dimension(:), intent(in), optional	MPARB,
		integer(ik), dimension(:), intent(in), optional	MTREEB,
		integer(ik), dimension(:), intent(in), optional	MSIFB,
		real(wp), dimension(:), intent(in), optional	valueB
	)

private

Performs some linear algebra operations for the Lanczos eigensolver.

Parameters

[out]	INFO	Error handler object, nullified on success
[in]	LPU	File unit number for res-file output
[in]	IFLAG	Option telling which operation to perform (see below)
[in]	Ndim	Dimension of the equation system
[in]	AllInt	If 'A', use full matrix, if 'I' use internal DOFs only
	X	Vector of dimension Ndim
[out]	Y	Vector of dimension Ndim
	MsgA	GSF information for matrix A
	structA	Symbolic assembly data for matrix A
	factorA	Factorization data for matrix A
	structB	Symbolic assembly data for matrix B
	coeffB	Coefficient assembly data for matrix B
	factorB	Factorization data for matrix B
[in]	diagB	The diagonal values for SPR-matrix B
[in]	MPARB	Sparse PARameters for SPR-matrix B
[in]	MTREEB	Elimination assembly TREES for SPR-matrix B
[in]	MSIFB	Storage Information for SPR-matrix B
[in]	valueB	Matrix values for SPR-matrix B

This subroutine calculates one of the following:

IFLAG = 1: X := (A-1)*UbT*X
IFLAG = 2: Y = (A-1)*UbT*X
IFLAG = 3: X := Ub*(A-1)*UbT*X
IFLAG = 4: Y = Ub*(A-1)*UbT*X
IFLAG = 5: X := (Ua-T)*B*(Ua-1)*X
IFLAG = 6: Y = (Ua-T)*B*(Ua-1)*X

where X and Y are vectors, A is a symmetric sparse matrix, represented by its factors La*Da*LaT, stored in structA and factorA, Ua is the Cholesky factor of A, also stored in structA,factorA, B is either a symmetric sparse matrix, stored in structB,coeffB, a symmetric sparse in-core matrix, stored in MPARB, ..., valueB, or a diagonal matrix, stored in diagB. Ub is the Cholesky factor of B, stored in structB,factorB or in MPARB, ..., valueB, or in diagB if B is just a diagonal matrix.

Author: Knut Morten Okstad

Date: 12 May 2005

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Variable Documentation

◆ work1

real(wp), dimension(:,:), allocatable, save felanczosmodule::work1

private

Internal work array.

◆ work2

real(wp), dimension(:,:), allocatable, save felanczosmodule::work2

private

Internal work array.

Functions/Subroutines

Variables

Detailed Description

Function/Subroutine Documentation

◆ fefindandfixzeropivots()

◆ felanczossolve()

◆ felfac()

◆ fesmm()

Variable Documentation

◆ work1

◆ work2