eigensystem – FIDASIM

A basic libary for calculating matrix eigen-decompositions and inverses

Used by

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Variables

long float double ONE TWO ZERO XMACH_EPS MAXIT

Functions

comabs outerprod

Subroutines

RSWAP balance balback elmhes elmtrans Comdiv hqrvec hqr2 eigen swap ludcmp lubksb matinv

Variables

Type	Visibility	Attributes		Name		Initial
integer,	public,	parameter	::	long	=	kind(int(1))
integer,	public,	parameter	::	float	=	kind(1.e0)
integer,	public,	parameter	::	double	=	kind(1.d0)
real(kind=double),	public,	parameter	::	ONE	=	1.d0
real(kind=double),	public,	parameter	::	TWO	=	2.d0
real(kind=double),	public,	parameter	::	ZERO	=	0.d0
real(kind=double),	public,	parameter	::	XMACH_EPS	=	2.22d-16
integer,	public,	parameter	::	MAXIT	=	50

Functions

public function comabs(ar, ai)

Calculates absolute value of a complex number a

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=double)				::	ar	Real part of `a`
real(kind=double)				::	ai	Imaginary part of `a`

Return Value real(kind=double)

Absolute value of a

public function outerprod(a, b)

Calculates outer product

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=double),	intent(in),		dimension(:)	::	a
real(kind=double),	intent(in),		dimension(:)	::	b

Return Value real(kind=double), dimension(size(a),size(b))

Subroutines

public subroutine RSWAP(a, b)

Swaps values a and b

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=double)				::	a
real(kind=double)				::	b

public subroutine balance(n, mat, scal, low, high)

Balances the matrix so that the rows with zero entries off the diagonal are isolated and the remaining columns and rows are resized to have one norm close to 1.

Arguments

Type	Intent		Name
integer,	intent(in)	::	n	Dimension of `mat`
real(kind=double)		::	mat(0:n-1,0:n-1)	`n`x`n` scaled matrix
real(kind=double)		::	scal(0:n-1)	Contains isolated eigenvalue in the positions 0-`low` and `high`-`n`-1 its other components contain the scaling factors for transforming `mat`
integer,	intent(out)	::	low
integer,	intent(out)	::	high

public subroutine balback(n, low, high, scal, eivec)

Reverses the balancing of balance for the eigenvectors

Arguments

Type	Intent		Name
integer,	intent(in)	::	n	Dimension of matrix
integer,	intent(in)	::	low	First nonzero row
integer,	intent(in)	::	high	Last nonzero row
real(kind=double),	intent(in)	::	scal(0:n-1)	Scaling data from balance
real(kind=double),	intent(inout)	::	eivec(0:n-1,0:n-1)

public subroutine elmhes(n, low, high, mat, perm)

Transforms the matrix mat to upper Hessenberg form.

Arguments

Type	Intent		Name
integer,	intent(in)	::	n	Dimension of `mat`
integer,	intent(in)	::	low	First nonzero row
integer,	intent(in)	::	high	Last nonzero row
real(kind=double),	intent(inout)	::	mat(0:n-1,0:n-1)	is stored in the lower triangle
integer,	intent(out)	::	perm(0:n-1)	Permutation vector for elmtrans

public subroutine elmtrans(n, low, high, mat, perm, h)

Elmtrans copies the Hessenberg matrix stored in mat to h

Arguments

Type	Intent		Name
integer,	intent(in)	::	n	Dimension of mat
integer,	intent(in)	::	low	First nonzero row
integer,	intent(in)	::	high	Last nonzero row
real(kind=double),	intent(in)	::	mat(0:n-1,0:n-1)	`n`x`n` input matrix
integer,	intent(in)	::	perm(0:n-1)	Permutation data from elmhes
real(kind=double),	intent(out)	::	h(0:n-1,0:n-1)	Hessenberg matrix

public subroutine Comdiv(ar, ai, br, bi, cr, ci, rc)

Performs complex division c = a / b

Arguments

Type		Name
real(kind=double)	::	ar	Real part of numerator
real(kind=double)	::	ai	Imaginary part of numerator
real(kind=double)	::	br	Real part of denominator
real(kind=double)	::	bi	Imaginary part of denominator
real(kind=double)	::	cr	Real part of quotient
real(kind=double)	::	ci	Imaginary part of quotient
integer	::	rc	return code

public subroutine hqrvec(n, low, high, h, wr, wi, eivec, rc)

Computes the eigenvectors for the eigenvalues found in hqr2

Arguments

Type	Intent		Name
integer,	intent(in)	::	n
integer,	intent(in)	::	low
integer,	intent(in)	::	high
real(kind=double)		::	h(0:n-1,0:n-1)
real(kind=double),	intent(in)	::	wr(0:n-1)
real(kind=double),	intent(in)	::	wi(0:n-1)
real(kind=double),	intent(out)	::	eivec(0:n-1,0:n-1)
integer		::	rc

public subroutine hqr2(n, low, high, h, wr, wi, eivec, cnt, rc)

Computes the eigenvalues and (if vec = True) the eigenvectors of an n * n upper Hessenberg matrix.

Arguments

Type	Intent		Name
integer,	intent(in)	::	n
integer,	intent(in)	::	low
integer,	intent(in)	::	high
real(kind=double),	intent(out)	::	h(0:n-1,0:n-1)
real(kind=double),	intent(out)	::	wr(0:n-1)
real(kind=double),	intent(out)	::	wi(0:n-1)
real(kind=double),	intent(out)	::	eivec(0:n-1,0:n-1)
integer,	intent(out)	::	cnt(0:n-1)
integer,	intent(out)	::	rc

public subroutine eigen(n, matrix, eigvec, eigval)

The subroutine eigen determines all eigenvalues and (if desired) all eigenvectors of a real square n * n matrix via the QR method in the version of Martin, Parlett, Peters, Reinsch and Wilkinson.

Arguments

Type	Intent	Attributes		Name
integer,	intent(in)		::	n
real(kind=double),	intent(in),	dimension(n,n)	::	matrix
real(kind=double),	intent(out),	dimension(n,n)	::	eigvec
real(kind=double),	intent(out),	dimension(n)	::	eigval

public subroutine swap(a, b)

Swap arrays a and b

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=double),	intent(inout),		dimension(:)	::	a
real(kind=double),	intent(inout),		dimension(:)	::	b

public subroutine ludcmp(a, indx, d)

Calculates LU decomposition

Arguments

Type	Intent	Attributes		Name
real(kind=double),	intent(inout),	dimension(:,:)	::	a
integer,	intent(out),	dimension(:)	::	indx
real(kind=double),	intent(out)		::	d

public subroutine lubksb(a, indx, b)

Does LU back substitution

Arguments

Type	Intent	Attributes		Name
real(kind=double),	intent(in),	dimension(:,:)	::	a
integer,	intent(in),	dimension(:)	::	indx
real(kind=double),	intent(inout),	dimension(:)	::	b

public subroutine matinv(a, b)

Matrix inversion with LU-decomposition

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=double),	intent(in),		dimension(:,:)	::	a
real(kind=double),	intent(out),		dimension(:,:)	::	b

eigensystem Module

Contents

Variables

Functions

Subroutines

Used by

Contents

Variables

Functions

Subroutines

Variables

Functions

public function comabs(ar, ai)

Arguments

Return Value real(kind=double)

public function outerprod(a, b)

Arguments

Return Value real(kind=double), dimension(size(a),size(b))

Subroutines

public subroutine RSWAP(a, b)

Arguments

public subroutine balance(n, mat, scal, low, high)

Arguments

public subroutine balback(n, low, high, scal, eivec)

Arguments

public subroutine elmhes(n, low, high, mat, perm)

Arguments

public subroutine elmtrans(n, low, high, mat, perm, h)

Arguments

public subroutine Comdiv(ar, ai, br, bi, cr, ci, rc)

Arguments

public subroutine hqrvec(n, low, high, h, wr, wi, eivec, rc)

Arguments

public subroutine hqr2(n, low, high, h, wr, wi, eivec, cnt, rc)

Arguments

public subroutine eigen(n, matrix, eigvec, eigval)

Arguments

public subroutine swap(a, b)

Arguments

public subroutine ludcmp(a, indx, d)

Arguments

public subroutine lubksb(a, indx, b)

Arguments

public subroutine matinv(a, b)

Arguments