eispack_module – fortran-astrodynamics-toolkit

Refactored SLATEC/EISPACK routines for computing eigenvalues and eigenvectors.

Uses

- kind_module
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Used by

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Nodes of different colours represent the following:

Solid arrows point from a submodule to the (sub)module which it is descended from. Dashed arrows point from a module or program unit to modules which it uses.

Subroutines

private subroutine balanc(Nm, n, a, Low, Igh, Scale)

Balance a real general matrix and isolate eigenvalues whenever possible.

Arguments

Type		Name
integer	::	Nm
integer	::	n
real(kind=wp)	::	a(Nm,*)
integer	::	Low
integer	::	Igh
real(kind=wp)	::	Scale(*)

private subroutine balbak(Nm, n, Low, Igh, Scale, m, z)

Form the eigenvectors of a real general matrix from the eigenvectors of matrix output from BALANC.

Arguments

Type		Name
integer	::	Nm
integer	::	n
integer	::	Low
integer	::	Igh
real(kind=wp)	::	Scale(*)
integer	::	m
real(kind=wp)	::	z(Nm,*)

private subroutine cdiv(Ar, Ai, Br, Bi, Cr, Ci)

Compute the complex quotient of two complex numbers.

Arguments

Type		Name
real(kind=wp)	::	Ar
real(kind=wp)	::	Ai
real(kind=wp)	::	Br
real(kind=wp)	::	Bi
real(kind=wp)	::	Cr
real(kind=wp)	::	Ci

private subroutine elmhes(Nm, n, Low, Igh, a, Intv)

Reduce a real general matrix to upper Hessenberg form using stabilized elementary similarity transformations.

Arguments

Type		Name
integer	::	Nm
integer	::	n
integer	::	Low
integer	::	Igh
real(kind=wp)	::	a(Nm,*)
integer	::	Intv(*)

private subroutine eltran(Nm, n, Low, Igh, a, Int, z)

Accumulates the stabilized elementary similarity transformations used in the reduction of a real general matrix to upper Hessenberg form by ELMHES.

Arguments

Type		Name
integer	::	Nm
integer	::	n
integer	::	Low
integer	::	Igh
real(kind=wp)	::	a(Nm,*)
integer	::	Int(*)
real(kind=wp)	::	z(Nm,*)

private subroutine hqr(Nm, n, Low, Igh, h, Wr, Wi, Ierr)

Compute the eigenvalues of a real upper Hessenberg matrix using the QR method.

Arguments

Type		Name
integer	::	Nm
integer	::	n
integer	::	Low
integer	::	Igh
real(kind=wp)	::	h(Nm,*)
real(kind=wp)	::	Wr(*)
real(kind=wp)	::	Wi(*)
integer	::	Ierr

private subroutine hqr2(Nm, n, Low, Igh, h, Wr, Wi, z, Ierr)

Compute the eigenvalues and eigenvectors of a real upper Hessenberg matrix using QR method.

Arguments

Type		Name
integer	::	Nm
integer	::	n
integer	::	Low
integer	::	Igh
real(kind=wp)	::	h(Nm,*)
real(kind=wp)	::	Wr(*)
real(kind=wp)	::	Wi(*)
real(kind=wp)	::	z(Nm,*)
integer	::	Ierr

private subroutine rg(Nm, n, a, Wr, Wi, Matz, z, Iv1, Fv1, Ierr)

Compute the eigenvalues and, optionally, the eigenvectors of a real general matrix.

Arguments

Type	Intent		Name
integer,	intent(in)	::	Nm	must be set to the row dimension of the two-dimensional array parameters, A and Z, as declared in the calling program dimension statement.
integer,	intent(in)	::	n	the order of the matrix A. N must be less than or equal to NM.
real(kind=wp),	intent(inout)	::	a(Nm,*)	contains the real general matrix. dimensioned A(NM,N). Note: A is destroyed on output.
real(kind=wp),	intent(out)	::	Wr(*)	real part of the eigenvalues. The eigenvalues are unordered except that complex conjugate pairs of eigenvalues appear consecutively with the eigenvalue having the positive imaginary part first. If an error exit is made, the eigenvalues should be correct for indices IERR+1, IERR+2, ..., N. WR and WI are one-dimensional REAL arrays, dimensioned WR(N) and WI(N).
real(kind=wp),	intent(out)	::	Wi(*)	imaginary part of the eigenvalues.
integer,	intent(in)	::	Matz	an INTEGER variable set equal to zero if only eigenvalues are desired. Otherwise, it is set to any non-zero integer for both eigenvalues and eigenvectors.
real(kind=wp),	intent(out)	::	z(Nm,*)	contains the real and imaginary parts of the eigenvectors if MATZ is not zero. If the J-th eigenvalue is real, the J-th column of Z contains its eigenvector. If the J-th eigenvalue is complex with positive imaginary part, the J-th and (J+1)-th columns of Z contain the real and imaginary parts of its eigenvector. The conjugate of this vector is the eigenvector for the conjugate eigenvalue. Z is a two-dimensional REAL array, dimensioned Z(NM,N).
integer,	intent(inout)	::	Iv1(*)	one-dimensional temporary storage arrays of dimension N.
real(kind=wp),	intent(inout)	::	Fv1(*)	one-dimensional temporary storage arrays of dimension N.
integer,	intent(out)	::	Ierr	an INTEGER flag set to: Read more…

public subroutine compute_eigenvalues_and_eigenvectors(n, a, w, z, ierr)

Compute the eigenvalues and, optionally, the eigenvectors of a real general matrix.

Arguments

Type	Intent	Attributes		Name
integer,	intent(in)		::	n	the order of the matrix `a`
real(kind=wp),	intent(in),	dimension(n,n)	::	a	contains the real general matrix
real(kind=wp),	intent(out),	dimension(n,2)	::	w	real and imaginary parts of the eigenvalues
real(kind=wp),	intent(out),	dimension(n,n)	::	z	real and imaginary parts of the eigenvectors
integer,	intent(out)		::	ierr	output flag from rg

public subroutine compute_real_eigenvalues_and_normalized_eigenvectors(n, a, e, v, n_results, ierr)

Returns only the real eigenvalues and the associated eigenvectors. Wrapper for compute_eigenvalues_and_eigenvectors.

Arguments

Type	Intent	Attributes		Name
integer,	intent(in)		::	n	the order of the matrix `a`
real(kind=wp),	intent(in),	dimension(n,n)	::	a	contains the real general matrix
real(kind=wp),	intent(out),	dimension(:), allocatable	::	e	eigenvalues (size `n_results`)
real(kind=wp),	intent(out),	dimension(:,:), allocatable	::	v	eigenvectors (size `n,n_results`)
integer,	intent(out)		::	n_results	number of real eigenvalues
integer,	intent(out)		::	ierr	output flag from rg

public subroutine eispack_test()

Unit test

Arguments

None

eispack_module Module

Contents

Subroutines

Uses

Used by

Subroutines

private subroutine balanc(Nm, n, a, Low, Igh, Scale)

Arguments

private subroutine balbak(Nm, n, Low, Igh, Scale, m, z)

Arguments

private subroutine cdiv(Ar, Ai, Br, Bi, Cr, Ci)

Arguments

private subroutine elmhes(Nm, n, Low, Igh, a, Intv)

Arguments

private subroutine eltran(Nm, n, Low, Igh, a, Int, z)

Arguments

private subroutine hqr(Nm, n, Low, Igh, h, Wr, Wi, Ierr)

Arguments

private subroutine hqr2(Nm, n, Low, Igh, h, Wr, Wi, z, Ierr)

Arguments

private subroutine rg(Nm, n, a, Wr, Wi, Matz, z, Iv1, Fv1, Ierr)

Arguments

public subroutine compute_eigenvalues_and_eigenvectors(n, a, w, z, ierr)

Arguments

public subroutine compute_real_eigenvalues_and_normalized_eigenvectors(n, a, e, v, n_results, ierr)

Arguments

public subroutine eispack_test()

Arguments