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references/igraph-1.0.1/vendor/lapack/dstein.c
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/* -- translated by f2c (version 20240504).
You must link the resulting object file with libf2c:
on Microsoft Windows system, link with libf2c.lib;
on Linux or Unix systems, link with .../path/to/libf2c.a -lm
or, if you install libf2c.a in a standard place, with -lf2c -lm
-- in that order, at the end of the command line, as in
cc *.o -lf2c -lm
Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
http://www.netlib.org/f2c/libf2c.zip
*/
#include "f2c.h"
/* Table of constant values */
static integer c__2 = 2;
static integer c__1 = 1;
static integer c_n1 = -1;
/* > \brief \b DSTEIN
=========== DOCUMENTATION ===========
Online html documentation available at
http://www.netlib.org/lapack/explore-html/
> \htmlonly
> Download DSTEIN + dependencies
> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dstein.
f">
> [TGZ]</a>
> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dstein.
f">
> [ZIP]</a>
> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dstein.
f">
> [TXT]</a>
> \endhtmlonly
Definition:
===========
SUBROUTINE DSTEIN( N, D, E, M, W, IBLOCK, ISPLIT, Z, LDZ, WORK,
IWORK, IFAIL, INFO )
INTEGER INFO, LDZ, M, N
INTEGER IBLOCK( * ), IFAIL( * ), ISPLIT( * ),
$ IWORK( * )
DOUBLE PRECISION D( * ), E( * ), W( * ), WORK( * ), Z( LDZ, * )
> \par Purpose:
=============
>
> \verbatim
>
> DSTEIN computes the eigenvectors of a real symmetric tridiagonal
> matrix T corresponding to specified eigenvalues, using inverse
> iteration.
>
> The maximum number of iterations allowed for each eigenvector is
> specified by an internal parameter MAXITS (currently set to 5).
> \endverbatim
Arguments:
==========
> \param[in] N
> \verbatim
> N is INTEGER
> The order of the matrix. N >= 0.
> \endverbatim
>
> \param[in] D
> \verbatim
> D is DOUBLE PRECISION array, dimension (N)
> The n diagonal elements of the tridiagonal matrix T.
> \endverbatim
>
> \param[in] E
> \verbatim
> E is DOUBLE PRECISION array, dimension (N-1)
> The (n-1) subdiagonal elements of the tridiagonal matrix
> T, in elements 1 to N-1.
> \endverbatim
>
> \param[in] M
> \verbatim
> M is INTEGER
> The number of eigenvectors to be found. 0 <= M <= N.
> \endverbatim
>
> \param[in] W
> \verbatim
> W is DOUBLE PRECISION array, dimension (N)
> The first M elements of W contain the eigenvalues for
> which eigenvectors are to be computed. The eigenvalues
> should be grouped by split-off block and ordered from
> smallest to largest within the block. ( The output array
> W from DSTEBZ with ORDER = 'B' is expected here. )
> \endverbatim
>
> \param[in] IBLOCK
> \verbatim
> IBLOCK is INTEGER array, dimension (N)
> The submatrix indices associated with the corresponding
> eigenvalues in W; IBLOCK(i)=1 if eigenvalue W(i) belongs to
> the first submatrix from the top, =2 if W(i) belongs to
> the second submatrix, etc. ( The output array IBLOCK
> from DSTEBZ is expected here. )
> \endverbatim
>
> \param[in] ISPLIT
> \verbatim
> ISPLIT is INTEGER array, dimension (N)
> The splitting points, at which T breaks up into submatrices.
> The first submatrix consists of rows/columns 1 to
> ISPLIT( 1 ), the second of rows/columns ISPLIT( 1 )+1
> through ISPLIT( 2 ), etc.
> ( The output array ISPLIT from DSTEBZ is expected here. )
> \endverbatim
>
> \param[out] Z
> \verbatim
> Z is DOUBLE PRECISION array, dimension (LDZ, M)
> The computed eigenvectors. The eigenvector associated
> with the eigenvalue W(i) is stored in the i-th column of
> Z. Any vector which fails to converge is set to its current
> iterate after MAXITS iterations.
> \endverbatim
>
> \param[in] LDZ
> \verbatim
> LDZ is INTEGER
> The leading dimension of the array Z. LDZ >= max(1,N).
> \endverbatim
>
> \param[out] WORK
> \verbatim
> WORK is DOUBLE PRECISION array, dimension (5*N)
> \endverbatim
>
> \param[out] IWORK
> \verbatim
> IWORK is INTEGER array, dimension (N)
> \endverbatim
>
> \param[out] IFAIL
> \verbatim
> IFAIL is INTEGER array, dimension (M)
> On normal exit, all elements of IFAIL are zero.
> If one or more eigenvectors fail to converge after
> MAXITS iterations, then their indices are stored in
> array IFAIL.
> \endverbatim
>
> \param[out] INFO
> \verbatim
> INFO is INTEGER
> = 0: successful exit.
> < 0: if INFO = -i, the i-th argument had an illegal value
> > 0: if INFO = i, then i eigenvectors failed to converge
> in MAXITS iterations. Their indices are stored in
> array IFAIL.
> \endverbatim
> \par Internal Parameters:
=========================
>
> \verbatim
> MAXITS INTEGER, default = 5
> The maximum number of iterations performed.
>
> EXTRA INTEGER, default = 2
> The number of iterations performed after norm growth
> criterion is satisfied, should be at least 1.
> \endverbatim
Authors:
========
> \author Univ. of Tennessee
> \author Univ. of California Berkeley
> \author Univ. of Colorado Denver
> \author NAG Ltd.
> \date November 2011
> \ingroup doubleOTHERcomputational
=====================================================================
Subroutine */ int igraphdstein_(integer *n, doublereal *d__, doublereal *e,
integer *m, doublereal *w, integer *iblock, integer *isplit,
doublereal *z__, integer *ldz, doublereal *work, integer *iwork,
integer *ifail, integer *info)
{
/* System generated locals */
integer z_dim1, z_offset, i__1, i__2, i__3;
doublereal d__1, d__2, d__3, d__4, d__5;
/* Builtin functions */
double sqrt(doublereal);
/* Local variables */
integer i__, j, b1, j1, bn;
doublereal xj, scl, eps, sep, nrm, tol;
integer its;
doublereal xjm, ztr, eps1;
integer jblk, nblk;
extern doublereal igraphddot_(integer *, doublereal *, integer *, doublereal *,
integer *);
integer jmax;
extern doublereal igraphdnrm2_(integer *, doublereal *, integer *);
extern /* Subroutine */ int igraphdscal_(integer *, doublereal *, doublereal *,
integer *);
integer iseed[4], gpind, iinfo;
extern doublereal igraphdasum_(integer *, doublereal *, integer *);
extern /* Subroutine */ int igraphdcopy_(integer *, doublereal *, integer *,
doublereal *, integer *), igraphdaxpy_(integer *, doublereal *,
doublereal *, integer *, doublereal *, integer *);
doublereal ortol;
integer indrv1, indrv2, indrv3, indrv4, indrv5;
extern doublereal igraphdlamch_(char *);
extern /* Subroutine */ int igraphdlagtf_(integer *, doublereal *, doublereal *,
doublereal *, doublereal *, doublereal *, doublereal *, integer *
, integer *);
extern integer igraphidamax_(integer *, doublereal *, integer *);
extern /* Subroutine */ int igraphxerbla_(char *, integer *, ftnlen), igraphdlagts_(
integer *, integer *, doublereal *, doublereal *, doublereal *,
doublereal *, integer *, doublereal *, doublereal *, integer *);
integer nrmchk;
extern /* Subroutine */ int igraphdlarnv_(integer *, integer *, integer *,
doublereal *);
integer blksiz;
doublereal onenrm, dtpcrt, pertol;
/* -- LAPACK computational routine (version 3.4.0) --
-- LAPACK is a software package provided by Univ. of Tennessee, --
-- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
November 2011
=====================================================================
Test the input parameters.
Parameter adjustments */
--d__;
--e;
--w;
--iblock;
--isplit;
z_dim1 = *ldz;
z_offset = 1 + z_dim1;
z__ -= z_offset;
--work;
--iwork;
--ifail;
/* Function Body */
*info = 0;
i__1 = *m;
for (i__ = 1; i__ <= i__1; ++i__) {
ifail[i__] = 0;
/* L10: */
}
if (*n < 0) {
*info = -1;
} else if (*m < 0 || *m > *n) {
*info = -4;
} else if (*ldz < max(1,*n)) {
*info = -9;
} else {
i__1 = *m;
for (j = 2; j <= i__1; ++j) {
if (iblock[j] < iblock[j - 1]) {
*info = -6;
goto L30;
}
if (iblock[j] == iblock[j - 1] && w[j] < w[j - 1]) {
*info = -5;
goto L30;
}
/* L20: */
}
L30:
;
}
if (*info != 0) {
i__1 = -(*info);
igraphxerbla_("DSTEIN", &i__1, (ftnlen)6);
return 0;
}
/* Quick return if possible */
if (*n == 0 || *m == 0) {
return 0;
} else if (*n == 1) {
z__[z_dim1 + 1] = 1.;
return 0;
}
/* Get machine constants. */
eps = igraphdlamch_("Precision");
/* Initialize seed for random number generator DLARNV. */
for (i__ = 1; i__ <= 4; ++i__) {
iseed[i__ - 1] = 1;
/* L40: */
}
/* Initialize pointers. */
indrv1 = 0;
indrv2 = indrv1 + *n;
indrv3 = indrv2 + *n;
indrv4 = indrv3 + *n;
indrv5 = indrv4 + *n;
/* Compute eigenvectors of matrix blocks. */
j1 = 1;
i__1 = iblock[*m];
for (nblk = 1; nblk <= i__1; ++nblk) {
/* Find starting and ending indices of block nblk. */
if (nblk == 1) {
b1 = 1;
} else {
b1 = isplit[nblk - 1] + 1;
}
bn = isplit[nblk];
blksiz = bn - b1 + 1;
if (blksiz == 1) {
goto L60;
}
gpind = b1;
/* Compute reorthogonalization criterion and stopping criterion. */
onenrm = (d__1 = d__[b1], abs(d__1)) + (d__2 = e[b1], abs(d__2));
/* Computing MAX */
d__3 = onenrm, d__4 = (d__1 = d__[bn], abs(d__1)) + (d__2 = e[bn - 1],
abs(d__2));
onenrm = max(d__3,d__4);
i__2 = bn - 1;
for (i__ = b1 + 1; i__ <= i__2; ++i__) {
/* Computing MAX */
d__4 = onenrm, d__5 = (d__1 = d__[i__], abs(d__1)) + (d__2 = e[
i__ - 1], abs(d__2)) + (d__3 = e[i__], abs(d__3));
onenrm = max(d__4,d__5);
/* L50: */
}
ortol = onenrm * .001;
dtpcrt = sqrt(.1 / blksiz);
/* Loop through eigenvalues of block nblk. */
L60:
jblk = 0;
i__2 = *m;
for (j = j1; j <= i__2; ++j) {
if (iblock[j] != nblk) {
j1 = j;
goto L160;
}
++jblk;
xj = w[j];
/* Skip all the work if the block size is one. */
if (blksiz == 1) {
work[indrv1 + 1] = 1.;
goto L120;
}
/* If eigenvalues j and j-1 are too close, add a relatively
small perturbation. */
if (jblk > 1) {
eps1 = (d__1 = eps * xj, abs(d__1));
pertol = eps1 * 10.;
sep = xj - xjm;
if (sep < pertol) {
xj = xjm + pertol;
}
}
its = 0;
nrmchk = 0;
/* Get random starting vector. */
igraphdlarnv_(&c__2, iseed, &blksiz, &work[indrv1 + 1]);
/* Copy the matrix T so it won't be destroyed in factorization. */
igraphdcopy_(&blksiz, &d__[b1], &c__1, &work[indrv4 + 1], &c__1);
i__3 = blksiz - 1;
igraphdcopy_(&i__3, &e[b1], &c__1, &work[indrv2 + 2], &c__1);
i__3 = blksiz - 1;
igraphdcopy_(&i__3, &e[b1], &c__1, &work[indrv3 + 1], &c__1);
/* Compute LU factors with partial pivoting ( PT = LU ) */
tol = 0.;
igraphdlagtf_(&blksiz, &work[indrv4 + 1], &xj, &work[indrv2 + 2], &work[
indrv3 + 1], &tol, &work[indrv5 + 1], &iwork[1], &iinfo);
/* Update iteration count. */
L70:
++its;
if (its > 5) {
goto L100;
}
/* Normalize and scale the righthand side vector Pb.
Computing MAX */
d__2 = eps, d__3 = (d__1 = work[indrv4 + blksiz], abs(d__1));
scl = blksiz * onenrm * max(d__2,d__3) / igraphdasum_(&blksiz, &work[
indrv1 + 1], &c__1);
igraphdscal_(&blksiz, &scl, &work[indrv1 + 1], &c__1);
/* Solve the system LU = Pb. */
igraphdlagts_(&c_n1, &blksiz, &work[indrv4 + 1], &work[indrv2 + 2], &
work[indrv3 + 1], &work[indrv5 + 1], &iwork[1], &work[
indrv1 + 1], &tol, &iinfo);
/* Reorthogonalize by modified Gram-Schmidt if eigenvalues are
close enough. */
if (jblk == 1) {
goto L90;
}
if ((d__1 = xj - xjm, abs(d__1)) > ortol) {
gpind = j;
}
if (gpind != j) {
i__3 = j - 1;
for (i__ = gpind; i__ <= i__3; ++i__) {
ztr = -igraphddot_(&blksiz, &work[indrv1 + 1], &c__1, &z__[b1 +
i__ * z_dim1], &c__1);
igraphdaxpy_(&blksiz, &ztr, &z__[b1 + i__ * z_dim1], &c__1, &
work[indrv1 + 1], &c__1);
/* L80: */
}
}
/* Check the infinity norm of the iterate. */
L90:
jmax = igraphidamax_(&blksiz, &work[indrv1 + 1], &c__1);
nrm = (d__1 = work[indrv1 + jmax], abs(d__1));
/* Continue for additional iterations after norm reaches
stopping criterion. */
if (nrm < dtpcrt) {
goto L70;
}
++nrmchk;
if (nrmchk < 3) {
goto L70;
}
goto L110;
/* If stopping criterion was not satisfied, update info and
store eigenvector number in array ifail. */
L100:
++(*info);
ifail[*info] = j;
/* Accept iterate as jth eigenvector. */
L110:
scl = 1. / igraphdnrm2_(&blksiz, &work[indrv1 + 1], &c__1);
jmax = igraphidamax_(&blksiz, &work[indrv1 + 1], &c__1);
if (work[indrv1 + jmax] < 0.) {
scl = -scl;
}
igraphdscal_(&blksiz, &scl, &work[indrv1 + 1], &c__1);
L120:
i__3 = *n;
for (i__ = 1; i__ <= i__3; ++i__) {
z__[i__ + j * z_dim1] = 0.;
/* L130: */
}
i__3 = blksiz;
for (i__ = 1; i__ <= i__3; ++i__) {
z__[b1 + i__ - 1 + j * z_dim1] = work[indrv1 + i__];
/* L140: */
}
/* Save the shift to check eigenvalue spacing at next
iteration. */
xjm = xj;
/* L150: */
}
L160:
;
}
return 0;
/* End of DSTEIN */
} /* igraphdstein_ */