/* -- translated by f2c (version 20100827).
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
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Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
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*/
#include "f2c.h"
/* Table of constant values */
static doublereal c_b9 = 0.;
static doublereal c_b10 = 1.;
static integer c__0 = 0;
static integer c__1 = 1;
static integer c__2 = 2;
/* > \brief \b DSTEQR
=========== DOCUMENTATION ===========
Online html documentation available at
http://www.netlib.org/lapack/explore-html/
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f">
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> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dsteqr.
f">
> [TXT]</a>
> \endhtmlonly
Definition:
===========
SUBROUTINE DSTEQR( COMPZ, N, D, E, Z, LDZ, WORK, INFO )
CHARACTER COMPZ
INTEGER INFO, LDZ, N
DOUBLE PRECISION D( * ), E( * ), WORK( * ), Z( LDZ, * )
> \par Purpose:
=============
>
> \verbatim
>
> DSTEQR computes all eigenvalues and, optionally, eigenvectors of a
> symmetric tridiagonal matrix using the implicit QL or QR method.
> The eigenvectors of a full or band symmetric matrix can also be found
> if DSYTRD or DSPTRD or DSBTRD has been used to reduce this matrix to
> tridiagonal form.
> \endverbatim
Arguments:
==========
> \param[in] COMPZ
> \verbatim
> COMPZ is CHARACTER*1
> = 'N': Compute eigenvalues only.
> = 'V': Compute eigenvalues and eigenvectors of the original
> symmetric matrix. On entry, Z must contain the
> orthogonal matrix used to reduce the original matrix
> to tridiagonal form.
> = 'I': Compute eigenvalues and eigenvectors of the
> tridiagonal matrix. Z is initialized to the identity
> matrix.
> \endverbatim
>
> \param[in] N
> \verbatim
> N is INTEGER
> The order of the matrix. N >= 0.
> \endverbatim
>
> \param[in,out] D
> \verbatim
> D is DOUBLE PRECISION array, dimension (N)
> On entry, the diagonal elements of the tridiagonal matrix.
> On exit, if INFO = 0, the eigenvalues in ascending order.
> \endverbatim
>
> \param[in,out] E
> \verbatim
> E is DOUBLE PRECISION array, dimension (N-1)
> On entry, the (n-1) subdiagonal elements of the tridiagonal
> matrix.
> On exit, E has been destroyed.
> \endverbatim
>
> \param[in,out] Z
> \verbatim
> Z is DOUBLE PRECISION array, dimension (LDZ, N)
> On entry, if COMPZ = 'V', then Z contains the orthogonal
> matrix used in the reduction to tridiagonal form.
> On exit, if INFO = 0, then if COMPZ = 'V', Z contains the
> orthonormal eigenvectors of the original symmetric matrix,
> and if COMPZ = 'I', Z contains the orthonormal eigenvectors
> of the symmetric tridiagonal matrix.
> If COMPZ = 'N', then Z is not referenced.
> \endverbatim
>
> \param[in] LDZ
> \verbatim
> LDZ is INTEGER
> The leading dimension of the array Z. LDZ >= 1, and if
> eigenvectors are desired, then LDZ >= max(1,N).
> \endverbatim
>
> \param[out] WORK
> \verbatim
> WORK is DOUBLE PRECISION array, dimension (max(1,2*N-2))
> If COMPZ = 'N', then WORK is not referenced.
> \endverbatim
>
> \param[out] INFO
> \verbatim
> INFO is INTEGER
> = 0: successful exit
> < 0: if INFO = -i, the i-th argument had an illegal value
> > 0: the algorithm has failed to find all the eigenvalues in
> a total of 30*N iterations; if INFO = i, then i
> elements of E have not converged to zero; on exit, D
> and E contain the elements of a symmetric tridiagonal
> matrix which is orthogonally similar to the original
> matrix.
> \endverbatim
Authors:
========
> \author Univ. of Tennessee
> \author Univ. of California Berkeley
> \author Univ. of Colorado Denver
> \author NAG Ltd.
> \date November 2011
> \ingroup auxOTHERcomputational
=====================================================================
Subroutine */ int igraphdsteqr_(char *compz, integer *n, doublereal *d__,
doublereal *e, doublereal *z__, integer *ldz, doublereal *work,
integer *info)
{
/* System generated locals */
integer z_dim1, z_offset, i__1, i__2;
doublereal d__1, d__2;
/* Builtin functions */
double sqrt(doublereal), d_sign(doublereal *, doublereal *);
/* Local variables */
doublereal b, c__, f, g;
integer i__, j, k, l, m;
doublereal p, r__, s;
integer l1, ii, mm, lm1, mm1, nm1;
doublereal rt1, rt2, eps;
integer lsv;
doublereal tst, eps2;
integer lend, jtot;
extern /* Subroutine */ int igraphdlae2_(doublereal *, doublereal *, doublereal
*, doublereal *, doublereal *);
extern logical igraphlsame_(char *, char *);
extern /* Subroutine */ int igraphdlasr_(char *, char *, char *, integer *,
integer *, doublereal *, doublereal *, doublereal *, integer *);
doublereal anorm;
extern /* Subroutine */ int igraphdswap_(integer *, doublereal *, integer *,
doublereal *, integer *), igraphdlaev2_(doublereal *, doublereal *,
doublereal *, doublereal *, doublereal *, doublereal *,
doublereal *);
integer lendm1, lendp1;
extern doublereal igraphdlapy2_(doublereal *, doublereal *), igraphdlamch_(char *);
integer iscale;
extern /* Subroutine */ int igraphdlascl_(char *, integer *, integer *,
doublereal *, doublereal *, integer *, integer *, doublereal *,
integer *, integer *), igraphdlaset_(char *, integer *, integer
*, doublereal *, doublereal *, doublereal *, integer *);
doublereal safmin;
extern /* Subroutine */ int igraphdlartg_(doublereal *, doublereal *,
doublereal *, doublereal *, doublereal *);
doublereal safmax;
extern /* Subroutine */ int igraphxerbla_(char *, integer *, ftnlen);
extern doublereal igraphdlanst_(char *, integer *, doublereal *, doublereal *);
extern /* Subroutine */ int igraphdlasrt_(char *, integer *, doublereal *,
integer *);
integer lendsv;
doublereal ssfmin;
integer nmaxit, icompz;
doublereal ssfmax;
/* -- 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;
z_dim1 = *ldz;
z_offset = 1 + z_dim1;
z__ -= z_offset;
--work;
/* Function Body */
*info = 0;
if (igraphlsame_(compz, "N")) {
icompz = 0;
} else if (igraphlsame_(compz, "V")) {
icompz = 1;
} else if (igraphlsame_(compz, "I")) {
icompz = 2;
} else {
icompz = -1;
}
if (icompz < 0) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*ldz < 1 || icompz > 0 && *ldz < max(1,*n)) {
*info = -6;
}
if (*info != 0) {
i__1 = -(*info);
igraphxerbla_("DSTEQR", &i__1, (ftnlen)6);
return 0;
}
/* Quick return if possible */
if (*n == 0) {
return 0;
}
if (*n == 1) {
if (icompz == 2) {
z__[z_dim1 + 1] = 1.;
}
return 0;
}
/* Determine the unit roundoff and over/underflow thresholds. */
eps = igraphdlamch_("E");
/* Computing 2nd power */
d__1 = eps;
eps2 = d__1 * d__1;
safmin = igraphdlamch_("S");
safmax = 1. / safmin;
ssfmax = sqrt(safmax) / 3.;
ssfmin = sqrt(safmin) / eps2;
/* Compute the eigenvalues and eigenvectors of the tridiagonal
matrix. */
if (icompz == 2) {
igraphdlaset_("Full", n, n, &c_b9, &c_b10, &z__[z_offset], ldz);
}
nmaxit = *n * 30;
jtot = 0;
/* Determine where the matrix splits and choose QL or QR iteration
for each block, according to whether top or bottom diagonal
element is smaller. */
l1 = 1;
nm1 = *n - 1;
L10:
if (l1 > *n) {
goto L160;
}
if (l1 > 1) {
e[l1 - 1] = 0.;
}
if (l1 <= nm1) {
i__1 = nm1;
for (m = l1; m <= i__1; ++m) {
tst = (d__1 = e[m], abs(d__1));
if (tst == 0.) {
goto L30;
}
if (tst <= sqrt((d__1 = d__[m], abs(d__1))) * sqrt((d__2 = d__[m
+ 1], abs(d__2))) * eps) {
e[m] = 0.;
goto L30;
}
/* L20: */
}
}
m = *n;
L30:
l = l1;
lsv = l;
lend = m;
lendsv = lend;
l1 = m + 1;
if (lend == l) {
goto L10;
}
/* Scale submatrix in rows and columns L to LEND */
i__1 = lend - l + 1;
anorm = igraphdlanst_("M", &i__1, &d__[l], &e[l]);
iscale = 0;
if (anorm == 0.) {
goto L10;
}
if (anorm > ssfmax) {
iscale = 1;
i__1 = lend - l + 1;
igraphdlascl_("G", &c__0, &c__0, &anorm, &ssfmax, &i__1, &c__1, &d__[l], n,
info);
i__1 = lend - l;
igraphdlascl_("G", &c__0, &c__0, &anorm, &ssfmax, &i__1, &c__1, &e[l], n,
info);
} else if (anorm < ssfmin) {
iscale = 2;
i__1 = lend - l + 1;
igraphdlascl_("G", &c__0, &c__0, &anorm, &ssfmin, &i__1, &c__1, &d__[l], n,
info);
i__1 = lend - l;
igraphdlascl_("G", &c__0, &c__0, &anorm, &ssfmin, &i__1, &c__1, &e[l], n,
info);
}
/* Choose between QL and QR iteration */
if ((d__1 = d__[lend], abs(d__1)) < (d__2 = d__[l], abs(d__2))) {
lend = lsv;
l = lendsv;
}
if (lend > l) {
/* QL Iteration
Look for small subdiagonal element. */
L40:
if (l != lend) {
lendm1 = lend - 1;
i__1 = lendm1;
for (m = l; m <= i__1; ++m) {
/* Computing 2nd power */
d__2 = (d__1 = e[m], abs(d__1));
tst = d__2 * d__2;
if (tst <= eps2 * (d__1 = d__[m], abs(d__1)) * (d__2 = d__[m
+ 1], abs(d__2)) + safmin) {
goto L60;
}
/* L50: */
}
}
m = lend;
L60:
if (m < lend) {
e[m] = 0.;
}
p = d__[l];
if (m == l) {
goto L80;
}
/* If remaining matrix is 2-by-2, use DLAE2 or SLAEV2
to compute its eigensystem. */
if (m == l + 1) {
if (icompz > 0) {
igraphdlaev2_(&d__[l], &e[l], &d__[l + 1], &rt1, &rt2, &c__, &s);
work[l] = c__;
work[*n - 1 + l] = s;
igraphdlasr_("R", "V", "B", n, &c__2, &work[l], &work[*n - 1 + l], &
z__[l * z_dim1 + 1], ldz);
} else {
igraphdlae2_(&d__[l], &e[l], &d__[l + 1], &rt1, &rt2);
}
d__[l] = rt1;
d__[l + 1] = rt2;
e[l] = 0.;
l += 2;
if (l <= lend) {
goto L40;
}
goto L140;
}
if (jtot == nmaxit) {
goto L140;
}
++jtot;
/* Form shift. */
g = (d__[l + 1] - p) / (e[l] * 2.);
r__ = igraphdlapy2_(&g, &c_b10);
g = d__[m] - p + e[l] / (g + d_sign(&r__, &g));
s = 1.;
c__ = 1.;
p = 0.;
/* Inner loop */
mm1 = m - 1;
i__1 = l;
for (i__ = mm1; i__ >= i__1; --i__) {
f = s * e[i__];
b = c__ * e[i__];
igraphdlartg_(&g, &f, &c__, &s, &r__);
if (i__ != m - 1) {
e[i__ + 1] = r__;
}
g = d__[i__ + 1] - p;
r__ = (d__[i__] - g) * s + c__ * 2. * b;
p = s * r__;
d__[i__ + 1] = g + p;
g = c__ * r__ - b;
/* If eigenvectors are desired, then save rotations. */
if (icompz > 0) {
work[i__] = c__;
work[*n - 1 + i__] = -s;
}
/* L70: */
}
/* If eigenvectors are desired, then apply saved rotations. */
if (icompz > 0) {
mm = m - l + 1;
igraphdlasr_("R", "V", "B", n, &mm, &work[l], &work[*n - 1 + l], &z__[l
* z_dim1 + 1], ldz);
}
d__[l] -= p;
e[l] = g;
goto L40;
/* Eigenvalue found. */
L80:
d__[l] = p;
++l;
if (l <= lend) {
goto L40;
}
goto L140;
} else {
/* QR Iteration
Look for small superdiagonal element. */
L90:
if (l != lend) {
lendp1 = lend + 1;
i__1 = lendp1;
for (m = l; m >= i__1; --m) {
/* Computing 2nd power */
d__2 = (d__1 = e[m - 1], abs(d__1));
tst = d__2 * d__2;
if (tst <= eps2 * (d__1 = d__[m], abs(d__1)) * (d__2 = d__[m
- 1], abs(d__2)) + safmin) {
goto L110;
}
/* L100: */
}
}
m = lend;
L110:
if (m > lend) {
e[m - 1] = 0.;
}
p = d__[l];
if (m == l) {
goto L130;
}
/* If remaining matrix is 2-by-2, use DLAE2 or SLAEV2
to compute its eigensystem. */
if (m == l - 1) {
if (icompz > 0) {
igraphdlaev2_(&d__[l - 1], &e[l - 1], &d__[l], &rt1, &rt2, &c__, &s)
;
work[m] = c__;
work[*n - 1 + m] = s;
igraphdlasr_("R", "V", "F", n, &c__2, &work[m], &work[*n - 1 + m], &
z__[(l - 1) * z_dim1 + 1], ldz);
} else {
igraphdlae2_(&d__[l - 1], &e[l - 1], &d__[l], &rt1, &rt2);
}
d__[l - 1] = rt1;
d__[l] = rt2;
e[l - 1] = 0.;
l += -2;
if (l >= lend) {
goto L90;
}
goto L140;
}
if (jtot == nmaxit) {
goto L140;
}
++jtot;
/* Form shift. */
g = (d__[l - 1] - p) / (e[l - 1] * 2.);
r__ = igraphdlapy2_(&g, &c_b10);
g = d__[m] - p + e[l - 1] / (g + d_sign(&r__, &g));
s = 1.;
c__ = 1.;
p = 0.;
/* Inner loop */
lm1 = l - 1;
i__1 = lm1;
for (i__ = m; i__ <= i__1; ++i__) {
f = s * e[i__];
b = c__ * e[i__];
igraphdlartg_(&g, &f, &c__, &s, &r__);
if (i__ != m) {
e[i__ - 1] = r__;
}
g = d__[i__] - p;
r__ = (d__[i__ + 1] - g) * s + c__ * 2. * b;
p = s * r__;
d__[i__] = g + p;
g = c__ * r__ - b;
/* If eigenvectors are desired, then save rotations. */
if (icompz > 0) {
work[i__] = c__;
work[*n - 1 + i__] = s;
}
/* L120: */
}
/* If eigenvectors are desired, then apply saved rotations. */
if (icompz > 0) {
mm = l - m + 1;
igraphdlasr_("R", "V", "F", n, &mm, &work[m], &work[*n - 1 + m], &z__[m
* z_dim1 + 1], ldz);
}
d__[l] -= p;
e[lm1] = g;
goto L90;
/* Eigenvalue found. */
L130:
d__[l] = p;
--l;
if (l >= lend) {
goto L90;
}
goto L140;
}
/* Undo scaling if necessary */
L140:
if (iscale == 1) {
i__1 = lendsv - lsv + 1;
igraphdlascl_("G", &c__0, &c__0, &ssfmax, &anorm, &i__1, &c__1, &d__[lsv],
n, info);
i__1 = lendsv - lsv;
igraphdlascl_("G", &c__0, &c__0, &ssfmax, &anorm, &i__1, &c__1, &e[lsv], n,
info);
} else if (iscale == 2) {
i__1 = lendsv - lsv + 1;
igraphdlascl_("G", &c__0, &c__0, &ssfmin, &anorm, &i__1, &c__1, &d__[lsv],
n, info);
i__1 = lendsv - lsv;
igraphdlascl_("G", &c__0, &c__0, &ssfmin, &anorm, &i__1, &c__1, &e[lsv], n,
info);
}
/* Check for no convergence to an eigenvalue after a total
of N*MAXIT iterations. */
if (jtot < nmaxit) {
goto L10;
}
i__1 = *n - 1;
for (i__ = 1; i__ <= i__1; ++i__) {
if (e[i__] != 0.) {
++(*info);
}
/* L150: */
}
goto L190;
/* Order eigenvalues and eigenvectors. */
L160:
if (icompz == 0) {
/* Use Quick Sort */
igraphdlasrt_("I", n, &d__[1], info);
} else {
/* Use Selection Sort to minimize swaps of eigenvectors */
i__1 = *n;
for (ii = 2; ii <= i__1; ++ii) {
i__ = ii - 1;
k = i__;
p = d__[i__];
i__2 = *n;
for (j = ii; j <= i__2; ++j) {
if (d__[j] < p) {
k = j;
p = d__[j];
}
/* L170: */
}
if (k != i__) {
d__[k] = d__[i__];
d__[i__] = p;
igraphdswap_(n, &z__[i__ * z_dim1 + 1], &c__1, &z__[k * z_dim1 + 1],
&c__1);
}
/* L180: */
}
}
L190:
return 0;
/* End of DSTEQR */
} /* igraphdsteqr_ */