535 lines
13 KiB
C++
535 lines
13 KiB
C++
/* fortran/dsterf.f -- translated by f2c (version 20200916).
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You must link the resulting object file with libf2c:
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on Microsoft Windows system, link with libf2c.lib;
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on Linux or Unix systems, link with .../path/to/libf2c.a -lm
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or, if you install libf2c.a in a standard place, with -lf2c -lm
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-- in that order, at the end of the command line, as in
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cc *.o -lf2c -lm
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Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
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http://www.netlib.org/f2c/libf2c.zip
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*/
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#ifdef __cplusplus
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extern "C" {
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#endif
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#include "lmp_f2c.h"
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/* Table of constant values */
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static integer c__0 = 0;
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static integer c__1 = 1;
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static doublereal c_b33 = 1.;
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/* > \brief \b DSTERF */
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/* =========== DOCUMENTATION =========== */
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/* Online html documentation available at */
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/* http://www.netlib.org/lapack/explore-html/ */
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/* > \htmlonly */
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/* > Download DSTERF + dependencies */
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/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dsterf.
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f"> */
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/* > [TGZ]</a> */
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/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dsterf.
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f"> */
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/* > [ZIP]</a> */
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/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dsterf.
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f"> */
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/* > [TXT]</a> */
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/* > \endhtmlonly */
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/* Definition: */
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/* =========== */
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/* SUBROUTINE DSTERF( N, D, E, INFO ) */
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/* .. Scalar Arguments .. */
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/* INTEGER INFO, N */
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/* .. */
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/* .. Array Arguments .. */
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/* DOUBLE PRECISION D( * ), E( * ) */
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/* .. */
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/* > \par Purpose: */
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/* ============= */
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/* > */
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/* > \verbatim */
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/* > */
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/* > DSTERF computes all eigenvalues of a symmetric tridiagonal matrix */
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/* > using the Pal-Walker-Kahan variant of the QL or QR algorithm. */
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/* > \endverbatim */
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/* Arguments: */
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/* ========== */
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/* > \param[in] N */
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/* > \verbatim */
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/* > N is INTEGER */
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/* > The order of the matrix. N >= 0. */
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/* > \endverbatim */
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/* > */
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/* > \param[in,out] D */
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/* > \verbatim */
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/* > D is DOUBLE PRECISION array, dimension (N) */
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/* > On entry, the n diagonal elements of the tridiagonal matrix. */
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/* > On exit, if INFO = 0, the eigenvalues in ascending order. */
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/* > \endverbatim */
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/* > */
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/* > \param[in,out] E */
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/* > \verbatim */
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/* > E is DOUBLE PRECISION array, dimension (N-1) */
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/* > On entry, the (n-1) subdiagonal elements of the tridiagonal */
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/* > matrix. */
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/* > On exit, E has been destroyed. */
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/* > \endverbatim */
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/* > */
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/* > \param[out] INFO */
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/* > \verbatim */
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/* > INFO is INTEGER */
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/* > = 0: successful exit */
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/* > < 0: if INFO = -i, the i-th argument had an illegal value */
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/* > > 0: the algorithm failed to find all of the eigenvalues in */
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/* > a total of 30*N iterations; if INFO = i, then i */
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/* > elements of E have not converged to zero. */
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/* > \endverbatim */
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/* Authors: */
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/* ======== */
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/* > \author Univ. of Tennessee */
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/* > \author Univ. of California Berkeley */
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/* > \author Univ. of Colorado Denver */
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/* > \author NAG Ltd. */
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/* > \ingroup auxOTHERcomputational */
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/* ===================================================================== */
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/* Subroutine */ int dsterf_(integer *n, doublereal *d__, doublereal *e,
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integer *info)
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{
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/* System generated locals */
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integer i__1;
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doublereal d__1, d__2, d__3;
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/* Builtin functions */
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double sqrt(doublereal), d_sign(doublereal *, doublereal *);
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/* Local variables */
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doublereal c__;
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integer i__, l, m;
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doublereal p, r__, s;
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integer l1;
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doublereal bb, rt1, rt2, eps, rte;
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integer lsv;
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doublereal eps2, oldc;
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integer lend;
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doublereal rmax;
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integer jtot;
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extern /* Subroutine */ int dlae2_(doublereal *, doublereal *, doublereal
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*, doublereal *, doublereal *);
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doublereal gamma, alpha, sigma, anorm;
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extern doublereal dlapy2_(doublereal *, doublereal *), dlamch_(char *,
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ftnlen);
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integer iscale;
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extern /* Subroutine */ int dlascl_(char *, integer *, integer *,
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doublereal *, doublereal *, integer *, integer *, doublereal *,
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integer *, integer *, ftnlen);
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doublereal oldgam, safmin;
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extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
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doublereal safmax;
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extern doublereal dlanst_(char *, integer *, doublereal *, doublereal *,
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ftnlen);
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extern /* Subroutine */ int dlasrt_(char *, integer *, doublereal *,
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integer *, ftnlen);
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integer lendsv;
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doublereal ssfmin;
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integer nmaxit;
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doublereal ssfmax;
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/* -- LAPACK computational routine -- */
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/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
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/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
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/* .. Scalar Arguments .. */
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/* .. */
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/* .. Array Arguments .. */
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/* .. */
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/* ===================================================================== */
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/* .. Parameters .. */
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/* .. */
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/* .. Local Scalars .. */
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/* .. */
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/* .. External Functions .. */
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/* .. */
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/* .. External Subroutines .. */
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/* .. */
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/* .. Intrinsic Functions .. */
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/* .. */
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/* .. Executable Statements .. */
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/* Test the input parameters. */
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/* Parameter adjustments */
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--e;
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--d__;
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/* Function Body */
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*info = 0;
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/* Quick return if possible */
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if (*n < 0) {
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*info = -1;
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i__1 = -(*info);
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xerbla_((char *)"DSTERF", &i__1, (ftnlen)6);
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return 0;
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}
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if (*n <= 1) {
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return 0;
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}
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/* Determine the unit roundoff for this environment. */
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eps = dlamch_((char *)"E", (ftnlen)1);
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/* Computing 2nd power */
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d__1 = eps;
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eps2 = d__1 * d__1;
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safmin = dlamch_((char *)"S", (ftnlen)1);
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safmax = 1. / safmin;
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ssfmax = sqrt(safmax) / 3.;
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ssfmin = sqrt(safmin) / eps2;
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rmax = dlamch_((char *)"O", (ftnlen)1);
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/* Compute the eigenvalues of the tridiagonal matrix. */
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nmaxit = *n * 30;
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sigma = 0.;
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jtot = 0;
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/* Determine where the matrix splits and choose QL or QR iteration */
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/* for each block, according to whether top or bottom diagonal */
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/* element is smaller. */
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l1 = 1;
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L10:
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if (l1 > *n) {
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goto L170;
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}
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if (l1 > 1) {
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e[l1 - 1] = 0.;
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}
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i__1 = *n - 1;
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for (m = l1; m <= i__1; ++m) {
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if ((d__3 = e[m], abs(d__3)) <= sqrt((d__1 = d__[m], abs(d__1))) *
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sqrt((d__2 = d__[m + 1], abs(d__2))) * eps) {
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e[m] = 0.;
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goto L30;
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}
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/* L20: */
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}
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m = *n;
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L30:
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l = l1;
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lsv = l;
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lend = m;
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lendsv = lend;
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l1 = m + 1;
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if (lend == l) {
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goto L10;
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}
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/* Scale submatrix in rows and columns L to LEND */
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i__1 = lend - l + 1;
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anorm = dlanst_((char *)"M", &i__1, &d__[l], &e[l], (ftnlen)1);
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iscale = 0;
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if (anorm == 0.) {
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goto L10;
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}
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if (anorm > ssfmax) {
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iscale = 1;
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i__1 = lend - l + 1;
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dlascl_((char *)"G", &c__0, &c__0, &anorm, &ssfmax, &i__1, &c__1, &d__[l], n,
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info, (ftnlen)1);
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i__1 = lend - l;
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dlascl_((char *)"G", &c__0, &c__0, &anorm, &ssfmax, &i__1, &c__1, &e[l], n,
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info, (ftnlen)1);
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} else if (anorm < ssfmin) {
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iscale = 2;
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i__1 = lend - l + 1;
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dlascl_((char *)"G", &c__0, &c__0, &anorm, &ssfmin, &i__1, &c__1, &d__[l], n,
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info, (ftnlen)1);
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i__1 = lend - l;
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dlascl_((char *)"G", &c__0, &c__0, &anorm, &ssfmin, &i__1, &c__1, &e[l], n,
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info, (ftnlen)1);
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}
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i__1 = lend - 1;
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for (i__ = l; i__ <= i__1; ++i__) {
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/* Computing 2nd power */
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d__1 = e[i__];
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e[i__] = d__1 * d__1;
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/* L40: */
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}
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/* Choose between QL and QR iteration */
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if ((d__1 = d__[lend], abs(d__1)) < (d__2 = d__[l], abs(d__2))) {
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lend = lsv;
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l = lendsv;
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}
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if (lend >= l) {
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/* QL Iteration */
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/* Look for small subdiagonal element. */
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L50:
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if (l != lend) {
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i__1 = lend - 1;
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for (m = l; m <= i__1; ++m) {
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if ((d__2 = e[m], abs(d__2)) <= eps2 * (d__1 = d__[m] * d__[m
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+ 1], abs(d__1))) {
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goto L70;
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}
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/* L60: */
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}
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}
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m = lend;
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L70:
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if (m < lend) {
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e[m] = 0.;
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}
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p = d__[l];
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if (m == l) {
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goto L90;
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}
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/* If remaining matrix is 2 by 2, use DLAE2 to compute its */
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/* eigenvalues. */
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if (m == l + 1) {
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rte = sqrt(e[l]);
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dlae2_(&d__[l], &rte, &d__[l + 1], &rt1, &rt2);
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d__[l] = rt1;
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d__[l + 1] = rt2;
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e[l] = 0.;
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l += 2;
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if (l <= lend) {
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goto L50;
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}
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goto L150;
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}
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if (jtot == nmaxit) {
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goto L150;
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}
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++jtot;
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/* Form shift. */
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rte = sqrt(e[l]);
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sigma = (d__[l + 1] - p) / (rte * 2.);
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r__ = dlapy2_(&sigma, &c_b33);
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sigma = p - rte / (sigma + d_sign(&r__, &sigma));
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c__ = 1.;
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s = 0.;
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gamma = d__[m] - sigma;
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p = gamma * gamma;
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/* Inner loop */
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i__1 = l;
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for (i__ = m - 1; i__ >= i__1; --i__) {
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bb = e[i__];
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r__ = p + bb;
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if (i__ != m - 1) {
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e[i__ + 1] = s * r__;
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}
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oldc = c__;
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c__ = p / r__;
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s = bb / r__;
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oldgam = gamma;
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alpha = d__[i__];
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gamma = c__ * (alpha - sigma) - s * oldgam;
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d__[i__ + 1] = oldgam + (alpha - gamma);
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if (c__ != 0.) {
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p = gamma * gamma / c__;
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} else {
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p = oldc * bb;
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}
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/* L80: */
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}
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e[l] = s * p;
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d__[l] = sigma + gamma;
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goto L50;
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/* Eigenvalue found. */
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L90:
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d__[l] = p;
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++l;
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if (l <= lend) {
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goto L50;
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}
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goto L150;
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} else {
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/* QR Iteration */
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/* Look for small superdiagonal element. */
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L100:
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i__1 = lend + 1;
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for (m = l; m >= i__1; --m) {
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if ((d__2 = e[m - 1], abs(d__2)) <= eps2 * (d__1 = d__[m] * d__[m
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- 1], abs(d__1))) {
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goto L120;
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}
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/* L110: */
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}
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m = lend;
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L120:
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if (m > lend) {
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e[m - 1] = 0.;
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}
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p = d__[l];
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if (m == l) {
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goto L140;
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}
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/* If remaining matrix is 2 by 2, use DLAE2 to compute its */
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/* eigenvalues. */
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if (m == l - 1) {
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rte = sqrt(e[l - 1]);
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dlae2_(&d__[l], &rte, &d__[l - 1], &rt1, &rt2);
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d__[l] = rt1;
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d__[l - 1] = rt2;
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e[l - 1] = 0.;
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l += -2;
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if (l >= lend) {
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goto L100;
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}
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goto L150;
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}
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if (jtot == nmaxit) {
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goto L150;
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}
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++jtot;
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/* Form shift. */
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rte = sqrt(e[l - 1]);
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sigma = (d__[l - 1] - p) / (rte * 2.);
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r__ = dlapy2_(&sigma, &c_b33);
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sigma = p - rte / (sigma + d_sign(&r__, &sigma));
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c__ = 1.;
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s = 0.;
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gamma = d__[m] - sigma;
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p = gamma * gamma;
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/* Inner loop */
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i__1 = l - 1;
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for (i__ = m; i__ <= i__1; ++i__) {
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bb = e[i__];
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r__ = p + bb;
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if (i__ != m) {
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e[i__ - 1] = s * r__;
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}
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oldc = c__;
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c__ = p / r__;
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s = bb / r__;
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oldgam = gamma;
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alpha = d__[i__ + 1];
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gamma = c__ * (alpha - sigma) - s * oldgam;
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d__[i__] = oldgam + (alpha - gamma);
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if (c__ != 0.) {
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p = gamma * gamma / c__;
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} else {
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p = oldc * bb;
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}
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/* L130: */
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}
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e[l - 1] = s * p;
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d__[l] = sigma + gamma;
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goto L100;
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/* Eigenvalue found. */
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L140:
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d__[l] = p;
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--l;
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if (l >= lend) {
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goto L100;
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}
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goto L150;
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}
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/* Undo scaling if necessary */
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L150:
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if (iscale == 1) {
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i__1 = lendsv - lsv + 1;
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dlascl_((char *)"G", &c__0, &c__0, &ssfmax, &anorm, &i__1, &c__1, &d__[lsv],
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n, info, (ftnlen)1);
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}
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if (iscale == 2) {
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i__1 = lendsv - lsv + 1;
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dlascl_((char *)"G", &c__0, &c__0, &ssfmin, &anorm, &i__1, &c__1, &d__[lsv],
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n, info, (ftnlen)1);
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}
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/* Check for no convergence to an eigenvalue after a total */
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/* of N*MAXIT iterations. */
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if (jtot < nmaxit) {
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goto L10;
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}
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i__1 = *n - 1;
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for (i__ = 1; i__ <= i__1; ++i__) {
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if (e[i__] != 0.) {
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++(*info);
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}
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/* L160: */
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}
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goto L180;
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/* Sort eigenvalues in increasing order. */
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L170:
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dlasrt_((char *)"I", n, &d__[1], info, (ftnlen)1);
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L180:
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return 0;
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/* End of DSTERF */
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} /* dsterf_ */
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#ifdef __cplusplus
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}
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#endif
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