618 lines
14 KiB
C
618 lines
14 KiB
C
/* ssteqr.f -- translated by f2c (version 20061008).
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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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#include "clapack.h"
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/* Table of constant values */
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static real c_b9 = 0.f;
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static real c_b10 = 1.f;
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static integer c__0 = 0;
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static integer c__1 = 1;
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static integer c__2 = 2;
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/* Subroutine */ int ssteqr_(char *compz, integer *n, real *d__, real *e,
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real *z__, integer *ldz, real *work, integer *info)
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{
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/* System generated locals */
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integer z_dim1, z_offset, i__1, i__2;
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real r__1, r__2;
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/* Builtin functions */
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double sqrt(doublereal), r_sign(real *, real *);
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/* Local variables */
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real b, c__, f, g;
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integer i__, j, k, l, m;
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real p, r__, s;
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integer l1, ii, mm, lm1, mm1, nm1;
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real rt1, rt2, eps;
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integer lsv;
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real tst, eps2;
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integer lend, jtot;
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extern /* Subroutine */ int slae2_(real *, real *, real *, real *, real *)
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;
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extern logical lsame_(char *, char *);
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real anorm;
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extern /* Subroutine */ int slasr_(char *, char *, char *, integer *,
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integer *, real *, real *, real *, integer *), sswap_(integer *, real *, integer *, real *, integer *);
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integer lendm1, lendp1;
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extern /* Subroutine */ int slaev2_(real *, real *, real *, real *, real *
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, real *, real *);
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extern doublereal slapy2_(real *, real *);
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integer iscale;
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extern doublereal slamch_(char *);
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real safmin;
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extern /* Subroutine */ int xerbla_(char *, integer *);
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real safmax;
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extern /* Subroutine */ int slascl_(char *, integer *, integer *, real *,
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real *, integer *, integer *, real *, integer *, integer *);
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integer lendsv;
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extern /* Subroutine */ int slartg_(real *, real *, real *, real *, real *
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), slaset_(char *, integer *, integer *, real *, real *, real *,
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integer *);
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real ssfmin;
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integer nmaxit, icompz;
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real ssfmax;
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extern doublereal slanst_(char *, integer *, real *, real *);
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extern /* Subroutine */ int slasrt_(char *, integer *, real *, integer *);
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/* -- LAPACK routine (version 3.2) -- */
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/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
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/* November 2006 */
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/* .. Scalar Arguments .. */
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/* .. */
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/* .. Array Arguments .. */
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/* .. */
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/* Purpose */
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/* ======= */
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/* SSTEQR computes all eigenvalues and, optionally, eigenvectors of a */
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/* symmetric tridiagonal matrix using the implicit QL or QR method. */
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/* The eigenvectors of a full or band symmetric matrix can also be found */
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/* if SSYTRD or SSPTRD or SSBTRD has been used to reduce this matrix to */
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/* tridiagonal form. */
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/* Arguments */
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/* ========= */
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/* COMPZ (input) CHARACTER*1 */
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/* = 'N': Compute eigenvalues only. */
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/* = 'V': Compute eigenvalues and eigenvectors of the original */
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/* symmetric matrix. On entry, Z must contain the */
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/* orthogonal matrix used to reduce the original matrix */
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/* to tridiagonal form. */
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/* = 'I': Compute eigenvalues and eigenvectors of the */
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/* tridiagonal matrix. Z is initialized to the identity */
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/* matrix. */
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/* N (input) INTEGER */
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/* The order of the matrix. N >= 0. */
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/* D (input/output) REAL array, dimension (N) */
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/* On entry, the diagonal elements of the tridiagonal matrix. */
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/* On exit, if INFO = 0, the eigenvalues in ascending order. */
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/* E (input/output) REAL 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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/* Z (input/output) REAL array, dimension (LDZ, N) */
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/* On entry, if COMPZ = 'V', then Z contains the orthogonal */
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/* matrix used in the reduction to tridiagonal form. */
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/* On exit, if INFO = 0, then if COMPZ = 'V', Z contains the */
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/* orthonormal eigenvectors of the original symmetric matrix, */
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/* and if COMPZ = 'I', Z contains the orthonormal eigenvectors */
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/* of the symmetric tridiagonal matrix. */
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/* If COMPZ = 'N', then Z is not referenced. */
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/* LDZ (input) INTEGER */
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/* The leading dimension of the array Z. LDZ >= 1, and if */
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/* eigenvectors are desired, then LDZ >= max(1,N). */
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/* WORK (workspace) REAL array, dimension (max(1,2*N-2)) */
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/* If COMPZ = 'N', then WORK is not referenced. */
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/* INFO (output) 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 has failed to find all 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; on exit, D */
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/* and E contain the elements of a symmetric tridiagonal */
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/* matrix which is orthogonally similar to the original */
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/* matrix. */
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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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--d__;
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--e;
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z_dim1 = *ldz;
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z_offset = 1 + z_dim1;
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z__ -= z_offset;
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--work;
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/* Function Body */
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*info = 0;
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if (lsame_(compz, "N")) {
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icompz = 0;
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} else if (lsame_(compz, "V")) {
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icompz = 1;
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} else if (lsame_(compz, "I")) {
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icompz = 2;
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} else {
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icompz = -1;
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}
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if (icompz < 0) {
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*info = -1;
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} else if (*n < 0) {
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*info = -2;
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} else if (*ldz < 1 || icompz > 0 && *ldz < max(1,*n)) {
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*info = -6;
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}
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if (*info != 0) {
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i__1 = -(*info);
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xerbla_("SSTEQR", &i__1);
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return 0;
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}
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/* Quick return if possible */
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if (*n == 0) {
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return 0;
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}
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if (*n == 1) {
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if (icompz == 2) {
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z__[z_dim1 + 1] = 1.f;
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}
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return 0;
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}
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/* Determine the unit roundoff and over/underflow thresholds. */
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eps = slamch_("E");
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/* Computing 2nd power */
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r__1 = eps;
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eps2 = r__1 * r__1;
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safmin = slamch_("S");
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safmax = 1.f / safmin;
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ssfmax = sqrt(safmax) / 3.f;
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ssfmin = sqrt(safmin) / eps2;
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/* Compute the eigenvalues and eigenvectors of the tridiagonal */
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/* matrix. */
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if (icompz == 2) {
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slaset_("Full", n, n, &c_b9, &c_b10, &z__[z_offset], ldz);
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}
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nmaxit = *n * 30;
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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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nm1 = *n - 1;
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L10:
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if (l1 > *n) {
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goto L160;
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}
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if (l1 > 1) {
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e[l1 - 1] = 0.f;
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}
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if (l1 <= nm1) {
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i__1 = nm1;
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for (m = l1; m <= i__1; ++m) {
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tst = (r__1 = e[m], dabs(r__1));
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if (tst == 0.f) {
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goto L30;
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}
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if (tst <= sqrt((r__1 = d__[m], dabs(r__1))) * sqrt((r__2 = d__[m
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+ 1], dabs(r__2))) * eps) {
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e[m] = 0.f;
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goto L30;
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}
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/* L20: */
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}
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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 = slanst_("I", &i__1, &d__[l], &e[l]);
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iscale = 0;
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if (anorm == 0.f) {
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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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slascl_("G", &c__0, &c__0, &anorm, &ssfmax, &i__1, &c__1, &d__[l], n,
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info);
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i__1 = lend - l;
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slascl_("G", &c__0, &c__0, &anorm, &ssfmax, &i__1, &c__1, &e[l], n,
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info);
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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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slascl_("G", &c__0, &c__0, &anorm, &ssfmin, &i__1, &c__1, &d__[l], n,
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info);
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i__1 = lend - l;
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slascl_("G", &c__0, &c__0, &anorm, &ssfmin, &i__1, &c__1, &e[l], n,
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info);
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}
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/* Choose between QL and QR iteration */
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if ((r__1 = d__[lend], dabs(r__1)) < (r__2 = d__[l], dabs(r__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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L40:
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if (l != lend) {
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lendm1 = lend - 1;
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i__1 = lendm1;
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for (m = l; m <= i__1; ++m) {
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/* Computing 2nd power */
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r__2 = (r__1 = e[m], dabs(r__1));
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tst = r__2 * r__2;
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if (tst <= eps2 * (r__1 = d__[m], dabs(r__1)) * (r__2 = d__[m
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+ 1], dabs(r__2)) + safmin) {
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goto L60;
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}
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/* L50: */
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}
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}
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m = lend;
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L60:
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if (m < lend) {
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e[m] = 0.f;
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}
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p = d__[l];
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if (m == l) {
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goto L80;
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}
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/* If remaining matrix is 2-by-2, use SLAE2 or SLAEV2 */
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/* to compute its eigensystem. */
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if (m == l + 1) {
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if (icompz > 0) {
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slaev2_(&d__[l], &e[l], &d__[l + 1], &rt1, &rt2, &c__, &s);
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work[l] = c__;
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work[*n - 1 + l] = s;
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slasr_("R", "V", "B", n, &c__2, &work[l], &work[*n - 1 + l], &
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z__[l * z_dim1 + 1], ldz);
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} else {
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slae2_(&d__[l], &e[l], &d__[l + 1], &rt1, &rt2);
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}
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d__[l] = rt1;
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d__[l + 1] = rt2;
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e[l] = 0.f;
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l += 2;
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if (l <= lend) {
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goto L40;
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}
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goto L140;
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}
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if (jtot == nmaxit) {
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goto L140;
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}
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++jtot;
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/* Form shift. */
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g = (d__[l + 1] - p) / (e[l] * 2.f);
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r__ = slapy2_(&g, &c_b10);
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g = d__[m] - p + e[l] / (g + r_sign(&r__, &g));
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s = 1.f;
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c__ = 1.f;
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p = 0.f;
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/* Inner loop */
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mm1 = m - 1;
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i__1 = l;
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for (i__ = mm1; i__ >= i__1; --i__) {
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f = s * e[i__];
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b = c__ * e[i__];
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slartg_(&g, &f, &c__, &s, &r__);
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if (i__ != m - 1) {
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e[i__ + 1] = r__;
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}
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g = d__[i__ + 1] - p;
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r__ = (d__[i__] - g) * s + c__ * 2.f * b;
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p = s * r__;
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d__[i__ + 1] = g + p;
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g = c__ * r__ - b;
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/* If eigenvectors are desired, then save rotations. */
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if (icompz > 0) {
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work[i__] = c__;
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work[*n - 1 + i__] = -s;
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}
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/* L70: */
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}
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/* If eigenvectors are desired, then apply saved rotations. */
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if (icompz > 0) {
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mm = m - l + 1;
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slasr_("R", "V", "B", n, &mm, &work[l], &work[*n - 1 + l], &z__[l
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* z_dim1 + 1], ldz);
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}
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d__[l] -= p;
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e[l] = g;
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goto L40;
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/* Eigenvalue found. */
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L80:
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d__[l] = p;
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++l;
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if (l <= lend) {
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goto L40;
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}
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goto L140;
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} else {
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/* QR Iteration */
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/* Look for small superdiagonal element. */
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L90:
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if (l != lend) {
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lendp1 = lend + 1;
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i__1 = lendp1;
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for (m = l; m >= i__1; --m) {
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/* Computing 2nd power */
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r__2 = (r__1 = e[m - 1], dabs(r__1));
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tst = r__2 * r__2;
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if (tst <= eps2 * (r__1 = d__[m], dabs(r__1)) * (r__2 = d__[m
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- 1], dabs(r__2)) + safmin) {
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goto L110;
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}
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/* L100: */
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}
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}
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m = lend;
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L110:
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if (m > lend) {
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e[m - 1] = 0.f;
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}
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p = d__[l];
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if (m == l) {
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goto L130;
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}
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/* If remaining matrix is 2-by-2, use SLAE2 or SLAEV2 */
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/* to compute its eigensystem. */
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if (m == l - 1) {
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if (icompz > 0) {
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slaev2_(&d__[l - 1], &e[l - 1], &d__[l], &rt1, &rt2, &c__, &s)
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;
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work[m] = c__;
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work[*n - 1 + m] = s;
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slasr_("R", "V", "F", n, &c__2, &work[m], &work[*n - 1 + m], &
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z__[(l - 1) * z_dim1 + 1], ldz);
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} else {
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slae2_(&d__[l - 1], &e[l - 1], &d__[l], &rt1, &rt2);
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}
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d__[l - 1] = rt1;
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d__[l] = rt2;
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e[l - 1] = 0.f;
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l += -2;
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if (l >= lend) {
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goto L90;
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}
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goto L140;
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}
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if (jtot == nmaxit) {
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goto L140;
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}
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++jtot;
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/* Form shift. */
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g = (d__[l - 1] - p) / (e[l - 1] * 2.f);
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r__ = slapy2_(&g, &c_b10);
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g = d__[m] - p + e[l - 1] / (g + r_sign(&r__, &g));
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s = 1.f;
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c__ = 1.f;
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p = 0.f;
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/* Inner loop */
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lm1 = l - 1;
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i__1 = lm1;
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for (i__ = m; i__ <= i__1; ++i__) {
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f = s * e[i__];
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b = c__ * e[i__];
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slartg_(&g, &f, &c__, &s, &r__);
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if (i__ != m) {
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e[i__ - 1] = r__;
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}
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g = d__[i__] - p;
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r__ = (d__[i__ + 1] - g) * s + c__ * 2.f * b;
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p = s * r__;
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d__[i__] = g + p;
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g = c__ * r__ - b;
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/* If eigenvectors are desired, then save rotations. */
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if (icompz > 0) {
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work[i__] = c__;
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work[*n - 1 + i__] = s;
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}
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/* L120: */
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}
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/* If eigenvectors are desired, then apply saved rotations. */
|
|
|
|
if (icompz > 0) {
|
|
mm = l - m + 1;
|
|
slasr_("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;
|
|
slascl_("G", &c__0, &c__0, &ssfmax, &anorm, &i__1, &c__1, &d__[lsv],
|
|
n, info);
|
|
i__1 = lendsv - lsv;
|
|
slascl_("G", &c__0, &c__0, &ssfmax, &anorm, &i__1, &c__1, &e[lsv], n,
|
|
info);
|
|
} else if (iscale == 2) {
|
|
i__1 = lendsv - lsv + 1;
|
|
slascl_("G", &c__0, &c__0, &ssfmin, &anorm, &i__1, &c__1, &d__[lsv],
|
|
n, info);
|
|
i__1 = lendsv - lsv;
|
|
slascl_("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.f) {
|
|
++(*info);
|
|
}
|
|
/* L150: */
|
|
}
|
|
goto L190;
|
|
|
|
/* Order eigenvalues and eigenvectors. */
|
|
|
|
L160:
|
|
if (icompz == 0) {
|
|
|
|
/* Use Quick Sort */
|
|
|
|
slasrt_("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;
|
|
sswap_(n, &z__[i__ * z_dim1 + 1], &c__1, &z__[k * z_dim1 + 1],
|
|
&c__1);
|
|
}
|
|
/* L180: */
|
|
}
|
|
}
|
|
|
|
L190:
|
|
return 0;
|
|
|
|
/* End of SSTEQR */
|
|
|
|
} /* ssteqr_ */
|