523 lines
18 KiB
C++
523 lines
18 KiB
C++
#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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static doublereal c_b15 = -.125;
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static integer c__1 = 1;
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static doublereal c_b49 = 1.;
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static doublereal c_b72 = -1.;
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int dbdsqr_(char *uplo, integer *n, integer *ncvt, integer *nru, integer *ncc, doublereal *d__,
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doublereal *e, doublereal *vt, integer *ldvt, doublereal *u, integer *ldu,
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doublereal *c__, integer *ldc, doublereal *work, integer *info, ftnlen uplo_len)
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{
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integer c_dim1, c_offset, u_dim1, u_offset, vt_dim1, vt_offset, i__1, i__2;
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doublereal d__1, d__2, d__3, d__4;
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double pow_lmp_dd(doublereal *, doublereal *), sqrt(doublereal), d_lmp_sign(doublereal *, doublereal *);
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integer iterdivn;
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doublereal f, g, h__;
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integer i__, j, m;
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doublereal r__;
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integer maxitdivn;
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doublereal cs;
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integer ll;
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doublereal sn, mu;
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integer nm1, nm12, nm13, lll;
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doublereal eps, sll, tol, abse;
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integer idir;
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doublereal abss;
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integer oldm;
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doublereal cosl;
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integer isub, iter;
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doublereal unfl, sinl, cosr, smin, smax, sinr;
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extern int drot_(integer *, doublereal *, integer *, doublereal *, integer *, doublereal *,
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doublereal *),
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dlas2_(doublereal *, doublereal *, doublereal *, doublereal *, doublereal *),
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dscal_(integer *, doublereal *, doublereal *, integer *);
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extern logical lsame_(char *, char *, ftnlen, ftnlen);
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doublereal oldcs;
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extern int dlasr_(char *, char *, char *, integer *, integer *, doublereal *, doublereal *,
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doublereal *, integer *, ftnlen, ftnlen, ftnlen);
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integer oldll;
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doublereal shift, sigmn, oldsn;
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extern int dswap_(integer *, doublereal *, integer *, doublereal *, integer *);
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doublereal sminl, sigmx;
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logical lower;
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extern int dlasq1_(integer *, doublereal *, doublereal *, doublereal *, integer *),
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dlasv2_(doublereal *, doublereal *, doublereal *, doublereal *, doublereal *, doublereal *,
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doublereal *, doublereal *, doublereal *);
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extern doublereal dlamch_(char *, ftnlen);
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extern int dlartg_(doublereal *, doublereal *, doublereal *, doublereal *, doublereal *),
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xerbla_(char *, integer *, ftnlen);
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doublereal sminoa, thresh;
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logical rotate;
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doublereal tolmul;
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--d__;
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--e;
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vt_dim1 = *ldvt;
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vt_offset = 1 + vt_dim1;
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vt -= vt_offset;
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u_dim1 = *ldu;
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u_offset = 1 + u_dim1;
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u -= u_offset;
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c_dim1 = *ldc;
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c_offset = 1 + c_dim1;
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c__ -= c_offset;
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--work;
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*info = 0;
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lower = lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1);
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if (!lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1) && !lower) {
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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 (*ncvt < 0) {
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*info = -3;
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} else if (*nru < 0) {
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*info = -4;
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} else if (*ncc < 0) {
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*info = -5;
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} else if (*ncvt == 0 && *ldvt < 1 || *ncvt > 0 && *ldvt < max(1, *n)) {
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*info = -9;
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} else if (*ldu < max(1, *nru)) {
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*info = -11;
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} else if (*ncc == 0 && *ldc < 1 || *ncc > 0 && *ldc < max(1, *n)) {
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*info = -13;
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}
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if (*info != 0) {
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i__1 = -(*info);
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xerbla_((char *)"DBDSQR", &i__1, (ftnlen)6);
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return 0;
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}
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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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goto L160;
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}
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rotate = *ncvt > 0 || *nru > 0 || *ncc > 0;
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if (!rotate) {
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dlasq1_(n, &d__[1], &e[1], &work[1], info);
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if (*info != 2) {
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return 0;
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}
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*info = 0;
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}
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nm1 = *n - 1;
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nm12 = nm1 + nm1;
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nm13 = nm12 + nm1;
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idir = 0;
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eps = dlamch_((char *)"Epsilon", (ftnlen)7);
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unfl = dlamch_((char *)"Safe minimum", (ftnlen)12);
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if (lower) {
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i__1 = *n - 1;
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for (i__ = 1; i__ <= i__1; ++i__) {
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dlartg_(&d__[i__], &e[i__], &cs, &sn, &r__);
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d__[i__] = r__;
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e[i__] = sn * d__[i__ + 1];
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d__[i__ + 1] = cs * d__[i__ + 1];
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work[i__] = cs;
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work[nm1 + i__] = sn;
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}
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if (*nru > 0) {
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dlasr_((char *)"R", (char *)"V", (char *)"F", nru, n, &work[1], &work[*n], &u[u_offset], ldu, (ftnlen)1,
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(ftnlen)1, (ftnlen)1);
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}
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if (*ncc > 0) {
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dlasr_((char *)"L", (char *)"V", (char *)"F", n, ncc, &work[1], &work[*n], &c__[c_offset], ldc, (ftnlen)1,
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(ftnlen)1, (ftnlen)1);
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}
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}
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d__3 = 100., d__4 = pow_lmp_dd(&eps, &c_b15);
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d__1 = 10., d__2 = min(d__3, d__4);
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tolmul = max(d__1, d__2);
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tol = tolmul * eps;
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smax = 0.;
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i__1 = *n;
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for (i__ = 1; i__ <= i__1; ++i__) {
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d__2 = smax, d__3 = (d__1 = d__[i__], abs(d__1));
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smax = max(d__2, d__3);
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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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d__2 = smax, d__3 = (d__1 = e[i__], abs(d__1));
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smax = max(d__2, d__3);
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}
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sminl = 0.;
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if (tol >= 0.) {
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sminoa = abs(d__[1]);
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if (sminoa == 0.) {
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goto L50;
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}
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mu = sminoa;
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i__1 = *n;
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for (i__ = 2; i__ <= i__1; ++i__) {
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mu = (d__2 = d__[i__], abs(d__2)) * (mu / (mu + (d__1 = e[i__ - 1], abs(d__1))));
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sminoa = min(sminoa, mu);
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if (sminoa == 0.) {
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goto L50;
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}
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}
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L50:
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sminoa /= sqrt((doublereal)(*n));
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d__1 = tol * sminoa, d__2 = *n * (*n * unfl) * 6;
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thresh = max(d__1, d__2);
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} else {
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d__1 = abs(tol) * smax, d__2 = *n * (*n * unfl) * 6;
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thresh = max(d__1, d__2);
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}
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maxitdivn = *n * 6;
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iterdivn = 0;
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iter = -1;
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oldll = -1;
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oldm = -1;
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m = *n;
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L60:
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if (m <= 1) {
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goto L160;
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}
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if (iter >= *n) {
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iter -= *n;
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++iterdivn;
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if (iterdivn >= maxitdivn) {
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goto L200;
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}
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}
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if (tol < 0. && (d__1 = d__[m], abs(d__1)) <= thresh) {
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d__[m] = 0.;
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}
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smax = (d__1 = d__[m], abs(d__1));
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smin = smax;
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i__1 = m - 1;
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for (lll = 1; lll <= i__1; ++lll) {
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ll = m - lll;
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abss = (d__1 = d__[ll], abs(d__1));
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abse = (d__1 = e[ll], abs(d__1));
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if (tol < 0. && abss <= thresh) {
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d__[ll] = 0.;
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}
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if (abse <= thresh) {
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goto L80;
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}
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smin = min(smin, abss);
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d__1 = max(smax, abss);
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smax = max(d__1, abse);
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}
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ll = 0;
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goto L90;
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L80:
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e[ll] = 0.;
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if (ll == m - 1) {
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--m;
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goto L60;
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}
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L90:
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++ll;
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if (ll == m - 1) {
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dlasv2_(&d__[m - 1], &e[m - 1], &d__[m], &sigmn, &sigmx, &sinr, &cosr, &sinl, &cosl);
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d__[m - 1] = sigmx;
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e[m - 1] = 0.;
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d__[m] = sigmn;
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if (*ncvt > 0) {
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drot_(ncvt, &vt[m - 1 + vt_dim1], ldvt, &vt[m + vt_dim1], ldvt, &cosr, &sinr);
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}
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if (*nru > 0) {
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drot_(nru, &u[(m - 1) * u_dim1 + 1], &c__1, &u[m * u_dim1 + 1], &c__1, &cosl, &sinl);
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}
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if (*ncc > 0) {
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drot_(ncc, &c__[m - 1 + c_dim1], ldc, &c__[m + c_dim1], ldc, &cosl, &sinl);
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}
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m += -2;
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goto L60;
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}
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if (ll > oldm || m < oldll) {
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if ((d__1 = d__[ll], abs(d__1)) >= (d__2 = d__[m], abs(d__2))) {
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idir = 1;
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} else {
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idir = 2;
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}
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}
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if (idir == 1) {
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if ((d__2 = e[m - 1], abs(d__2)) <= abs(tol) * (d__1 = d__[m], abs(d__1)) ||
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tol < 0. && (d__3 = e[m - 1], abs(d__3)) <= thresh) {
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e[m - 1] = 0.;
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goto L60;
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}
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if (tol >= 0.) {
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mu = (d__1 = d__[ll], abs(d__1));
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sminl = mu;
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i__1 = m - 1;
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for (lll = ll; lll <= i__1; ++lll) {
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if ((d__1 = e[lll], abs(d__1)) <= tol * mu) {
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e[lll] = 0.;
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goto L60;
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}
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mu = (d__2 = d__[lll + 1], abs(d__2)) * (mu / (mu + (d__1 = e[lll], abs(d__1))));
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sminl = min(sminl, mu);
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}
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}
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} else {
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if ((d__2 = e[ll], abs(d__2)) <= abs(tol) * (d__1 = d__[ll], abs(d__1)) ||
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tol < 0. && (d__3 = e[ll], abs(d__3)) <= thresh) {
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e[ll] = 0.;
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goto L60;
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}
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if (tol >= 0.) {
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mu = (d__1 = d__[m], abs(d__1));
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sminl = mu;
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i__1 = ll;
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for (lll = m - 1; lll >= i__1; --lll) {
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if ((d__1 = e[lll], abs(d__1)) <= tol * mu) {
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e[lll] = 0.;
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goto L60;
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}
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mu = (d__2 = d__[lll], abs(d__2)) * (mu / (mu + (d__1 = e[lll], abs(d__1))));
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sminl = min(sminl, mu);
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}
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}
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}
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oldll = ll;
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oldm = m;
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d__1 = eps, d__2 = tol * .01;
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if (tol >= 0. && *n * tol * (sminl / smax) <= max(d__1, d__2)) {
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shift = 0.;
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} else {
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if (idir == 1) {
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sll = (d__1 = d__[ll], abs(d__1));
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dlas2_(&d__[m - 1], &e[m - 1], &d__[m], &shift, &r__);
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} else {
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sll = (d__1 = d__[m], abs(d__1));
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dlas2_(&d__[ll], &e[ll], &d__[ll + 1], &shift, &r__);
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}
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if (sll > 0.) {
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d__1 = shift / sll;
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if (d__1 * d__1 < eps) {
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shift = 0.;
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}
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}
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}
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iter = iter + m - ll;
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if (shift == 0.) {
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if (idir == 1) {
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cs = 1.;
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oldcs = 1.;
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i__1 = m - 1;
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for (i__ = ll; i__ <= i__1; ++i__) {
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d__1 = d__[i__] * cs;
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dlartg_(&d__1, &e[i__], &cs, &sn, &r__);
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if (i__ > ll) {
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e[i__ - 1] = oldsn * r__;
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}
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d__1 = oldcs * r__;
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d__2 = d__[i__ + 1] * sn;
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dlartg_(&d__1, &d__2, &oldcs, &oldsn, &d__[i__]);
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work[i__ - ll + 1] = cs;
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work[i__ - ll + 1 + nm1] = sn;
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work[i__ - ll + 1 + nm12] = oldcs;
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work[i__ - ll + 1 + nm13] = oldsn;
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}
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h__ = d__[m] * cs;
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d__[m] = h__ * oldcs;
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e[m - 1] = h__ * oldsn;
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if (*ncvt > 0) {
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i__1 = m - ll + 1;
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dlasr_((char *)"L", (char *)"V", (char *)"F", &i__1, ncvt, &work[1], &work[*n], &vt[ll + vt_dim1], ldvt,
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(ftnlen)1, (ftnlen)1, (ftnlen)1);
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}
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if (*nru > 0) {
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i__1 = m - ll + 1;
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dlasr_((char *)"R", (char *)"V", (char *)"F", nru, &i__1, &work[nm12 + 1], &work[nm13 + 1],
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&u[ll * u_dim1 + 1], ldu, (ftnlen)1, (ftnlen)1, (ftnlen)1);
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}
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if (*ncc > 0) {
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i__1 = m - ll + 1;
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dlasr_((char *)"L", (char *)"V", (char *)"F", &i__1, ncc, &work[nm12 + 1], &work[nm13 + 1],
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&c__[ll + c_dim1], ldc, (ftnlen)1, (ftnlen)1, (ftnlen)1);
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}
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if ((d__1 = e[m - 1], abs(d__1)) <= thresh) {
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e[m - 1] = 0.;
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}
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} else {
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cs = 1.;
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oldcs = 1.;
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i__1 = ll + 1;
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for (i__ = m; i__ >= i__1; --i__) {
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d__1 = d__[i__] * cs;
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dlartg_(&d__1, &e[i__ - 1], &cs, &sn, &r__);
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if (i__ < m) {
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e[i__] = oldsn * r__;
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}
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d__1 = oldcs * r__;
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d__2 = d__[i__ - 1] * sn;
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dlartg_(&d__1, &d__2, &oldcs, &oldsn, &d__[i__]);
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work[i__ - ll] = cs;
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work[i__ - ll + nm1] = -sn;
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work[i__ - ll + nm12] = oldcs;
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work[i__ - ll + nm13] = -oldsn;
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}
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h__ = d__[ll] * cs;
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d__[ll] = h__ * oldcs;
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e[ll] = h__ * oldsn;
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if (*ncvt > 0) {
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i__1 = m - ll + 1;
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dlasr_((char *)"L", (char *)"V", (char *)"B", &i__1, ncvt, &work[nm12 + 1], &work[nm13 + 1],
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&vt[ll + vt_dim1], ldvt, (ftnlen)1, (ftnlen)1, (ftnlen)1);
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}
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if (*nru > 0) {
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i__1 = m - ll + 1;
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dlasr_((char *)"R", (char *)"V", (char *)"B", nru, &i__1, &work[1], &work[*n], &u[ll * u_dim1 + 1], ldu,
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(ftnlen)1, (ftnlen)1, (ftnlen)1);
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}
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if (*ncc > 0) {
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i__1 = m - ll + 1;
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dlasr_((char *)"L", (char *)"V", (char *)"B", &i__1, ncc, &work[1], &work[*n], &c__[ll + c_dim1], ldc,
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(ftnlen)1, (ftnlen)1, (ftnlen)1);
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}
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if ((d__1 = e[ll], abs(d__1)) <= thresh) {
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e[ll] = 0.;
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}
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}
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} else {
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if (idir == 1) {
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f = ((d__1 = d__[ll], abs(d__1)) - shift) *
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(d_lmp_sign(&c_b49, &d__[ll]) + shift / d__[ll]);
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g = e[ll];
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i__1 = m - 1;
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for (i__ = ll; i__ <= i__1; ++i__) {
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dlartg_(&f, &g, &cosr, &sinr, &r__);
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if (i__ > ll) {
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e[i__ - 1] = r__;
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}
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f = cosr * d__[i__] + sinr * e[i__];
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e[i__] = cosr * e[i__] - sinr * d__[i__];
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g = sinr * d__[i__ + 1];
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d__[i__ + 1] = cosr * d__[i__ + 1];
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dlartg_(&f, &g, &cosl, &sinl, &r__);
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d__[i__] = r__;
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f = cosl * e[i__] + sinl * d__[i__ + 1];
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d__[i__ + 1] = cosl * d__[i__ + 1] - sinl * e[i__];
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if (i__ < m - 1) {
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g = sinl * e[i__ + 1];
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e[i__ + 1] = cosl * e[i__ + 1];
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}
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work[i__ - ll + 1] = cosr;
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work[i__ - ll + 1 + nm1] = sinr;
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work[i__ - ll + 1 + nm12] = cosl;
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work[i__ - ll + 1 + nm13] = sinl;
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}
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e[m - 1] = f;
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if (*ncvt > 0) {
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i__1 = m - ll + 1;
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dlasr_((char *)"L", (char *)"V", (char *)"F", &i__1, ncvt, &work[1], &work[*n], &vt[ll + vt_dim1], ldvt,
|
|
(ftnlen)1, (ftnlen)1, (ftnlen)1);
|
|
}
|
|
if (*nru > 0) {
|
|
i__1 = m - ll + 1;
|
|
dlasr_((char *)"R", (char *)"V", (char *)"F", nru, &i__1, &work[nm12 + 1], &work[nm13 + 1],
|
|
&u[ll * u_dim1 + 1], ldu, (ftnlen)1, (ftnlen)1, (ftnlen)1);
|
|
}
|
|
if (*ncc > 0) {
|
|
i__1 = m - ll + 1;
|
|
dlasr_((char *)"L", (char *)"V", (char *)"F", &i__1, ncc, &work[nm12 + 1], &work[nm13 + 1],
|
|
&c__[ll + c_dim1], ldc, (ftnlen)1, (ftnlen)1, (ftnlen)1);
|
|
}
|
|
if ((d__1 = e[m - 1], abs(d__1)) <= thresh) {
|
|
e[m - 1] = 0.;
|
|
}
|
|
} else {
|
|
f = ((d__1 = d__[m], abs(d__1)) - shift) * (d_lmp_sign(&c_b49, &d__[m]) + shift / d__[m]);
|
|
g = e[m - 1];
|
|
i__1 = ll + 1;
|
|
for (i__ = m; i__ >= i__1; --i__) {
|
|
dlartg_(&f, &g, &cosr, &sinr, &r__);
|
|
if (i__ < m) {
|
|
e[i__] = r__;
|
|
}
|
|
f = cosr * d__[i__] + sinr * e[i__ - 1];
|
|
e[i__ - 1] = cosr * e[i__ - 1] - sinr * d__[i__];
|
|
g = sinr * d__[i__ - 1];
|
|
d__[i__ - 1] = cosr * d__[i__ - 1];
|
|
dlartg_(&f, &g, &cosl, &sinl, &r__);
|
|
d__[i__] = r__;
|
|
f = cosl * e[i__ - 1] + sinl * d__[i__ - 1];
|
|
d__[i__ - 1] = cosl * d__[i__ - 1] - sinl * e[i__ - 1];
|
|
if (i__ > ll + 1) {
|
|
g = sinl * e[i__ - 2];
|
|
e[i__ - 2] = cosl * e[i__ - 2];
|
|
}
|
|
work[i__ - ll] = cosr;
|
|
work[i__ - ll + nm1] = -sinr;
|
|
work[i__ - ll + nm12] = cosl;
|
|
work[i__ - ll + nm13] = -sinl;
|
|
}
|
|
e[ll] = f;
|
|
if ((d__1 = e[ll], abs(d__1)) <= thresh) {
|
|
e[ll] = 0.;
|
|
}
|
|
if (*ncvt > 0) {
|
|
i__1 = m - ll + 1;
|
|
dlasr_((char *)"L", (char *)"V", (char *)"B", &i__1, ncvt, &work[nm12 + 1], &work[nm13 + 1],
|
|
&vt[ll + vt_dim1], ldvt, (ftnlen)1, (ftnlen)1, (ftnlen)1);
|
|
}
|
|
if (*nru > 0) {
|
|
i__1 = m - ll + 1;
|
|
dlasr_((char *)"R", (char *)"V", (char *)"B", nru, &i__1, &work[1], &work[*n], &u[ll * u_dim1 + 1], ldu,
|
|
(ftnlen)1, (ftnlen)1, (ftnlen)1);
|
|
}
|
|
if (*ncc > 0) {
|
|
i__1 = m - ll + 1;
|
|
dlasr_((char *)"L", (char *)"V", (char *)"B", &i__1, ncc, &work[1], &work[*n], &c__[ll + c_dim1], ldc,
|
|
(ftnlen)1, (ftnlen)1, (ftnlen)1);
|
|
}
|
|
}
|
|
}
|
|
goto L60;
|
|
L160:
|
|
i__1 = *n;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
if (d__[i__] < 0.) {
|
|
d__[i__] = -d__[i__];
|
|
if (*ncvt > 0) {
|
|
dscal_(ncvt, &c_b72, &vt[i__ + vt_dim1], ldvt);
|
|
}
|
|
}
|
|
}
|
|
i__1 = *n - 1;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
isub = 1;
|
|
smin = d__[1];
|
|
i__2 = *n + 1 - i__;
|
|
for (j = 2; j <= i__2; ++j) {
|
|
if (d__[j] <= smin) {
|
|
isub = j;
|
|
smin = d__[j];
|
|
}
|
|
}
|
|
if (isub != *n + 1 - i__) {
|
|
d__[isub] = d__[*n + 1 - i__];
|
|
d__[*n + 1 - i__] = smin;
|
|
if (*ncvt > 0) {
|
|
dswap_(ncvt, &vt[isub + vt_dim1], ldvt, &vt[*n + 1 - i__ + vt_dim1], ldvt);
|
|
}
|
|
if (*nru > 0) {
|
|
dswap_(nru, &u[isub * u_dim1 + 1], &c__1, &u[(*n + 1 - i__) * u_dim1 + 1], &c__1);
|
|
}
|
|
if (*ncc > 0) {
|
|
dswap_(ncc, &c__[isub + c_dim1], ldc, &c__[*n + 1 - i__ + c_dim1], ldc);
|
|
}
|
|
}
|
|
}
|
|
goto L220;
|
|
L200:
|
|
*info = 0;
|
|
i__1 = *n - 1;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
if (e[i__] != 0.) {
|
|
++(*info);
|
|
}
|
|
}
|
|
L220:
|
|
return 0;
|
|
}
|
|
#ifdef __cplusplus
|
|
}
|
|
#endif
|