#ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" static doublereal c_b15 = -.125; static integer c__1 = 1; static doublereal c_b49 = 1.; static doublereal c_b72 = -1.; int dbdsqr_(char *uplo, integer *n, integer *ncvt, integer *nru, integer *ncc, doublereal *d__, doublereal *e, doublereal *vt, integer *ldvt, doublereal *u, integer *ldu, doublereal *c__, integer *ldc, doublereal *work, integer *info, ftnlen uplo_len) { integer c_dim1, c_offset, u_dim1, u_offset, vt_dim1, vt_offset, i__1, i__2; doublereal d__1, d__2, d__3, d__4; double pow_lmp_dd(doublereal *, doublereal *), sqrt(doublereal), d_lmp_sign(doublereal *, doublereal *); integer iterdivn; doublereal f, g, h__; integer i__, j, m; doublereal r__; integer maxitdivn; doublereal cs; integer ll; doublereal sn, mu; integer nm1, nm12, nm13, lll; doublereal eps, sll, tol, abse; integer idir; doublereal abss; integer oldm; doublereal cosl; integer isub, iter; doublereal unfl, sinl, cosr, smin, smax, sinr; extern int drot_(integer *, doublereal *, integer *, doublereal *, integer *, doublereal *, doublereal *), dlas2_(doublereal *, doublereal *, doublereal *, doublereal *, doublereal *), dscal_(integer *, doublereal *, doublereal *, integer *); extern logical lsame_(char *, char *, ftnlen, ftnlen); doublereal oldcs; extern int dlasr_(char *, char *, char *, integer *, integer *, doublereal *, doublereal *, doublereal *, integer *, ftnlen, ftnlen, ftnlen); integer oldll; doublereal shift, sigmn, oldsn; extern int dswap_(integer *, doublereal *, integer *, doublereal *, integer *); doublereal sigmx; logical lower; extern int dlasq1_(integer *, doublereal *, doublereal *, doublereal *, integer *), dlasv2_(doublereal *, doublereal *, doublereal *, doublereal *, doublereal *, doublereal *, doublereal *, doublereal *, doublereal *); extern doublereal dlamch_(char *, ftnlen); extern int dlartg_(doublereal *, doublereal *, doublereal *, doublereal *, doublereal *), xerbla_(char *, integer *, ftnlen); doublereal sminoa, thresh; logical rotate; doublereal tolmul; --d__; --e; vt_dim1 = *ldvt; vt_offset = 1 + vt_dim1; vt -= vt_offset; u_dim1 = *ldu; u_offset = 1 + u_dim1; u -= u_offset; c_dim1 = *ldc; c_offset = 1 + c_dim1; c__ -= c_offset; --work; *info = 0; lower = lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1); if (!lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1) && !lower) { *info = -1; } else if (*n < 0) { *info = -2; } else if (*ncvt < 0) { *info = -3; } else if (*nru < 0) { *info = -4; } else if (*ncc < 0) { *info = -5; } else if (*ncvt == 0 && *ldvt < 1 || *ncvt > 0 && *ldvt < max(1, *n)) { *info = -9; } else if (*ldu < max(1, *nru)) { *info = -11; } else if (*ncc == 0 && *ldc < 1 || *ncc > 0 && *ldc < max(1, *n)) { *info = -13; } if (*info != 0) { i__1 = -(*info); xerbla_((char *)"DBDSQR", &i__1, (ftnlen)6); return 0; } if (*n == 0) { return 0; } if (*n == 1) { goto L160; } rotate = *ncvt > 0 || *nru > 0 || *ncc > 0; if (!rotate) { dlasq1_(n, &d__[1], &e[1], &work[1], info); if (*info != 2) { return 0; } *info = 0; } nm1 = *n - 1; nm12 = nm1 + nm1; nm13 = nm12 + nm1; idir = 0; eps = dlamch_((char *)"Epsilon", (ftnlen)7); unfl = dlamch_((char *)"Safe minimum", (ftnlen)12); if (lower) { i__1 = *n - 1; for (i__ = 1; i__ <= i__1; ++i__) { dlartg_(&d__[i__], &e[i__], &cs, &sn, &r__); d__[i__] = r__; e[i__] = sn * d__[i__ + 1]; d__[i__ + 1] = cs * d__[i__ + 1]; work[i__] = cs; work[nm1 + i__] = sn; } if (*nru > 0) { dlasr_((char *)"R", (char *)"V", (char *)"F", nru, n, &work[1], &work[*n], &u[u_offset], ldu, (ftnlen)1, (ftnlen)1, (ftnlen)1); } if (*ncc > 0) { dlasr_((char *)"L", (char *)"V", (char *)"F", n, ncc, &work[1], &work[*n], &c__[c_offset], ldc, (ftnlen)1, (ftnlen)1, (ftnlen)1); } } d__3 = 100., d__4 = pow_lmp_dd(&eps, &c_b15); d__1 = 10., d__2 = min(d__3, d__4); tolmul = max(d__1, d__2); tol = tolmul * eps; smax = 0.; i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { d__2 = smax, d__3 = (d__1 = d__[i__], abs(d__1)); smax = max(d__2, d__3); } i__1 = *n - 1; for (i__ = 1; i__ <= i__1; ++i__) { d__2 = smax, d__3 = (d__1 = e[i__], abs(d__1)); smax = max(d__2, d__3); } smin = 0.; if (tol >= 0.) { sminoa = abs(d__[1]); if (sminoa == 0.) { goto L50; } mu = sminoa; i__1 = *n; for (i__ = 2; i__ <= i__1; ++i__) { mu = (d__2 = d__[i__], abs(d__2)) * (mu / (mu + (d__1 = e[i__ - 1], abs(d__1)))); sminoa = min(sminoa, mu); if (sminoa == 0.) { goto L50; } } L50: sminoa /= sqrt((doublereal)(*n)); d__1 = tol * sminoa, d__2 = *n * (*n * unfl) * 6; thresh = max(d__1, d__2); } else { d__1 = abs(tol) * smax, d__2 = *n * (*n * unfl) * 6; thresh = max(d__1, d__2); } maxitdivn = *n * 6; iterdivn = 0; iter = -1; oldll = -1; oldm = -1; m = *n; L60: if (m <= 1) { goto L160; } if (iter >= *n) { iter -= *n; ++iterdivn; if (iterdivn >= maxitdivn) { goto L200; } } if (tol < 0. && (d__1 = d__[m], abs(d__1)) <= thresh) { d__[m] = 0.; } smax = (d__1 = d__[m], abs(d__1)); i__1 = m - 1; for (lll = 1; lll <= i__1; ++lll) { ll = m - lll; abss = (d__1 = d__[ll], abs(d__1)); abse = (d__1 = e[ll], abs(d__1)); if (tol < 0. && abss <= thresh) { d__[ll] = 0.; } if (abse <= thresh) { goto L80; } d__1 = max(smax, abss); smax = max(d__1, abse); } ll = 0; goto L90; L80: e[ll] = 0.; if (ll == m - 1) { --m; goto L60; } L90: ++ll; if (ll == m - 1) { dlasv2_(&d__[m - 1], &e[m - 1], &d__[m], &sigmn, &sigmx, &sinr, &cosr, &sinl, &cosl); d__[m - 1] = sigmx; e[m - 1] = 0.; d__[m] = sigmn; if (*ncvt > 0) { drot_(ncvt, &vt[m - 1 + vt_dim1], ldvt, &vt[m + vt_dim1], ldvt, &cosr, &sinr); } if (*nru > 0) { drot_(nru, &u[(m - 1) * u_dim1 + 1], &c__1, &u[m * u_dim1 + 1], &c__1, &cosl, &sinl); } if (*ncc > 0) { drot_(ncc, &c__[m - 1 + c_dim1], ldc, &c__[m + c_dim1], ldc, &cosl, &sinl); } m += -2; goto L60; } if (ll > oldm || m < oldll) { if ((d__1 = d__[ll], abs(d__1)) >= (d__2 = d__[m], abs(d__2))) { idir = 1; } else { idir = 2; } } if (idir == 1) { if ((d__2 = e[m - 1], abs(d__2)) <= abs(tol) * (d__1 = d__[m], abs(d__1)) || tol < 0. && (d__3 = e[m - 1], abs(d__3)) <= thresh) { e[m - 1] = 0.; goto L60; } if (tol >= 0.) { mu = (d__1 = d__[ll], abs(d__1)); smin = mu; i__1 = m - 1; for (lll = ll; lll <= i__1; ++lll) { if ((d__1 = e[lll], abs(d__1)) <= tol * mu) { e[lll] = 0.; goto L60; } mu = (d__2 = d__[lll + 1], abs(d__2)) * (mu / (mu + (d__1 = e[lll], abs(d__1)))); smin = min(smin, mu); } } } else { if ((d__2 = e[ll], abs(d__2)) <= abs(tol) * (d__1 = d__[ll], abs(d__1)) || tol < 0. && (d__3 = e[ll], abs(d__3)) <= thresh) { e[ll] = 0.; goto L60; } if (tol >= 0.) { mu = (d__1 = d__[m], abs(d__1)); smin = mu; i__1 = ll; for (lll = m - 1; lll >= i__1; --lll) { if ((d__1 = e[lll], abs(d__1)) <= tol * mu) { e[lll] = 0.; goto L60; } mu = (d__2 = d__[lll], abs(d__2)) * (mu / (mu + (d__1 = e[lll], abs(d__1)))); smin = min(smin, mu); } } } oldll = ll; oldm = m; d__1 = eps, d__2 = tol * .01; if (tol >= 0. && *n * tol * (smin / smax) <= max(d__1, d__2)) { shift = 0.; } else { if (idir == 1) { sll = (d__1 = d__[ll], abs(d__1)); dlas2_(&d__[m - 1], &e[m - 1], &d__[m], &shift, &r__); } else { sll = (d__1 = d__[m], abs(d__1)); dlas2_(&d__[ll], &e[ll], &d__[ll + 1], &shift, &r__); } if (sll > 0.) { d__1 = shift / sll; if (d__1 * d__1 < eps) { shift = 0.; } } } iter = iter + m - ll; if (shift == 0.) { if (idir == 1) { cs = 1.; oldcs = 1.; i__1 = m - 1; for (i__ = ll; i__ <= i__1; ++i__) { d__1 = d__[i__] * cs; dlartg_(&d__1, &e[i__], &cs, &sn, &r__); if (i__ > ll) { e[i__ - 1] = oldsn * r__; } d__1 = oldcs * r__; d__2 = d__[i__ + 1] * sn; dlartg_(&d__1, &d__2, &oldcs, &oldsn, &d__[i__]); work[i__ - ll + 1] = cs; work[i__ - ll + 1 + nm1] = sn; work[i__ - ll + 1 + nm12] = oldcs; work[i__ - ll + 1 + nm13] = oldsn; } h__ = d__[m] * cs; d__[m] = h__ * oldcs; e[m - 1] = h__ * oldsn; if (*ncvt > 0) { i__1 = m - ll + 1; 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 { cs = 1.; oldcs = 1.; i__1 = ll + 1; for (i__ = m; i__ >= i__1; --i__) { d__1 = d__[i__] * cs; dlartg_(&d__1, &e[i__ - 1], &cs, &sn, &r__); if (i__ < m) { e[i__] = oldsn * r__; } d__1 = oldcs * r__; d__2 = d__[i__ - 1] * sn; dlartg_(&d__1, &d__2, &oldcs, &oldsn, &d__[i__]); work[i__ - ll] = cs; work[i__ - ll + nm1] = -sn; work[i__ - ll + nm12] = oldcs; work[i__ - ll + nm13] = -oldsn; } h__ = d__[ll] * cs; d__[ll] = h__ * oldcs; e[ll] = h__ * oldsn; 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); } if ((d__1 = e[ll], abs(d__1)) <= thresh) { e[ll] = 0.; } } } else { if (idir == 1) { f = ((d__1 = d__[ll], abs(d__1)) - shift) * (d_lmp_sign(&c_b49, &d__[ll]) + shift / d__[ll]); g = e[ll]; i__1 = m - 1; for (i__ = ll; i__ <= i__1; ++i__) { dlartg_(&f, &g, &cosr, &sinr, &r__); if (i__ > ll) { e[i__ - 1] = r__; } f = cosr * d__[i__] + sinr * e[i__]; e[i__] = cosr * e[i__] - 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__] + sinl * d__[i__ + 1]; d__[i__ + 1] = cosl * d__[i__ + 1] - sinl * e[i__]; if (i__ < m - 1) { g = sinl * e[i__ + 1]; e[i__ + 1] = cosl * e[i__ + 1]; } work[i__ - ll + 1] = cosr; work[i__ - ll + 1 + nm1] = sinr; work[i__ - ll + 1 + nm12] = cosl; work[i__ - ll + 1 + nm13] = sinl; } e[m - 1] = f; if (*ncvt > 0) { i__1 = m - ll + 1; 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