#ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" static integer c__6 = 6; static integer c_n1 = -1; static integer c__9 = 9; static integer c__0 = 0; static integer c__1 = 1; static doublereal c_b82 = 0.; int dgelsd_(integer *m, integer *n, integer *nrhs, doublereal *a, integer *lda, doublereal *b, integer *ldb, doublereal *s, doublereal *rcond, integer *rank, doublereal *work, integer *lwork, integer *iwork, integer *info) { integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3, i__4; double log(doublereal); integer ie, il, mm; doublereal eps, anrm, bnrm; integer itau, nlvl, iascl, ibscl; doublereal sfmin; integer minmn, maxmn, itaup, itauq, mnthr, nwork; extern int dgebrd_(integer *, integer *, doublereal *, integer *, doublereal *, doublereal *, doublereal *, doublereal *, doublereal *, integer *, integer *); extern doublereal dlamch_(char *, ftnlen), dlange_(char *, integer *, integer *, doublereal *, integer *, doublereal *, ftnlen); extern int dgelqf_(integer *, integer *, doublereal *, integer *, doublereal *, doublereal *, integer *, integer *), dlalsd_(char *, integer *, integer *, integer *, doublereal *, doublereal *, doublereal *, integer *, doublereal *, integer *, doublereal *, integer *, integer *, ftnlen), dlascl_(char *, integer *, integer *, doublereal *, doublereal *, integer *, integer *, doublereal *, integer *, integer *, ftnlen), dgeqrf_(integer *, integer *, doublereal *, integer *, doublereal *, doublereal *, integer *, integer *), dlacpy_(char *, integer *, integer *, doublereal *, integer *, doublereal *, integer *, ftnlen), dlaset_(char *, integer *, integer *, doublereal *, doublereal *, doublereal *, integer *, ftnlen), xerbla_(char *, integer *, ftnlen); extern integer ilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *, ftnlen, ftnlen); doublereal bignum; extern int dormbr_(char *, char *, char *, integer *, integer *, integer *, doublereal *, integer *, doublereal *, doublereal *, integer *, doublereal *, integer *, integer *, ftnlen, ftnlen, ftnlen); integer wlalsd; extern int dormlq_(char *, char *, integer *, integer *, integer *, doublereal *, integer *, doublereal *, doublereal *, integer *, doublereal *, integer *, integer *, ftnlen, ftnlen); integer ldwork; extern int dormqr_(char *, char *, integer *, integer *, integer *, doublereal *, integer *, doublereal *, doublereal *, integer *, doublereal *, integer *, integer *, ftnlen, ftnlen); integer liwork, minwrk, maxwrk; doublereal smlnum; logical lquery; integer smlsiz; a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; b_dim1 = *ldb; b_offset = 1 + b_dim1; b -= b_offset; --s; --work; --iwork; *info = 0; minmn = min(*m, *n); maxmn = max(*m, *n); mnthr = ilaenv_(&c__6, (char *)"DGELSD", (char *)" ", m, n, nrhs, &c_n1, (ftnlen)6, (ftnlen)1); lquery = *lwork == -1; if (*m < 0) { *info = -1; } else if (*n < 0) { *info = -2; } else if (*nrhs < 0) { *info = -3; } else if (*lda < max(1, *m)) { *info = -5; } else if (*ldb < max(1, maxmn)) { *info = -7; } smlsiz = ilaenv_(&c__9, (char *)"DGELSD", (char *)" ", &c__0, &c__0, &c__0, &c__0, (ftnlen)6, (ftnlen)1); minwrk = 1; liwork = 1; minmn = max(1, minmn); i__1 = (integer)(log((doublereal)minmn / (doublereal)(smlsiz + 1)) / log(2.)) + 1; nlvl = max(i__1, 0); if (*info == 0) { maxwrk = 0; liwork = minmn * 3 * nlvl + minmn * 11; mm = *m; if (*m >= *n && *m >= mnthr) { mm = *n; i__1 = maxwrk, i__2 = *n + *n * ilaenv_(&c__1, (char *)"DGEQRF", (char *)" ", m, n, &c_n1, &c_n1, (ftnlen)6, (ftnlen)1); maxwrk = max(i__1, i__2); i__1 = maxwrk, i__2 = *n + *nrhs * ilaenv_(&c__1, (char *)"DORMQR", (char *)"LT", m, nrhs, n, &c_n1, (ftnlen)6, (ftnlen)2); maxwrk = max(i__1, i__2); } if (*m >= *n) { i__1 = maxwrk, i__2 = *n * 3 + (mm + *n) * ilaenv_(&c__1, (char *)"DGEBRD", (char *)" ", &mm, n, &c_n1, &c_n1, (ftnlen)6, (ftnlen)1); maxwrk = max(i__1, i__2); i__1 = maxwrk, i__2 = *n * 3 + *nrhs * ilaenv_(&c__1, (char *)"DORMBR", (char *)"QLT", &mm, nrhs, n, &c_n1, (ftnlen)6, (ftnlen)3); maxwrk = max(i__1, i__2); i__1 = maxwrk, i__2 = *n * 3 + (*n - 1) * ilaenv_(&c__1, (char *)"DORMBR", (char *)"PLN", n, nrhs, n, &c_n1, (ftnlen)6, (ftnlen)3); maxwrk = max(i__1, i__2); i__1 = smlsiz + 1; wlalsd = *n * 9 + (*n << 1) * smlsiz + (*n << 3) * nlvl + *n * *nrhs + i__1 * i__1; i__1 = maxwrk, i__2 = *n * 3 + wlalsd; maxwrk = max(i__1, i__2); i__1 = *n * 3 + mm, i__2 = *n * 3 + *nrhs, i__1 = max(i__1, i__2), i__2 = *n * 3 + wlalsd; minwrk = max(i__1, i__2); } if (*n > *m) { i__1 = smlsiz + 1; wlalsd = *m * 9 + (*m << 1) * smlsiz + (*m << 3) * nlvl + *m * *nrhs + i__1 * i__1; if (*n >= mnthr) { maxwrk = *m + *m * ilaenv_(&c__1, (char *)"DGELQF", (char *)" ", m, n, &c_n1, &c_n1, (ftnlen)6, (ftnlen)1); i__1 = maxwrk, i__2 = *m * *m + (*m << 2) + (*m << 1) * ilaenv_(&c__1, (char *)"DGEBRD", (char *)" ", m, m, &c_n1, &c_n1, (ftnlen)6, (ftnlen)1); maxwrk = max(i__1, i__2); i__1 = maxwrk, i__2 = *m * *m + (*m << 2) + *nrhs * ilaenv_(&c__1, (char *)"DORMBR", (char *)"QLT", m, nrhs, m, &c_n1, (ftnlen)6, (ftnlen)3); maxwrk = max(i__1, i__2); i__1 = maxwrk, i__2 = *m * *m + (*m << 2) + (*m - 1) * ilaenv_(&c__1, (char *)"DORMBR", (char *)"PLN", m, nrhs, m, &c_n1, (ftnlen)6, (ftnlen)3); maxwrk = max(i__1, i__2); if (*nrhs > 1) { i__1 = maxwrk, i__2 = *m * *m + *m + *m * *nrhs; maxwrk = max(i__1, i__2); } else { i__1 = maxwrk, i__2 = *m * *m + (*m << 1); maxwrk = max(i__1, i__2); } i__1 = maxwrk, i__2 = *m + *nrhs * ilaenv_(&c__1, (char *)"DORMLQ", (char *)"LT", n, nrhs, m, &c_n1, (ftnlen)6, (ftnlen)2); maxwrk = max(i__1, i__2); i__1 = maxwrk, i__2 = *m * *m + (*m << 2) + wlalsd; maxwrk = max(i__1, i__2); i__3 = *m, i__4 = (*m << 1) - 4, i__3 = max(i__3, i__4), i__3 = max(i__3, *nrhs), i__4 = *n - *m * 3; i__1 = maxwrk, i__2 = (*m << 2) + *m * *m + max(i__3, i__4); maxwrk = max(i__1, i__2); } else { maxwrk = *m * 3 + (*n + *m) * ilaenv_(&c__1, (char *)"DGEBRD", (char *)" ", m, n, &c_n1, &c_n1, (ftnlen)6, (ftnlen)1); i__1 = maxwrk, i__2 = *m * 3 + *nrhs * ilaenv_(&c__1, (char *)"DORMBR", (char *)"QLT", m, nrhs, n, &c_n1, (ftnlen)6, (ftnlen)3); maxwrk = max(i__1, i__2); i__1 = maxwrk, i__2 = *m * 3 + *m * ilaenv_(&c__1, (char *)"DORMBR", (char *)"PLN", n, nrhs, m, &c_n1, (ftnlen)6, (ftnlen)3); maxwrk = max(i__1, i__2); i__1 = maxwrk, i__2 = *m * 3 + wlalsd; maxwrk = max(i__1, i__2); } i__1 = *m * 3 + *nrhs, i__2 = *m * 3 + *m, i__1 = max(i__1, i__2), i__2 = *m * 3 + wlalsd; minwrk = max(i__1, i__2); } minwrk = min(minwrk, maxwrk); work[1] = (doublereal)maxwrk; iwork[1] = liwork; if (*lwork < minwrk && !lquery) { *info = -12; } } if (*info != 0) { i__1 = -(*info); xerbla_((char *)"DGELSD", &i__1, (ftnlen)6); return 0; } else if (lquery) { goto L10; } if (*m == 0 || *n == 0) { *rank = 0; return 0; } eps = dlamch_((char *)"P", (ftnlen)1); sfmin = dlamch_((char *)"S", (ftnlen)1); smlnum = sfmin / eps; bignum = 1. / smlnum; anrm = dlange_((char *)"M", m, n, &a[a_offset], lda, &work[1], (ftnlen)1); iascl = 0; if (anrm > 0. && anrm < smlnum) { dlascl_((char *)"G", &c__0, &c__0, &anrm, &smlnum, m, n, &a[a_offset], lda, info, (ftnlen)1); iascl = 1; } else if (anrm > bignum) { dlascl_((char *)"G", &c__0, &c__0, &anrm, &bignum, m, n, &a[a_offset], lda, info, (ftnlen)1); iascl = 2; } else if (anrm == 0.) { i__1 = max(*m, *n); dlaset_((char *)"F", &i__1, nrhs, &c_b82, &c_b82, &b[b_offset], ldb, (ftnlen)1); dlaset_((char *)"F", &minmn, &c__1, &c_b82, &c_b82, &s[1], &c__1, (ftnlen)1); *rank = 0; goto L10; } bnrm = dlange_((char *)"M", m, nrhs, &b[b_offset], ldb, &work[1], (ftnlen)1); ibscl = 0; if (bnrm > 0. && bnrm < smlnum) { dlascl_((char *)"G", &c__0, &c__0, &bnrm, &smlnum, m, nrhs, &b[b_offset], ldb, info, (ftnlen)1); ibscl = 1; } else if (bnrm > bignum) { dlascl_((char *)"G", &c__0, &c__0, &bnrm, &bignum, m, nrhs, &b[b_offset], ldb, info, (ftnlen)1); ibscl = 2; } if (*m < *n) { i__1 = *n - *m; dlaset_((char *)"F", &i__1, nrhs, &c_b82, &c_b82, &b[*m + 1 + b_dim1], ldb, (ftnlen)1); } if (*m >= *n) { mm = *m; if (*m >= mnthr) { mm = *n; itau = 1; nwork = itau + *n; i__1 = *lwork - nwork + 1; dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &i__1, info); i__1 = *lwork - nwork + 1; dormqr_((char *)"L", (char *)"T", m, nrhs, n, &a[a_offset], lda, &work[itau], &b[b_offset], ldb, &work[nwork], &i__1, info, (ftnlen)1, (ftnlen)1); if (*n > 1) { i__1 = *n - 1; i__2 = *n - 1; dlaset_((char *)"L", &i__1, &i__2, &c_b82, &c_b82, &a[a_dim1 + 2], lda, (ftnlen)1); } } ie = 1; itauq = ie + *n; itaup = itauq + *n; nwork = itaup + *n; i__1 = *lwork - nwork + 1; dgebrd_(&mm, n, &a[a_offset], lda, &s[1], &work[ie], &work[itauq], &work[itaup], &work[nwork], &i__1, info); i__1 = *lwork - nwork + 1; dormbr_((char *)"Q", (char *)"L", (char *)"T", &mm, nrhs, n, &a[a_offset], lda, &work[itauq], &b[b_offset], ldb, &work[nwork], &i__1, info, (ftnlen)1, (ftnlen)1, (ftnlen)1); dlalsd_((char *)"U", &smlsiz, n, nrhs, &s[1], &work[ie], &b[b_offset], ldb, rcond, rank, &work[nwork], &iwork[1], info, (ftnlen)1); if (*info != 0) { goto L10; } i__1 = *lwork - nwork + 1; dormbr_((char *)"P", (char *)"L", (char *)"N", n, nrhs, n, &a[a_offset], lda, &work[itaup], &b[b_offset], ldb, &work[nwork], &i__1, info, (ftnlen)1, (ftnlen)1, (ftnlen)1); } else { i__1 = *m, i__2 = (*m << 1) - 4, i__1 = max(i__1, i__2), i__1 = max(i__1, *nrhs), i__2 = *n - *m * 3, i__1 = max(i__1, i__2); if (*n >= mnthr && *lwork >= (*m << 2) + *m * *m + max(i__1, wlalsd)) { ldwork = *m; i__3 = *m, i__4 = (*m << 1) - 4, i__3 = max(i__3, i__4), i__3 = max(i__3, *nrhs), i__4 = *n - *m * 3; i__1 = (*m << 2) + *m * *lda + max(i__3, i__4), i__2 = *m * *lda + *m + *m * *nrhs, i__1 = max(i__1, i__2), i__2 = (*m << 2) + *m * *lda + wlalsd; if (*lwork >= max(i__1, i__2)) { ldwork = *lda; } itau = 1; nwork = *m + 1; i__1 = *lwork - nwork + 1; dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &i__1, info); il = nwork; dlacpy_((char *)"L", m, m, &a[a_offset], lda, &work[il], &ldwork, (ftnlen)1); i__1 = *m - 1; i__2 = *m - 1; dlaset_((char *)"U", &i__1, &i__2, &c_b82, &c_b82, &work[il + ldwork], &ldwork, (ftnlen)1); ie = il + ldwork * *m; itauq = ie + *m; itaup = itauq + *m; nwork = itaup + *m; i__1 = *lwork - nwork + 1; dgebrd_(m, m, &work[il], &ldwork, &s[1], &work[ie], &work[itauq], &work[itaup], &work[nwork], &i__1, info); i__1 = *lwork - nwork + 1; dormbr_((char *)"Q", (char *)"L", (char *)"T", m, nrhs, m, &work[il], &ldwork, &work[itauq], &b[b_offset], ldb, &work[nwork], &i__1, info, (ftnlen)1, (ftnlen)1, (ftnlen)1); dlalsd_((char *)"U", &smlsiz, m, nrhs, &s[1], &work[ie], &b[b_offset], ldb, rcond, rank, &work[nwork], &iwork[1], info, (ftnlen)1); if (*info != 0) { goto L10; } i__1 = *lwork - nwork + 1; dormbr_((char *)"P", (char *)"L", (char *)"N", m, nrhs, m, &work[il], &ldwork, &work[itaup], &b[b_offset], ldb, &work[nwork], &i__1, info, (ftnlen)1, (ftnlen)1, (ftnlen)1); i__1 = *n - *m; dlaset_((char *)"F", &i__1, nrhs, &c_b82, &c_b82, &b[*m + 1 + b_dim1], ldb, (ftnlen)1); nwork = itau + *m; i__1 = *lwork - nwork + 1; dormlq_((char *)"L", (char *)"T", n, nrhs, m, &a[a_offset], lda, &work[itau], &b[b_offset], ldb, &work[nwork], &i__1, info, (ftnlen)1, (ftnlen)1); } else { ie = 1; itauq = ie + *m; itaup = itauq + *m; nwork = itaup + *m; i__1 = *lwork - nwork + 1; dgebrd_(m, n, &a[a_offset], lda, &s[1], &work[ie], &work[itauq], &work[itaup], &work[nwork], &i__1, info); i__1 = *lwork - nwork + 1; dormbr_((char *)"Q", (char *)"L", (char *)"T", m, nrhs, n, &a[a_offset], lda, &work[itauq], &b[b_offset], ldb, &work[nwork], &i__1, info, (ftnlen)1, (ftnlen)1, (ftnlen)1); dlalsd_((char *)"L", &smlsiz, m, nrhs, &s[1], &work[ie], &b[b_offset], ldb, rcond, rank, &work[nwork], &iwork[1], info, (ftnlen)1); if (*info != 0) { goto L10; } i__1 = *lwork - nwork + 1; dormbr_((char *)"P", (char *)"L", (char *)"N", n, nrhs, m, &a[a_offset], lda, &work[itaup], &b[b_offset], ldb, &work[nwork], &i__1, info, (ftnlen)1, (ftnlen)1, (ftnlen)1); } } if (iascl == 1) { dlascl_((char *)"G", &c__0, &c__0, &anrm, &smlnum, n, nrhs, &b[b_offset], ldb, info, (ftnlen)1); dlascl_((char *)"G", &c__0, &c__0, &smlnum, &anrm, &minmn, &c__1, &s[1], &minmn, info, (ftnlen)1); } else if (iascl == 2) { dlascl_((char *)"G", &c__0, &c__0, &anrm, &bignum, n, nrhs, &b[b_offset], ldb, info, (ftnlen)1); dlascl_((char *)"G", &c__0, &c__0, &bignum, &anrm, &minmn, &c__1, &s[1], &minmn, info, (ftnlen)1); } if (ibscl == 1) { dlascl_((char *)"G", &c__0, &c__0, &smlnum, &bnrm, n, nrhs, &b[b_offset], ldb, info, (ftnlen)1); } else if (ibscl == 2) { dlascl_((char *)"G", &c__0, &c__0, &bignum, &bnrm, n, nrhs, &b[b_offset], ldb, info, (ftnlen)1); } L10: work[1] = (doublereal)maxwrk; iwork[1] = liwork; return 0; } #ifdef __cplusplus } #endif