#ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" static integer c__6 = 6; static integer c_n1 = -1; static integer c__0 = 0; static doublereal c_b46 = 0.; static integer c__1 = 1; static doublereal c_b79 = 1.; int dgelss_(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 *info) { integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3, i__4; doublereal d__1; integer i__, bl, ie, il, mm; doublereal dum[1], eps, thr, anrm, bnrm; integer itau, lwork_dgebrd__, lwork_dgelqf__, lwork_dgeqrf__, lwork_dorgbr__, lwork_dormbr__, lwork_dormlq__, lwork_dormqr__; extern int dgemm_(char *, char *, integer *, integer *, integer *, doublereal *, doublereal *, integer *, doublereal *, integer *, doublereal *, doublereal *, integer *, ftnlen, ftnlen); integer iascl, ibscl; extern int dgemv_(char *, integer *, integer *, doublereal *, doublereal *, integer *, doublereal *, integer *, doublereal *, doublereal *, integer *, ftnlen), drscl_(integer *, doublereal *, doublereal *, integer *); integer chunk; doublereal sfmin; integer minmn; extern int dcopy_(integer *, doublereal *, integer *, doublereal *, integer *); integer maxmn, itaup, itauq, mnthr, iwork; 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); integer bdspac; extern int dgelqf_(integer *, integer *, doublereal *, integer *, doublereal *, doublereal *, integer *, integer *), 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), dbdsqr_(char *, integer *, integer *, integer *, integer *, doublereal *, doublereal *, doublereal *, integer *, doublereal *, integer *, doublereal *, integer *, doublereal *, integer *, ftnlen), dorgbr_(char *, integer *, integer *, integer *, doublereal *, integer *, doublereal *, doublereal *, integer *, integer *, ftnlen); doublereal bignum; extern integer ilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *, ftnlen, ftnlen); extern int dormbr_(char *, char *, char *, integer *, integer *, integer *, doublereal *, integer *, doublereal *, doublereal *, integer *, doublereal *, integer *, integer *, ftnlen, ftnlen, ftnlen), 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 minwrk, maxwrk; doublereal smlnum; logical lquery; a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; b_dim1 = *ldb; b_offset = 1 + b_dim1; b -= b_offset; --s; --work; *info = 0; minmn = min(*m, *n); maxmn = max(*m, *n); 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; } if (*info == 0) { minwrk = 1; maxwrk = 1; if (minmn > 0) { mm = *m; mnthr = ilaenv_(&c__6, (char *)"DGELSS", (char *)" ", m, n, nrhs, &c_n1, (ftnlen)6, (ftnlen)1); if (*m >= *n && *m >= mnthr) { dgeqrf_(m, n, &a[a_offset], lda, dum, dum, &c_n1, info); lwork_dgeqrf__ = (integer)dum[0]; dormqr_((char *)"L", (char *)"T", m, nrhs, n, &a[a_offset], lda, dum, &b[b_offset], ldb, dum, &c_n1, info, (ftnlen)1, (ftnlen)1); lwork_dormqr__ = (integer)dum[0]; mm = *n; i__1 = maxwrk, i__2 = *n + lwork_dgeqrf__; maxwrk = max(i__1, i__2); i__1 = maxwrk, i__2 = *n + lwork_dormqr__; maxwrk = max(i__1, i__2); } if (*m >= *n) { i__1 = 1, i__2 = *n * 5; bdspac = max(i__1, i__2); dgebrd_(&mm, n, &a[a_offset], lda, &s[1], dum, dum, dum, dum, &c_n1, info); lwork_dgebrd__ = (integer)dum[0]; dormbr_((char *)"Q", (char *)"L", (char *)"T", &mm, nrhs, n, &a[a_offset], lda, dum, &b[b_offset], ldb, dum, &c_n1, info, (ftnlen)1, (ftnlen)1, (ftnlen)1); lwork_dormbr__ = (integer)dum[0]; dorgbr_((char *)"P", n, n, n, &a[a_offset], lda, dum, dum, &c_n1, info, (ftnlen)1); lwork_dorgbr__ = (integer)dum[0]; i__1 = maxwrk, i__2 = *n * 3 + lwork_dgebrd__; maxwrk = max(i__1, i__2); i__1 = maxwrk, i__2 = *n * 3 + lwork_dormbr__; maxwrk = max(i__1, i__2); i__1 = maxwrk, i__2 = *n * 3 + lwork_dorgbr__; maxwrk = max(i__1, i__2); maxwrk = max(maxwrk, bdspac); i__1 = maxwrk, i__2 = *n * *nrhs; maxwrk = max(i__1, i__2); i__1 = *n * 3 + mm, i__2 = *n * 3 + *nrhs, i__1 = max(i__1, i__2); minwrk = max(i__1, bdspac); maxwrk = max(minwrk, maxwrk); } if (*n > *m) { i__1 = 1, i__2 = *m * 5; bdspac = max(i__1, i__2); i__1 = *m * 3 + *nrhs, i__2 = *m * 3 + *n, i__1 = max(i__1, i__2); minwrk = max(i__1, bdspac); if (*n >= mnthr) { dgelqf_(m, n, &a[a_offset], lda, dum, dum, &c_n1, info); lwork_dgelqf__ = (integer)dum[0]; dgebrd_(m, m, &a[a_offset], lda, &s[1], dum, dum, dum, dum, &c_n1, info); lwork_dgebrd__ = (integer)dum[0]; dormbr_((char *)"Q", (char *)"L", (char *)"T", m, nrhs, n, &a[a_offset], lda, dum, &b[b_offset], ldb, dum, &c_n1, info, (ftnlen)1, (ftnlen)1, (ftnlen)1); lwork_dormbr__ = (integer)dum[0]; dorgbr_((char *)"P", m, m, m, &a[a_offset], lda, dum, dum, &c_n1, info, (ftnlen)1); lwork_dorgbr__ = (integer)dum[0]; dormlq_((char *)"L", (char *)"T", n, nrhs, m, &a[a_offset], lda, dum, &b[b_offset], ldb, dum, &c_n1, info, (ftnlen)1, (ftnlen)1); lwork_dormlq__ = (integer)dum[0]; maxwrk = *m + lwork_dgelqf__; i__1 = maxwrk, i__2 = *m * *m + (*m << 2) + lwork_dgebrd__; maxwrk = max(i__1, i__2); i__1 = maxwrk, i__2 = *m * *m + (*m << 2) + lwork_dormbr__; maxwrk = max(i__1, i__2); i__1 = maxwrk, i__2 = *m * *m + (*m << 2) + lwork_dorgbr__; maxwrk = max(i__1, i__2); i__1 = maxwrk, i__2 = *m * *m + *m + bdspac; 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 + lwork_dormlq__; maxwrk = max(i__1, i__2); } else { dgebrd_(m, n, &a[a_offset], lda, &s[1], dum, dum, dum, dum, &c_n1, info); lwork_dgebrd__ = (integer)dum[0]; dormbr_((char *)"Q", (char *)"L", (char *)"T", m, nrhs, m, &a[a_offset], lda, dum, &b[b_offset], ldb, dum, &c_n1, info, (ftnlen)1, (ftnlen)1, (ftnlen)1); lwork_dormbr__ = (integer)dum[0]; dorgbr_((char *)"P", m, n, m, &a[a_offset], lda, dum, dum, &c_n1, info, (ftnlen)1); lwork_dorgbr__ = (integer)dum[0]; maxwrk = *m * 3 + lwork_dgebrd__; i__1 = maxwrk, i__2 = *m * 3 + lwork_dormbr__; maxwrk = max(i__1, i__2); i__1 = maxwrk, i__2 = *m * 3 + lwork_dorgbr__; maxwrk = max(i__1, i__2); maxwrk = max(maxwrk, bdspac); i__1 = maxwrk, i__2 = *n * *nrhs; maxwrk = max(i__1, i__2); } } maxwrk = max(minwrk, maxwrk); } work[1] = (doublereal)maxwrk; if (*lwork < minwrk && !lquery) { *info = -12; } } if (*info != 0) { i__1 = -(*info); xerbla_((char *)"DGELSS", &i__1, (ftnlen)6); return 0; } else if (lquery) { return 0; } 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_b46, &c_b46, &b[b_offset], ldb, (ftnlen)1); dlaset_((char *)"F", &minmn, &c__1, &c_b46, &c_b46, &s[1], &minmn, (ftnlen)1); *rank = 0; goto L70; } 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) { mm = *m; if (*m >= mnthr) { mm = *n; itau = 1; iwork = itau + *n; i__1 = *lwork - iwork + 1; dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork], &i__1, info); i__1 = *lwork - iwork + 1; dormqr_((char *)"L", (char *)"T", m, nrhs, n, &a[a_offset], lda, &work[itau], &b[b_offset], ldb, &work[iwork], &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_b46, &c_b46, &a[a_dim1 + 2], lda, (ftnlen)1); } } ie = 1; itauq = ie + *n; itaup = itauq + *n; iwork = itaup + *n; i__1 = *lwork - iwork + 1; dgebrd_(&mm, n, &a[a_offset], lda, &s[1], &work[ie], &work[itauq], &work[itaup], &work[iwork], &i__1, info); i__1 = *lwork - iwork + 1; dormbr_((char *)"Q", (char *)"L", (char *)"T", &mm, nrhs, n, &a[a_offset], lda, &work[itauq], &b[b_offset], ldb, &work[iwork], &i__1, info, (ftnlen)1, (ftnlen)1, (ftnlen)1); i__1 = *lwork - iwork + 1; dorgbr_((char *)"P", n, n, n, &a[a_offset], lda, &work[itaup], &work[iwork], &i__1, info, (ftnlen)1); iwork = ie + *n; dbdsqr_((char *)"U", n, n, &c__0, nrhs, &s[1], &work[ie], &a[a_offset], lda, dum, &c__1, &b[b_offset], ldb, &work[iwork], info, (ftnlen)1); if (*info != 0) { goto L70; } d__1 = *rcond * s[1]; thr = max(d__1, sfmin); if (*rcond < 0.) { d__1 = eps * s[1]; thr = max(d__1, sfmin); } *rank = 0; i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { if (s[i__] > thr) { drscl_(nrhs, &s[i__], &b[i__ + b_dim1], ldb); ++(*rank); } else { dlaset_((char *)"F", &c__1, nrhs, &c_b46, &c_b46, &b[i__ + b_dim1], ldb, (ftnlen)1); } } if (*lwork >= *ldb * *nrhs && *nrhs > 1) { dgemm_((char *)"T", (char *)"N", n, nrhs, n, &c_b79, &a[a_offset], lda, &b[b_offset], ldb, &c_b46, &work[1], ldb, (ftnlen)1, (ftnlen)1); dlacpy_((char *)"G", n, nrhs, &work[1], ldb, &b[b_offset], ldb, (ftnlen)1); } else if (*nrhs > 1) { chunk = *lwork / *n; i__1 = *nrhs; i__2 = chunk; for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) { i__3 = *nrhs - i__ + 1; bl = min(i__3, chunk); dgemm_((char *)"T", (char *)"N", n, &bl, n, &c_b79, &a[a_offset], lda, &b[i__ * b_dim1 + 1], ldb, &c_b46, &work[1], n, (ftnlen)1, (ftnlen)1); dlacpy_((char *)"G", n, &bl, &work[1], n, &b[i__ * b_dim1 + 1], ldb, (ftnlen)1); } } else if (*nrhs == 1) { dgemv_((char *)"T", n, n, &c_b79, &a[a_offset], lda, &b[b_offset], &c__1, &c_b46, &work[1], &c__1, (ftnlen)1); dcopy_(n, &work[1], &c__1, &b[b_offset], &c__1); } } else { i__2 = *m, i__1 = (*m << 1) - 4, i__2 = max(i__2, i__1), i__2 = max(i__2, *nrhs), i__1 = *n - *m * 3; if (*n >= mnthr && *lwork >= (*m << 2) + *m * *m + max(i__2, i__1)) { 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__2 = (*m << 2) + *m * *lda + max(i__3, i__4), i__1 = *m * *lda + *m + *m * *nrhs; if (*lwork >= max(i__2, i__1)) { ldwork = *lda; } itau = 1; iwork = *m + 1; i__2 = *lwork - iwork + 1; dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork], &i__2, info); il = iwork; dlacpy_((char *)"L", m, m, &a[a_offset], lda, &work[il], &ldwork, (ftnlen)1); i__2 = *m - 1; i__1 = *m - 1; dlaset_((char *)"U", &i__2, &i__1, &c_b46, &c_b46, &work[il + ldwork], &ldwork, (ftnlen)1); ie = il + ldwork * *m; itauq = ie + *m; itaup = itauq + *m; iwork = itaup + *m; i__2 = *lwork - iwork + 1; dgebrd_(m, m, &work[il], &ldwork, &s[1], &work[ie], &work[itauq], &work[itaup], &work[iwork], &i__2, info); i__2 = *lwork - iwork + 1; dormbr_((char *)"Q", (char *)"L", (char *)"T", m, nrhs, m, &work[il], &ldwork, &work[itauq], &b[b_offset], ldb, &work[iwork], &i__2, info, (ftnlen)1, (ftnlen)1, (ftnlen)1); i__2 = *lwork - iwork + 1; dorgbr_((char *)"P", m, m, m, &work[il], &ldwork, &work[itaup], &work[iwork], &i__2, info, (ftnlen)1); iwork = ie + *m; dbdsqr_((char *)"U", m, m, &c__0, nrhs, &s[1], &work[ie], &work[il], &ldwork, &a[a_offset], lda, &b[b_offset], ldb, &work[iwork], info, (ftnlen)1); if (*info != 0) { goto L70; } d__1 = *rcond * s[1]; thr = max(d__1, sfmin); if (*rcond < 0.) { d__1 = eps * s[1]; thr = max(d__1, sfmin); } *rank = 0; i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { if (s[i__] > thr) { drscl_(nrhs, &s[i__], &b[i__ + b_dim1], ldb); ++(*rank); } else { dlaset_((char *)"F", &c__1, nrhs, &c_b46, &c_b46, &b[i__ + b_dim1], ldb, (ftnlen)1); } } iwork = ie; if (*lwork >= *ldb * *nrhs + iwork - 1 && *nrhs > 1) { dgemm_((char *)"T", (char *)"N", m, nrhs, m, &c_b79, &work[il], &ldwork, &b[b_offset], ldb, &c_b46, &work[iwork], ldb, (ftnlen)1, (ftnlen)1); dlacpy_((char *)"G", m, nrhs, &work[iwork], ldb, &b[b_offset], ldb, (ftnlen)1); } else if (*nrhs > 1) { chunk = (*lwork - iwork + 1) / *m; i__2 = *nrhs; i__1 = chunk; for (i__ = 1; i__1 < 0 ? i__ >= i__2 : i__ <= i__2; i__ += i__1) { i__3 = *nrhs - i__ + 1; bl = min(i__3, chunk); dgemm_((char *)"T", (char *)"N", m, &bl, m, &c_b79, &work[il], &ldwork, &b[i__ * b_dim1 + 1], ldb, &c_b46, &work[iwork], m, (ftnlen)1, (ftnlen)1); dlacpy_((char *)"G", m, &bl, &work[iwork], m, &b[i__ * b_dim1 + 1], ldb, (ftnlen)1); } } else if (*nrhs == 1) { dgemv_((char *)"T", m, m, &c_b79, &work[il], &ldwork, &b[b_dim1 + 1], &c__1, &c_b46, &work[iwork], &c__1, (ftnlen)1); dcopy_(m, &work[iwork], &c__1, &b[b_dim1 + 1], &c__1); } i__1 = *n - *m; dlaset_((char *)"F", &i__1, nrhs, &c_b46, &c_b46, &b[*m + 1 + b_dim1], ldb, (ftnlen)1); iwork = itau + *m; i__1 = *lwork - iwork + 1; dormlq_((char *)"L", (char *)"T", n, nrhs, m, &a[a_offset], lda, &work[itau], &b[b_offset], ldb, &work[iwork], &i__1, info, (ftnlen)1, (ftnlen)1); } else { ie = 1; itauq = ie + *m; itaup = itauq + *m; iwork = itaup + *m; i__1 = *lwork - iwork + 1; dgebrd_(m, n, &a[a_offset], lda, &s[1], &work[ie], &work[itauq], &work[itaup], &work[iwork], &i__1, info); i__1 = *lwork - iwork + 1; dormbr_((char *)"Q", (char *)"L", (char *)"T", m, nrhs, n, &a[a_offset], lda, &work[itauq], &b[b_offset], ldb, &work[iwork], &i__1, info, (ftnlen)1, (ftnlen)1, (ftnlen)1); i__1 = *lwork - iwork + 1; dorgbr_((char *)"P", m, n, m, &a[a_offset], lda, &work[itaup], &work[iwork], &i__1, info, (ftnlen)1); iwork = ie + *m; dbdsqr_((char *)"L", m, n, &c__0, nrhs, &s[1], &work[ie], &a[a_offset], lda, dum, &c__1, &b[b_offset], ldb, &work[iwork], info, (ftnlen)1); if (*info != 0) { goto L70; } d__1 = *rcond * s[1]; thr = max(d__1, sfmin); if (*rcond < 0.) { d__1 = eps * s[1]; thr = max(d__1, sfmin); } *rank = 0; i__1 = *m; for (i__ = 1; i__ <= i__1; ++i__) { if (s[i__] > thr) { drscl_(nrhs, &s[i__], &b[i__ + b_dim1], ldb); ++(*rank); } else { dlaset_((char *)"F", &c__1, nrhs, &c_b46, &c_b46, &b[i__ + b_dim1], ldb, (ftnlen)1); } } if (*lwork >= *ldb * *nrhs && *nrhs > 1) { dgemm_((char *)"T", (char *)"N", n, nrhs, m, &c_b79, &a[a_offset], lda, &b[b_offset], ldb, &c_b46, &work[1], ldb, (ftnlen)1, (ftnlen)1); dlacpy_((char *)"F", n, nrhs, &work[1], ldb, &b[b_offset], ldb, (ftnlen)1); } else if (*nrhs > 1) { chunk = *lwork / *n; i__1 = *nrhs; i__2 = chunk; for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) { i__3 = *nrhs - i__ + 1; bl = min(i__3, chunk); dgemm_((char *)"T", (char *)"N", n, &bl, m, &c_b79, &a[a_offset], lda, &b[i__ * b_dim1 + 1], ldb, &c_b46, &work[1], n, (ftnlen)1, (ftnlen)1); dlacpy_((char *)"F", n, &bl, &work[1], n, &b[i__ * b_dim1 + 1], ldb, (ftnlen)1); } } else if (*nrhs == 1) { dgemv_((char *)"T", m, n, &c_b79, &a[a_offset], lda, &b[b_offset], &c__1, &c_b46, &work[1], &c__1, (ftnlen)1); dcopy_(n, &work[1], &c__1, &b[b_offset], &c__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); } L70: work[1] = (doublereal)maxwrk; return 0; } #ifdef __cplusplus } #endif