#ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" static integer c__1 = 1; static doublereal c_b6 = 0.; static integer c__0 = 0; static doublereal c_b11 = 1.; int dlalsd_(char *uplo, integer *smlsiz, integer *n, integer *nrhs, doublereal *d__, doublereal *e, doublereal *b, integer *ldb, doublereal *rcond, integer *rank, doublereal *work, integer *iwork, integer *info, ftnlen uplo_len) { integer b_dim1, b_offset, i__1, i__2; doublereal d__1; double log(doublereal), d_lmp_sign(doublereal *, doublereal *); integer c__, i__, j, k; doublereal r__; integer s, u, z__; doublereal cs; integer bx; doublereal sn; integer st, vt, nm1, st1; doublereal eps; integer iwk; doublereal tol; integer difl, difr; doublereal rcnd; integer perm, nsub; extern int drot_(integer *, doublereal *, integer *, doublereal *, integer *, doublereal *, doublereal *); integer nlvl, sqre, bxst; extern int dgemm_(char *, char *, integer *, integer *, integer *, doublereal *, doublereal *, integer *, doublereal *, integer *, doublereal *, doublereal *, integer *, ftnlen, ftnlen), dcopy_(integer *, doublereal *, integer *, doublereal *, integer *); integer poles, sizei, nsize, nwork, icmpq1, icmpq2; extern doublereal dlamch_(char *, ftnlen); extern int dlasda_(integer *, integer *, integer *, integer *, doublereal *, doublereal *, doublereal *, integer *, doublereal *, integer *, doublereal *, doublereal *, doublereal *, doublereal *, integer *, integer *, integer *, integer *, doublereal *, doublereal *, doublereal *, doublereal *, integer *, integer *), dlalsa_(integer *, integer *, integer *, integer *, doublereal *, integer *, doublereal *, integer *, doublereal *, integer *, doublereal *, integer *, doublereal *, doublereal *, doublereal *, doublereal *, integer *, integer *, integer *, integer *, doublereal *, doublereal *, doublereal *, doublereal *, integer *, integer *), dlascl_(char *, integer *, integer *, doublereal *, doublereal *, integer *, integer *, doublereal *, integer *, integer *, ftnlen); extern integer idamax_(integer *, doublereal *, integer *); extern int dlasdq_(char *, integer *, integer *, integer *, integer *, integer *, doublereal *, doublereal *, doublereal *, integer *, doublereal *, integer *, doublereal *, integer *, doublereal *, integer *, ftnlen), dlacpy_(char *, integer *, integer *, doublereal *, integer *, doublereal *, integer *, ftnlen), dlartg_(doublereal *, doublereal *, doublereal *, doublereal *, doublereal *), dlaset_(char *, integer *, integer *, doublereal *, doublereal *, doublereal *, integer *, ftnlen), xerbla_(char *, integer *, ftnlen); integer givcol; extern doublereal dlanst_(char *, integer *, doublereal *, doublereal *, ftnlen); extern int dlasrt_(char *, integer *, doublereal *, integer *, ftnlen); doublereal orgnrm; integer givnum, givptr, smlszp; --d__; --e; b_dim1 = *ldb; b_offset = 1 + b_dim1; b -= b_offset; --work; --iwork; *info = 0; if (*n < 0) { *info = -3; } else if (*nrhs < 1) { *info = -4; } else if (*ldb < 1 || *ldb < *n) { *info = -8; } if (*info != 0) { i__1 = -(*info); xerbla_((char *)"DLALSD", &i__1, (ftnlen)6); return 0; } eps = dlamch_((char *)"Epsilon", (ftnlen)7); if (*rcond <= 0. || *rcond >= 1.) { rcnd = eps; } else { rcnd = *rcond; } *rank = 0; if (*n == 0) { return 0; } else if (*n == 1) { if (d__[1] == 0.) { dlaset_((char *)"A", &c__1, nrhs, &c_b6, &c_b6, &b[b_offset], ldb, (ftnlen)1); } else { *rank = 1; dlascl_((char *)"G", &c__0, &c__0, &d__[1], &c_b11, &c__1, nrhs, &b[b_offset], ldb, info, (ftnlen)1); d__[1] = abs(d__[1]); } return 0; } if (*(unsigned char *)uplo == 'L') { 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]; if (*nrhs == 1) { drot_(&c__1, &b[i__ + b_dim1], &c__1, &b[i__ + 1 + b_dim1], &c__1, &cs, &sn); } else { work[(i__ << 1) - 1] = cs; work[i__ * 2] = sn; } } if (*nrhs > 1) { i__1 = *nrhs; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = *n - 1; for (j = 1; j <= i__2; ++j) { cs = work[(j << 1) - 1]; sn = work[j * 2]; drot_(&c__1, &b[j + i__ * b_dim1], &c__1, &b[j + 1 + i__ * b_dim1], &c__1, &cs, &sn); } } } } nm1 = *n - 1; orgnrm = dlanst_((char *)"M", n, &d__[1], &e[1], (ftnlen)1); if (orgnrm == 0.) { dlaset_((char *)"A", n, nrhs, &c_b6, &c_b6, &b[b_offset], ldb, (ftnlen)1); return 0; } dlascl_((char *)"G", &c__0, &c__0, &orgnrm, &c_b11, n, &c__1, &d__[1], n, info, (ftnlen)1); dlascl_((char *)"G", &c__0, &c__0, &orgnrm, &c_b11, &nm1, &c__1, &e[1], &nm1, info, (ftnlen)1); if (*n <= *smlsiz) { nwork = *n * *n + 1; dlaset_((char *)"A", n, n, &c_b6, &c_b11, &work[1], n, (ftnlen)1); dlasdq_((char *)"U", &c__0, n, n, &c__0, nrhs, &d__[1], &e[1], &work[1], n, &work[1], n, &b[b_offset], ldb, &work[nwork], info, (ftnlen)1); if (*info != 0) { return 0; } tol = rcnd * (d__1 = d__[idamax_(n, &d__[1], &c__1)], abs(d__1)); i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { if (d__[i__] <= tol) { dlaset_((char *)"A", &c__1, nrhs, &c_b6, &c_b6, &b[i__ + b_dim1], ldb, (ftnlen)1); } else { dlascl_((char *)"G", &c__0, &c__0, &d__[i__], &c_b11, &c__1, nrhs, &b[i__ + b_dim1], ldb, info, (ftnlen)1); ++(*rank); } } dgemm_((char *)"T", (char *)"N", n, nrhs, n, &c_b11, &work[1], n, &b[b_offset], ldb, &c_b6, &work[nwork], n, (ftnlen)1, (ftnlen)1); dlacpy_((char *)"A", n, nrhs, &work[nwork], n, &b[b_offset], ldb, (ftnlen)1); dlascl_((char *)"G", &c__0, &c__0, &c_b11, &orgnrm, n, &c__1, &d__[1], n, info, (ftnlen)1); dlasrt_((char *)"D", n, &d__[1], info, (ftnlen)1); dlascl_((char *)"G", &c__0, &c__0, &orgnrm, &c_b11, n, nrhs, &b[b_offset], ldb, info, (ftnlen)1); return 0; } nlvl = (integer)(log((doublereal)(*n) / (doublereal)(*smlsiz + 1)) / log(2.)) + 1; smlszp = *smlsiz + 1; u = 1; vt = *smlsiz * *n + 1; difl = vt + smlszp * *n; difr = difl + nlvl * *n; z__ = difr + (nlvl * *n << 1); c__ = z__ + nlvl * *n; s = c__ + *n; poles = s + *n; givnum = poles + (nlvl << 1) * *n; bx = givnum + (nlvl << 1) * *n; nwork = bx + *n * *nrhs; sizei = *n + 1; k = sizei + *n; givptr = k + *n; perm = givptr + *n; givcol = perm + nlvl * *n; iwk = givcol + (nlvl * *n << 1); st = 1; sqre = 0; icmpq1 = 1; icmpq2 = 0; nsub = 0; i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { if ((d__1 = d__[i__], abs(d__1)) < eps) { d__[i__] = d_lmp_sign(&eps, &d__[i__]); } } i__1 = nm1; for (i__ = 1; i__ <= i__1; ++i__) { if ((d__1 = e[i__], abs(d__1)) < eps || i__ == nm1) { ++nsub; iwork[nsub] = st; if (i__ < nm1) { nsize = i__ - st + 1; iwork[sizei + nsub - 1] = nsize; } else if ((d__1 = e[i__], abs(d__1)) >= eps) { nsize = *n - st + 1; iwork[sizei + nsub - 1] = nsize; } else { nsize = i__ - st + 1; iwork[sizei + nsub - 1] = nsize; ++nsub; iwork[nsub] = *n; iwork[sizei + nsub - 1] = 1; dcopy_(nrhs, &b[*n + b_dim1], ldb, &work[bx + nm1], n); } st1 = st - 1; if (nsize == 1) { dcopy_(nrhs, &b[st + b_dim1], ldb, &work[bx + st1], n); } else if (nsize <= *smlsiz) { dlaset_((char *)"A", &nsize, &nsize, &c_b6, &c_b11, &work[vt + st1], n, (ftnlen)1); dlasdq_((char *)"U", &c__0, &nsize, &nsize, &c__0, nrhs, &d__[st], &e[st], &work[vt + st1], n, &work[nwork], n, &b[st + b_dim1], ldb, &work[nwork], info, (ftnlen)1); if (*info != 0) { return 0; } dlacpy_((char *)"A", &nsize, nrhs, &b[st + b_dim1], ldb, &work[bx + st1], n, (ftnlen)1); } else { dlasda_(&icmpq1, smlsiz, &nsize, &sqre, &d__[st], &e[st], &work[u + st1], n, &work[vt + st1], &iwork[k + st1], &work[difl + st1], &work[difr + st1], &work[z__ + st1], &work[poles + st1], &iwork[givptr + st1], &iwork[givcol + st1], n, &iwork[perm + st1], &work[givnum + st1], &work[c__ + st1], &work[s + st1], &work[nwork], &iwork[iwk], info); if (*info != 0) { return 0; } bxst = bx + st1; dlalsa_(&icmpq2, smlsiz, &nsize, nrhs, &b[st + b_dim1], ldb, &work[bxst], n, &work[u + st1], n, &work[vt + st1], &iwork[k + st1], &work[difl + st1], &work[difr + st1], &work[z__ + st1], &work[poles + st1], &iwork[givptr + st1], &iwork[givcol + st1], n, &iwork[perm + st1], &work[givnum + st1], &work[c__ + st1], &work[s + st1], &work[nwork], &iwork[iwk], info); if (*info != 0) { return 0; } } st = i__ + 1; } } tol = rcnd * (d__1 = d__[idamax_(n, &d__[1], &c__1)], abs(d__1)); i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { if ((d__1 = d__[i__], abs(d__1)) <= tol) { dlaset_((char *)"A", &c__1, nrhs, &c_b6, &c_b6, &work[bx + i__ - 1], n, (ftnlen)1); } else { ++(*rank); dlascl_((char *)"G", &c__0, &c__0, &d__[i__], &c_b11, &c__1, nrhs, &work[bx + i__ - 1], n, info, (ftnlen)1); } d__[i__] = (d__1 = d__[i__], abs(d__1)); } icmpq2 = 1; i__1 = nsub; for (i__ = 1; i__ <= i__1; ++i__) { st = iwork[i__]; st1 = st - 1; nsize = iwork[sizei + i__ - 1]; bxst = bx + st1; if (nsize == 1) { dcopy_(nrhs, &work[bxst], n, &b[st + b_dim1], ldb); } else if (nsize <= *smlsiz) { dgemm_((char *)"T", (char *)"N", &nsize, nrhs, &nsize, &c_b11, &work[vt + st1], n, &work[bxst], n, &c_b6, &b[st + b_dim1], ldb, (ftnlen)1, (ftnlen)1); } else { dlalsa_(&icmpq2, smlsiz, &nsize, nrhs, &work[bxst], n, &b[st + b_dim1], ldb, &work[u + st1], n, &work[vt + st1], &iwork[k + st1], &work[difl + st1], &work[difr + st1], &work[z__ + st1], &work[poles + st1], &iwork[givptr + st1], &iwork[givcol + st1], n, &iwork[perm + st1], &work[givnum + st1], &work[c__ + st1], &work[s + st1], &work[nwork], &iwork[iwk], info); if (*info != 0) { return 0; } } } dlascl_((char *)"G", &c__0, &c__0, &c_b11, &orgnrm, n, &c__1, &d__[1], n, info, (ftnlen)1); dlasrt_((char *)"D", n, &d__[1], info, (ftnlen)1); dlascl_((char *)"G", &c__0, &c__0, &orgnrm, &c_b11, n, nrhs, &b[b_offset], ldb, info, (ftnlen)1); return 0; } #ifdef __cplusplus } #endif