#include "f2c.h" #include "blaswrap.h" /* Table of constant values */ static complex c_b1 = {0.f,0.f}; static integer c__9 = 9; static integer c__0 = 0; static integer c__6 = 6; static integer c_n1 = -1; static integer c__1 = 1; static real c_b80 = 0.f; /* Subroutine */ int cgelsd_(integer *m, integer *n, integer *nrhs, complex * a, integer *lda, complex *b, integer *ldb, real *s, real *rcond, integer *rank, complex *work, integer *lwork, real *rwork, integer * iwork, integer *info) { /* System generated locals */ integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3, i__4; /* Builtin functions */ double log(doublereal); /* Local variables */ integer ie, il, mm; real eps, anrm, bnrm; integer itau, nlvl, iascl, ibscl; real sfmin; integer minmn, maxmn, itaup, itauq, mnthr, nwork; extern /* Subroutine */ int cgebrd_(integer *, integer *, complex *, integer *, real *, real *, complex *, complex *, complex *, integer *, integer *), slabad_(real *, real *); extern doublereal clange_(char *, integer *, integer *, complex *, integer *, real *); extern /* Subroutine */ int cgelqf_(integer *, integer *, complex *, integer *, complex *, complex *, integer *, integer *), clalsd_( char *, integer *, integer *, integer *, real *, real *, complex * , integer *, real *, integer *, complex *, real *, integer *, integer *), clascl_(char *, integer *, integer *, real *, real *, integer *, integer *, complex *, integer *, integer *), cgeqrf_(integer *, integer *, complex *, integer *, complex *, complex *, integer *, integer *); extern doublereal slamch_(char *); extern /* Subroutine */ int clacpy_(char *, integer *, integer *, complex *, integer *, complex *, integer *), claset_(char *, integer *, integer *, complex *, complex *, complex *, integer *), xerbla_(char *, integer *); extern integer ilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *); real bignum; extern /* Subroutine */ int slascl_(char *, integer *, integer *, real *, real *, integer *, integer *, real *, integer *, integer *), cunmbr_(char *, char *, char *, integer *, integer *, integer *, complex *, integer *, complex *, complex *, integer *, complex *, integer *, integer *), slaset_( char *, integer *, integer *, real *, real *, real *, integer *), cunmlq_(char *, char *, integer *, integer *, integer *, complex *, integer *, complex *, complex *, integer *, complex *, integer *, integer *); integer ldwork; extern /* Subroutine */ int cunmqr_(char *, char *, integer *, integer *, integer *, complex *, integer *, complex *, complex *, integer *, complex *, integer *, integer *); integer liwork, minwrk, maxwrk; real smlnum; integer lrwork; logical lquery; integer nrwork, smlsiz; /* -- LAPACK driver routine (version 3.1) -- */ /* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ /* November 2006 */ /* .. Scalar Arguments .. */ /* .. */ /* .. Array Arguments .. */ /* .. */ /* Purpose */ /* ======= */ /* CGELSD computes the minimum-norm solution to a real linear least */ /* squares problem: */ /* minimize 2-norm(| b - A*x |) */ /* using the singular value decomposition (SVD) of A. A is an M-by-N */ /* matrix which may be rank-deficient. */ /* Several right hand side vectors b and solution vectors x can be */ /* handled in a single call; they are stored as the columns of the */ /* M-by-NRHS right hand side matrix B and the N-by-NRHS solution */ /* matrix X. */ /* The problem is solved in three steps: */ /* (1) Reduce the coefficient matrix A to bidiagonal form with */ /* Householder tranformations, reducing the original problem */ /* into a "bidiagonal least squares problem" (BLS) */ /* (2) Solve the BLS using a divide and conquer approach. */ /* (3) Apply back all the Householder tranformations to solve */ /* the original least squares problem. */ /* The effective rank of A is determined by treating as zero those */ /* singular values which are less than RCOND times the largest singular */ /* value. */ /* The divide and conquer algorithm makes very mild assumptions about */ /* floating point arithmetic. It will work on machines with a guard */ /* digit in add/subtract, or on those binary machines without guard */ /* digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or */ /* Cray-2. It could conceivably fail on hexadecimal or decimal machines */ /* without guard digits, but we know of none. */ /* Arguments */ /* ========= */ /* M (input) INTEGER */ /* The number of rows of the matrix A. M >= 0. */ /* N (input) INTEGER */ /* The number of columns of the matrix A. N >= 0. */ /* NRHS (input) INTEGER */ /* The number of right hand sides, i.e., the number of columns */ /* of the matrices B and X. NRHS >= 0. */ /* A (input/output) COMPLEX array, dimension (LDA,N) */ /* On entry, the M-by-N matrix A. */ /* On exit, A has been destroyed. */ /* LDA (input) INTEGER */ /* The leading dimension of the array A. LDA >= max(1,M). */ /* B (input/output) COMPLEX array, dimension (LDB,NRHS) */ /* On entry, the M-by-NRHS right hand side matrix B. */ /* On exit, B is overwritten by the N-by-NRHS solution matrix X. */ /* If m >= n and RANK = n, the residual sum-of-squares for */ /* the solution in the i-th column is given by the sum of */ /* squares of the modulus of elements n+1:m in that column. */ /* LDB (input) INTEGER */ /* The leading dimension of the array B. LDB >= max(1,M,N). */ /* S (output) REAL array, dimension (min(M,N)) */ /* The singular values of A in decreasing order. */ /* The condition number of A in the 2-norm = S(1)/S(min(m,n)). */ /* RCOND (input) REAL */ /* RCOND is used to determine the effective rank of A. */ /* Singular values S(i) <= RCOND*S(1) are treated as zero. */ /* If RCOND < 0, machine precision is used instead. */ /* RANK (output) INTEGER */ /* The effective rank of A, i.e., the number of singular values */ /* which are greater than RCOND*S(1). */ /* WORK (workspace/output) COMPLEX array, dimension (MAX(1,LWORK)) */ /* On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */ /* LWORK (input) INTEGER */ /* The dimension of the array WORK. LWORK must be at least 1. */ /* The exact minimum amount of workspace needed depends on M, */ /* N and NRHS. As long as LWORK is at least */ /* 2 * N + N * NRHS */ /* if M is greater than or equal to N or */ /* 2 * M + M * NRHS */ /* if M is less than N, the code will execute correctly. */ /* For good performance, LWORK should generally be larger. */ /* If LWORK = -1, then a workspace query is assumed; the routine */ /* only calculates the optimal size of the array WORK and the */ /* minimum sizes of the arrays RWORK and IWORK, and returns */ /* these values as the first entries of the WORK, RWORK and */ /* IWORK arrays, and no error message related to LWORK is issued */ /* by XERBLA. */ /* RWORK (workspace) REAL array, dimension (MAX(1,LRWORK)) */ /* LRWORK >= */ /* 10*N + 2*N*SMLSIZ + 8*N*NLVL + 3*SMLSIZ*NRHS + */ /* (SMLSIZ+1)**2 */ /* if M is greater than or equal to N or */ /* 10*M + 2*M*SMLSIZ + 8*M*NLVL + 3*SMLSIZ*NRHS + */ /* (SMLSIZ+1)**2 */ /* if M is less than N, the code will execute correctly. */ /* SMLSIZ is returned by ILAENV and is equal to the maximum */ /* size of the subproblems at the bottom of the computation */ /* tree (usually about 25), and */ /* NLVL = MAX( 0, INT( LOG_2( MIN( M,N )/(SMLSIZ+1) ) ) + 1 ) */ /* On exit, if INFO = 0, RWORK(1) returns the minimum LRWORK. */ /* IWORK (workspace) INTEGER array, dimension (MAX(1,LIWORK)) */ /* LIWORK >= max(1, 3*MINMN*NLVL + 11*MINMN), */ /* where MINMN = MIN( M,N ). */ /* On exit, if INFO = 0, IWORK(1) returns the minimum LIWORK. */ /* INFO (output) INTEGER */ /* = 0: successful exit */ /* < 0: if INFO = -i, the i-th argument had an illegal value. */ /* > 0: the algorithm for computing the SVD failed to converge; */ /* if INFO = i, i off-diagonal elements of an intermediate */ /* bidiagonal form did not converge to zero. */ /* Further Details */ /* =============== */ /* Based on contributions by */ /* Ming Gu and Ren-Cang Li, Computer Science Division, University of */ /* California at Berkeley, USA */ /* Osni Marques, LBNL/NERSC, USA */ /* ===================================================================== */ /* .. Parameters .. */ /* .. */ /* .. Local Scalars .. */ /* .. */ /* .. External Subroutines .. */ /* .. */ /* .. External Functions .. */ /* .. */ /* .. Intrinsic Functions .. */ /* .. */ /* .. Executable Statements .. */ /* Test the input arguments. */ /* Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; b_dim1 = *ldb; b_offset = 1 + b_dim1; b -= b_offset; --s; --work; --rwork; --iwork; /* Function Body */ *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; } /* Compute workspace. */ /* (Note: Comments in the code beginning "Workspace:" describe the */ /* minimal amount of workspace needed at that point in the code, */ /* as well as the preferred amount for good performance. */ /* NB refers to the optimal block size for the immediately */ /* following subroutine, as returned by ILAENV.) */ if (*info == 0) { minwrk = 1; maxwrk = 1; liwork = 1; lrwork = 1; if (minmn > 0) { smlsiz = ilaenv_(&c__9, "CGELSD", " ", &c__0, &c__0, &c__0, &c__0); mnthr = ilaenv_(&c__6, "CGELSD", " ", m, n, nrhs, &c_n1); /* Computing MAX */ i__1 = (integer) (log((real) minmn / (real) (smlsiz + 1)) / log( 2.f)) + 1; nlvl = max(i__1,0); liwork = minmn * 3 * nlvl + minmn * 11; mm = *m; if (*m >= *n && *m >= mnthr) { /* Path 1a - overdetermined, with many more rows than */ /* columns. */ mm = *n; /* Computing MAX */ i__1 = maxwrk, i__2 = *n * ilaenv_(&c__1, "CGEQRF", " ", m, n, &c_n1, &c_n1); maxwrk = max(i__1,i__2); /* Computing MAX */ i__1 = maxwrk, i__2 = *nrhs * ilaenv_(&c__1, "CUNMQR", "LC", m, nrhs, n, &c_n1); maxwrk = max(i__1,i__2); } if (*m >= *n) { /* Path 1 - overdetermined or exactly determined. */ /* Computing 2nd power */ i__1 = smlsiz + 1; lrwork = *n * 10 + (*n << 1) * smlsiz + (*n << 3) * nlvl + smlsiz * 3 * *nrhs + i__1 * i__1; /* Computing MAX */ i__1 = maxwrk, i__2 = (*n << 1) + (mm + *n) * ilaenv_(&c__1, "CGEBRD", " ", &mm, n, &c_n1, &c_n1); maxwrk = max(i__1,i__2); /* Computing MAX */ i__1 = maxwrk, i__2 = (*n << 1) + *nrhs * ilaenv_(&c__1, "CUNMBR", "QLC", &mm, nrhs, n, &c_n1); maxwrk = max(i__1,i__2); /* Computing MAX */ i__1 = maxwrk, i__2 = (*n << 1) + (*n - 1) * ilaenv_(&c__1, "CUNMBR", "PLN", n, nrhs, n, &c_n1); maxwrk = max(i__1,i__2); /* Computing MAX */ i__1 = maxwrk, i__2 = (*n << 1) + *n * *nrhs; maxwrk = max(i__1,i__2); /* Computing MAX */ i__1 = (*n << 1) + mm, i__2 = (*n << 1) + *n * *nrhs; minwrk = max(i__1,i__2); } if (*n > *m) { /* Computing 2nd power */ i__1 = smlsiz + 1; lrwork = *m * 10 + (*m << 1) * smlsiz + (*m << 3) * nlvl + smlsiz * 3 * *nrhs + i__1 * i__1; if (*n >= mnthr) { /* Path 2a - underdetermined, with many more columns */ /* than rows. */ maxwrk = *m + *m * ilaenv_(&c__1, "CGELQF", " ", m, n, & c_n1, &c_n1); /* Computing MAX */ i__1 = maxwrk, i__2 = *m * *m + (*m << 2) + (*m << 1) * ilaenv_(&c__1, "CGEBRD", " ", m, m, &c_n1, &c_n1); maxwrk = max(i__1,i__2); /* Computing MAX */ i__1 = maxwrk, i__2 = *m * *m + (*m << 2) + *nrhs * ilaenv_(&c__1, "CUNMBR", "QLC", m, nrhs, m, &c_n1); maxwrk = max(i__1,i__2); /* Computing MAX */ i__1 = maxwrk, i__2 = *m * *m + (*m << 2) + (*m - 1) * ilaenv_(&c__1, "CUNMLQ", "LC", n, nrhs, m, &c_n1); maxwrk = max(i__1,i__2); if (*nrhs > 1) { /* Computing MAX */ i__1 = maxwrk, i__2 = *m * *m + *m + *m * *nrhs; maxwrk = max(i__1,i__2); } else { /* Computing MAX */ i__1 = maxwrk, i__2 = *m * *m + (*m << 1); maxwrk = max(i__1,i__2); } /* Computing MAX */ i__1 = maxwrk, i__2 = *m * *m + (*m << 2) + *m * *nrhs; maxwrk = max(i__1,i__2); } else { /* Path 2 - underdetermined. */ maxwrk = (*m << 1) + (*n + *m) * ilaenv_(&c__1, "CGEBRD", " ", m, n, &c_n1, &c_n1); /* Computing MAX */ i__1 = maxwrk, i__2 = (*m << 1) + *nrhs * ilaenv_(&c__1, "CUNMBR", "QLC", m, nrhs, m, &c_n1); maxwrk = max(i__1,i__2); /* Computing MAX */ i__1 = maxwrk, i__2 = (*m << 1) + *m * ilaenv_(&c__1, "CUNMBR", "PLN", n, nrhs, m, &c_n1); maxwrk = max(i__1,i__2); /* Computing MAX */ i__1 = maxwrk, i__2 = (*m << 1) + *m * *nrhs; maxwrk = max(i__1,i__2); } /* Computing MAX */ i__1 = (*m << 1) + *n, i__2 = (*m << 1) + *m * *nrhs; minwrk = max(i__1,i__2); } } minwrk = min(minwrk,maxwrk); work[1].r = (real) maxwrk, work[1].i = 0.f; iwork[1] = liwork; rwork[1] = (real) lrwork; if (*lwork < minwrk && ! lquery) { *info = -12; } } if (*info != 0) { i__1 = -(*info); xerbla_("CGELSD", &i__1); return 0; } else if (lquery) { return 0; } /* Quick return if possible. */ if (*m == 0 || *n == 0) { *rank = 0; return 0; } /* Get machine parameters. */ eps = slamch_("P"); sfmin = slamch_("S"); smlnum = sfmin / eps; bignum = 1.f / smlnum; slabad_(&smlnum, &bignum); /* Scale A if max entry outside range [SMLNUM,BIGNUM]. */ anrm = clange_("M", m, n, &a[a_offset], lda, &rwork[1]); iascl = 0; if (anrm > 0.f && anrm < smlnum) { /* Scale matrix norm up to SMLNUM */ clascl_("G", &c__0, &c__0, &anrm, &smlnum, m, n, &a[a_offset], lda, info); iascl = 1; } else if (anrm > bignum) { /* Scale matrix norm down to BIGNUM. */ clascl_("G", &c__0, &c__0, &anrm, &bignum, m, n, &a[a_offset], lda, info); iascl = 2; } else if (anrm == 0.f) { /* Matrix all zero. Return zero solution. */ i__1 = max(*m,*n); claset_("F", &i__1, nrhs, &c_b1, &c_b1, &b[b_offset], ldb); slaset_("F", &minmn, &c__1, &c_b80, &c_b80, &s[1], &c__1); *rank = 0; goto L10; } /* Scale B if max entry outside range [SMLNUM,BIGNUM]. */ bnrm = clange_("M", m, nrhs, &b[b_offset], ldb, &rwork[1]); ibscl = 0; if (bnrm > 0.f && bnrm < smlnum) { /* Scale matrix norm up to SMLNUM. */ clascl_("G", &c__0, &c__0, &bnrm, &smlnum, m, nrhs, &b[b_offset], ldb, info); ibscl = 1; } else if (bnrm > bignum) { /* Scale matrix norm down to BIGNUM. */ clascl_("G", &c__0, &c__0, &bnrm, &bignum, m, nrhs, &b[b_offset], ldb, info); ibscl = 2; } /* If M < N make sure B(M+1:N,:) = 0 */ if (*m < *n) { i__1 = *n - *m; claset_("F", &i__1, nrhs, &c_b1, &c_b1, &b[*m + 1 + b_dim1], ldb); } /* Overdetermined case. */ if (*m >= *n) { /* Path 1 - overdetermined or exactly determined. */ mm = *m; if (*m >= mnthr) { /* Path 1a - overdetermined, with many more rows than columns */ mm = *n; itau = 1; nwork = itau + *n; /* Compute A=Q*R. */ /* (RWorkspace: need N) */ /* (CWorkspace: need N, prefer N*NB) */ i__1 = *lwork - nwork + 1; cgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &i__1, info); /* Multiply B by transpose(Q). */ /* (RWorkspace: need N) */ /* (CWorkspace: need NRHS, prefer NRHS*NB) */ i__1 = *lwork - nwork + 1; cunmqr_("L", "C", m, nrhs, n, &a[a_offset], lda, &work[itau], &b[ b_offset], ldb, &work[nwork], &i__1, info); /* Zero out below R. */ if (*n > 1) { i__1 = *n - 1; i__2 = *n - 1; claset_("L", &i__1, &i__2, &c_b1, &c_b1, &a[a_dim1 + 2], lda); } } itauq = 1; itaup = itauq + *n; nwork = itaup + *n; ie = 1; nrwork = ie + *n; /* Bidiagonalize R in A. */ /* (RWorkspace: need N) */ /* (CWorkspace: need 2*N+MM, prefer 2*N+(MM+N)*NB) */ i__1 = *lwork - nwork + 1; cgebrd_(&mm, n, &a[a_offset], lda, &s[1], &rwork[ie], &work[itauq], & work[itaup], &work[nwork], &i__1, info); /* Multiply B by transpose of left bidiagonalizing vectors of R. */ /* (CWorkspace: need 2*N+NRHS, prefer 2*N+NRHS*NB) */ i__1 = *lwork - nwork + 1; cunmbr_("Q", "L", "C", &mm, nrhs, n, &a[a_offset], lda, &work[itauq], &b[b_offset], ldb, &work[nwork], &i__1, info); /* Solve the bidiagonal least squares problem. */ clalsd_("U", &smlsiz, n, nrhs, &s[1], &rwork[ie], &b[b_offset], ldb, rcond, rank, &work[nwork], &rwork[nrwork], &iwork[1], info); if (*info != 0) { goto L10; } /* Multiply B by right bidiagonalizing vectors of R. */ i__1 = *lwork - nwork + 1; cunmbr_("P", "L", "N", n, nrhs, n, &a[a_offset], lda, &work[itaup], & b[b_offset], ldb, &work[nwork], &i__1, info); } else /* if(complicated condition) */ { /* Computing MAX */ 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; if (*n >= mnthr && *lwork >= (*m << 2) + *m * *m + max(i__1,i__2)) { /* Path 2a - underdetermined, with many more columns than rows */ /* and sufficient workspace for an efficient algorithm. */ ldwork = *m; /* Computing MAX */ /* Computing MAX */ 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; if (*lwork >= max(i__1,i__2)) { ldwork = *lda; } itau = 1; nwork = *m + 1; /* Compute A=L*Q. */ /* (CWorkspace: need 2*M, prefer M+M*NB) */ i__1 = *lwork - nwork + 1; cgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &i__1, info); il = nwork; /* Copy L to WORK(IL), zeroing out above its diagonal. */ clacpy_("L", m, m, &a[a_offset], lda, &work[il], &ldwork); i__1 = *m - 1; i__2 = *m - 1; claset_("U", &i__1, &i__2, &c_b1, &c_b1, &work[il + ldwork], & ldwork); itauq = il + ldwork * *m; itaup = itauq + *m; nwork = itaup + *m; ie = 1; nrwork = ie + *m; /* Bidiagonalize L in WORK(IL). */ /* (RWorkspace: need M) */ /* (CWorkspace: need M*M+4*M, prefer M*M+4*M+2*M*NB) */ i__1 = *lwork - nwork + 1; cgebrd_(m, m, &work[il], &ldwork, &s[1], &rwork[ie], &work[itauq], &work[itaup], &work[nwork], &i__1, info); /* Multiply B by transpose of left bidiagonalizing vectors of L. */ /* (CWorkspace: need M*M+4*M+NRHS, prefer M*M+4*M+NRHS*NB) */ i__1 = *lwork - nwork + 1; cunmbr_("Q", "L", "C", m, nrhs, m, &work[il], &ldwork, &work[ itauq], &b[b_offset], ldb, &work[nwork], &i__1, info); /* Solve the bidiagonal least squares problem. */ clalsd_("U", &smlsiz, m, nrhs, &s[1], &rwork[ie], &b[b_offset], ldb, rcond, rank, &work[nwork], &rwork[nrwork], &iwork[1], info); if (*info != 0) { goto L10; } /* Multiply B by right bidiagonalizing vectors of L. */ i__1 = *lwork - nwork + 1; cunmbr_("P", "L", "N", m, nrhs, m, &work[il], &ldwork, &work[ itaup], &b[b_offset], ldb, &work[nwork], &i__1, info); /* Zero out below first M rows of B. */ i__1 = *n - *m; claset_("F", &i__1, nrhs, &c_b1, &c_b1, &b[*m + 1 + b_dim1], ldb); nwork = itau + *m; /* Multiply transpose(Q) by B. */ /* (CWorkspace: need NRHS, prefer NRHS*NB) */ i__1 = *lwork - nwork + 1; cunmlq_("L", "C", n, nrhs, m, &a[a_offset], lda, &work[itau], &b[ b_offset], ldb, &work[nwork], &i__1, info); } else { /* Path 2 - remaining underdetermined cases. */ itauq = 1; itaup = itauq + *m; nwork = itaup + *m; ie = 1; nrwork = ie + *m; /* Bidiagonalize A. */ /* (RWorkspace: need M) */ /* (CWorkspace: need 2*M+N, prefer 2*M+(M+N)*NB) */ i__1 = *lwork - nwork + 1; cgebrd_(m, n, &a[a_offset], lda, &s[1], &rwork[ie], &work[itauq], &work[itaup], &work[nwork], &i__1, info); /* Multiply B by transpose of left bidiagonalizing vectors. */ /* (CWorkspace: need 2*M+NRHS, prefer 2*M+NRHS*NB) */ i__1 = *lwork - nwork + 1; cunmbr_("Q", "L", "C", m, nrhs, n, &a[a_offset], lda, &work[itauq] , &b[b_offset], ldb, &work[nwork], &i__1, info); /* Solve the bidiagonal least squares problem. */ clalsd_("L", &smlsiz, m, nrhs, &s[1], &rwork[ie], &b[b_offset], ldb, rcond, rank, &work[nwork], &rwork[nrwork], &iwork[1], info); if (*info != 0) { goto L10; } /* Multiply B by right bidiagonalizing vectors of A. */ i__1 = *lwork - nwork + 1; cunmbr_("P", "L", "N", n, nrhs, m, &a[a_offset], lda, &work[itaup] , &b[b_offset], ldb, &work[nwork], &i__1, info); } } /* Undo scaling. */ if (iascl == 1) { clascl_("G", &c__0, &c__0, &anrm, &smlnum, n, nrhs, &b[b_offset], ldb, info); slascl_("G", &c__0, &c__0, &smlnum, &anrm, &minmn, &c__1, &s[1], & minmn, info); } else if (iascl == 2) { clascl_("G", &c__0, &c__0, &anrm, &bignum, n, nrhs, &b[b_offset], ldb, info); slascl_("G", &c__0, &c__0, &bignum, &anrm, &minmn, &c__1, &s[1], & minmn, info); } if (ibscl == 1) { clascl_("G", &c__0, &c__0, &smlnum, &bnrm, n, nrhs, &b[b_offset], ldb, info); } else if (ibscl == 2) { clascl_("G", &c__0, &c__0, &bignum, &bnrm, n, nrhs, &b[b_offset], ldb, info); } L10: work[1].r = (real) maxwrk, work[1].i = 0.f; iwork[1] = liwork; rwork[1] = (real) lrwork; return 0; /* End of CGELSD */ } /* cgelsd_ */