#include "f2c.h" #include "blaswrap.h" /* Table of constant values */ static complex c_b1 = {0.f,0.f}; static complex c_b2 = {1.f,0.f}; static integer c__6 = 6; static integer c_n1 = -1; static integer c__1 = 1; static integer c__0 = 0; static real c_b78 = 0.f; /* Subroutine */ int cgelss_(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 * info) { /* System generated locals */ integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3; real r__1; /* Local variables */ integer i__, bl, ie, il, mm; real eps, thr, anrm, bnrm; integer itau; complex vdum[1]; extern /* Subroutine */ int cgemm_(char *, char *, integer *, integer *, integer *, complex *, complex *, integer *, complex *, integer *, complex *, complex *, integer *); integer iascl, ibscl; extern /* Subroutine */ int cgemv_(char *, integer *, integer *, complex * , complex *, integer *, complex *, integer *, complex *, complex * , integer *); integer chunk; real sfmin; extern /* Subroutine */ int ccopy_(integer *, complex *, integer *, complex *, integer *); integer minmn, maxmn, itaup, itauq, mnthr, iwork; 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 *), 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 *), cbdsqr_(char *, integer *, integer *, integer *, integer *, real *, real *, complex *, integer *, complex *, integer *, complex *, integer *, real *, integer *); extern integer ilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *); real bignum; extern /* Subroutine */ int cungbr_(char *, integer *, integer *, integer *, complex *, integer *, complex *, complex *, integer *, integer *), 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 *), csrscl_(integer *, real *, complex *, 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 minwrk, maxwrk; real smlnum; integer irwork; logical lquery; /* -- LAPACK driver routine (version 3.1) -- */ /* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ /* November 2006 */ /* .. Scalar Arguments .. */ /* .. */ /* .. Array Arguments .. */ /* .. */ /* Purpose */ /* ======= */ /* CGELSS computes the minimum norm solution to a complex 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 effective rank of A is determined by treating as zero those */ /* singular values which are less than RCOND times the largest singular */ /* value. */ /* 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, the first min(m,n) rows of A are overwritten with */ /* its right singular vectors, stored rowwise. */ /* 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 >= 1, and also: */ /* LWORK >= 2*min(M,N) + max(M,N,NRHS) */ /* 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 WORK array, returns */ /* this value as the first entry of the WORK array, and no error */ /* message related to LWORK is issued by XERBLA. */ /* RWORK (workspace) REAL array, dimension (5*min(M,N)) */ /* 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. */ /* ===================================================================== */ /* .. Parameters .. */ /* .. */ /* .. Local Scalars .. */ /* .. */ /* .. Local Arrays .. */ /* .. */ /* .. 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; /* 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. */ /* CWorkspace refers to complex workspace, and RWorkspace refers */ /* to real workspace. NB refers to the optimal block size for the */ /* immediately following subroutine, as returned by ILAENV.) */ if (*info == 0) { minwrk = 1; maxwrk = 1; if (minmn > 0) { mm = *m; mnthr = ilaenv_(&c__6, "CGELSS", " ", m, n, nrhs, &c_n1); if (*m >= *n && *m >= mnthr) { /* Path 1a - overdetermined, with many more rows than */ /* columns */ mm = *n; /* Computing MAX */ i__1 = maxwrk, i__2 = *n + *n * ilaenv_(&c__1, "CGEQRF", " ", m, n, &c_n1, &c_n1); maxwrk = max(i__1,i__2); /* Computing MAX */ i__1 = maxwrk, i__2 = *n + *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 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, "CUNGBR", "P", n, n, n, &c_n1); maxwrk = max(i__1,i__2); /* Computing MAX */ i__1 = maxwrk, i__2 = *n * *nrhs; maxwrk = max(i__1,i__2); minwrk = (*n << 1) + max(*nrhs,*m); } if (*n > *m) { minwrk = (*m << 1) + max(*nrhs,*n); 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 * 3 + *m * *m + (*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 * 3 + *m * *m + *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 * 3 + *m * *m + (*m - 1) * ilaenv_(&c__1, "CUNGBR", "P", m, m, 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 + *nrhs * ilaenv_(&c__1, "CUNMLQ" , "LC", n, nrhs, m, &c_n1); 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, "CUNGBR", "P", m, n, m, &c_n1); maxwrk = max(i__1,i__2); /* Computing MAX */ i__1 = maxwrk, i__2 = *n * *nrhs; maxwrk = max(i__1,i__2); } } maxwrk = max(minwrk,maxwrk); } work[1].r = (real) maxwrk, work[1].i = 0.f; if (*lwork < minwrk && ! lquery) { *info = -12; } } if (*info != 0) { i__1 = -(*info); xerbla_("CGELSS", &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 element 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_b78, &c_b78, &s[1], &minmn); *rank = 0; goto L70; } /* Scale B if max element 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; } /* 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; iwork = itau + *n; /* Compute A=Q*R */ /* (CWorkspace: need 2*N, prefer N+N*NB) */ /* (RWorkspace: none) */ i__1 = *lwork - iwork + 1; cgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork], &i__1, info); /* Multiply B by transpose(Q) */ /* (CWorkspace: need N+NRHS, prefer N+NRHS*NB) */ /* (RWorkspace: none) */ i__1 = *lwork - iwork + 1; cunmqr_("L", "C", m, nrhs, n, &a[a_offset], lda, &work[itau], &b[ b_offset], ldb, &work[iwork], &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); } } ie = 1; itauq = 1; itaup = itauq + *n; iwork = itaup + *n; /* Bidiagonalize R in A */ /* (CWorkspace: need 2*N+MM, prefer 2*N+(MM+N)*NB) */ /* (RWorkspace: need N) */ i__1 = *lwork - iwork + 1; cgebrd_(&mm, n, &a[a_offset], lda, &s[1], &rwork[ie], &work[itauq], & work[itaup], &work[iwork], &i__1, info); /* Multiply B by transpose of left bidiagonalizing vectors of R */ /* (CWorkspace: need 2*N+NRHS, prefer 2*N+NRHS*NB) */ /* (RWorkspace: none) */ i__1 = *lwork - iwork + 1; cunmbr_("Q", "L", "C", &mm, nrhs, n, &a[a_offset], lda, &work[itauq], &b[b_offset], ldb, &work[iwork], &i__1, info); /* Generate right bidiagonalizing vectors of R in A */ /* (CWorkspace: need 3*N-1, prefer 2*N+(N-1)*NB) */ /* (RWorkspace: none) */ i__1 = *lwork - iwork + 1; cungbr_("P", n, n, n, &a[a_offset], lda, &work[itaup], &work[iwork], & i__1, info); irwork = ie + *n; /* Perform bidiagonal QR iteration */ /* multiply B by transpose of left singular vectors */ /* compute right singular vectors in A */ /* (CWorkspace: none) */ /* (RWorkspace: need BDSPAC) */ cbdsqr_("U", n, n, &c__0, nrhs, &s[1], &rwork[ie], &a[a_offset], lda, vdum, &c__1, &b[b_offset], ldb, &rwork[irwork], info); if (*info != 0) { goto L70; } /* Multiply B by reciprocals of singular values */ /* Computing MAX */ r__1 = *rcond * s[1]; thr = dmax(r__1,sfmin); if (*rcond < 0.f) { /* Computing MAX */ r__1 = eps * s[1]; thr = dmax(r__1,sfmin); } *rank = 0; i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { if (s[i__] > thr) { csrscl_(nrhs, &s[i__], &b[i__ + b_dim1], ldb); ++(*rank); } else { claset_("F", &c__1, nrhs, &c_b1, &c_b1, &b[i__ + b_dim1], ldb); } /* L10: */ } /* Multiply B by right singular vectors */ /* (CWorkspace: need N, prefer N*NRHS) */ /* (RWorkspace: none) */ if (*lwork >= *ldb * *nrhs && *nrhs > 1) { cgemm_("C", "N", n, nrhs, n, &c_b2, &a[a_offset], lda, &b[ b_offset], ldb, &c_b1, &work[1], ldb); clacpy_("G", n, nrhs, &work[1], ldb, &b[b_offset], ldb) ; } 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) { /* Computing MIN */ i__3 = *nrhs - i__ + 1; bl = min(i__3,chunk); cgemm_("C", "N", n, &bl, n, &c_b2, &a[a_offset], lda, &b[i__ * b_dim1 + 1], ldb, &c_b1, &work[1], n); clacpy_("G", n, &bl, &work[1], n, &b[i__ * b_dim1 + 1], ldb); /* L20: */ } } else { cgemv_("C", n, n, &c_b2, &a[a_offset], lda, &b[b_offset], &c__1, & c_b1, &work[1], &c__1); ccopy_(n, &work[1], &c__1, &b[b_offset], &c__1); } } else /* if(complicated condition) */ { /* Computing MAX */ i__2 = max(*m,*nrhs), i__1 = *n - (*m << 1); if (*n >= mnthr && *lwork >= *m * 3 + *m * *m + max(i__2,i__1)) { /* Underdetermined case, M much less than N */ /* Path 2a - underdetermined, with many more columns than rows */ /* and sufficient workspace for an efficient algorithm */ ldwork = *m; /* Computing MAX */ i__2 = max(*m,*nrhs), i__1 = *n - (*m << 1); if (*lwork >= *m * 3 + *m * *lda + max(i__2,i__1)) { ldwork = *lda; } itau = 1; iwork = *m + 1; /* Compute A=L*Q */ /* (CWorkspace: need 2*M, prefer M+M*NB) */ /* (RWorkspace: none) */ i__2 = *lwork - iwork + 1; cgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork], &i__2, info); il = iwork; /* Copy L to WORK(IL), zeroing out above it */ clacpy_("L", m, m, &a[a_offset], lda, &work[il], &ldwork); i__2 = *m - 1; i__1 = *m - 1; claset_("U", &i__2, &i__1, &c_b1, &c_b1, &work[il + ldwork], & ldwork); ie = 1; itauq = il + ldwork * *m; itaup = itauq + *m; iwork = itaup + *m; /* Bidiagonalize L in WORK(IL) */ /* (CWorkspace: need M*M+4*M, prefer M*M+3*M+2*M*NB) */ /* (RWorkspace: need M) */ i__2 = *lwork - iwork + 1; cgebrd_(m, m, &work[il], &ldwork, &s[1], &rwork[ie], &work[itauq], &work[itaup], &work[iwork], &i__2, info); /* Multiply B by transpose of left bidiagonalizing vectors of L */ /* (CWorkspace: need M*M+3*M+NRHS, prefer M*M+3*M+NRHS*NB) */ /* (RWorkspace: none) */ i__2 = *lwork - iwork + 1; cunmbr_("Q", "L", "C", m, nrhs, m, &work[il], &ldwork, &work[ itauq], &b[b_offset], ldb, &work[iwork], &i__2, info); /* Generate right bidiagonalizing vectors of R in WORK(IL) */ /* (CWorkspace: need M*M+4*M-1, prefer M*M+3*M+(M-1)*NB) */ /* (RWorkspace: none) */ i__2 = *lwork - iwork + 1; cungbr_("P", m, m, m, &work[il], &ldwork, &work[itaup], &work[ iwork], &i__2, info); irwork = ie + *m; /* Perform bidiagonal QR iteration, computing right singular */ /* vectors of L in WORK(IL) and multiplying B by transpose of */ /* left singular vectors */ /* (CWorkspace: need M*M) */ /* (RWorkspace: need BDSPAC) */ cbdsqr_("U", m, m, &c__0, nrhs, &s[1], &rwork[ie], &work[il], & ldwork, &a[a_offset], lda, &b[b_offset], ldb, &rwork[ irwork], info); if (*info != 0) { goto L70; } /* Multiply B by reciprocals of singular values */ /* Computing MAX */ r__1 = *rcond * s[1]; thr = dmax(r__1,sfmin); if (*rcond < 0.f) { /* Computing MAX */ r__1 = eps * s[1]; thr = dmax(r__1,sfmin); } *rank = 0; i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { if (s[i__] > thr) { csrscl_(nrhs, &s[i__], &b[i__ + b_dim1], ldb); ++(*rank); } else { claset_("F", &c__1, nrhs, &c_b1, &c_b1, &b[i__ + b_dim1], ldb); } /* L30: */ } iwork = il + *m * ldwork; /* Multiply B by right singular vectors of L in WORK(IL) */ /* (CWorkspace: need M*M+2*M, prefer M*M+M+M*NRHS) */ /* (RWorkspace: none) */ if (*lwork >= *ldb * *nrhs + iwork - 1 && *nrhs > 1) { cgemm_("C", "N", m, nrhs, m, &c_b2, &work[il], &ldwork, &b[ b_offset], ldb, &c_b1, &work[iwork], ldb); clacpy_("G", m, nrhs, &work[iwork], ldb, &b[b_offset], ldb); } 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) { /* Computing MIN */ i__3 = *nrhs - i__ + 1; bl = min(i__3,chunk); cgemm_("C", "N", m, &bl, m, &c_b2, &work[il], &ldwork, &b[ i__ * b_dim1 + 1], ldb, &c_b1, &work[iwork], m); clacpy_("G", m, &bl, &work[iwork], m, &b[i__ * b_dim1 + 1] , ldb); /* L40: */ } } else { cgemv_("C", m, m, &c_b2, &work[il], &ldwork, &b[b_dim1 + 1], & c__1, &c_b1, &work[iwork], &c__1); ccopy_(m, &work[iwork], &c__1, &b[b_dim1 + 1], &c__1); } /* 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); iwork = itau + *m; /* Multiply transpose(Q) by B */ /* (CWorkspace: need M+NRHS, prefer M+NHRS*NB) */ /* (RWorkspace: none) */ i__1 = *lwork - iwork + 1; cunmlq_("L", "C", n, nrhs, m, &a[a_offset], lda, &work[itau], &b[ b_offset], ldb, &work[iwork], &i__1, info); } else { /* Path 2 - remaining underdetermined cases */ ie = 1; itauq = 1; itaup = itauq + *m; iwork = itaup + *m; /* Bidiagonalize A */ /* (CWorkspace: need 3*M, prefer 2*M+(M+N)*NB) */ /* (RWorkspace: need N) */ i__1 = *lwork - iwork + 1; cgebrd_(m, n, &a[a_offset], lda, &s[1], &rwork[ie], &work[itauq], &work[itaup], &work[iwork], &i__1, info); /* Multiply B by transpose of left bidiagonalizing vectors */ /* (CWorkspace: need 2*M+NRHS, prefer 2*M+NRHS*NB) */ /* (RWorkspace: none) */ i__1 = *lwork - iwork + 1; cunmbr_("Q", "L", "C", m, nrhs, n, &a[a_offset], lda, &work[itauq] , &b[b_offset], ldb, &work[iwork], &i__1, info); /* Generate right bidiagonalizing vectors in A */ /* (CWorkspace: need 3*M, prefer 2*M+M*NB) */ /* (RWorkspace: none) */ i__1 = *lwork - iwork + 1; cungbr_("P", m, n, m, &a[a_offset], lda, &work[itaup], &work[ iwork], &i__1, info); irwork = ie + *m; /* Perform bidiagonal QR iteration, */ /* computing right singular vectors of A in A and */ /* multiplying B by transpose of left singular vectors */ /* (CWorkspace: none) */ /* (RWorkspace: need BDSPAC) */ cbdsqr_("L", m, n, &c__0, nrhs, &s[1], &rwork[ie], &a[a_offset], lda, vdum, &c__1, &b[b_offset], ldb, &rwork[irwork], info); if (*info != 0) { goto L70; } /* Multiply B by reciprocals of singular values */ /* Computing MAX */ r__1 = *rcond * s[1]; thr = dmax(r__1,sfmin); if (*rcond < 0.f) { /* Computing MAX */ r__1 = eps * s[1]; thr = dmax(r__1,sfmin); } *rank = 0; i__1 = *m; for (i__ = 1; i__ <= i__1; ++i__) { if (s[i__] > thr) { csrscl_(nrhs, &s[i__], &b[i__ + b_dim1], ldb); ++(*rank); } else { claset_("F", &c__1, nrhs, &c_b1, &c_b1, &b[i__ + b_dim1], ldb); } /* L50: */ } /* Multiply B by right singular vectors of A */ /* (CWorkspace: need N, prefer N*NRHS) */ /* (RWorkspace: none) */ if (*lwork >= *ldb * *nrhs && *nrhs > 1) { cgemm_("C", "N", n, nrhs, m, &c_b2, &a[a_offset], lda, &b[ b_offset], ldb, &c_b1, &work[1], ldb); clacpy_("G", n, nrhs, &work[1], ldb, &b[b_offset], ldb); } 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) { /* Computing MIN */ i__3 = *nrhs - i__ + 1; bl = min(i__3,chunk); cgemm_("C", "N", n, &bl, m, &c_b2, &a[a_offset], lda, &b[ i__ * b_dim1 + 1], ldb, &c_b1, &work[1], n); clacpy_("F", n, &bl, &work[1], n, &b[i__ * b_dim1 + 1], ldb); /* L60: */ } } else { cgemv_("C", m, n, &c_b2, &a[a_offset], lda, &b[b_offset], & c__1, &c_b1, &work[1], &c__1); ccopy_(n, &work[1], &c__1, &b[b_offset], &c__1); } } } /* 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); } L70: work[1].r = (real) maxwrk, work[1].i = 0.f; return 0; /* End of CGELSS */ } /* cgelss_ */