/* cgelss.f -- translated by f2c (version 20061008).
You must link the resulting object file with libf2c:
on Microsoft Windows system, link with libf2c.lib;
on Linux or Unix systems, link with .../path/to/libf2c.a -lm
or, if you install libf2c.a in a standard place, with -lf2c -lm
-- in that order, at the end of the command line, as in
cc *.o -lf2c -lm
Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
http://www.netlib.org/f2c/libf2c.zip
*/
#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 3.2) -- */
/* 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_ */