/* Subroutine */ int cgels_(char *trans, integer *m, integer *n, integer *
nrhs, complex *a, integer *lda, complex *b, integer *ldb, complex *
work, integer *lwork, 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__, j, nb, mn;
real anrm, bnrm;
integer brow;
logical tpsd;
integer iascl, ibscl;
extern logical lsame_(char *, char *);
integer wsize;
real rwork[1];
extern /* Subroutine */ int 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 *);
extern doublereal slamch_(char *);
extern /* Subroutine */ int cgeqrf_(integer *, integer *, complex *,
integer *, complex *, complex *, integer *, integer *), claset_(
char *, integer *, integer *, complex *, complex *, complex *,
integer *), xerbla_(char *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *);
integer scllen;
real bignum;
extern /* Subroutine */ int cunmlq_(char *, char *, integer *, integer *,
integer *, complex *, integer *, complex *, complex *, integer *,
complex *, integer *, integer *), cunmqr_(char *,
char *, integer *, integer *, integer *, complex *, integer *,
complex *, complex *, integer *, complex *, integer *, integer *);
real smlnum;
logical lquery;
extern /* Subroutine */ int ctrtrs_(char *, char *, char *, integer *,
integer *, complex *, integer *, complex *, integer *, integer *);
/* -- LAPACK driver routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* CGELS solves overdetermined or underdetermined complex linear systems */
/* involving an M-by-N matrix A, or its conjugate-transpose, using a QR */
/* or LQ factorization of A. It is assumed that A has full rank. */
/* The following options are provided: */
/* 1. If TRANS = 'N' and m >= n: find the least squares solution of */
/* an overdetermined system, i.e., solve the least squares problem */
/* minimize || B - A*X ||. */
/* 2. If TRANS = 'N' and m < n: find the minimum norm solution of */
/* an underdetermined system A * X = B. */
/* 3. If TRANS = 'C' and m >= n: find the minimum norm solution of */
/* an undetermined system A**H * X = B. */
/* 4. If TRANS = 'C' and m < n: find the least squares solution of */
/* an overdetermined system, i.e., solve the least squares problem */
/* minimize || B - A**H * X ||. */
/* 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. */
/* Arguments */
/* ========= */
/* TRANS (input) CHARACTER*1 */
/* = 'N': the linear system involves A; */
/* = 'C': the linear system involves A**H. */
/* 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. */
/* if M >= N, A is overwritten by details of its QR */
/* factorization as returned by CGEQRF; */
/* if M < N, A is overwritten by details of its LQ */
/* factorization as returned by CGELQF. */
/* 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 matrix B of right hand side vectors, stored */
/* columnwise; B is M-by-NRHS if TRANS = 'N', or N-by-NRHS */
/* if TRANS = 'C'. */
/* On exit, if INFO = 0, B is overwritten by the solution */
/* vectors, stored columnwise: */
/* if TRANS = 'N' and m >= n, rows 1 to n of B contain the least */
/* squares solution vectors; the residual sum of squares for the */
/* solution in each column is given by the sum of squares of the */
/* modulus of elements N+1 to M in that column; */
/* if TRANS = 'N' and m < n, rows 1 to N of B contain the */
/* minimum norm solution vectors; */
/* if TRANS = 'C' and m >= n, rows 1 to M of B contain the */
/* minimum norm solution vectors; */
/* if TRANS = 'C' and m < n, rows 1 to M of B contain the */
/* least squares solution vectors; the residual sum of squares */
/* for the solution in each column is given by the sum of */
/* squares of the modulus of elements M+1 to N in that column. */
/* LDB (input) INTEGER */
/* The leading dimension of the array B. LDB >= MAX(1,M,N). */
/* 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 >= max( 1, MN + max( MN, NRHS ) ). */
/* For optimal performance, */
/* LWORK >= max( 1, MN + max( MN, NRHS )*NB ). */
/* where MN = min(M,N) and NB is the optimum block size. */
/* 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. */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value */
/* > 0: if INFO = i, the i-th diagonal element of the */
/* triangular factor of A is zero, so that A does not have */
/* full rank; the least squares solution could not be */
/* computed. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. 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;
--work;
/* Function Body */
*info = 0;
mn = min(*m,*n);
lquery = *lwork == -1;
if (! (lsame_(trans, "N") || lsame_(trans, "C"))) {
*info = -1;
} else if (*m < 0) {
*info = -2;
} else if (*n < 0) {
*info = -3;
} else if (*nrhs < 0) {
*info = -4;
} else if (*lda < max(1,*m)) {
*info = -6;
} else /* if(complicated condition) */ {
/* Computing MAX */
i__1 = max(1,*m);
if (*ldb < max(i__1,*n)) {
*info = -8;
} else /* if(complicated condition) */ {
/* Computing MAX */
i__1 = 1, i__2 = mn + max(mn,*nrhs);
if (*lwork < max(i__1,i__2) && ! lquery) {
*info = -10;
}
}
}
/* Figure out optimal block size */
if (*info == 0 || *info == -10) {
tpsd = TRUE_;
if (lsame_(trans, "N")) {
tpsd = FALSE_;
}
if (*m >= *n) {
nb = ilaenv_(&c__1, "CGEQRF", " ", m, n, &c_n1, &c_n1);
if (tpsd) {
/* Computing MAX */
i__1 = nb, i__2 = ilaenv_(&c__1, "CUNMQR", "LN", m, nrhs, n, &
c_n1);
nb = max(i__1,i__2);
} else {
/* Computing MAX */
i__1 = nb, i__2 = ilaenv_(&c__1, "CUNMQR", "LC", m, nrhs, n, &
c_n1);
nb = max(i__1,i__2);
}
} else {
nb = ilaenv_(&c__1, "CGELQF", " ", m, n, &c_n1, &c_n1);
if (tpsd) {
/* Computing MAX */
i__1 = nb, i__2 = ilaenv_(&c__1, "CUNMLQ", "LC", n, nrhs, m, &
c_n1);
nb = max(i__1,i__2);
} else {
/* Computing MAX */
i__1 = nb, i__2 = ilaenv_(&c__1, "CUNMLQ", "LN", n, nrhs, m, &
c_n1);
nb = max(i__1,i__2);
}
}
/* Computing MAX */
i__1 = 1, i__2 = mn + max(mn,*nrhs) * nb;
wsize = max(i__1,i__2);
r__1 = (real) wsize;
work[1].r = r__1, work[1].i = 0.f;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("CGELS ", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible */
/* Computing MIN */
i__1 = min(*m,*n);
if (min(i__1,*nrhs) == 0) {
i__1 = max(*m,*n);
claset_("Full", &i__1, nrhs, &c_b1, &c_b1, &b[b_offset], ldb);
return 0;
}
/* Get machine parameters */
smlnum = slamch_("S") / slamch_("P");
bignum = 1.f / smlnum;
slabad_(&smlnum, &bignum);
/* Scale A, B if max element outside range [SMLNUM,BIGNUM] */
anrm = clange_("M", m, n, &a[a_offset], lda, rwork);
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);
goto L50;
}
brow = *m;
if (tpsd) {
brow = *n;
}
bnrm = clange_("M", &brow, nrhs, &b[b_offset], ldb, rwork);
ibscl = 0;
if (bnrm > 0.f && bnrm < smlnum) {
/* Scale matrix norm up to SMLNUM */
clascl_("G", &c__0, &c__0, &bnrm, &smlnum, &brow, 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, &brow, nrhs, &b[b_offset],
ldb, info);
ibscl = 2;
}
if (*m >= *n) {
/* compute QR factorization of A */
i__1 = *lwork - mn;
cgeqrf_(m, n, &a[a_offset], lda, &work[1], &work[mn + 1], &i__1, info)
;
/* workspace at least N, optimally N*NB */
if (! tpsd) {
/* Least-Squares Problem min || A * X - B || */
/* B(1:M,1:NRHS) := Q' * B(1:M,1:NRHS) */
i__1 = *lwork - mn;
cunmqr_("Left", "Conjugate transpose", m, nrhs, n, &a[a_offset],
lda, &work[1], &b[b_offset], ldb, &work[mn + 1], &i__1,
info);
/* workspace at least NRHS, optimally NRHS*NB */
/* B(1:N,1:NRHS) := inv(R) * B(1:N,1:NRHS) */
ctrtrs_("Upper", "No transpose", "Non-unit", n, nrhs, &a[a_offset]
, lda, &b[b_offset], ldb, info);
if (*info > 0) {
return 0;
}
scllen = *n;
} else {
/* Overdetermined system of equations A' * X = B */
/* B(1:N,1:NRHS) := inv(R') * B(1:N,1:NRHS) */
ctrtrs_("Upper", "Conjugate transpose", "Non-unit", n, nrhs, &a[
a_offset], lda, &b[b_offset], ldb, info);
if (*info > 0) {
return 0;
}
/* B(N+1:M,1:NRHS) = ZERO */
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = *n + 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * b_dim1;
b[i__3].r = 0.f, b[i__3].i = 0.f;
/* L10: */
}
/* L20: */
}
/* B(1:M,1:NRHS) := Q(1:N,:) * B(1:N,1:NRHS) */
i__1 = *lwork - mn;
cunmqr_("Left", "No transpose", m, nrhs, n, &a[a_offset], lda, &
work[1], &b[b_offset], ldb, &work[mn + 1], &i__1, info);
/* workspace at least NRHS, optimally NRHS*NB */
scllen = *m;
}
} else {
/* Compute LQ factorization of A */
i__1 = *lwork - mn;
cgelqf_(m, n, &a[a_offset], lda, &work[1], &work[mn + 1], &i__1, info)
;
/* workspace at least M, optimally M*NB. */
if (! tpsd) {
/* underdetermined system of equations A * X = B */
/* B(1:M,1:NRHS) := inv(L) * B(1:M,1:NRHS) */
ctrtrs_("Lower", "No transpose", "Non-unit", m, nrhs, &a[a_offset]
, lda, &b[b_offset], ldb, info);
if (*info > 0) {
return 0;
}
/* B(M+1:N,1:NRHS) = 0 */
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
i__2 = *n;
for (i__ = *m + 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * b_dim1;
b[i__3].r = 0.f, b[i__3].i = 0.f;
/* L30: */
}
/* L40: */
}
/* B(1:N,1:NRHS) := Q(1:N,:)' * B(1:M,1:NRHS) */
i__1 = *lwork - mn;
cunmlq_("Left", "Conjugate transpose", n, nrhs, m, &a[a_offset],
lda, &work[1], &b[b_offset], ldb, &work[mn + 1], &i__1,
info);
/* workspace at least NRHS, optimally NRHS*NB */
scllen = *n;
} else {
/* overdetermined system min || A' * X - B || */
/* B(1:N,1:NRHS) := Q * B(1:N,1:NRHS) */
i__1 = *lwork - mn;
cunmlq_("Left", "No transpose", n, nrhs, m, &a[a_offset], lda, &
work[1], &b[b_offset], ldb, &work[mn + 1], &i__1, info);
/* workspace at least NRHS, optimally NRHS*NB */
/* B(1:M,1:NRHS) := inv(L') * B(1:M,1:NRHS) */
ctrtrs_("Lower", "Conjugate transpose", "Non-unit", m, nrhs, &a[
a_offset], lda, &b[b_offset], ldb, info);
if (*info > 0) {
return 0;
}
scllen = *m;
}
}
/* Undo scaling */
if (iascl == 1) {
clascl_("G", &c__0, &c__0, &anrm, &smlnum, &scllen, nrhs, &b[b_offset]
, ldb, info);
} else if (iascl == 2) {
clascl_("G", &c__0, &c__0, &anrm, &bignum, &scllen, nrhs, &b[b_offset]
, ldb, info);
}
if (ibscl == 1) {
clascl_("G", &c__0, &c__0, &smlnum, &bnrm, &scllen, nrhs, &b[b_offset]
, ldb, info);
} else if (ibscl == 2) {
clascl_("G", &c__0, &c__0, &bignum, &bnrm, &scllen, nrhs, &b[b_offset]
, ldb, info);
}
L50:
r__1 = (real) wsize;
work[1].r = r__1, work[1].i = 0.f;
return 0;
/* End of CGELS */
} /* cgels_ */
/* 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 real 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 real 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 3.4.0) -- */
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
/* November 2011 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* ===================================================================== */
/* .. 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); // , expr subst
maxwrk = max(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk;
i__2 = *nrhs * ilaenv_(&c__1, "CUNMQR", "LC", m, nrhs, n, &c_n1); // , expr subst
maxwrk = max(i__1,i__2);
}
if (*m >= *n)
{
/* Path 1 - overdetermined or exactly determined. */
/* Computing MAX */
/* Computing 2nd power */
i__3 = smlsiz + 1;
i__1 = i__3 * i__3;
i__2 = *n * (*nrhs + 1) + (*nrhs << 1); // , expr subst
lrwork = *n * 10 + (*n << 1) * smlsiz + (*n << 3) * nlvl + smlsiz * 3 * *nrhs + max(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk;
i__2 = (*n << 1) + (mm + *n) * ilaenv_(&c__1, "CGEBRD", " ", &mm, n, &c_n1, &c_n1); // , expr subst
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); // , expr subst
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); // , expr subst
maxwrk = max(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk;
i__2 = (*n << 1) + *n * *nrhs; // , expr subst
maxwrk = max(i__1,i__2);
/* Computing MAX */
i__1 = (*n << 1) + mm;
i__2 = (*n << 1) + *n * *nrhs; // , expr subst
minwrk = max(i__1,i__2);
}
if (*n > *m)
{
/* Computing MAX */
/* Computing 2nd power */
i__3 = smlsiz + 1;
i__1 = i__3 * i__3;
i__2 = *n * (*nrhs + 1) + (*nrhs << 1); // , expr subst
lrwork = *m * 10 + (*m << 1) * smlsiz + (*m << 3) * nlvl + smlsiz * 3 * *nrhs + max(i__1,i__2);
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); // , expr subst
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); // , expr subst
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); // , expr subst
maxwrk = max(i__1,i__2);
if (*nrhs > 1)
{
/* Computing MAX */
i__1 = maxwrk;
i__2 = *m * *m + *m + *m * *nrhs; // , expr subst
maxwrk = max(i__1,i__2);
}
else
{
/* Computing MAX */
i__1 = maxwrk;
i__2 = *m * *m + (*m << 1); // , expr subst
maxwrk = max(i__1,i__2);
}
/* Computing MAX */
i__1 = maxwrk;
i__2 = *m * *m + (*m << 2) + *m * *nrhs; // , expr subst
maxwrk = max(i__1,i__2);
/* XXX: Ensure the Path 2a case below is triggered. The workspace */
/* calculation should use queries for all routines eventually. */
/* 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; // ; expr subst
i__1 = maxwrk;
i__2 = (*m << 2) + *m * *m + max(i__3,i__4) ; // , expr subst
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); // , expr subst
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); // , expr subst
maxwrk = max(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk;
i__2 = (*m << 1) + *m * *nrhs; // , expr subst
maxwrk = max(i__1,i__2);
}
/* Computing MAX */
i__1 = (*m << 1) + *n;
i__2 = (*m << 1) + *m * *nrhs; // , expr subst
minwrk = max(i__1,i__2);
}
}
minwrk = min(minwrk,maxwrk);
work[1].r = (real) maxwrk;
work[1].i = 0.f; // , expr subst
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; // ; expr subst
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; // ; expr subst
i__1 = (*m << 2) + *m * *lda + max(i__3,i__4);
i__2 = *m * *lda + *m + *m * *nrhs; // , expr subst
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; // , expr subst
iwork[1] = liwork;
rwork[1] = (real) lrwork;
return 0;
/* End of CGELSD */
}
/* Subroutine */ int clqt01_(integer *m, integer *n, complex *a, complex *af,
complex *q, complex *l, integer *lda, complex *tau, complex *work,
integer *lwork, real *rwork, real *result)
{
/* System generated locals */
integer a_dim1, a_offset, af_dim1, af_offset, l_dim1, l_offset, q_dim1,
q_offset, i__1;
/* Builtin functions
Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen);
/* Local variables */
static integer info;
extern /* Subroutine */ int cgemm_(char *, char *, integer *, integer *,
integer *, complex *, complex *, integer *, complex *, integer *,
complex *, complex *, integer *), cherk_(char *,
char *, integer *, integer *, real *, complex *, integer *, real *
, complex *, integer *);
static real resid, anorm;
static integer minmn;
extern doublereal clange_(char *, integer *, integer *, complex *,
integer *, real *);
extern /* Subroutine */ int cgelqf_(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 *);
extern doublereal clansy_(char *, char *, integer *, complex *, integer *,
real *);
extern /* Subroutine */ int cunglq_(integer *, integer *, integer *,
complex *, integer *, complex *, complex *, integer *, integer *);
static real eps;
#define q_subscr(a_1,a_2) (a_2)*q_dim1 + a_1
#define q_ref(a_1,a_2) q[q_subscr(a_1,a_2)]
#define af_subscr(a_1,a_2) (a_2)*af_dim1 + a_1
#define af_ref(a_1,a_2) af[af_subscr(a_1,a_2)]
/* -- LAPACK test routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
September 30, 1994
Purpose
=======
CLQT01 tests CGELQF, which computes the LQ factorization of an m-by-n
matrix A, and partially tests CUNGLQ which forms the n-by-n
orthogonal matrix Q.
CLQT01 compares L with A*Q', and checks that Q is orthogonal.
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.
A (input) COMPLEX array, dimension (LDA,N)
The m-by-n matrix A.
AF (output) COMPLEX array, dimension (LDA,N)
Details of the LQ factorization of A, as returned by CGELQF.
See CGELQF for further details.
Q (output) COMPLEX array, dimension (LDA,N)
The n-by-n orthogonal matrix Q.
L (workspace) COMPLEX array, dimension (LDA,max(M,N))
LDA (input) INTEGER
The leading dimension of the arrays A, AF, Q and L.
LDA >= max(M,N).
TAU (output) COMPLEX array, dimension (min(M,N))
The scalar factors of the elementary reflectors, as returned
by CGELQF.
WORK (workspace) COMPLEX array, dimension (LWORK)
LWORK (input) INTEGER
The dimension of the array WORK.
RWORK (workspace) REAL array, dimension (max(M,N))
RESULT (output) REAL array, dimension (2)
The test ratios:
RESULT(1) = norm( L - A*Q' ) / ( N * norm(A) * EPS )
RESULT(2) = norm( I - Q*Q' ) / ( N * EPS )
=====================================================================
Parameter adjustments */
l_dim1 = *lda;
l_offset = 1 + l_dim1 * 1;
l -= l_offset;
q_dim1 = *lda;
q_offset = 1 + q_dim1 * 1;
q -= q_offset;
af_dim1 = *lda;
af_offset = 1 + af_dim1 * 1;
af -= af_offset;
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
--tau;
--work;
--rwork;
--result;
/* Function Body */
minmn = min(*m,*n);
eps = slamch_("Epsilon");
/* Copy the matrix A to the array AF. */
clacpy_("Full", m, n, &a[a_offset], lda, &af[af_offset], lda);
/* Factorize the matrix A in the array AF. */
s_copy(srnamc_1.srnamt, "CGELQF", (ftnlen)6, (ftnlen)6);
cgelqf_(m, n, &af[af_offset], lda, &tau[1], &work[1], lwork, &info);
/* Copy details of Q */
claset_("Full", n, n, &c_b1, &c_b1, &q[q_offset], lda);
if (*n > 1) {
i__1 = *n - 1;
clacpy_("Upper", m, &i__1, &af_ref(1, 2), lda, &q_ref(1, 2), lda);
}
/* Generate the n-by-n matrix Q */
s_copy(srnamc_1.srnamt, "CUNGLQ", (ftnlen)6, (ftnlen)6);
cunglq_(n, n, &minmn, &q[q_offset], lda, &tau[1], &work[1], lwork, &info);
/* Copy L */
claset_("Full", m, n, &c_b10, &c_b10, &l[l_offset], lda);
clacpy_("Lower", m, n, &af[af_offset], lda, &l[l_offset], lda);
/* Compute L - A*Q' */
cgemm_("No transpose", "Conjugate transpose", m, n, n, &c_b15, &a[
a_offset], lda, &q[q_offset], lda, &c_b16, &l[l_offset], lda);
/* Compute norm( L - Q'*A ) / ( N * norm(A) * EPS ) . */
anorm = clange_("1", m, n, &a[a_offset], lda, &rwork[1]);
resid = clange_("1", m, n, &l[l_offset], lda, &rwork[1]);
if (anorm > 0.f) {
result[1] = resid / (real) max(1,*n) / anorm / eps;
} else {
result[1] = 0.f;
}
/* Compute I - Q*Q' */
claset_("Full", n, n, &c_b10, &c_b16, &l[l_offset], lda);
cherk_("Upper", "No transpose", n, n, &c_b24, &q[q_offset], lda, &c_b25, &
l[l_offset], lda);
/* Compute norm( I - Q*Q' ) / ( N * EPS ) . */
resid = clansy_("1", "Upper", n, &l[l_offset], lda, &rwork[1]);
result[2] = resid / (real) max(1,*n) / eps;
return 0;
/* End of CLQT01 */
} /* clqt01_ */
/* 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;
complex dum[1];
real eps, thr, anrm, bnrm;
integer itau, lwork_cgebrd__, lwork_cgelqf__, lwork_cgeqrf__, lwork_cungbr__, lwork_cunmbr__, lwork_cunmlq__, lwork_cunmqr__;
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_(), slabad_(real *, real *);
extern real 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 real 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 3.4.0) -- */
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
/* November 2011 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* ===================================================================== */
/* .. 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 */
/* Compute space needed for CGEQRF */
cgeqrf_(m, n, &a[a_offset], lda, dum, dum, &c_n1, info);
lwork_cgeqrf__ = dum[0].r;
/* Compute space needed for CUNMQR */
cunmqr_("L", "C", m, nrhs, n, &a[a_offset], lda, dum, &b[ b_offset], ldb, dum, &c_n1, info);
lwork_cunmqr__ = dum[0].r;
mm = *n;
/* Computing MAX */
i__1 = maxwrk;
i__2 = *n + *n * ilaenv_(&c__1, "CGEQRF", " ", m, n, &c_n1, &c_n1); // , expr subst
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); // , expr subst
maxwrk = max(i__1,i__2);
}
if (*m >= *n)
{
/* Path 1 - overdetermined or exactly determined */
/* Compute space needed for CGEBRD */
cgebrd_(&mm, n, &a[a_offset], lda, &s[1], dum, dum, dum, dum, &c_n1, info);
lwork_cgebrd__ = dum[0].r;
/* Compute space needed for CUNMBR */
cunmbr_("Q", "L", "C", &mm, nrhs, n, &a[a_offset], lda, dum, & b[b_offset], ldb, dum, &c_n1, info);
lwork_cunmbr__ = dum[0].r;
/* Compute space needed for CUNGBR */
cungbr_("P", n, n, n, &a[a_offset], lda, dum, dum, &c_n1, info);
lwork_cungbr__ = dum[0].r;
/* Compute total workspace needed */
/* Computing MAX */
i__1 = maxwrk;
i__2 = (*n << 1) + lwork_cgebrd__; // , expr subst
maxwrk = max(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk;
i__2 = (*n << 1) + lwork_cunmbr__; // , expr subst
maxwrk = max(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk;
i__2 = (*n << 1) + lwork_cungbr__; // , expr subst
maxwrk = max(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk;
i__2 = *n * *nrhs; // , expr subst
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 */
/* Compute space needed for CGELQF */
cgelqf_(m, n, &a[a_offset], lda, dum, dum, &c_n1, info);
lwork_cgelqf__ = dum[0].r;
/* Compute space needed for CGEBRD */
cgebrd_(m, m, &a[a_offset], lda, &s[1], dum, dum, dum, dum, &c_n1, info);
lwork_cgebrd__ = dum[0].r;
/* Compute space needed for CUNMBR */
cunmbr_("Q", "L", "C", m, nrhs, n, &a[a_offset], lda, dum, &b[b_offset], ldb, dum, &c_n1, info);
lwork_cunmbr__ = dum[0].r;
/* Compute space needed for CUNGBR */
cungbr_("P", m, m, m, &a[a_offset], lda, dum, dum, &c_n1, info);
lwork_cungbr__ = dum[0].r;
/* Compute space needed for CUNMLQ */
cunmlq_("L", "C", n, nrhs, m, &a[a_offset], lda, dum, &b[ b_offset], ldb, dum, &c_n1, info);
lwork_cunmlq__ = dum[0].r;
/* Compute total workspace needed */
maxwrk = *m + lwork_cgelqf__;
/* Computing MAX */
i__1 = maxwrk;
i__2 = *m * 3 + *m * *m + lwork_cgebrd__; // , expr subst
maxwrk = max(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk;
i__2 = *m * 3 + *m * *m + lwork_cunmbr__; // , expr subst
maxwrk = max(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk;
i__2 = *m * 3 + *m * *m + lwork_cungbr__; // , expr subst
maxwrk = max(i__1,i__2);
if (*nrhs > 1)
{
/* Computing MAX */
i__1 = maxwrk;
i__2 = *m * *m + *m + *m * *nrhs; // , expr subst
maxwrk = max(i__1,i__2);
}
else
{
/* Computing MAX */
i__1 = maxwrk;
i__2 = *m * *m + (*m << 1); // , expr subst
maxwrk = max(i__1,i__2);
}
/* Computing MAX */
i__1 = maxwrk;
i__2 = *m + lwork_cunmlq__; // , expr subst
maxwrk = max(i__1,i__2);
}
else
{
/* Path 2 - underdetermined */
/* Compute space needed for CGEBRD */
cgebrd_(m, n, &a[a_offset], lda, &s[1], dum, dum, dum, dum, &c_n1, info);
lwork_cgebrd__ = dum[0].r;
/* Compute space needed for CUNMBR */
cunmbr_("Q", "L", "C", m, nrhs, m, &a[a_offset], lda, dum, &b[b_offset], ldb, dum, &c_n1, info);
lwork_cunmbr__ = dum[0].r;
/* Compute space needed for CUNGBR */
cungbr_("P", m, n, m, &a[a_offset], lda, dum, dum, &c_n1, info);
lwork_cungbr__ = dum[0].r;
maxwrk = (*m << 1) + lwork_cgebrd__;
/* Computing MAX */
i__1 = maxwrk;
i__2 = (*m << 1) + lwork_cunmbr__; // , expr subst
maxwrk = max(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk;
i__2 = (*m << 1) + lwork_cungbr__; // , expr subst
maxwrk = max(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk;
i__2 = *n * *nrhs; // , expr subst
maxwrk = max(i__1,i__2);
}
}
maxwrk = max(minwrk,maxwrk);
}
work[1].r = (real) maxwrk;
work[1].i = 0.f; // , expr subst
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_b59, &c_b59, &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, dum, &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 = max(r__1,sfmin);
if (*rcond < 0.f)
{
/* Computing MAX */
r__1 = eps * s[1];
thr = max(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); // , expr subst
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); // , expr subst
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 = max(r__1,sfmin);
if (*rcond < 0.f)
{
/* Computing MAX */
r__1 = eps * s[1];
thr = max(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, dum, &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 = max(r__1,sfmin);
if (*rcond < 0.f)
{
/* Computing MAX */
r__1 = eps * s[1];
thr = max(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; // , expr subst
return 0;
/* End of CGELSS */
}
/* Subroutine */ int ctimlq_(char *line, integer *nm, integer *mval, integer *
nval, integer *nk, integer *kval, integer *nnb, integer *nbval,
integer *nxval, integer *nlda, integer *ldaval, real *timmin, complex
*a, complex *tau, complex *b, complex *work, real *rwork, real *
reslts, integer *ldr1, integer *ldr2, integer *ldr3, integer *nout,
ftnlen line_len)
{
/* Initialized data */
static char subnam[6*3] = "CGELQF" "CUNGLQ" "CUNMLQ";
static char sides[1*2] = "L" "R";
static char transs[1*2] = "N" "C";
static integer iseed[4] = { 0,0,0,1 };
/* Format strings */
static char fmt_9999[] = "(1x,a6,\002 timing run not attempted\002,/)";
static char fmt_9998[] = "(/\002 *** Speed of \002,a6,\002 in megaflops "
"***\002)";
static char fmt_9997[] = "(5x,\002line \002,i2,\002 with LDA = \002,i5)";
static char fmt_9996[] = "(5x,\002K = min(M,N)\002,/)";
static char fmt_9995[] = "(/5x,a6,\002 with SIDE = '\002,a1,\002', TRANS"
" = '\002,a1,\002', \002,a1,\002 =\002,i6,/)";
static char fmt_9994[] = "(\002 *** No pairs (M,N) found with M <= N: "
" \002,a6,\002 not timed\002)";
/* System generated locals */
integer reslts_dim1, reslts_dim2, reslts_dim3, reslts_offset, i__1, i__2,
i__3, i__4, i__5, i__6;
/* Builtin functions
Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen);
integer s_wsfe(cilist *), do_fio(integer *, char *, ftnlen), e_wsfe(void),
s_wsle(cilist *), e_wsle(void);
/* Local variables */
static integer ilda;
static char labm[1], side[1];
static integer info;
static char path[3];
static real time;
static integer isub, muse[12], nuse[12], i__, k, m, n;
static char cname[6];
static integer iside, itoff, itran, minmn;
extern doublereal sopla_(char *, integer *, integer *, integer *, integer
*, integer *);
extern /* Subroutine */ int icopy_(integer *, integer *, integer *,
integer *, integer *);
static char trans[1];
static integer k1, i4, m1, n1;
static real s1, s2;
static integer ic;
extern /* Subroutine */ int sprtb4_(char *, char *, char *, integer *,
integer *, integer *, integer *, integer *, integer *, integer *,
real *, integer *, integer *, integer *, ftnlen, ftnlen, ftnlen),
sprtb5_(char *, char *, char *, integer *, integer *, integer *,
integer *, integer *, integer *, real *, integer *, integer *,
integer *, ftnlen, ftnlen, ftnlen);
static integer nb, ik, im;
extern /* Subroutine */ int cgelqf_(integer *, integer *, complex *,
integer *, complex *, complex *, integer *, integer *);
static integer lw, nx, reseed[4];
extern /* Subroutine */ int atimck_(integer *, char *, integer *, integer
*, integer *, integer *, integer *, integer *, ftnlen);
extern doublereal second_(void);
extern /* Subroutine */ int clacpy_(char *, integer *, integer *, complex
*, integer *, complex *, integer *), ctimmg_(integer *,
integer *, integer *, complex *, integer *, integer *, integer *),
atimin_(char *, char *, integer *, char *, logical *, integer *,
integer *, ftnlen, ftnlen, ftnlen), clatms_(integer *, integer *,
char *, integer *, char *, real *, integer *, real *, real *,
integer *, integer *, char *, complex *, integer *, complex *,
integer *), cunglq_(integer *, integer *,
integer *, complex *, integer *, complex *, complex *, integer *,
integer *), xlaenv_(integer *, integer *), cunmlq_(char *, char *,
integer *, integer *, integer *, complex *, integer *, complex *,
complex *, integer *, complex *, integer *, integer *);
extern doublereal smflop_(real *, real *, integer *);
static real untime;
static logical timsub[3];
static integer lda, icl, inb, imx;
static real ops;
/* Fortran I/O blocks */
static cilist io___9 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___29 = { 0, 0, 0, fmt_9998, 0 };
static cilist io___31 = { 0, 0, 0, fmt_9997, 0 };
static cilist io___32 = { 0, 0, 0, 0, 0 };
static cilist io___33 = { 0, 0, 0, fmt_9996, 0 };
static cilist io___34 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___49 = { 0, 0, 0, fmt_9998, 0 };
static cilist io___50 = { 0, 0, 0, fmt_9997, 0 };
static cilist io___51 = { 0, 0, 0, fmt_9995, 0 };
static cilist io___53 = { 0, 0, 0, fmt_9995, 0 };
static cilist io___54 = { 0, 0, 0, fmt_9994, 0 };
#define subnam_ref(a_0,a_1) &subnam[(a_1)*6 + a_0 - 6]
#define reslts_ref(a_1,a_2,a_3,a_4) reslts[(((a_4)*reslts_dim3 + (a_3))*\
reslts_dim2 + (a_2))*reslts_dim1 + a_1]
/* -- LAPACK timing routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
March 31, 1993
Purpose
=======
CTIMLQ times the LAPACK routines to perform the LQ factorization of
a COMPLEX general matrix.
Arguments
=========
LINE (input) CHARACTER*80
The input line that requested this routine. The first six
characters contain either the name of a subroutine or a
generic path name. The remaining characters may be used to
specify the individual routines to be timed. See ATIMIN for
a full description of the format of the input line.
NM (input) INTEGER
The number of values of M and N contained in the vectors
MVAL and NVAL. The matrix sizes are used in pairs (M,N).
MVAL (input) INTEGER array, dimension (NM)
The values of the matrix row dimension M.
NVAL (input) INTEGER array, dimension (NM)
The values of the matrix column dimension N.
NK (input) INTEGER
The number of values of K in the vector KVAL.
KVAL (input) INTEGER array, dimension (NK)
The values of the matrix dimension K, used in CUNMLQ.
NNB (input) INTEGER
The number of values of NB and NX contained in the
vectors NBVAL and NXVAL. The blocking parameters are used
in pairs (NB,NX).
NBVAL (input) INTEGER array, dimension (NNB)
The values of the blocksize NB.
NXVAL (input) INTEGER array, dimension (NNB)
The values of the crossover point NX.
NLDA (input) INTEGER
The number of values of LDA contained in the vector LDAVAL.
LDAVAL (input) INTEGER array, dimension (NLDA)
The values of the leading dimension of the array A.
TIMMIN (input) REAL
The minimum time a subroutine will be timed.
A (workspace) COMPLEX array, dimension (LDAMAX*NMAX)
where LDAMAX and NMAX are the maximum values of LDA and N.
TAU (workspace) COMPLEX array, dimension (min(M,N))
B (workspace) COMPLEX array, dimension (LDAMAX*NMAX)
WORK (workspace) COMPLEX array, dimension (LDAMAX*NBMAX)
where NBMAX is the maximum value of NB.
RWORK (workspace) REAL array, dimension
(min(MMAX,NMAX))
RESLTS (workspace) REAL array, dimension
(LDR1,LDR2,LDR3,2*NK)
The timing results for each subroutine over the relevant
values of (M,N), (NB,NX), and LDA.
LDR1 (input) INTEGER
The first dimension of RESLTS. LDR1 >= max(1,NNB).
LDR2 (input) INTEGER
The second dimension of RESLTS. LDR2 >= max(1,NM).
LDR3 (input) INTEGER
The third dimension of RESLTS. LDR3 >= max(1,NLDA).
NOUT (input) INTEGER
The unit number for output.
Internal Parameters
===================
MODE INTEGER
The matrix type. MODE = 3 is a geometric distribution of
eigenvalues. See CLATMS for further details.
COND REAL
The condition number of the matrix. The singular values are
set to values from DMAX to DMAX/COND.
DMAX REAL
The magnitude of the largest singular value.
=====================================================================
Parameter adjustments */
--mval;
--nval;
--kval;
--nbval;
--nxval;
--ldaval;
--a;
--tau;
--b;
--work;
--rwork;
reslts_dim1 = *ldr1;
reslts_dim2 = *ldr2;
reslts_dim3 = *ldr3;
reslts_offset = 1 + reslts_dim1 * (1 + reslts_dim2 * (1 + reslts_dim3 * 1)
);
reslts -= reslts_offset;
/* Function Body
Extract the timing request from the input line. */
s_copy(path, "Complex precision", (ftnlen)1, (ftnlen)17);
s_copy(path + 1, "LQ", (ftnlen)2, (ftnlen)2);
atimin_(path, line, &c__3, subnam, timsub, nout, &info, (ftnlen)3, (
ftnlen)80, (ftnlen)6);
if (info != 0) {
goto L230;
}
/* Check that M <= LDA for the input values. */
s_copy(cname, line, (ftnlen)6, (ftnlen)6);
atimck_(&c__1, cname, nm, &mval[1], nlda, &ldaval[1], nout, &info, (
ftnlen)6);
if (info > 0) {
io___9.ciunit = *nout;
s_wsfe(&io___9);
do_fio(&c__1, cname, (ftnlen)6);
e_wsfe();
goto L230;
}
/* Do for each pair of values (M,N): */
i__1 = *nm;
for (im = 1; im <= i__1; ++im) {
m = mval[im];
n = nval[im];
minmn = min(m,n);
icopy_(&c__4, iseed, &c__1, reseed, &c__1);
/* Do for each value of LDA: */
i__2 = *nlda;
for (ilda = 1; ilda <= i__2; ++ilda) {
lda = ldaval[ilda];
/* Do for each pair of values (NB, NX) in NBVAL and NXVAL. */
i__3 = *nnb;
for (inb = 1; inb <= i__3; ++inb) {
nb = nbval[inb];
xlaenv_(&c__1, &nb);
nx = nxval[inb];
xlaenv_(&c__3, &nx);
/* Computing MAX */
i__4 = 1, i__5 = m * max(1,nb);
lw = max(i__4,i__5);
/* Generate a test matrix of size M by N. */
icopy_(&c__4, reseed, &c__1, iseed, &c__1);
clatms_(&m, &n, "Uniform", iseed, "Nonsymm", &rwork[1], &c__3,
&c_b24, &c_b25, &m, &n, "No packing", &b[1], &lda, &
work[1], &info);
if (timsub[0]) {
/* CGELQF: LQ factorization */
clacpy_("Full", &m, &n, &b[1], &lda, &a[1], &lda);
ic = 0;
s1 = second_();
L10:
cgelqf_(&m, &n, &a[1], &lda, &tau[1], &work[1], &lw, &
info);
s2 = second_();
time = s2 - s1;
++ic;
if (time < *timmin) {
clacpy_("Full", &m, &n, &b[1], &lda, &a[1], &lda);
goto L10;
}
/* Subtract the time used in CLACPY. */
icl = 1;
s1 = second_();
L20:
s2 = second_();
untime = s2 - s1;
++icl;
if (icl <= ic) {
clacpy_("Full", &m, &n, &a[1], &lda, &b[1], &lda);
goto L20;
}
time = (time - untime) / (real) ic;
ops = sopla_("CGELQF", &m, &n, &c__0, &c__0, &nb);
reslts_ref(inb, im, ilda, 1) = smflop_(&ops, &time, &info)
;
} else {
/* If CGELQF was not timed, generate a matrix and factor
it using CGELQF anyway so that the factored form of
the matrix can be used in timing the other routines. */
clacpy_("Full", &m, &n, &b[1], &lda, &a[1], &lda);
cgelqf_(&m, &n, &a[1], &lda, &tau[1], &work[1], &lw, &
info);
}
if (timsub[1]) {
/* CUNGLQ: Generate orthogonal matrix Q from the LQ
factorization */
clacpy_("Full", &minmn, &n, &a[1], &lda, &b[1], &lda);
ic = 0;
s1 = second_();
L30:
cunglq_(&minmn, &n, &minmn, &b[1], &lda, &tau[1], &work[1]
, &lw, &info);
s2 = second_();
time = s2 - s1;
++ic;
if (time < *timmin) {
clacpy_("Full", &minmn, &n, &a[1], &lda, &b[1], &lda);
goto L30;
}
/* Subtract the time used in CLACPY. */
icl = 1;
s1 = second_();
L40:
s2 = second_();
untime = s2 - s1;
++icl;
if (icl <= ic) {
clacpy_("Full", &minmn, &n, &a[1], &lda, &b[1], &lda);
goto L40;
}
time = (time - untime) / (real) ic;
ops = sopla_("CUNGLQ", &minmn, &n, &minmn, &c__0, &nb);
reslts_ref(inb, im, ilda, 2) = smflop_(&ops, &time, &info)
;
}
/* L50: */
}
/* L60: */
}
/* L70: */
}
/* Print tables of results */
for (isub = 1; isub <= 2; ++isub) {
if (! timsub[isub - 1]) {
goto L90;
}
io___29.ciunit = *nout;
s_wsfe(&io___29);
do_fio(&c__1, subnam_ref(0, isub), (ftnlen)6);
e_wsfe();
if (*nlda > 1) {
i__1 = *nlda;
for (i__ = 1; i__ <= i__1; ++i__) {
io___31.ciunit = *nout;
s_wsfe(&io___31);
do_fio(&c__1, (char *)&i__, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&ldaval[i__], (ftnlen)sizeof(integer));
e_wsfe();
/* L80: */
}
}
io___32.ciunit = *nout;
s_wsle(&io___32);
e_wsle();
if (isub == 2) {
io___33.ciunit = *nout;
s_wsfe(&io___33);
e_wsfe();
}
sprtb4_("( NB, NX)", "M", "N", nnb, &nbval[1], &nxval[1], nm, &mval[
1], &nval[1], nlda, &reslts_ref(1, 1, 1, isub), ldr1, ldr2,
nout, (ftnlen)11, (ftnlen)1, (ftnlen)1);
L90:
;
}
/* Time CUNMLQ separately. Here the starting matrix is M by N, and
K is the free dimension of the matrix multiplied by Q. */
if (timsub[2]) {
/* Check that K <= LDA for the input values. */
atimck_(&c__3, cname, nk, &kval[1], nlda, &ldaval[1], nout, &info, (
ftnlen)6);
if (info > 0) {
io___34.ciunit = *nout;
s_wsfe(&io___34);
do_fio(&c__1, subnam_ref(0, 3), (ftnlen)6);
e_wsfe();
goto L230;
}
/* Use only the pairs (M,N) where M <= N. */
imx = 0;
i__1 = *nm;
for (im = 1; im <= i__1; ++im) {
if (mval[im] <= nval[im]) {
++imx;
muse[imx - 1] = mval[im];
nuse[imx - 1] = nval[im];
}
/* L100: */
}
/* CUNMLQ: Multiply by Q stored as a product of elementary
transformations
Do for each pair of values (M,N): */
i__1 = imx;
for (im = 1; im <= i__1; ++im) {
m = muse[im - 1];
n = nuse[im - 1];
/* Do for each value of LDA: */
i__2 = *nlda;
for (ilda = 1; ilda <= i__2; ++ilda) {
lda = ldaval[ilda];
/* Generate an M by N matrix and form its LQ decomposition. */
clatms_(&m, &n, "Uniform", iseed, "Nonsymm", &rwork[1], &c__3,
&c_b24, &c_b25, &m, &n, "No packing", &a[1], &lda, &
work[1], &info);
/* Computing MAX */
i__3 = 1, i__4 = m * max(1,nb);
lw = max(i__3,i__4);
cgelqf_(&m, &n, &a[1], &lda, &tau[1], &work[1], &lw, &info);
/* Do first for SIDE = 'L', then for SIDE = 'R' */
i4 = 0;
for (iside = 1; iside <= 2; ++iside) {
*(unsigned char *)side = *(unsigned char *)&sides[iside -
1];
/* Do for each pair of values (NB, NX) in NBVAL and
NXVAL. */
i__3 = *nnb;
for (inb = 1; inb <= i__3; ++inb) {
nb = nbval[inb];
xlaenv_(&c__1, &nb);
nx = nxval[inb];
xlaenv_(&c__3, &nx);
/* Do for each value of K in KVAL */
i__4 = *nk;
for (ik = 1; ik <= i__4; ++ik) {
k = kval[ik];
/* Sort out which variable is which */
if (iside == 1) {
k1 = m;
m1 = n;
n1 = k;
/* Computing MAX */
i__5 = 1, i__6 = n1 * max(1,nb);
lw = max(i__5,i__6);
} else {
k1 = m;
n1 = n;
m1 = k;
/* Computing MAX */
i__5 = 1, i__6 = m1 * max(1,nb);
lw = max(i__5,i__6);
}
/* Do first for TRANS = 'N', then for TRANS = 'T' */
itoff = 0;
for (itran = 1; itran <= 2; ++itran) {
*(unsigned char *)trans = *(unsigned char *)&
transs[itran - 1];
ctimmg_(&c__0, &m1, &n1, &b[1], &lda, &c__0, &
c__0);
ic = 0;
s1 = second_();
L110:
cunmlq_(side, trans, &m1, &n1, &k1, &a[1], &
lda, &tau[1], &b[1], &lda, &work[1], &
lw, &info);
s2 = second_();
time = s2 - s1;
++ic;
if (time < *timmin) {
ctimmg_(&c__0, &m1, &n1, &b[1], &lda, &
c__0, &c__0);
goto L110;
}
/* Subtract the time used in CTIMMG. */
icl = 1;
s1 = second_();
L120:
s2 = second_();
untime = s2 - s1;
++icl;
if (icl <= ic) {
ctimmg_(&c__0, &m1, &n1, &b[1], &lda, &
c__0, &c__0);
goto L120;
}
time = (time - untime) / (real) ic;
i__5 = iside - 1;
ops = sopla_("CUNMLQ", &m1, &n1, &k1, &i__5, &
nb);
reslts_ref(inb, im, ilda, i4 + itoff + ik) =
smflop_(&ops, &time, &info);
itoff = *nk;
/* L130: */
}
/* L140: */
}
/* L150: */
}
i4 = *nk << 1;
/* L160: */
}
/* L170: */
}
/* L180: */
}
/* Print tables of results */
isub = 3;
i4 = 1;
if (imx >= 1) {
for (iside = 1; iside <= 2; ++iside) {
*(unsigned char *)side = *(unsigned char *)&sides[iside - 1];
if (iside == 1) {
io___49.ciunit = *nout;
s_wsfe(&io___49);
do_fio(&c__1, subnam_ref(0, isub), (ftnlen)6);
e_wsfe();
if (*nlda > 1) {
i__1 = *nlda;
for (i__ = 1; i__ <= i__1; ++i__) {
io___50.ciunit = *nout;
s_wsfe(&io___50);
do_fio(&c__1, (char *)&i__, (ftnlen)sizeof(
integer));
do_fio(&c__1, (char *)&ldaval[i__], (ftnlen)
sizeof(integer));
e_wsfe();
/* L190: */
}
}
}
for (itran = 1; itran <= 2; ++itran) {
*(unsigned char *)trans = *(unsigned char *)&transs[itran
- 1];
i__1 = *nk;
for (ik = 1; ik <= i__1; ++ik) {
if (iside == 1) {
n = kval[ik];
io___51.ciunit = *nout;
s_wsfe(&io___51);
do_fio(&c__1, subnam_ref(0, isub), (ftnlen)6);
do_fio(&c__1, side, (ftnlen)1);
do_fio(&c__1, trans, (ftnlen)1);
do_fio(&c__1, "N", (ftnlen)1);
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer))
;
e_wsfe();
*(unsigned char *)labm = 'M';
} else {
m = kval[ik];
io___53.ciunit = *nout;
s_wsfe(&io___53);
do_fio(&c__1, subnam_ref(0, isub), (ftnlen)6);
do_fio(&c__1, side, (ftnlen)1);
do_fio(&c__1, trans, (ftnlen)1);
do_fio(&c__1, "M", (ftnlen)1);
do_fio(&c__1, (char *)&m, (ftnlen)sizeof(integer))
;
e_wsfe();
*(unsigned char *)labm = 'N';
}
sprtb5_("NB", "K", labm, nnb, &nbval[1], &imx, muse,
nuse, nlda, &reslts_ref(1, 1, 1, i4), ldr1,
ldr2, nout, (ftnlen)2, (ftnlen)1, (ftnlen)1);
++i4;
/* L200: */
}
/* L210: */
}
/* L220: */
}
} else {
io___54.ciunit = *nout;
s_wsfe(&io___54);
do_fio(&c__1, subnam_ref(0, isub), (ftnlen)6);
e_wsfe();
}
}
L230:
return 0;
/* End of CTIMLQ */
} /* ctimlq_ */
/* Subroutine */ int clqt01_(integer *m, integer *n, complex *a, complex *af,
complex *q, complex *l, integer *lda, complex *tau, complex *work,
integer *lwork, real *rwork, real *result)
{
/* System generated locals */
integer a_dim1, a_offset, af_dim1, af_offset, l_dim1, l_offset, q_dim1,
q_offset, i__1;
/* Builtin functions */
/* Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen);
/* Local variables */
real eps;
integer info;
extern /* Subroutine */ int cgemm_(char *, char *, integer *, integer *,
integer *, complex *, complex *, integer *, complex *, integer *,
complex *, complex *, integer *), cherk_(char *,
char *, integer *, integer *, real *, complex *, integer *, real *
, complex *, integer *);
real resid, anorm;
integer minmn;
extern doublereal clange_(char *, integer *, integer *, complex *,
integer *, real *);
extern /* Subroutine */ int cgelqf_(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 *);
extern doublereal clansy_(char *, char *, integer *, complex *, integer *,
real *);
extern /* Subroutine */ int cunglq_(integer *, integer *, integer *,
complex *, integer *, complex *, complex *, integer *, integer *);
/* -- LAPACK test routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* CLQT01 tests CGELQF, which computes the LQ factorization of an m-by-n */
/* matrix A, and partially tests CUNGLQ which forms the n-by-n */
/* orthogonal matrix Q. */
/* CLQT01 compares L with A*Q', and checks that Q is orthogonal. */
/* 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. */
/* A (input) COMPLEX array, dimension (LDA,N) */
/* The m-by-n matrix A. */
/* AF (output) COMPLEX array, dimension (LDA,N) */
/* Details of the LQ factorization of A, as returned by CGELQF. */
/* See CGELQF for further details. */
/* Q (output) COMPLEX array, dimension (LDA,N) */
/* The n-by-n orthogonal matrix Q. */
/* L (workspace) COMPLEX array, dimension (LDA,max(M,N)) */
/* LDA (input) INTEGER */
/* The leading dimension of the arrays A, AF, Q and L. */
/* LDA >= max(M,N). */
/* TAU (output) COMPLEX array, dimension (min(M,N)) */
/* The scalar factors of the elementary reflectors, as returned */
/* by CGELQF. */
/* WORK (workspace) COMPLEX array, dimension (LWORK) */
/* LWORK (input) INTEGER */
/* The dimension of the array WORK. */
/* RWORK (workspace) REAL array, dimension (max(M,N)) */
/* RESULT (output) REAL array, dimension (2) */
/* The test ratios: */
/* RESULT(1) = norm( L - A*Q' ) / ( N * norm(A) * EPS ) */
/* RESULT(2) = norm( I - Q*Q' ) / ( N * EPS ) */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Scalars in Common .. */
/* .. */
/* .. Common blocks .. */
/* .. */
/* .. Executable Statements .. */
/* Parameter adjustments */
l_dim1 = *lda;
l_offset = 1 + l_dim1;
l -= l_offset;
q_dim1 = *lda;
q_offset = 1 + q_dim1;
q -= q_offset;
af_dim1 = *lda;
af_offset = 1 + af_dim1;
af -= af_offset;
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--tau;
--work;
--rwork;
--result;
/* Function Body */
minmn = min(*m,*n);
eps = slamch_("Epsilon");
/* Copy the matrix A to the array AF. */
clacpy_("Full", m, n, &a[a_offset], lda, &af[af_offset], lda);
/* Factorize the matrix A in the array AF. */
s_copy(srnamc_1.srnamt, "CGELQF", (ftnlen)6, (ftnlen)6);
cgelqf_(m, n, &af[af_offset], lda, &tau[1], &work[1], lwork, &info);
/* Copy details of Q */
claset_("Full", n, n, &c_b1, &c_b1, &q[q_offset], lda);
if (*n > 1) {
i__1 = *n - 1;
clacpy_("Upper", m, &i__1, &af[(af_dim1 << 1) + 1], lda, &q[(q_dim1 <<
1) + 1], lda);
}
/* Generate the n-by-n matrix Q */
s_copy(srnamc_1.srnamt, "CUNGLQ", (ftnlen)6, (ftnlen)6);
cunglq_(n, n, &minmn, &q[q_offset], lda, &tau[1], &work[1], lwork, &info);
/* Copy L */
claset_("Full", m, n, &c_b10, &c_b10, &l[l_offset], lda);
clacpy_("Lower", m, n, &af[af_offset], lda, &l[l_offset], lda);
/* Compute L - A*Q' */
cgemm_("No transpose", "Conjugate transpose", m, n, n, &c_b15, &a[
a_offset], lda, &q[q_offset], lda, &c_b16, &l[l_offset], lda);
/* Compute norm( L - Q'*A ) / ( N * norm(A) * EPS ) . */
anorm = clange_("1", m, n, &a[a_offset], lda, &rwork[1]);
resid = clange_("1", m, n, &l[l_offset], lda, &rwork[1]);
if (anorm > 0.f) {
result[1] = resid / (real) max(1,*n) / anorm / eps;
} else {
result[1] = 0.f;
}
/* Compute I - Q*Q' */
claset_("Full", n, n, &c_b10, &c_b16, &l[l_offset], lda);
cherk_("Upper", "No transpose", n, n, &c_b24, &q[q_offset], lda, &c_b25, &
l[l_offset], lda);
/* Compute norm( I - Q*Q' ) / ( N * EPS ) . */
resid = clansy_("1", "Upper", n, &l[l_offset], lda, &rwork[1]);
result[2] = resid / (real) max(1,*n) / eps;
return 0;
/* End of CLQT01 */
} /* clqt01_ */
/* 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;
real r__1;
complex q__1;
/* Local variables */
static real anrm, bnrm;
static integer itau, iascl, ibscl;
static real sfmin;
static integer minmn, maxmn, itaup, itauq, mnthr, nwork, ie, il;
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 *);
static integer mm;
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 *, ftnlen, ftnlen);
static 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 *);
static integer ldwork;
extern /* Subroutine */ int cunmqr_(char *, char *, integer *, integer *,
integer *, complex *, integer *, complex *, complex *, integer *,
complex *, integer *, integer *);
static integer minwrk, maxwrk;
static real smlnum;
static logical lquery;
static integer nrwork, smlsiz;
static real eps;
#define a_subscr(a_1,a_2) (a_2)*a_dim1 + a_1
#define a_ref(a_1,a_2) a[a_subscr(a_1,a_2)]
#define b_subscr(a_1,a_2) (a_2)*b_dim1 + a_1
#define b_ref(a_1,a_2) b[b_subscr(a_1,a_2)]
/* -- LAPACK driver routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
October 31, 1999
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 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 (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 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 at least
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 )
IWORK (workspace) INTEGER array, dimension (LIWORK)
LIWORK >= 3 * MINMN * NLVL + 11 * MINMN,
where MINMN = 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.
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
=====================================================================
Test the input arguments.
Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
b_dim1 = *ldb;
b_offset = 1 + b_dim1 * 1;
b -= b_offset;
--s;
--work;
--rwork;
--iwork;
/* Function Body */
*info = 0;
minmn = min(*m,*n);
maxmn = max(*m,*n);
mnthr = ilaenv_(&c__6, "CGELSD", " ", m, n, nrhs, &c_n1, (ftnlen)6, (
ftnlen)1);
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;
}
smlsiz = ilaenv_(&c__9, "CGELSD", " ", &c__0, &c__0, &c__0, &c__0, (
ftnlen)6, (ftnlen)1);
/* 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.) */
minwrk = 1;
if (*info == 0) {
maxwrk = 0;
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, (ftnlen)6, (ftnlen)1);
maxwrk = max(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk, i__2 = *nrhs * ilaenv_(&c__1, "CUNMQR", "LC", m,
nrhs, n, &c_n1, (ftnlen)6, (ftnlen)2);
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, (ftnlen)6, (ftnlen)1)
;
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, (ftnlen)6, (ftnlen)3);
maxwrk = max(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk, i__2 = (*n << 1) + (*n - 1) * ilaenv_(&c__1, "CUN"
"MBR", "PLN", n, nrhs, n, &c_n1, (ftnlen)6, (ftnlen)3);
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) {
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, (ftnlen)6, (ftnlen)1);
/* Computing MAX */
i__1 = maxwrk, i__2 = *m * *m + (*m << 2) + (*m << 1) *
ilaenv_(&c__1, "CGEBRD", " ", m, m, &c_n1, &c_n1, (
ftnlen)6, (ftnlen)1);
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, (ftnlen)6, (
ftnlen)3);
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, (
ftnlen)6, (ftnlen)2);
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, (ftnlen)6, (ftnlen)1);
/* Computing MAX */
i__1 = maxwrk, i__2 = (*m << 1) + *nrhs * ilaenv_(&c__1,
"CUNMBR", "QLC", m, nrhs, m, &c_n1, (ftnlen)6, (
ftnlen)3);
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, (ftnlen)6, (ftnlen)3);
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);
r__1 = (real) maxwrk;
q__1.r = r__1, q__1.i = 0.f;
work[1].r = q__1.r, work[1].i = q__1.i;
if (*lwork < minwrk && ! lquery) {
*info = -12;
}
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("CGELSD", &i__1);
return 0;
} else if (lquery) {
goto L10;
}
/* 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_b81, &c_b81, &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_ref(*m + 1, 1), 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_ref(2, 1), 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_ref(*m + 1, 1), 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:
r__1 = (real) maxwrk;
q__1.r = r__1, q__1.i = 0.f;
work[1].r = q__1.r, work[1].i = q__1.i;
return 0;
/* End of CGELSD */
} /* cgelsd_ */