/* zgelsd.f -- translated by f2c (version 20061008).
You must link the resulting object file with libf2c:
on Microsoft Windows system, link with libf2c.lib;
on Linux or Unix systems, link with .../path/to/libf2c.a -lm
or, if you install libf2c.a in a standard place, with -lf2c -lm
-- in that order, at the end of the command line, as in
cc *.o -lf2c -lm
Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
http://www.netlib.org/f2c/libf2c.zip
*/
#include "f2c.h"
#include "blaswrap.h"
/* Table of constant values */
static doublecomplex c_b1 = {0.,0.};
static integer c__9 = 9;
static integer c__0 = 0;
static integer c__6 = 6;
static integer c_n1 = -1;
static integer c__1 = 1;
static doublereal c_b80 = 0.;
/* Subroutine */ int zgelsd_(integer *m, integer *n, integer *nrhs,
doublecomplex *a, integer *lda, doublecomplex *b, integer *ldb,
doublereal *s, doublereal *rcond, integer *rank, doublecomplex *work,
integer *lwork, doublereal *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;
doublereal eps, anrm, bnrm;
integer itau, nlvl, iascl, ibscl;
doublereal sfmin;
integer minmn, maxmn, itaup, itauq, mnthr, nwork;
extern /* Subroutine */ int dlabad_(doublereal *, doublereal *);
extern doublereal dlamch_(char *);
extern /* Subroutine */ int dlascl_(char *, integer *, integer *,
doublereal *, doublereal *, integer *, integer *, doublereal *,
integer *, integer *), dlaset_(char *, integer *, integer
*, doublereal *, doublereal *, doublereal *, integer *),
xerbla_(char *, integer *), zgebrd_(integer *, integer *,
doublecomplex *, integer *, doublereal *, doublereal *,
doublecomplex *, doublecomplex *, doublecomplex *, integer *,
integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *);
extern doublereal zlange_(char *, integer *, integer *, doublecomplex *,
integer *, doublereal *);
doublereal bignum;
extern /* Subroutine */ int zgelqf_(integer *, integer *, doublecomplex *,
integer *, doublecomplex *, doublecomplex *, integer *, integer *
), zlalsd_(char *, integer *, integer *, integer *, doublereal *,
doublereal *, doublecomplex *, integer *, doublereal *, integer *,
doublecomplex *, doublereal *, integer *, integer *),
zlascl_(char *, integer *, integer *, doublereal *, doublereal *,
integer *, integer *, doublecomplex *, integer *, integer *), zgeqrf_(integer *, integer *, doublecomplex *, integer *,
doublecomplex *, doublecomplex *, integer *, integer *);
integer ldwork;
extern /* Subroutine */ int zlacpy_(char *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *),
zlaset_(char *, integer *, integer *, doublecomplex *,
doublecomplex *, doublecomplex *, integer *);
integer liwork, minwrk, maxwrk;
doublereal smlnum;
extern /* Subroutine */ int zunmbr_(char *, char *, char *, integer *,
integer *, integer *, doublecomplex *, integer *, doublecomplex *,
doublecomplex *, integer *, doublecomplex *, integer *, integer *
);
integer lrwork;
logical lquery;
integer nrwork, smlsiz;
extern /* Subroutine */ int zunmlq_(char *, char *, integer *, integer *,
integer *, doublecomplex *, integer *, doublecomplex *,
doublecomplex *, integer *, doublecomplex *, integer *, integer *), zunmqr_(char *, char *, integer *, integer *,
integer *, doublecomplex *, integer *, doublecomplex *,
doublecomplex *, integer *, doublecomplex *, integer *, integer *);
/* -- LAPACK driver routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* ZGELSD 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) COMPLEX*16 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*16 array, dimension (LDB,NRHS) */
/* On entry, the M-by-NRHS right hand side matrix B. */
/* On exit, B is overwritten by the N-by-NRHS solution matrix X. */
/* If m >= n and RANK = n, the residual sum-of-squares for */
/* the solution in the i-th column is given by the sum of */
/* squares of the modulus of elements n+1:m in that column. */
/* LDB (input) INTEGER */
/* The leading dimension of the array B. LDB >= max(1,M,N). */
/* S (output) DOUBLE PRECISION 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) DOUBLE PRECISION */
/* 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*16 array, dimension (MAX(1,LWORK)) */
/* On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
/* LWORK (input) INTEGER */
/* The dimension of the array WORK. LWORK must be at least 1. */
/* The exact minimum amount of workspace needed depends on M, */
/* N and NRHS. As long as LWORK is at least */
/* 2*N + N*NRHS */
/* if M is greater than or equal to N or */
/* 2*M + M*NRHS */
/* if M is less than N, the code will execute correctly. */
/* For good performance, LWORK should generally be larger. */
/* If LWORK = -1, then a workspace query is assumed; the routine */
/* only calculates the optimal size of the array WORK and the */
/* minimum sizes of the arrays RWORK and IWORK, and returns */
/* these values as the first entries of the WORK, RWORK and */
/* IWORK arrays, and no error message related to LWORK is issued */
/* by XERBLA. */
/* RWORK (workspace) DOUBLE PRECISION array, dimension (MAX(1,LRWORK)) */
/* LRWORK >= */
/* 10*N + 2*N*SMLSIZ + 8*N*NLVL + 3*SMLSIZ*NRHS + */
/* (SMLSIZ+1)**2 */
/* if M is greater than or equal to N or */
/* 10*M + 2*M*SMLSIZ + 8*M*NLVL + 3*SMLSIZ*NRHS + */
/* (SMLSIZ+1)**2 */
/* if M is less than N, the code will execute correctly. */
/* SMLSIZ is returned by ILAENV and is equal to the maximum */
/* size of the subproblems at the bottom of the computation */
/* tree (usually about 25), and */
/* NLVL = MAX( 0, INT( LOG_2( MIN( M,N )/(SMLSIZ+1) ) ) + 1 ) */
/* On exit, if INFO = 0, RWORK(1) returns the minimum LRWORK. */
/* IWORK (workspace) INTEGER array, dimension (MAX(1,LIWORK)) */
/* LIWORK >= max(1, 3*MINMN*NLVL + 11*MINMN), */
/* where MINMN = MIN( M,N ). */
/* On exit, if INFO = 0, IWORK(1) returns the minimum LIWORK. */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value. */
/* > 0: the algorithm for computing the SVD failed to converge; */
/* if INFO = i, i off-diagonal elements of an intermediate */
/* bidiagonal form did not converge to zero. */
/* Further Details */
/* =============== */
/* Based on contributions by */
/* Ming Gu and Ren-Cang Li, Computer Science Division, University of */
/* California at Berkeley, USA */
/* Osni Marques, LBNL/NERSC, USA */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input arguments. */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
--s;
--work;
--rwork;
--iwork;
/* Function Body */
*info = 0;
minmn = min(*m,*n);
maxmn = max(*m,*n);
lquery = *lwork == -1;
if (*m < 0) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*nrhs < 0) {
*info = -3;
} else if (*lda < max(1,*m)) {
*info = -5;
} else if (*ldb < max(1,maxmn)) {
*info = -7;
}
/* Compute workspace. */
/* (Note: Comments in the code beginning "Workspace:" describe the */
/* minimal amount of workspace needed at that point in the code, */
/* as well as the preferred amount for good performance. */
/* NB refers to the optimal block size for the immediately */
/* following subroutine, as returned by ILAENV.) */
if (*info == 0) {
minwrk = 1;
maxwrk = 1;
liwork = 1;
lrwork = 1;
if (minmn > 0) {
smlsiz = ilaenv_(&c__9, "ZGELSD", " ", &c__0, &c__0, &c__0, &c__0);
mnthr = ilaenv_(&c__6, "ZGELSD", " ", m, n, nrhs, &c_n1);
/* Computing MAX */
i__1 = (integer) (log((doublereal) minmn / (doublereal) (smlsiz +
1)) / log(2.)) + 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, "ZGEQRF", " ", m, n,
&c_n1, &c_n1);
maxwrk = max(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk, i__2 = *nrhs * ilaenv_(&c__1, "ZUNMQR", "LC",
m, nrhs, n, &c_n1);
maxwrk = max(i__1,i__2);
}
if (*m >= *n) {
/* Path 1 - overdetermined or exactly determined. */
/* Computing 2nd power */
i__1 = smlsiz + 1;
lrwork = *n * 10 + (*n << 1) * smlsiz + (*n << 3) * nlvl +
smlsiz * 3 * *nrhs + i__1 * i__1;
/* Computing MAX */
i__1 = maxwrk, i__2 = (*n << 1) + (mm + *n) * ilaenv_(&c__1,
"ZGEBRD", " ", &mm, n, &c_n1, &c_n1);
maxwrk = max(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk, i__2 = (*n << 1) + *nrhs * ilaenv_(&c__1,
"ZUNMBR", "QLC", &mm, nrhs, n, &c_n1);
maxwrk = max(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk, i__2 = (*n << 1) + (*n - 1) * ilaenv_(&c__1,
"ZUNMBR", "PLN", n, nrhs, n, &c_n1);
maxwrk = max(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk, i__2 = (*n << 1) + *n * *nrhs;
maxwrk = max(i__1,i__2);
/* Computing MAX */
i__1 = (*n << 1) + mm, i__2 = (*n << 1) + *n * *nrhs;
minwrk = max(i__1,i__2);
}
if (*n > *m) {
/* Computing 2nd power */
i__1 = smlsiz + 1;
lrwork = *m * 10 + (*m << 1) * smlsiz + (*m << 3) * nlvl +
smlsiz * 3 * *nrhs + i__1 * i__1;
if (*n >= mnthr) {
/* Path 2a - underdetermined, with many more columns */
/* than rows. */
maxwrk = *m + *m * ilaenv_(&c__1, "ZGELQF", " ", m, n, &
c_n1, &c_n1);
/* Computing MAX */
i__1 = maxwrk, i__2 = *m * *m + (*m << 2) + (*m << 1) *
ilaenv_(&c__1, "ZGEBRD", " ", m, m, &c_n1, &c_n1);
maxwrk = max(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk, i__2 = *m * *m + (*m << 2) + *nrhs *
ilaenv_(&c__1, "ZUNMBR", "QLC", m, nrhs, m, &c_n1);
maxwrk = max(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk, i__2 = *m * *m + (*m << 2) + (*m - 1) *
ilaenv_(&c__1, "ZUNMLQ", "LC", n, nrhs, m, &c_n1);
maxwrk = max(i__1,i__2);
if (*nrhs > 1) {
/* Computing MAX */
i__1 = maxwrk, i__2 = *m * *m + *m + *m * *nrhs;
maxwrk = max(i__1,i__2);
} else {
/* Computing MAX */
i__1 = maxwrk, i__2 = *m * *m + (*m << 1);
maxwrk = max(i__1,i__2);
}
/* Computing MAX */
i__1 = maxwrk, i__2 = *m * *m + (*m << 2) + *m * *nrhs;
maxwrk = max(i__1,i__2);
/* 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;
i__1 = maxwrk, i__2 = (*m << 2) + *m * *m + max(i__3,i__4)
;
maxwrk = max(i__1,i__2);
} else {
/* Path 2 - underdetermined. */
maxwrk = (*m << 1) + (*n + *m) * ilaenv_(&c__1, "ZGEBRD",
" ", m, n, &c_n1, &c_n1);
/* Computing MAX */
i__1 = maxwrk, i__2 = (*m << 1) + *nrhs * ilaenv_(&c__1,
"ZUNMBR", "QLC", m, nrhs, m, &c_n1);
maxwrk = max(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk, i__2 = (*m << 1) + *m * ilaenv_(&c__1,
"ZUNMBR", "PLN", n, nrhs, m, &c_n1);
maxwrk = max(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk, i__2 = (*m << 1) + *m * *nrhs;
maxwrk = max(i__1,i__2);
}
/* Computing MAX */
i__1 = (*m << 1) + *n, i__2 = (*m << 1) + *m * *nrhs;
minwrk = max(i__1,i__2);
}
}
minwrk = min(minwrk,maxwrk);
work[1].r = (doublereal) maxwrk, work[1].i = 0.;
iwork[1] = liwork;
rwork[1] = (doublereal) lrwork;
if (*lwork < minwrk && ! lquery) {
*info = -12;
}
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZGELSD", &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 = dlamch_("P");
sfmin = dlamch_("S");
smlnum = sfmin / eps;
bignum = 1. / smlnum;
dlabad_(&smlnum, &bignum);
/* Scale A if max entry outside range [SMLNUM,BIGNUM]. */
anrm = zlange_("M", m, n, &a[a_offset], lda, &rwork[1]);
iascl = 0;
if (anrm > 0. && anrm < smlnum) {
/* Scale matrix norm up to SMLNUM */
zlascl_("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. */
zlascl_("G", &c__0, &c__0, &anrm, &bignum, m, n, &a[a_offset], lda,
info);
iascl = 2;
} else if (anrm == 0.) {
/* Matrix all zero. Return zero solution. */
i__1 = max(*m,*n);
zlaset_("F", &i__1, nrhs, &c_b1, &c_b1, &b[b_offset], ldb);
dlaset_("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 = zlange_("M", m, nrhs, &b[b_offset], ldb, &rwork[1]);
ibscl = 0;
if (bnrm > 0. && bnrm < smlnum) {
/* Scale matrix norm up to SMLNUM. */
zlascl_("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. */
zlascl_("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;
zlaset_("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;
zgeqrf_(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;
zunmqr_("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;
zlaset_("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;
zgebrd_(&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;
zunmbr_("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. */
zlalsd_("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;
zunmbr_("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;
zgelqf_(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. */
zlacpy_("L", m, m, &a[a_offset], lda, &work[il], &ldwork);
i__1 = *m - 1;
i__2 = *m - 1;
zlaset_("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;
zgebrd_(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;
zunmbr_("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. */
zlalsd_("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;
zunmbr_("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;
zlaset_("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;
zunmlq_("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;
zgebrd_(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;
zunmbr_("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. */
zlalsd_("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;
zunmbr_("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) {
zlascl_("G", &c__0, &c__0, &anrm, &smlnum, n, nrhs, &b[b_offset], ldb,
info);
dlascl_("G", &c__0, &c__0, &smlnum, &anrm, &minmn, &c__1, &s[1], &
minmn, info);
} else if (iascl == 2) {
zlascl_("G", &c__0, &c__0, &anrm, &bignum, n, nrhs, &b[b_offset], ldb,
info);
dlascl_("G", &c__0, &c__0, &bignum, &anrm, &minmn, &c__1, &s[1], &
minmn, info);
}
if (ibscl == 1) {
zlascl_("G", &c__0, &c__0, &smlnum, &bnrm, n, nrhs, &b[b_offset], ldb,
info);
} else if (ibscl == 2) {
zlascl_("G", &c__0, &c__0, &bignum, &bnrm, n, nrhs, &b[b_offset], ldb,
info);
}
L10:
work[1].r = (doublereal) maxwrk, work[1].i = 0.;
iwork[1] = liwork;
rwork[1] = (doublereal) lrwork;
return 0;
/* End of ZGELSD */
} /* zgelsd_ */
