/* zgelsy.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 doublecomplex c_b2 = {1.,0.};
static integer c__1 = 1;
static integer c_n1 = -1;
static integer c__0 = 0;
static integer c__2 = 2;
/* Subroutine */ int zgelsy_(integer *m, integer *n, integer *nrhs,
doublecomplex *a, integer *lda, doublecomplex *b, integer *ldb,
integer *jpvt, doublereal *rcond, integer *rank, doublecomplex *work,
integer *lwork, doublereal *rwork, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3, i__4;
doublereal d__1, d__2;
doublecomplex z__1;
/* Builtin functions */
double z_abs(doublecomplex *);
/* Local variables */
integer i__, j;
doublecomplex c1, c2, s1, s2;
integer nb, mn, nb1, nb2, nb3, nb4;
doublereal anrm, bnrm, smin, smax;
integer iascl, ibscl, ismin, ismax;
doublereal wsize;
extern /* Subroutine */ int zcopy_(integer *, doublecomplex *, integer *,
doublecomplex *, integer *), ztrsm_(char *, char *, char *, char *
, integer *, integer *, doublecomplex *, doublecomplex *, integer
*, doublecomplex *, integer *),
zlaic1_(integer *, integer *, doublecomplex *, doublereal *,
doublecomplex *, doublecomplex *, doublereal *, doublecomplex *,
doublecomplex *), dlabad_(doublereal *, doublereal *), zgeqp3_(
integer *, integer *, doublecomplex *, integer *, integer *,
doublecomplex *, doublecomplex *, integer *, doublereal *,
integer *);
extern doublereal dlamch_(char *);
extern /* Subroutine */ int xerbla_(char *, 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 zlascl_(char *, integer *, integer *,
doublereal *, doublereal *, integer *, integer *, doublecomplex *,
integer *, integer *), zlaset_(char *, integer *,
integer *, doublecomplex *, doublecomplex *, doublecomplex *,
integer *);
doublereal sminpr, smaxpr, smlnum;
integer lwkopt;
logical lquery;
extern /* Subroutine */ int zunmqr_(char *, char *, integer *, integer *,
integer *, doublecomplex *, integer *, doublecomplex *,
doublecomplex *, integer *, doublecomplex *, integer *, integer *), zunmrz_(char *, char *, integer *, integer *,
integer *, integer *, doublecomplex *, integer *, doublecomplex *,
doublecomplex *, integer *, doublecomplex *, integer *, integer *
), ztzrzf_(integer *, integer *, doublecomplex *,
integer *, doublecomplex *, 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 */
/* ======= */
/* ZGELSY computes the minimum-norm solution to a complex linear least */
/* squares problem: */
/* minimize || A * X - B || */
/* using a complete orthogonal factorization 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 routine first computes a QR factorization with column pivoting: */
/* A * P = Q * [ R11 R12 ] */
/* [ 0 R22 ] */
/* with R11 defined as the largest leading submatrix whose estimated */
/* condition number is less than 1/RCOND. The order of R11, RANK, */
/* is the effective rank of A. */
/* Then, R22 is considered to be negligible, and R12 is annihilated */
/* by unitary transformations from the right, arriving at the */
/* complete orthogonal factorization: */
/* A * P = Q * [ T11 0 ] * Z */
/* [ 0 0 ] */
/* The minimum-norm solution is then */
/* X = P * Z' [ inv(T11)*Q1'*B ] */
/* [ 0 ] */
/* where Q1 consists of the first RANK columns of Q. */
/* This routine is basically identical to the original xGELSX except */
/* three differences: */
/* o The permutation of matrix B (the right hand side) is faster and */
/* more simple. */
/* o The call to the subroutine xGEQPF has been substituted by the */
/* the call to the subroutine xGEQP3. This subroutine is a Blas-3 */
/* version of the QR factorization with column pivoting. */
/* o Matrix B (the right hand side) is updated with Blas-3. */
/* 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 matrices B and X. NRHS >= 0. */
/* A (input/output) COMPLEX*16 array, dimension (LDA,N) */
/* On entry, the M-by-N matrix A. */
/* On exit, A has been overwritten by details of its */
/* complete orthogonal factorization. */
/* 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, the N-by-NRHS solution matrix X. */
/* LDB (input) INTEGER */
/* The leading dimension of the array B. LDB >= max(1,M,N). */
/* JPVT (input/output) INTEGER array, dimension (N) */
/* On entry, if JPVT(i) .ne. 0, the i-th column of A is permuted */
/* to the front of AP, otherwise column i is a free column. */
/* On exit, if JPVT(i) = k, then the i-th column of A*P */
/* was the k-th column of A. */
/* RCOND (input) DOUBLE PRECISION */
/* RCOND is used to determine the effective rank of A, which */
/* is defined as the order of the largest leading triangular */
/* submatrix R11 in the QR factorization with pivoting of A, */
/* whose estimated condition number < 1/RCOND. */
/* RANK (output) INTEGER */
/* The effective rank of A, i.e., the order of the submatrix */
/* R11. This is the same as the order of the submatrix T11 */
/* in the complete orthogonal factorization of A. */
/* 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. */
/* The unblocked strategy requires that: */
/* LWORK >= MN + MAX( 2*MN, N+1, MN+NRHS ) */
/* where MN = min(M,N). */
/* The block algorithm requires that: */
/* LWORK >= MN + MAX( 2*MN, NB*(N+1), MN+MN*NB, MN+NB*NRHS ) */
/* where NB is an upper bound on the blocksize returned */
/* by ILAENV for the routines ZGEQP3, ZTZRZF, CTZRQF, ZUNMQR, */
/* and ZUNMRZ. */
/* 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) DOUBLE PRECISION array, dimension (2*N) */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value */
/* Further Details */
/* =============== */
/* Based on contributions by */
/* A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA */
/* E. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain */
/* G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
--jpvt;
--work;
--rwork;
/* Function Body */
mn = min(*m,*n);
ismin = mn + 1;
ismax = (mn << 1) + 1;
/* Test the input arguments. */
*info = 0;
nb1 = ilaenv_(&c__1, "ZGEQRF", " ", m, n, &c_n1, &c_n1);
nb2 = ilaenv_(&c__1, "ZGERQF", " ", m, n, &c_n1, &c_n1);
nb3 = ilaenv_(&c__1, "ZUNMQR", " ", m, n, nrhs, &c_n1);
nb4 = ilaenv_(&c__1, "ZUNMRQ", " ", m, n, nrhs, &c_n1);
/* Computing MAX */
i__1 = max(nb1,nb2), i__1 = max(i__1,nb3);
nb = max(i__1,nb4);
/* Computing MAX */
i__1 = 1, i__2 = mn + (*n << 1) + nb * (*n + 1), i__1 = max(i__1,i__2),
i__2 = (mn << 1) + nb * *nrhs;
lwkopt = max(i__1,i__2);
z__1.r = (doublereal) lwkopt, z__1.i = 0.;
work[1].r = z__1.r, work[1].i = z__1.i;
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(complicated condition) */ {
/* Computing MAX */
i__1 = max(1,*m);
if (*ldb < max(i__1,*n)) {
*info = -7;
} else /* if(complicated condition) */ {
/* Computing MAX */
i__1 = mn << 1, i__2 = *n + 1, i__1 = max(i__1,i__2), i__2 = mn +
*nrhs;
if (*lwork < mn + max(i__1,i__2) && ! lquery) {
*info = -12;
}
}
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZGELSY", &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) {
*rank = 0;
return 0;
}
/* Get machine parameters */
smlnum = dlamch_("S") / dlamch_("P");
bignum = 1. / smlnum;
dlabad_(&smlnum, &bignum);
/* Scale A, B if max entries 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);
*rank = 0;
goto L70;
}
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;
}
/* Compute QR factorization with column pivoting of A: */
/* A * P = Q * R */
i__1 = *lwork - mn;
zgeqp3_(m, n, &a[a_offset], lda, &jpvt[1], &work[1], &work[mn + 1], &i__1,
&rwork[1], info);
i__1 = mn + 1;
wsize = mn + work[i__1].r;
/* complex workspace: MN+NB*(N+1). real workspace 2*N. */
/* Details of Householder rotations stored in WORK(1:MN). */
/* Determine RANK using incremental condition estimation */
i__1 = ismin;
work[i__1].r = 1., work[i__1].i = 0.;
i__1 = ismax;
work[i__1].r = 1., work[i__1].i = 0.;
smax = z_abs(&a[a_dim1 + 1]);
smin = smax;
if (z_abs(&a[a_dim1 + 1]) == 0.) {
*rank = 0;
i__1 = max(*m,*n);
zlaset_("F", &i__1, nrhs, &c_b1, &c_b1, &b[b_offset], ldb);
goto L70;
} else {
*rank = 1;
}
L10:
if (*rank < mn) {
i__ = *rank + 1;
zlaic1_(&c__2, rank, &work[ismin], &smin, &a[i__ * a_dim1 + 1], &a[
i__ + i__ * a_dim1], &sminpr, &s1, &c1);
zlaic1_(&c__1, rank, &work[ismax], &smax, &a[i__ * a_dim1 + 1], &a[
i__ + i__ * a_dim1], &smaxpr, &s2, &c2);
if (smaxpr * *rcond <= sminpr) {
i__1 = *rank;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = ismin + i__ - 1;
i__3 = ismin + i__ - 1;
z__1.r = s1.r * work[i__3].r - s1.i * work[i__3].i, z__1.i =
s1.r * work[i__3].i + s1.i * work[i__3].r;
work[i__2].r = z__1.r, work[i__2].i = z__1.i;
i__2 = ismax + i__ - 1;
i__3 = ismax + i__ - 1;
z__1.r = s2.r * work[i__3].r - s2.i * work[i__3].i, z__1.i =
s2.r * work[i__3].i + s2.i * work[i__3].r;
work[i__2].r = z__1.r, work[i__2].i = z__1.i;
/* L20: */
}
i__1 = ismin + *rank;
work[i__1].r = c1.r, work[i__1].i = c1.i;
i__1 = ismax + *rank;
work[i__1].r = c2.r, work[i__1].i = c2.i;
smin = sminpr;
smax = smaxpr;
++(*rank);
goto L10;
}
}
/* complex workspace: 3*MN. */
/* Logically partition R = [ R11 R12 ] */
/* [ 0 R22 ] */
/* where R11 = R(1:RANK,1:RANK) */
/* [R11,R12] = [ T11, 0 ] * Y */
if (*rank < *n) {
i__1 = *lwork - (mn << 1);
ztzrzf_(rank, n, &a[a_offset], lda, &work[mn + 1], &work[(mn << 1) +
1], &i__1, info);
}
/* complex workspace: 2*MN. */
/* Details of Householder rotations stored in WORK(MN+1:2*MN) */
/* B(1:M,1:NRHS) := Q' * B(1:M,1:NRHS) */
i__1 = *lwork - (mn << 1);
zunmqr_("Left", "Conjugate transpose", m, nrhs, &mn, &a[a_offset], lda, &
work[1], &b[b_offset], ldb, &work[(mn << 1) + 1], &i__1, info);
/* Computing MAX */
i__1 = (mn << 1) + 1;
d__1 = wsize, d__2 = (mn << 1) + work[i__1].r;
wsize = max(d__1,d__2);
/* complex workspace: 2*MN+NB*NRHS. */
/* B(1:RANK,1:NRHS) := inv(T11) * B(1:RANK,1:NRHS) */
ztrsm_("Left", "Upper", "No transpose", "Non-unit", rank, nrhs, &c_b2, &a[
a_offset], lda, &b[b_offset], ldb);
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
i__2 = *n;
for (i__ = *rank + 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * b_dim1;
b[i__3].r = 0., b[i__3].i = 0.;
/* L30: */
}
/* L40: */
}
/* B(1:N,1:NRHS) := Y' * B(1:N,1:NRHS) */
if (*rank < *n) {
i__1 = *n - *rank;
i__2 = *lwork - (mn << 1);
zunmrz_("Left", "Conjugate transpose", n, nrhs, rank, &i__1, &a[
a_offset], lda, &work[mn + 1], &b[b_offset], ldb, &work[(mn <<
1) + 1], &i__2, info);
}
/* complex workspace: 2*MN+NRHS. */
/* B(1:N,1:NRHS) := P * B(1:N,1:NRHS) */
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = jpvt[i__];
i__4 = i__ + j * b_dim1;
work[i__3].r = b[i__4].r, work[i__3].i = b[i__4].i;
/* L50: */
}
zcopy_(n, &work[1], &c__1, &b[j * b_dim1 + 1], &c__1);
/* L60: */
}
/* complex workspace: N. */
/* Undo scaling */
if (iascl == 1) {
zlascl_("G", &c__0, &c__0, &anrm, &smlnum, n, nrhs, &b[b_offset], ldb,
info);
zlascl_("U", &c__0, &c__0, &smlnum, &anrm, rank, rank, &a[a_offset],
lda, info);
} else if (iascl == 2) {
zlascl_("G", &c__0, &c__0, &anrm, &bignum, n, nrhs, &b[b_offset], ldb,
info);
zlascl_("U", &c__0, &c__0, &bignum, &anrm, rank, rank, &a[a_offset],
lda, 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);
}
L70:
z__1.r = (doublereal) lwkopt, z__1.i = 0.;
work[1].r = z__1.r, work[1].i = z__1.i;
return 0;
/* End of ZGELSY */
} /* zgelsy_ */
