/* Subroutine */ int zgelqf_(integer *m, integer *n, doublecomplex *a,
integer *lda, doublecomplex *tau, doublecomplex *work, integer *lwork,
integer *info)
{
/* -- LAPACK routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
June 30, 1999
Purpose
=======
ZGELQF computes an LQ factorization of a complex M-by-N matrix A:
A = L * Q.
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/output) COMPLEX*16 array, dimension (LDA,N)
On entry, the M-by-N matrix A.
On exit, the elements on and below the diagonal of the array
contain the m-by-min(m,n) lower trapezoidal matrix L (L is
lower triangular if m <= n); the elements above the diagonal,
with the array TAU, represent the unitary matrix Q as a
product of elementary reflectors (see Further Details).
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,M).
TAU (output) COMPLEX*16 array, dimension (min(M,N))
The scalar factors of the elementary reflectors (see Further
Details).
WORK (workspace/output) COMPLEX*16 array, dimension (LWORK)
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input) INTEGER
The dimension of the array WORK. LWORK >= max(1,M).
For optimum performance LWORK >= M*NB, where NB is the
optimal blocksize.
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
Further Details
===============
The matrix Q is represented as a product of elementary reflectors
Q = H(k)' . . . H(2)' H(1)', where k = min(m,n).
Each H(i) has the form
H(i) = I - tau * v * v'
where tau is a complex scalar, and v is a complex vector with
v(1:i-1) = 0 and v(i) = 1; conjg(v(i+1:n)) is stored on exit in
A(i,i+1:n), and tau in TAU(i).
=====================================================================
Test the input arguments
Parameter adjustments */
/* Table of constant values */
static integer c__1 = 1;
static integer c_n1 = -1;
static integer c__3 = 3;
static integer c__2 = 2;
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3, i__4;
/* Local variables */
static integer i__, k, nbmin, iinfo;
extern /* Subroutine */ int zgelq2_(integer *, integer *, doublecomplex *,
integer *, doublecomplex *, doublecomplex *, integer *);
static integer ib, nb, nx;
extern /* Subroutine */ int xerbla_(char *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *, ftnlen, ftnlen);
extern /* Subroutine */ int zlarfb_(char *, char *, char *, char *,
integer *, integer *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *);
static integer ldwork;
extern /* Subroutine */ int zlarft_(char *, char *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, doublecomplex *,
integer *);
static integer lwkopt;
static logical lquery;
static integer iws;
#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)]
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
--tau;
--work;
/* Function Body */
*info = 0;
nb = ilaenv_(&c__1, "ZGELQF", " ", m, n, &c_n1, &c_n1, (ftnlen)6, (ftnlen)
1);
lwkopt = *m * nb;
work[1].r = (doublereal) lwkopt, work[1].i = 0.;
lquery = *lwork == -1;
if (*m < 0) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*lda < max(1,*m)) {
*info = -4;
} else if (*lwork < max(1,*m) && ! lquery) {
*info = -7;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZGELQF", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible */
k = min(*m,*n);
if (k == 0) {
work[1].r = 1., work[1].i = 0.;
return 0;
}
nbmin = 2;
nx = 0;
iws = *m;
if (nb > 1 && nb < k) {
/* Determine when to cross over from blocked to unblocked code.
Computing MAX */
i__1 = 0, i__2 = ilaenv_(&c__3, "ZGELQF", " ", m, n, &c_n1, &c_n1, (
ftnlen)6, (ftnlen)1);
nx = max(i__1,i__2);
if (nx < k) {
/* Determine if workspace is large enough for blocked code. */
ldwork = *m;
iws = ldwork * nb;
if (*lwork < iws) {
/* Not enough workspace to use optimal NB: reduce NB and
determine the minimum value of NB. */
nb = *lwork / ldwork;
/* Computing MAX */
i__1 = 2, i__2 = ilaenv_(&c__2, "ZGELQF", " ", m, n, &c_n1, &
c_n1, (ftnlen)6, (ftnlen)1);
nbmin = max(i__1,i__2);
}
}
}
if (nb >= nbmin && nb < k && nx < k) {
/* Use blocked code initially */
i__1 = k - nx;
i__2 = nb;
for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) {
/* Computing MIN */
i__3 = k - i__ + 1;
ib = min(i__3,nb);
/* Compute the LQ factorization of the current block
A(i:i+ib-1,i:n) */
i__3 = *n - i__ + 1;
zgelq2_(&ib, &i__3, &a_ref(i__, i__), lda, &tau[i__], &work[1], &
iinfo);
if (i__ + ib <= *m) {
/* Form the triangular factor of the block reflector
H = H(i) H(i+1) . . . H(i+ib-1) */
i__3 = *n - i__ + 1;
zlarft_("Forward", "Rowwise", &i__3, &ib, &a_ref(i__, i__),
lda, &tau[i__], &work[1], &ldwork);
/* Apply H to A(i+ib:m,i:n) from the right */
i__3 = *m - i__ - ib + 1;
i__4 = *n - i__ + 1;
zlarfb_("Right", "No transpose", "Forward", "Rowwise", &i__3,
&i__4, &ib, &a_ref(i__, i__), lda, &work[1], &ldwork,
&a_ref(i__ + ib, i__), lda, &work[ib + 1], &ldwork);
}
/* L10: */
}
} else {
i__ = 1;
}
/* Use unblocked code to factor the last or only block. */
if (i__ <= k) {
i__2 = *m - i__ + 1;
i__1 = *n - i__ + 1;
zgelq2_(&i__2, &i__1, &a_ref(i__, i__), lda, &tau[i__], &work[1], &
iinfo);
}
work[1].r = (doublereal) iws, work[1].i = 0.;
return 0;
/* End of ZGELQF */
} /* zgelqf_ */
doublereal zqrt14_(char *trans, integer *m, integer *n, integer *nrhs,
doublecomplex *a, integer *lda, doublecomplex *x, integer *ldx,
doublecomplex *work, integer *lwork)
{
/* System generated locals */
integer a_dim1, a_offset, x_dim1, x_offset, i__1, i__2, i__3;
doublereal ret_val, d__1, d__2;
doublecomplex z__1;
/* Builtin functions */
double z_abs(doublecomplex *);
void d_cnjg(doublecomplex *, doublecomplex *);
/* Local variables */
static integer info;
static doublereal anrm;
static logical tpsd;
static doublereal xnrm;
static integer i__, j;
extern logical lsame_(char *, char *);
static doublereal rwork[1];
extern /* Subroutine */ int zgelq2_(integer *, integer *, doublecomplex *,
integer *, doublecomplex *, doublecomplex *, integer *), zgeqr2_(
integer *, integer *, doublecomplex *, integer *, doublecomplex *,
doublecomplex *, integer *);
extern doublereal dlamch_(char *);
extern /* Subroutine */ int xerbla_(char *, integer *);
extern doublereal zlange_(char *, integer *, integer *, doublecomplex *,
integer *, doublereal *);
extern /* Subroutine */ int zlascl_(char *, integer *, integer *,
doublereal *, doublereal *, integer *, integer *, doublecomplex *,
integer *, integer *);
static integer ldwork;
extern /* Subroutine */ int zlacpy_(char *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *);
static doublereal err;
#define x_subscr(a_1,a_2) (a_2)*x_dim1 + a_1
#define x_ref(a_1,a_2) x[x_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
February 29, 1992
Purpose
=======
ZQRT14 checks whether X is in the row space of A or A'. It does so
by scaling both X and A such that their norms are in the range
[sqrt(eps), 1/sqrt(eps)], then computing a QR factorization of [A,X]
(if TRANS = 'C') or an LQ factorization of [A',X]' (if TRANS = 'N'),
and returning the norm of the trailing triangle, scaled by
MAX(M,N,NRHS)*eps.
Arguments
=========
TRANS (input) CHARACTER*1
= 'N': No transpose, check for X in the row space of A
= 'C': Conjugate transpose, check for X in row space of A'.
M (input) INTEGER
The number of rows of the matrix A.
N (input) INTEGER
The number of columns of the matrix A.
NRHS (input) INTEGER
The number of right hand sides, i.e., the number of columns
of X.
A (input) COMPLEX*16 array, dimension (LDA,N)
The M-by-N matrix A.
LDA (input) INTEGER
The leading dimension of the array A.
X (input) COMPLEX*16 array, dimension (LDX,NRHS)
If TRANS = 'N', the N-by-NRHS matrix X.
IF TRANS = 'C', the M-by-NRHS matrix X.
LDX (input) INTEGER
The leading dimension of the array X.
WORK (workspace) COMPLEX*16 array dimension (LWORK)
LWORK (input) INTEGER
length of workspace array required
If TRANS = 'N', LWORK >= (M+NRHS)*(N+2);
if TRANS = 'C', LWORK >= (N+NRHS)*(M+2).
=====================================================================
Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
x_dim1 = *ldx;
x_offset = 1 + x_dim1 * 1;
x -= x_offset;
--work;
/* Function Body */
ret_val = 0.;
if (lsame_(trans, "N")) {
ldwork = *m + *nrhs;
tpsd = FALSE_;
if (*lwork < (*m + *nrhs) * (*n + 2)) {
xerbla_("ZQRT14", &c__10);
return ret_val;
} else if (*n <= 0 || *nrhs <= 0) {
return ret_val;
}
} else if (lsame_(trans, "C")) {
ldwork = *m;
tpsd = TRUE_;
if (*lwork < (*n + *nrhs) * (*m + 2)) {
xerbla_("ZQRT14", &c__10);
return ret_val;
} else if (*m <= 0 || *nrhs <= 0) {
return ret_val;
}
} else {
xerbla_("ZQRT14", &c__1);
return ret_val;
}
/* Copy and scale A */
zlacpy_("All", m, n, &a[a_offset], lda, &work[1], &ldwork);
anrm = zlange_("M", m, n, &work[1], &ldwork, rwork);
if (anrm != 0.) {
zlascl_("G", &c__0, &c__0, &anrm, &c_b15, m, n, &work[1], &ldwork, &
info);
}
/* Copy X or X' into the right place and scale it */
if (tpsd) {
/* Copy X into columns n+1:n+nrhs of work */
zlacpy_("All", m, nrhs, &x[x_offset], ldx, &work[*n * ldwork + 1], &
ldwork);
xnrm = zlange_("M", m, nrhs, &work[*n * ldwork + 1], &ldwork, rwork);
if (xnrm != 0.) {
zlascl_("G", &c__0, &c__0, &xnrm, &c_b15, m, nrhs, &work[*n *
ldwork + 1], &ldwork, &info);
}
i__1 = *n + *nrhs;
anrm = zlange_("One-norm", m, &i__1, &work[1], &ldwork, rwork);
/* Compute QR factorization of X */
i__1 = *n + *nrhs;
/* Computing MIN */
i__2 = *m, i__3 = *n + *nrhs;
zgeqr2_(m, &i__1, &work[1], &ldwork, &work[ldwork * (*n + *nrhs) + 1],
&work[ldwork * (*n + *nrhs) + min(i__2,i__3) + 1], &info);
/* Compute largest entry in upper triangle of
work(n+1:m,n+1:n+nrhs) */
err = 0.;
i__1 = *n + *nrhs;
for (j = *n + 1; j <= i__1; ++j) {
i__2 = min(*m,j);
for (i__ = *n + 1; i__ <= i__2; ++i__) {
/* Computing MAX */
d__1 = err, d__2 = z_abs(&work[i__ + (j - 1) * *m]);
err = max(d__1,d__2);
/* L10: */
}
/* L20: */
}
} else {
/* Copy X' into rows m+1:m+nrhs of work */
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = *nrhs;
for (j = 1; j <= i__2; ++j) {
i__3 = *m + j + (i__ - 1) * ldwork;
d_cnjg(&z__1, &x_ref(i__, j));
work[i__3].r = z__1.r, work[i__3].i = z__1.i;
/* L30: */
}
/* L40: */
}
xnrm = zlange_("M", nrhs, n, &work[*m + 1], &ldwork, rwork)
;
if (xnrm != 0.) {
zlascl_("G", &c__0, &c__0, &xnrm, &c_b15, nrhs, n, &work[*m + 1],
&ldwork, &info);
}
/* Compute LQ factorization of work */
zgelq2_(&ldwork, n, &work[1], &ldwork, &work[ldwork * *n + 1], &work[
ldwork * (*n + 1) + 1], &info);
/* Compute largest entry in lower triangle in
work(m+1:m+nrhs,m+1:n) */
err = 0.;
i__1 = *n;
for (j = *m + 1; j <= i__1; ++j) {
i__2 = ldwork;
for (i__ = j; i__ <= i__2; ++i__) {
/* Computing MAX */
d__1 = err, d__2 = z_abs(&work[i__ + (j - 1) * ldwork]);
err = max(d__1,d__2);
/* L50: */
}
/* L60: */
}
}
/* Computing MAX */
i__1 = max(*m,*n);
ret_val = err / ((doublereal) max(i__1,*nrhs) * dlamch_("Epsilon"));
return ret_val;
/* End of ZQRT14 */
} /* zqrt14_ */
/* Subroutine */ int zerrlq_(char *path, integer *nunit)
{
/* System generated locals */
integer i__1;
doublereal d__1, d__2;
doublecomplex z__1;
/* Builtin functions */
integer s_wsle(cilist *), e_wsle(void);
/* Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen);
/* Local variables */
doublecomplex a[4] /* was [2][2] */, b[2];
integer i__, j;
doublecomplex w[2], x[2], af[4] /* was [2][2] */;
integer info;
extern /* Subroutine */ int zgelq2_(integer *, integer *, doublecomplex *,
integer *, doublecomplex *, doublecomplex *, integer *), zungl2_(
integer *, integer *, integer *, doublecomplex *, integer *,
doublecomplex *, doublecomplex *, integer *), zunml2_(char *,
char *, integer *, integer *, integer *, doublecomplex *, integer
*, doublecomplex *, doublecomplex *, integer *, doublecomplex *,
integer *), alaesm_(char *, logical *, integer *), chkxer_(char *, integer *, integer *, logical *, logical
*), zgelqf_(integer *, integer *, doublecomplex *,
integer *, doublecomplex *, doublecomplex *, integer *, integer *)
, zgelqs_(integer *, integer *, integer *, doublecomplex *,
integer *, doublecomplex *, doublecomplex *, integer *,
doublecomplex *, integer *, integer *), zunglq_(integer *,
integer *, integer *, doublecomplex *, integer *, doublecomplex *,
doublecomplex *, integer *, integer *), zunmlq_(char *, char *,
integer *, integer *, integer *, doublecomplex *, integer *,
doublecomplex *, doublecomplex *, integer *, doublecomplex *,
integer *, integer *);
/* Fortran I/O blocks */
static cilist io___1 = { 0, 0, 0, 0, 0 };
/* -- LAPACK test routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* ZERRLQ tests the error exits for the COMPLEX*16 routines */
/* that use the LQ decomposition of a general matrix. */
/* Arguments */
/* ========= */
/* PATH (input) CHARACTER*3 */
/* The LAPACK path name for the routines to be tested. */
/* NUNIT (input) INTEGER */
/* The unit number for output. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Scalars in Common .. */
/* .. */
/* .. Common blocks .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
infoc_1.nout = *nunit;
io___1.ciunit = infoc_1.nout;
s_wsle(&io___1);
e_wsle();
/* Set the variables to innocuous values. */
for (j = 1; j <= 2; ++j) {
for (i__ = 1; i__ <= 2; ++i__) {
i__1 = i__ + (j << 1) - 3;
d__1 = 1. / (doublereal) (i__ + j);
d__2 = -1. / (doublereal) (i__ + j);
z__1.r = d__1, z__1.i = d__2;
a[i__1].r = z__1.r, a[i__1].i = z__1.i;
i__1 = i__ + (j << 1) - 3;
d__1 = 1. / (doublereal) (i__ + j);
d__2 = -1. / (doublereal) (i__ + j);
z__1.r = d__1, z__1.i = d__2;
af[i__1].r = z__1.r, af[i__1].i = z__1.i;
/* L10: */
}
i__1 = j - 1;
b[i__1].r = 0., b[i__1].i = 0.;
i__1 = j - 1;
w[i__1].r = 0., w[i__1].i = 0.;
i__1 = j - 1;
x[i__1].r = 0., x[i__1].i = 0.;
/* L20: */
}
infoc_1.ok = TRUE_;
/* Error exits for LQ factorization */
/* ZGELQF */
s_copy(srnamc_1.srnamt, "ZGELQF", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
zgelqf_(&c_n1, &c__0, a, &c__1, b, w, &c__1, &info);
chkxer_("ZGELQF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
zgelqf_(&c__0, &c_n1, a, &c__1, b, w, &c__1, &info);
chkxer_("ZGELQF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
zgelqf_(&c__2, &c__1, a, &c__1, b, w, &c__2, &info);
chkxer_("ZGELQF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
zgelqf_(&c__2, &c__1, a, &c__2, b, w, &c__1, &info);
chkxer_("ZGELQF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* ZGELQ2 */
s_copy(srnamc_1.srnamt, "ZGELQ2", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
zgelq2_(&c_n1, &c__0, a, &c__1, b, w, &info);
chkxer_("ZGELQ2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
zgelq2_(&c__0, &c_n1, a, &c__1, b, w, &info);
chkxer_("ZGELQ2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
zgelq2_(&c__2, &c__1, a, &c__1, b, w, &info);
chkxer_("ZGELQ2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* ZGELQS */
s_copy(srnamc_1.srnamt, "ZGELQS", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
zgelqs_(&c_n1, &c__0, &c__0, a, &c__1, x, b, &c__1, w, &c__1, &info);
chkxer_("ZGELQS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
zgelqs_(&c__0, &c_n1, &c__0, a, &c__1, x, b, &c__1, w, &c__1, &info);
chkxer_("ZGELQS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
zgelqs_(&c__2, &c__1, &c__0, a, &c__2, x, b, &c__1, w, &c__1, &info);
chkxer_("ZGELQS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
zgelqs_(&c__0, &c__0, &c_n1, a, &c__1, x, b, &c__1, w, &c__1, &info);
chkxer_("ZGELQS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
zgelqs_(&c__2, &c__2, &c__0, a, &c__1, x, b, &c__2, w, &c__1, &info);
chkxer_("ZGELQS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 8;
zgelqs_(&c__1, &c__2, &c__0, a, &c__1, x, b, &c__1, w, &c__1, &info);
chkxer_("ZGELQS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 10;
zgelqs_(&c__1, &c__1, &c__2, a, &c__1, x, b, &c__1, w, &c__1, &info);
chkxer_("ZGELQS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* ZUNGLQ */
s_copy(srnamc_1.srnamt, "ZUNGLQ", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
zunglq_(&c_n1, &c__0, &c__0, a, &c__1, x, w, &c__1, &info);
chkxer_("ZUNGLQ", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
zunglq_(&c__0, &c_n1, &c__0, a, &c__1, x, w, &c__1, &info);
chkxer_("ZUNGLQ", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
zunglq_(&c__2, &c__1, &c__0, a, &c__2, x, w, &c__2, &info);
chkxer_("ZUNGLQ", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
zunglq_(&c__0, &c__0, &c_n1, a, &c__1, x, w, &c__1, &info);
chkxer_("ZUNGLQ", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
zunglq_(&c__1, &c__1, &c__2, a, &c__1, x, w, &c__1, &info);
chkxer_("ZUNGLQ", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
zunglq_(&c__2, &c__2, &c__0, a, &c__1, x, w, &c__2, &info);
chkxer_("ZUNGLQ", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 8;
zunglq_(&c__2, &c__2, &c__0, a, &c__2, x, w, &c__1, &info);
chkxer_("ZUNGLQ", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* ZUNGL2 */
s_copy(srnamc_1.srnamt, "ZUNGL2", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
zungl2_(&c_n1, &c__0, &c__0, a, &c__1, x, w, &info);
chkxer_("ZUNGL2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
zungl2_(&c__0, &c_n1, &c__0, a, &c__1, x, w, &info);
chkxer_("ZUNGL2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
zungl2_(&c__2, &c__1, &c__0, a, &c__2, x, w, &info);
chkxer_("ZUNGL2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
zungl2_(&c__0, &c__0, &c_n1, a, &c__1, x, w, &info);
chkxer_("ZUNGL2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
zungl2_(&c__1, &c__1, &c__2, a, &c__1, x, w, &info);
chkxer_("ZUNGL2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
zungl2_(&c__2, &c__2, &c__0, a, &c__1, x, w, &info);
chkxer_("ZUNGL2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* ZUNMLQ */
s_copy(srnamc_1.srnamt, "ZUNMLQ", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
zunmlq_("/", "N", &c__0, &c__0, &c__0, a, &c__1, x, af, &c__1, w, &c__1, &
info);
chkxer_("ZUNMLQ", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
zunmlq_("L", "/", &c__0, &c__0, &c__0, a, &c__1, x, af, &c__1, w, &c__1, &
info);
chkxer_("ZUNMLQ", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
zunmlq_("L", "N", &c_n1, &c__0, &c__0, a, &c__1, x, af, &c__1, w, &c__1, &
info);
chkxer_("ZUNMLQ", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
zunmlq_("L", "N", &c__0, &c_n1, &c__0, a, &c__1, x, af, &c__1, w, &c__1, &
info);
chkxer_("ZUNMLQ", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
zunmlq_("L", "N", &c__0, &c__0, &c_n1, a, &c__1, x, af, &c__1, w, &c__1, &
info);
chkxer_("ZUNMLQ", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
zunmlq_("L", "N", &c__0, &c__1, &c__1, a, &c__1, x, af, &c__1, w, &c__1, &
info);
chkxer_("ZUNMLQ", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
zunmlq_("R", "N", &c__1, &c__0, &c__1, a, &c__1, x, af, &c__1, w, &c__1, &
info);
chkxer_("ZUNMLQ", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
zunmlq_("L", "N", &c__2, &c__0, &c__2, a, &c__1, x, af, &c__2, w, &c__1, &
info);
chkxer_("ZUNMLQ", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
zunmlq_("R", "N", &c__0, &c__2, &c__2, a, &c__1, x, af, &c__1, w, &c__1, &
info);
chkxer_("ZUNMLQ", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 10;
zunmlq_("L", "N", &c__2, &c__1, &c__0, a, &c__2, x, af, &c__1, w, &c__1, &
info);
chkxer_("ZUNMLQ", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 12;
zunmlq_("L", "N", &c__1, &c__2, &c__0, a, &c__1, x, af, &c__1, w, &c__1, &
info);
chkxer_("ZUNMLQ", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 12;
zunmlq_("R", "N", &c__2, &c__1, &c__0, a, &c__1, x, af, &c__2, w, &c__1, &
info);
chkxer_("ZUNMLQ", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* ZUNML2 */
s_copy(srnamc_1.srnamt, "ZUNML2", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
zunml2_("/", "N", &c__0, &c__0, &c__0, a, &c__1, x, af, &c__1, w, &info);
chkxer_("ZUNML2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
zunml2_("L", "/", &c__0, &c__0, &c__0, a, &c__1, x, af, &c__1, w, &info);
chkxer_("ZUNML2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
zunml2_("L", "N", &c_n1, &c__0, &c__0, a, &c__1, x, af, &c__1, w, &info);
chkxer_("ZUNML2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
zunml2_("L", "N", &c__0, &c_n1, &c__0, a, &c__1, x, af, &c__1, w, &info);
chkxer_("ZUNML2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
zunml2_("L", "N", &c__0, &c__0, &c_n1, a, &c__1, x, af, &c__1, w, &info);
chkxer_("ZUNML2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
zunml2_("L", "N", &c__0, &c__1, &c__1, a, &c__1, x, af, &c__1, w, &info);
chkxer_("ZUNML2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
zunml2_("R", "N", &c__1, &c__0, &c__1, a, &c__1, x, af, &c__1, w, &info);
chkxer_("ZUNML2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
zunml2_("L", "N", &c__2, &c__1, &c__2, a, &c__1, x, af, &c__2, w, &info);
chkxer_("ZUNML2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
zunml2_("R", "N", &c__1, &c__2, &c__2, a, &c__1, x, af, &c__1, w, &info);
chkxer_("ZUNML2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 10;
zunml2_("L", "N", &c__2, &c__1, &c__0, a, &c__2, x, af, &c__1, w, &info);
chkxer_("ZUNML2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* Print a summary line. */
alaesm_(path, &infoc_1.ok, &infoc_1.nout);
return 0;
/* End of ZERRLQ */
} /* zerrlq_ */
/* Subroutine */ int zgelqf_(integer *m, integer *n, doublecomplex *a,
integer *lda, doublecomplex *tau, doublecomplex *work, integer *lwork,
integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3, i__4;
/* Local variables */
integer i__, k, ib, nb, nx, iws, nbmin, iinfo;
extern /* Subroutine */ int zgelq2_(integer *, integer *, doublecomplex *,
integer *, doublecomplex *, doublecomplex *, integer *), xerbla_(
char *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *);
extern /* Subroutine */ int zlarfb_(char *, char *, char *, char *,
integer *, integer *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *);
integer ldwork;
extern /* Subroutine */ int zlarft_(char *, char *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, doublecomplex *,
integer *);
integer lwkopt;
logical lquery;
/* -- LAPACK routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* ZGELQF computes an LQ factorization of a complex M-by-N matrix A: */
/* A = L * Q. */
/* 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/output) COMPLEX*16 array, dimension (LDA,N) */
/* On entry, the M-by-N matrix A. */
/* On exit, the elements on and below the diagonal of the array */
/* contain the m-by-min(m,n) lower trapezoidal matrix L (L is */
/* lower triangular if m <= n); the elements above the diagonal, */
/* with the array TAU, represent the unitary matrix Q as a */
/* product of elementary reflectors (see Further Details). */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= max(1,M). */
/* TAU (output) COMPLEX*16 array, dimension (min(M,N)) */
/* The scalar factors of the elementary reflectors (see Further */
/* Details). */
/* 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 >= max(1,M). */
/* For optimum performance LWORK >= M*NB, where NB is the */
/* optimal blocksize. */
/* 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 */
/* Further Details */
/* =============== */
/* The matrix Q is represented as a product of elementary reflectors */
/* Q = H(k)' . . . H(2)' H(1)', where k = min(m,n). */
/* Each H(i) has the form */
/* H(i) = I - tau * v * v' */
/* where tau is a complex scalar, and v is a complex vector with */
/* v(1:i-1) = 0 and v(i) = 1; conjg(v(i+1:n)) is stored on exit in */
/* A(i,i+1:n), and tau in TAU(i). */
/* ===================================================================== */
/* .. Local Scalars .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input arguments */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--tau;
--work;
/* Function Body */
*info = 0;
nb = ilaenv_(&c__1, "ZGELQF", " ", m, n, &c_n1, &c_n1);
lwkopt = *m * nb;
work[1].r = (doublereal) lwkopt, work[1].i = 0.;
lquery = *lwork == -1;
if (*m < 0) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*lda < max(1,*m)) {
*info = -4;
} else if (*lwork < max(1,*m) && ! lquery) {
*info = -7;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZGELQF", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible */
k = min(*m,*n);
if (k == 0) {
work[1].r = 1., work[1].i = 0.;
return 0;
}
nbmin = 2;
nx = 0;
iws = *m;
if (nb > 1 && nb < k) {
/* Determine when to cross over from blocked to unblocked code. */
/* Computing MAX */
i__1 = 0, i__2 = ilaenv_(&c__3, "ZGELQF", " ", m, n, &c_n1, &c_n1);
nx = max(i__1,i__2);
if (nx < k) {
/* Determine if workspace is large enough for blocked code. */
ldwork = *m;
iws = ldwork * nb;
if (*lwork < iws) {
/* Not enough workspace to use optimal NB: reduce NB and */
/* determine the minimum value of NB. */
nb = *lwork / ldwork;
/* Computing MAX */
i__1 = 2, i__2 = ilaenv_(&c__2, "ZGELQF", " ", m, n, &c_n1, &
c_n1);
nbmin = max(i__1,i__2);
}
}
}
if (nb >= nbmin && nb < k && nx < k) {
/* Use blocked code initially */
i__1 = k - nx;
i__2 = nb;
for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) {
/* Computing MIN */
i__3 = k - i__ + 1;
ib = min(i__3,nb);
/* Compute the LQ factorization of the current block */
/* A(i:i+ib-1,i:n) */
i__3 = *n - i__ + 1;
zgelq2_(&ib, &i__3, &a[i__ + i__ * a_dim1], lda, &tau[i__], &work[
1], &iinfo);
if (i__ + ib <= *m) {
/* Form the triangular factor of the block reflector */
/* H = H(i) H(i+1) . . . H(i+ib-1) */
i__3 = *n - i__ + 1;
zlarft_("Forward", "Rowwise", &i__3, &ib, &a[i__ + i__ *
a_dim1], lda, &tau[i__], &work[1], &ldwork);
/* Apply H to A(i+ib:m,i:n) from the right */
i__3 = *m - i__ - ib + 1;
i__4 = *n - i__ + 1;
zlarfb_("Right", "No transpose", "Forward", "Rowwise", &i__3,
&i__4, &ib, &a[i__ + i__ * a_dim1], lda, &work[1], &
ldwork, &a[i__ + ib + i__ * a_dim1], lda, &work[ib +
1], &ldwork);
}
/* L10: */
}
} else {
i__ = 1;
}
/* Use unblocked code to factor the last or only block. */
if (i__ <= k) {
i__2 = *m - i__ + 1;
i__1 = *n - i__ + 1;
zgelq2_(&i__2, &i__1, &a[i__ + i__ * a_dim1], lda, &tau[i__], &work[1]
, &iinfo);
}
work[1].r = (doublereal) iws, work[1].i = 0.;
return 0;
/* End of ZGELQF */
} /* zgelqf_ */
