/* Subroutine */ int cqlt01_(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, i__2;
/* 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 cgeqlf_(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 cungql_(integer *, integer *, integer *,
complex *, integer *, complex *, complex *, integer *, integer *);
static real eps;
#define l_subscr(a_1,a_2) (a_2)*l_dim1 + a_1
#define l_ref(a_1,a_2) l[l_subscr(a_1,a_2)]
#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
=======
CQLT01 tests CGEQLF, which computes the QL factorization of an m-by-n
matrix A, and partially tests CUNGQL which forms the m-by-m
orthogonal matrix Q.
CQLT01 compares L with Q'*A, 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 QL factorization of A, as returned by CGEQLF.
See CGEQLF for further details.
Q (output) COMPLEX array, dimension (LDA,M)
The m-by-m 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 R.
LDA >= max(M,N).
TAU (output) COMPLEX array, dimension (min(M,N))
The scalar factors of the elementary reflectors, as returned
by CGEQLF.
WORK (workspace) COMPLEX array, dimension (LWORK)
LWORK (input) INTEGER
The dimension of the array WORK.
RWORK (workspace) REAL array, dimension (M)
RESULT (output) REAL array, dimension (2)
The test ratios:
RESULT(1) = norm( L - Q'*A ) / ( M * norm(A) * EPS )
RESULT(2) = norm( I - Q'*Q ) / ( M * 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, "CGEQLF", (ftnlen)6, (ftnlen)6);
cgeqlf_(m, n, &af[af_offset], lda, &tau[1], &work[1], lwork, &info);
/* Copy details of Q */
claset_("Full", m, m, &c_b1, &c_b1, &q[q_offset], lda);
if (*m >= *n) {
if (*n < *m && *n > 0) {
i__1 = *m - *n;
clacpy_("Full", &i__1, n, &af[af_offset], lda, &q_ref(1, *m - *n
+ 1), lda);
}
if (*n > 1) {
i__1 = *n - 1;
i__2 = *n - 1;
clacpy_("Upper", &i__1, &i__2, &af_ref(*m - *n + 1, 2), lda, &
q_ref(*m - *n + 1, *m - *n + 2), lda);
}
} else {
if (*m > 1) {
i__1 = *m - 1;
i__2 = *m - 1;
clacpy_("Upper", &i__1, &i__2, &af_ref(1, *n - *m + 2), lda, &
q_ref(1, 2), lda);
}
}
/* Generate the m-by-m matrix Q */
s_copy(srnamc_1.srnamt, "CUNGQL", (ftnlen)6, (ftnlen)6);
cungql_(m, m, &minmn, &q[q_offset], lda, &tau[1], &work[1], lwork, &info);
/* Copy L */
claset_("Full", m, n, &c_b12, &c_b12, &l[l_offset], lda);
if (*m >= *n) {
if (*n > 0) {
clacpy_("Lower", n, n, &af_ref(*m - *n + 1, 1), lda, &l_ref(*m - *
n + 1, 1), lda);
}
} else {
if (*n > *m && *m > 0) {
i__1 = *n - *m;
clacpy_("Full", m, &i__1, &af[af_offset], lda, &l[l_offset], lda);
}
if (*m > 0) {
clacpy_("Lower", m, m, &af_ref(1, *n - *m + 1), lda, &l_ref(1, *n
- *m + 1), lda);
}
}
/* Compute L - Q'*A */
cgemm_("Conjugate transpose", "No transpose", m, n, m, &c_b19, &q[
q_offset], lda, &a[a_offset], lda, &c_b20, &l[l_offset], lda);
/* Compute norm( L - Q'*A ) / ( M * 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,*m) / anorm / eps;
} else {
result[1] = 0.f;
}
/* Compute I - Q'*Q */
claset_("Full", m, m, &c_b12, &c_b20, &l[l_offset], lda);
cherk_("Upper", "Conjugate transpose", m, m, &c_b28, &q[q_offset], lda, &
c_b29, &l[l_offset], lda);
/* Compute norm( I - Q'*Q ) / ( M * EPS ) . */
resid = clansy_("1", "Upper", m, &l[l_offset], lda, &rwork[1]);
result[2] = resid / (real) max(1,*m) / eps;
return 0;
/* End of CQLT01 */
} /* cqlt01_ */
/* Subroutine */ int cqlt01_(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, i__2;
/* 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 cgeqlf_(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 cungql_(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 */
/* ======= */
/* CQLT01 tests CGEQLF, which computes the QL factorization of an m-by-n */
/* matrix A, and partially tests CUNGQL which forms the m-by-m */
/* orthogonal matrix Q. */
/* CQLT01 compares L with Q'*A, 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 QL factorization of A, as returned by CGEQLF. */
/* See CGEQLF for further details. */
/* Q (output) COMPLEX array, dimension (LDA,M) */
/* The m-by-m 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 R. */
/* LDA >= max(M,N). */
/* TAU (output) COMPLEX array, dimension (min(M,N)) */
/* The scalar factors of the elementary reflectors, as returned */
/* by CGEQLF. */
/* WORK (workspace) COMPLEX array, dimension (LWORK) */
/* LWORK (input) INTEGER */
/* The dimension of the array WORK. */
/* RWORK (workspace) REAL array, dimension (M) */
/* RESULT (output) REAL array, dimension (2) */
/* The test ratios: */
/* RESULT(1) = norm( L - Q'*A ) / ( M * norm(A) * EPS ) */
/* RESULT(2) = norm( I - Q'*Q ) / ( M * 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, "CGEQLF", (ftnlen)6, (ftnlen)6);
cgeqlf_(m, n, &af[af_offset], lda, &tau[1], &work[1], lwork, &info);
/* Copy details of Q */
claset_("Full", m, m, &c_b1, &c_b1, &q[q_offset], lda);
if (*m >= *n) {
if (*n < *m && *n > 0) {
i__1 = *m - *n;
clacpy_("Full", &i__1, n, &af[af_offset], lda, &q[(*m - *n + 1) *
q_dim1 + 1], lda);
}
if (*n > 1) {
i__1 = *n - 1;
i__2 = *n - 1;
clacpy_("Upper", &i__1, &i__2, &af[*m - *n + 1 + (af_dim1 << 1)],
lda, &q[*m - *n + 1 + (*m - *n + 2) * q_dim1], lda);
}
} else {
if (*m > 1) {
i__1 = *m - 1;
i__2 = *m - 1;
clacpy_("Upper", &i__1, &i__2, &af[(*n - *m + 2) * af_dim1 + 1],
lda, &q[(q_dim1 << 1) + 1], lda);
}
}
/* Generate the m-by-m matrix Q */
s_copy(srnamc_1.srnamt, "CUNGQL", (ftnlen)6, (ftnlen)6);
cungql_(m, m, &minmn, &q[q_offset], lda, &tau[1], &work[1], lwork, &info);
/* Copy L */
claset_("Full", m, n, &c_b12, &c_b12, &l[l_offset], lda);
if (*m >= *n) {
if (*n > 0) {
clacpy_("Lower", n, n, &af[*m - *n + 1 + af_dim1], lda, &l[*m - *
n + 1 + l_dim1], lda);
}
} else {
if (*n > *m && *m > 0) {
i__1 = *n - *m;
clacpy_("Full", m, &i__1, &af[af_offset], lda, &l[l_offset], lda);
}
if (*m > 0) {
clacpy_("Lower", m, m, &af[(*n - *m + 1) * af_dim1 + 1], lda, &l[(
*n - *m + 1) * l_dim1 + 1], lda);
}
}
/* Compute L - Q'*A */
cgemm_("Conjugate transpose", "No transpose", m, n, m, &c_b19, &q[
q_offset], lda, &a[a_offset], lda, &c_b20, &l[l_offset], lda);
/* Compute norm( L - Q'*A ) / ( M * 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,*m) / anorm / eps;
} else {
result[1] = 0.f;
}
/* Compute I - Q'*Q */
claset_("Full", m, m, &c_b12, &c_b20, &l[l_offset], lda);
cherk_("Upper", "Conjugate transpose", m, m, &c_b28, &q[q_offset], lda, &
c_b29, &l[l_offset], lda);
/* Compute norm( I - Q'*Q ) / ( M * EPS ) . */
resid = clansy_("1", "Upper", m, &l[l_offset], lda, &rwork[1]);
result[2] = resid / (real) max(1,*m) / eps;
return 0;
/* End of CQLT01 */
} /* cqlt01_ */
/* Subroutine */ int cerrql_(char *path, integer *nunit)
{
/* System generated locals */
integer i__1;
real r__1, r__2;
complex q__1;
/* Builtin functions */
integer s_wsle(cilist *), e_wsle(void);
/* Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen);
/* Local variables */
complex a[4] /* was [2][2] */, b[2];
integer i__, j;
complex w[2], x[2], af[4] /* was [2][2] */;
integer info;
extern /* Subroutine */ int cgeql2_(integer *, integer *, complex *,
integer *, complex *, complex *, integer *), cung2l_(integer *,
integer *, integer *, complex *, integer *, complex *, complex *,
integer *), cunm2l_(char *, char *, integer *, integer *, integer
*, complex *, integer *, complex *, complex *, integer *, complex
*, integer *), cgeqlf_(integer *, integer *,
complex *, integer *, complex *, complex *, integer *, integer *),
alaesm_(char *, logical *, integer *), cgeqls_(integer *,
integer *, integer *, complex *, integer *, complex *, complex *,
integer *, complex *, integer *, integer *), chkxer_(char *,
integer *, integer *, logical *, logical *), cungql_(
integer *, integer *, integer *, complex *, integer *, complex *,
complex *, integer *, integer *), cunmql_(char *, char *, integer
*, integer *, integer *, complex *, integer *, complex *, complex
*, integer *, complex *, 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 */
/* ======= */
/* CERRQL tests the error exits for the COMPLEX routines */
/* that use the QL 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;
r__1 = 1.f / (real) (i__ + j);
r__2 = -1.f / (real) (i__ + j);
q__1.r = r__1, q__1.i = r__2;
a[i__1].r = q__1.r, a[i__1].i = q__1.i;
i__1 = i__ + (j << 1) - 3;
r__1 = 1.f / (real) (i__ + j);
r__2 = -1.f / (real) (i__ + j);
q__1.r = r__1, q__1.i = r__2;
af[i__1].r = q__1.r, af[i__1].i = q__1.i;
/* L10: */
}
i__1 = j - 1;
b[i__1].r = 0.f, b[i__1].i = 0.f;
i__1 = j - 1;
w[i__1].r = 0.f, w[i__1].i = 0.f;
i__1 = j - 1;
x[i__1].r = 0.f, x[i__1].i = 0.f;
/* L20: */
}
infoc_1.ok = TRUE_;
/* Error exits for QL factorization */
/* CGEQLF */
s_copy(srnamc_1.srnamt, "CGEQLF", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
cgeqlf_(&c_n1, &c__0, a, &c__1, b, w, &c__1, &info);
chkxer_("CGEQLF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
cgeqlf_(&c__0, &c_n1, a, &c__1, b, w, &c__1, &info);
chkxer_("CGEQLF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
cgeqlf_(&c__2, &c__1, a, &c__1, b, w, &c__1, &info);
chkxer_("CGEQLF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
cgeqlf_(&c__1, &c__2, a, &c__1, b, w, &c__1, &info);
chkxer_("CGEQLF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* CGEQL2 */
s_copy(srnamc_1.srnamt, "CGEQL2", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
cgeql2_(&c_n1, &c__0, a, &c__1, b, w, &info);
chkxer_("CGEQL2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
cgeql2_(&c__0, &c_n1, a, &c__1, b, w, &info);
chkxer_("CGEQL2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
cgeql2_(&c__2, &c__1, a, &c__1, b, w, &info);
chkxer_("CGEQL2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* CGEQLS */
s_copy(srnamc_1.srnamt, "CGEQLS", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
cgeqls_(&c_n1, &c__0, &c__0, a, &c__1, x, b, &c__1, w, &c__1, &info);
chkxer_("CGEQLS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
cgeqls_(&c__0, &c_n1, &c__0, a, &c__1, x, b, &c__1, w, &c__1, &info);
chkxer_("CGEQLS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
cgeqls_(&c__1, &c__2, &c__0, a, &c__1, x, b, &c__1, w, &c__1, &info);
chkxer_("CGEQLS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
cgeqls_(&c__0, &c__0, &c_n1, a, &c__1, x, b, &c__1, w, &c__1, &info);
chkxer_("CGEQLS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
cgeqls_(&c__2, &c__1, &c__0, a, &c__1, x, b, &c__2, w, &c__1, &info);
chkxer_("CGEQLS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 8;
cgeqls_(&c__2, &c__1, &c__0, a, &c__2, x, b, &c__1, w, &c__1, &info);
chkxer_("CGEQLS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 10;
cgeqls_(&c__1, &c__1, &c__2, a, &c__1, x, b, &c__1, w, &c__1, &info);
chkxer_("CGEQLS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* CUNGQL */
s_copy(srnamc_1.srnamt, "CUNGQL", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
cungql_(&c_n1, &c__0, &c__0, a, &c__1, x, w, &c__1, &info);
chkxer_("CUNGQL", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
cungql_(&c__0, &c_n1, &c__0, a, &c__1, x, w, &c__1, &info);
chkxer_("CUNGQL", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
cungql_(&c__1, &c__2, &c__0, a, &c__1, x, w, &c__2, &info);
chkxer_("CUNGQL", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
cungql_(&c__0, &c__0, &c_n1, a, &c__1, x, w, &c__1, &info);
chkxer_("CUNGQL", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
cungql_(&c__1, &c__1, &c__2, a, &c__1, x, w, &c__1, &info);
chkxer_("CUNGQL", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
cungql_(&c__2, &c__1, &c__0, a, &c__1, x, w, &c__1, &info);
chkxer_("CUNGQL", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 8;
cungql_(&c__2, &c__2, &c__0, a, &c__2, x, w, &c__1, &info);
chkxer_("CUNGQL", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* CUNG2L */
s_copy(srnamc_1.srnamt, "CUNG2L", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
cung2l_(&c_n1, &c__0, &c__0, a, &c__1, x, w, &info);
chkxer_("CUNG2L", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
cung2l_(&c__0, &c_n1, &c__0, a, &c__1, x, w, &info);
chkxer_("CUNG2L", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
cung2l_(&c__1, &c__2, &c__0, a, &c__1, x, w, &info);
chkxer_("CUNG2L", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
cung2l_(&c__0, &c__0, &c_n1, a, &c__1, x, w, &info);
chkxer_("CUNG2L", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
cung2l_(&c__2, &c__1, &c__2, a, &c__2, x, w, &info);
chkxer_("CUNG2L", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
cung2l_(&c__2, &c__1, &c__0, a, &c__1, x, w, &info);
chkxer_("CUNG2L", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* CUNMQL */
s_copy(srnamc_1.srnamt, "CUNMQL", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
cunmql_("/", "N", &c__0, &c__0, &c__0, a, &c__1, x, af, &c__1, w, &c__1, &
info);
chkxer_("CUNMQL", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
cunmql_("L", "/", &c__0, &c__0, &c__0, a, &c__1, x, af, &c__1, w, &c__1, &
info);
chkxer_("CUNMQL", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
cunmql_("L", "N", &c_n1, &c__0, &c__0, a, &c__1, x, af, &c__1, w, &c__1, &
info);
chkxer_("CUNMQL", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
cunmql_("L", "N", &c__0, &c_n1, &c__0, a, &c__1, x, af, &c__1, w, &c__1, &
info);
chkxer_("CUNMQL", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
cunmql_("L", "N", &c__0, &c__0, &c_n1, a, &c__1, x, af, &c__1, w, &c__1, &
info);
chkxer_("CUNMQL", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
cunmql_("L", "N", &c__0, &c__1, &c__1, a, &c__1, x, af, &c__1, w, &c__1, &
info);
chkxer_("CUNMQL", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
cunmql_("R", "N", &c__1, &c__0, &c__1, a, &c__1, x, af, &c__1, w, &c__1, &
info);
chkxer_("CUNMQL", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
cunmql_("L", "N", &c__2, &c__1, &c__0, a, &c__1, x, af, &c__2, w, &c__1, &
info);
chkxer_("CUNMQL", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
cunmql_("R", "N", &c__1, &c__2, &c__0, a, &c__1, x, af, &c__1, w, &c__1, &
info);
chkxer_("CUNMQL", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 10;
cunmql_("L", "N", &c__2, &c__1, &c__0, a, &c__2, x, af, &c__1, w, &c__1, &
info);
chkxer_("CUNMQL", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 12;
cunmql_("L", "N", &c__1, &c__2, &c__0, a, &c__1, x, af, &c__1, w, &c__1, &
info);
chkxer_("CUNMQL", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 12;
cunmql_("R", "N", &c__2, &c__1, &c__0, a, &c__1, x, af, &c__2, w, &c__1, &
info);
chkxer_("CUNMQL", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* CUNM2L */
s_copy(srnamc_1.srnamt, "CUNM2L", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
cunm2l_("/", "N", &c__0, &c__0, &c__0, a, &c__1, x, af, &c__1, w, &info);
chkxer_("CUNM2L", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
cunm2l_("L", "/", &c__0, &c__0, &c__0, a, &c__1, x, af, &c__1, w, &info);
chkxer_("CUNM2L", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
cunm2l_("L", "N", &c_n1, &c__0, &c__0, a, &c__1, x, af, &c__1, w, &info);
chkxer_("CUNM2L", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
cunm2l_("L", "N", &c__0, &c_n1, &c__0, a, &c__1, x, af, &c__1, w, &info);
chkxer_("CUNM2L", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
cunm2l_("L", "N", &c__0, &c__0, &c_n1, a, &c__1, x, af, &c__1, w, &info);
chkxer_("CUNM2L", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
cunm2l_("L", "N", &c__0, &c__1, &c__1, a, &c__1, x, af, &c__1, w, &info);
chkxer_("CUNM2L", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
cunm2l_("R", "N", &c__1, &c__0, &c__1, a, &c__1, x, af, &c__1, w, &info);
chkxer_("CUNM2L", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
cunm2l_("L", "N", &c__2, &c__1, &c__0, a, &c__1, x, af, &c__2, w, &info);
chkxer_("CUNM2L", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
cunm2l_("R", "N", &c__1, &c__2, &c__0, a, &c__1, x, af, &c__1, w, &info);
chkxer_("CUNM2L", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 10;
cunm2l_("L", "N", &c__2, &c__1, &c__0, a, &c__2, x, af, &c__1, w, &info);
chkxer_("CUNM2L", &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 CERRQL */
} /* cerrql_ */
/* Subroutine */ int cqlt03_(integer *m, integer *n, integer *k, complex *af,
complex *c__, complex *cc, complex *q, integer *lda, complex *tau,
complex *work, integer *lwork, real *rwork, real *result)
{
/* Initialized data */
static integer iseed[4] = { 1988,1989,1990,1991 };
/* System generated locals */
integer af_dim1, af_offset, c_dim1, c_offset, cc_dim1, cc_offset, q_dim1,
q_offset, i__1, i__2;
/* Local variables */
integer j, mc, nc;
real eps;
char side[1];
integer info;
integer iside;
real resid;
integer minmn;
real cnorm;
char trans[1];
integer itrans;
/* -- LAPACK test routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* CQLT03 tests CUNMQL, which computes Q*C, Q'*C, C*Q or C*Q'. */
/* CQLT03 compares the results of a call to CUNMQL with the results of */
/* forming Q explicitly by a call to CUNGQL and then performing matrix */
/* multiplication by a call to CGEMM. */
/* Arguments */
/* ========= */
/* M (input) INTEGER */
/* The order of the orthogonal matrix Q. M >= 0. */
/* N (input) INTEGER */
/* The number of rows or columns of the matrix C; C is m-by-n if */
/* Q is applied from the left, or n-by-m if Q is applied from */
/* the right. N >= 0. */
/* K (input) INTEGER */
/* The number of elementary reflectors whose product defines the */
/* orthogonal matrix Q. M >= K >= 0. */
/* AF (input) COMPLEX array, dimension (LDA,N) */
/* Details of the QL factorization of an m-by-n matrix, as */
/* returned by CGEQLF. See CGEQLF for further details. */
/* C (workspace) COMPLEX array, dimension (LDA,N) */
/* CC (workspace) COMPLEX array, dimension (LDA,N) */
/* Q (workspace) COMPLEX array, dimension (LDA,M) */
/* LDA (input) INTEGER */
/* The leading dimension of the arrays AF, C, CC, and Q. */
/* TAU (input) COMPLEX array, dimension (min(M,N)) */
/* The scalar factors of the elementary reflectors corresponding */
/* to the QL factorization in AF. */
/* WORK (workspace) COMPLEX array, dimension (LWORK) */
/* LWORK (input) INTEGER */
/* The length of WORK. LWORK must be at least M, and should be */
/* M*NB, where NB is the blocksize for this environment. */
/* RWORK (workspace) REAL array, dimension (M) */
/* RESULT (output) REAL array, dimension (4) */
/* The test ratios compare two techniques for multiplying a */
/* random matrix C by an m-by-m orthogonal matrix Q. */
/* RESULT(1) = norm( Q*C - Q*C ) / ( M * norm(C) * EPS ) */
/* RESULT(2) = norm( C*Q - C*Q ) / ( M * norm(C) * EPS ) */
/* RESULT(3) = norm( Q'*C - Q'*C )/ ( M * norm(C) * EPS ) */
/* RESULT(4) = norm( C*Q' - C*Q' )/ ( M * norm(C) * EPS ) */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Scalars in Common .. */
/* .. */
/* .. Common blocks .. */
/* .. */
/* .. Data statements .. */
/* Parameter adjustments */
q_dim1 = *lda;
q_offset = 1 + q_dim1;
q -= q_offset;
cc_dim1 = *lda;
cc_offset = 1 + cc_dim1;
cc -= cc_offset;
c_dim1 = *lda;
c_offset = 1 + c_dim1;
c__ -= c_offset;
af_dim1 = *lda;
af_offset = 1 + af_dim1;
af -= af_offset;
--tau;
--work;
--rwork;
--result;
/* Function Body */
/* .. */
/* .. Executable Statements .. */
eps = slamch_("Epsilon");
minmn = min(*m,*n);
/* Quick return if possible */
if (minmn == 0) {
result[1] = 0.f;
result[2] = 0.f;
result[3] = 0.f;
result[4] = 0.f;
return 0;
}
/* Copy the last k columns of the factorization to the array Q */
claset_("Full", m, m, &c_b1, &c_b1, &q[q_offset], lda);
if (*k > 0 && *m > *k) {
i__1 = *m - *k;
clacpy_("Full", &i__1, k, &af[(*n - *k + 1) * af_dim1 + 1], lda, &q[(*
m - *k + 1) * q_dim1 + 1], lda);
}
if (*k > 1) {
i__1 = *k - 1;
i__2 = *k - 1;
clacpy_("Upper", &i__1, &i__2, &af[*m - *k + 1 + (*n - *k + 2) *
af_dim1], lda, &q[*m - *k + 1 + (*m - *k + 2) * q_dim1], lda);
}
/* Generate the m-by-m matrix Q */
s_copy(srnamc_1.srnamt, "CUNGQL", (ftnlen)32, (ftnlen)6);
cungql_(m, m, k, &q[q_offset], lda, &tau[minmn - *k + 1], &work[1], lwork,
&info);
for (iside = 1; iside <= 2; ++iside) {
if (iside == 1) {
*(unsigned char *)side = 'L';
mc = *m;
nc = *n;
} else {
*(unsigned char *)side = 'R';
mc = *n;
nc = *m;
}
/* Generate MC by NC matrix C */
i__1 = nc;
for (j = 1; j <= i__1; ++j) {
clarnv_(&c__2, iseed, &mc, &c__[j * c_dim1 + 1]);
/* L10: */
}
cnorm = clange_("1", &mc, &nc, &c__[c_offset], lda, &rwork[1]);
if (cnorm == 0.f) {
cnorm = 1.f;
}
for (itrans = 1; itrans <= 2; ++itrans) {
if (itrans == 1) {
*(unsigned char *)trans = 'N';
} else {
*(unsigned char *)trans = 'C';
}
/* Copy C */
clacpy_("Full", &mc, &nc, &c__[c_offset], lda, &cc[cc_offset],
lda);
/* Apply Q or Q' to C */
s_copy(srnamc_1.srnamt, "CUNMQL", (ftnlen)32, (ftnlen)6);
if (*k > 0) {
cunmql_(side, trans, &mc, &nc, k, &af[(*n - *k + 1) * af_dim1
+ 1], lda, &tau[minmn - *k + 1], &cc[cc_offset], lda,
&work[1], lwork, &info);
}
/* Form explicit product and subtract */
if (lsame_(side, "L")) {
cgemm_(trans, "No transpose", &mc, &nc, &mc, &c_b21, &q[
q_offset], lda, &c__[c_offset], lda, &c_b22, &cc[
cc_offset], lda);
} else {
cgemm_("No transpose", trans, &mc, &nc, &nc, &c_b21, &c__[
c_offset], lda, &q[q_offset], lda, &c_b22, &cc[
cc_offset], lda);
}
/* Compute error in the difference */
resid = clange_("1", &mc, &nc, &cc[cc_offset], lda, &rwork[1]);
result[(iside - 1 << 1) + itrans] = resid / ((real) max(1,*m) *
cnorm * eps);
/* L20: */
}
/* L30: */
}
return 0;
/* End of CQLT03 */
} /* cqlt03_ */
/* Subroutine */ int cungtr_(char *uplo, integer *n, complex *a, integer *lda,
complex *tau, complex *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__, j, nb;
integer iinfo;
logical upper;
integer lwkopt;
logical lquery;
/* -- LAPACK routine (version 3.2) -- */
/* November 2006 */
/* Purpose */
/* ======= */
/* CUNGTR generates a complex unitary matrix Q which is defined as the */
/* product of n-1 elementary reflectors of order N, as returned by */
/* CHETRD: */
/* if UPLO = 'U', Q = H(n-1) . . . H(2) H(1), */
/* if UPLO = 'L', Q = H(1) H(2) . . . H(n-1). */
/* Arguments */
/* ========= */
/* UPLO (input) CHARACTER*1 */
/* = 'U': Upper triangle of A contains elementary reflectors */
/* from CHETRD; */
/* = 'L': Lower triangle of A contains elementary reflectors */
/* from CHETRD. */
/* N (input) INTEGER */
/* The order of the matrix Q. N >= 0. */
/* A (input/output) COMPLEX array, dimension (LDA,N) */
/* On entry, the vectors which define the elementary reflectors, */
/* as returned by CHETRD. */
/* On exit, the N-by-N unitary matrix Q. */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= N. */
/* TAU (input) COMPLEX array, dimension (N-1) */
/* TAU(i) must contain the scalar factor of the elementary */
/* reflector H(i), as returned by CHETRD. */
/* 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 >= N-1. */
/* For optimum performance LWORK >= (N-1)*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 */
/* ===================================================================== */
/* Test the input arguments */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--tau;
--work;
/* Function Body */
*info = 0;
lquery = *lwork == -1;
upper = lsame_(uplo, "U");
if (! upper && ! lsame_(uplo, "L")) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*lda < max(1,*n)) {
*info = -4;
} else /* if(complicated condition) */ {
/* Computing MAX */
i__1 = 1, i__2 = *n - 1;
if (*lwork < max(i__1,i__2) && ! lquery) {
*info = -7;
}
}
if (*info == 0) {
if (upper) {
i__1 = *n - 1;
i__2 = *n - 1;
i__3 = *n - 1;
nb = ilaenv_(&c__1, "CUNGQL", " ", &i__1, &i__2, &i__3, &c_n1);
} else {
i__1 = *n - 1;
i__2 = *n - 1;
i__3 = *n - 1;
nb = ilaenv_(&c__1, "CUNGQR", " ", &i__1, &i__2, &i__3, &c_n1);
}
/* Computing MAX */
i__1 = 1, i__2 = *n - 1;
lwkopt = max(i__1,i__2) * nb;
work[1].r = (real) lwkopt, work[1].i = 0.f;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("CUNGTR", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible */
if (*n == 0) {
work[1].r = 1.f, work[1].i = 0.f;
return 0;
}
if (upper) {
/* Q was determined by a call to CHETRD with UPLO = 'U' */
/* Shift the vectors which define the elementary reflectors one */
/* column to the left, and set the last row and column of Q to */
/* those of the unit matrix */
i__1 = *n - 1;
for (j = 1; j <= i__1; ++j) {
i__2 = j - 1;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * a_dim1;
i__4 = i__ + (j + 1) * a_dim1;
a[i__3].r = a[i__4].r, a[i__3].i = a[i__4].i;
}
i__2 = *n + j * a_dim1;
a[i__2].r = 0.f, a[i__2].i = 0.f;
}
i__1 = *n - 1;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__ + *n * a_dim1;
a[i__2].r = 0.f, a[i__2].i = 0.f;
}
i__1 = *n + *n * a_dim1;
a[i__1].r = 1.f, a[i__1].i = 0.f;
/* Generate Q(1:n-1,1:n-1) */
i__1 = *n - 1;
i__2 = *n - 1;
i__3 = *n - 1;
cungql_(&i__1, &i__2, &i__3, &a[a_offset], lda, &tau[1], &work[1],
lwork, &iinfo);
} else {
/* Q was determined by a call to CHETRD with UPLO = 'L'. */
/* Shift the vectors which define the elementary reflectors one */
/* column to the right, and set the first row and column of Q to */
/* those of the unit matrix */
for (j = *n; j >= 2; --j) {
i__1 = j * a_dim1 + 1;
a[i__1].r = 0.f, a[i__1].i = 0.f;
i__1 = *n;
for (i__ = j + 1; i__ <= i__1; ++i__) {
i__2 = i__ + j * a_dim1;
i__3 = i__ + (j - 1) * a_dim1;
a[i__2].r = a[i__3].r, a[i__2].i = a[i__3].i;
}
}
i__1 = a_dim1 + 1;
a[i__1].r = 1.f, a[i__1].i = 0.f;
i__1 = *n;
for (i__ = 2; i__ <= i__1; ++i__) {
i__2 = i__ + a_dim1;
a[i__2].r = 0.f, a[i__2].i = 0.f;
}
if (*n > 1) {
/* Generate Q(2:n,2:n) */
i__1 = *n - 1;
i__2 = *n - 1;
i__3 = *n - 1;
cungqr_(&i__1, &i__2, &i__3, &a[(a_dim1 << 1) + 2], lda, &tau[1],
&work[1], lwork, &iinfo);
}
}
work[1].r = (real) lwkopt, work[1].i = 0.f;
return 0;
/* End of CUNGTR */
} /* cungtr_ */
/* Subroutine */ int cqlt02_(integer *m, integer *n, integer *k, 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, i__2;
/* 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;
extern doublereal clange_(char *, integer *, integer *, complex *,
integer *, real *), 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 cungql_(integer *, integer *, integer *,
complex *, integer *, complex *, complex *, integer *, integer *);
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 l_subscr(a_1,a_2) (a_2)*l_dim1 + a_1
#define l_ref(a_1,a_2) l[l_subscr(a_1,a_2)]
#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
=======
CQLT02 tests CUNGQL, which generates an m-by-n matrix Q with
orthonornmal columns that is defined as the product of k elementary
reflectors.
Given the QL factorization of an m-by-n matrix A, CQLT02 generates
the orthogonal matrix Q defined by the factorization of the last k
columns of A; it compares L(m-n+1:m,n-k+1:n) with
Q(1:m,m-n+1:m)'*A(1:m,n-k+1:n), and checks that the columns of Q are
orthonormal.
Arguments
=========
M (input) INTEGER
The number of rows of the matrix Q to be generated. M >= 0.
N (input) INTEGER
The number of columns of the matrix Q to be generated.
M >= N >= 0.
K (input) INTEGER
The number of elementary reflectors whose product defines the
matrix Q. N >= K >= 0.
A (input) COMPLEX array, dimension (LDA,N)
The m-by-n matrix A which was factorized by CQLT01.
AF (input) COMPLEX array, dimension (LDA,N)
Details of the QL factorization of A, as returned by CGEQLF.
See CGEQLF for further details.
Q (workspace) COMPLEX array, dimension (LDA,N)
L (workspace) COMPLEX array, dimension (LDA,N)
LDA (input) INTEGER
The leading dimension of the arrays A, AF, Q and L. LDA >= M.
TAU (input) COMPLEX array, dimension (N)
The scalar factors of the elementary reflectors corresponding
to the QL factorization in AF.
WORK (workspace) COMPLEX array, dimension (LWORK)
LWORK (input) INTEGER
The dimension of the array WORK.
RWORK (workspace) REAL array, dimension (M)
RESULT (output) REAL array, dimension (2)
The test ratios:
RESULT(1) = norm( L - Q'*A ) / ( M * norm(A) * EPS )
RESULT(2) = norm( I - Q'*Q ) / ( M * EPS )
=====================================================================
Quick return if possible
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 */
if (*m == 0 || *n == 0 || *k == 0) {
result[1] = 0.f;
result[2] = 0.f;
return 0;
}
eps = slamch_("Epsilon");
/* Copy the last k columns of the factorization to the array Q */
claset_("Full", m, n, &c_b1, &c_b1, &q[q_offset], lda);
if (*k < *m) {
i__1 = *m - *k;
clacpy_("Full", &i__1, k, &af_ref(1, *n - *k + 1), lda, &q_ref(1, *n
- *k + 1), lda);
}
if (*k > 1) {
i__1 = *k - 1;
i__2 = *k - 1;
clacpy_("Upper", &i__1, &i__2, &af_ref(*m - *k + 1, *n - *k + 2), lda,
&q_ref(*m - *k + 1, *n - *k + 2), lda);
}
/* Generate the last n columns of the matrix Q */
s_copy(srnamc_1.srnamt, "CUNGQL", (ftnlen)6, (ftnlen)6);
cungql_(m, n, k, &q[q_offset], lda, &tau[*n - *k + 1], &work[1], lwork, &
info);
/* Copy L(m-n+1:m,n-k+1:n) */
claset_("Full", n, k, &c_b9, &c_b9, &l_ref(*m - *n + 1, *n - *k + 1), lda);
clacpy_("Lower", k, k, &af_ref(*m - *k + 1, *n - *k + 1), lda, &l_ref(*m
- *k + 1, *n - *k + 1), lda);
/* Compute L(m-n+1:m,n-k+1:n) - Q(1:m,m-n+1:m)' * A(1:m,n-k+1:n) */
cgemm_("Conjugate transpose", "No transpose", n, k, m, &c_b14, &q[
q_offset], lda, &a_ref(1, *n - *k + 1), lda, &c_b15, &l_ref(*m - *
n + 1, *n - *k + 1), lda);
/* Compute norm( L - Q'*A ) / ( M * norm(A) * EPS ) . */
anorm = clange_("1", m, k, &a_ref(1, *n - *k + 1), lda, &rwork[1]);
resid = clange_("1", n, k, &l_ref(*m - *n + 1, *n - *k + 1), lda, &rwork[
1]);
if (anorm > 0.f) {
result[1] = resid / (real) max(1,*m) / anorm / eps;
} else {
result[1] = 0.f;
}
/* Compute I - Q'*Q */
claset_("Full", n, n, &c_b9, &c_b15, &l[l_offset], lda);
cherk_("Upper", "Conjugate transpose", n, m, &c_b23, &q[q_offset], lda, &
c_b24, &l[l_offset], lda);
/* Compute norm( I - Q'*Q ) / ( M * EPS ) . */
resid = clansy_("1", "Upper", n, &l[l_offset], lda, &rwork[1]);
result[2] = resid / (real) max(1,*m) / eps;
return 0;
/* End of CQLT02 */
} /* cqlt02_ */
