/* Subroutine */ int crqt02_(integer *m, integer *n, integer *k, complex *a,
complex *af, complex *q, complex *r__, integer *lda, complex *tau,
complex *work, integer *lwork, real *rwork, real *result)
{
/* System generated locals */
integer a_dim1, a_offset, af_dim1, af_offset, q_dim1, q_offset, r_dim1,
r_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;
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 cungrq_(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 */
/* ======= */
/* CRQT02 tests CUNGRQ, which generates an m-by-n matrix Q with */
/* orthonornmal rows that is defined as the product of k elementary */
/* reflectors. */
/* Given the RQ factorization of an m-by-n matrix A, CRQT02 generates */
/* the orthogonal matrix Q defined by the factorization of the last k */
/* rows of A; it compares R(m-k+1:m,n-m+1:n) with */
/* A(m-k+1:m,1:n)*Q(n-m+1:n,1:n)', and checks that the rows 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. */
/* N >= M >= 0. */
/* K (input) INTEGER */
/* The number of elementary reflectors whose product defines the */
/* matrix Q. M >= K >= 0. */
/* A (input) COMPLEX array, dimension (LDA,N) */
/* The m-by-n matrix A which was factorized by CRQT01. */
/* AF (input) COMPLEX array, dimension (LDA,N) */
/* Details of the RQ factorization of A, as returned by CGERQF. */
/* See CGERQF for further details. */
/* Q (workspace) COMPLEX array, dimension (LDA,N) */
/* R (workspace) COMPLEX array, dimension (LDA,M) */
/* LDA (input) INTEGER */
/* The leading dimension of the arrays A, AF, Q and L. LDA >= N. */
/* TAU (input) COMPLEX array, dimension (M) */
/* The scalar factors of the elementary reflectors corresponding */
/* to the RQ 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( R - A*Q' ) / ( N * norm(A) * EPS ) */
/* RESULT(2) = norm( I - Q*Q' ) / ( N * EPS ) */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Scalars in Common .. */
/* .. */
/* .. Common blocks .. */
/* .. */
/* .. Executable Statements .. */
/* Quick return if possible */
/* Parameter adjustments */
r_dim1 = *lda;
r_offset = 1 + r_dim1;
r__ -= r_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 */
if (*m == 0 || *n == 0 || *k == 0) {
result[1] = 0.f;
result[2] = 0.f;
return 0;
}
eps = slamch_("Epsilon");
/* Copy the last k rows of the factorization to the array Q */
claset_("Full", m, n, &c_b1, &c_b1, &q[q_offset], lda);
if (*k < *n) {
i__1 = *n - *k;
clacpy_("Full", k, &i__1, &af[*m - *k + 1 + af_dim1], lda, &q[*m - *k
+ 1 + q_dim1], lda);
}
if (*k > 1) {
i__1 = *k - 1;
i__2 = *k - 1;
clacpy_("Lower", &i__1, &i__2, &af[*m - *k + 2 + (*n - *k + 1) *
af_dim1], lda, &q[*m - *k + 2 + (*n - *k + 1) * q_dim1], lda);
}
/* Generate the last n rows of the matrix Q */
s_copy(srnamc_1.srnamt, "CUNGRQ", (ftnlen)32, (ftnlen)6);
cungrq_(m, n, k, &q[q_offset], lda, &tau[*m - *k + 1], &work[1], lwork, &
info);
/* Copy R(m-k+1:m,n-m+1:n) */
claset_("Full", k, m, &c_b9, &c_b9, &r__[*m - *k + 1 + (*n - *m + 1) *
r_dim1], lda);
clacpy_("Upper", k, k, &af[*m - *k + 1 + (*n - *k + 1) * af_dim1], lda, &
r__[*m - *k + 1 + (*n - *k + 1) * r_dim1], lda);
/* Compute R(m-k+1:m,n-m+1:n) - A(m-k+1:m,1:n) * Q(n-m+1:n,1:n)' */
cgemm_("No transpose", "Conjugate transpose", k, m, n, &c_b14, &a[*m - *k
+ 1 + a_dim1], lda, &q[q_offset], lda, &c_b15, &r__[*m - *k + 1 +
(*n - *m + 1) * r_dim1], lda);
/* Compute norm( R - A*Q' ) / ( N * norm(A) * EPS ) . */
anorm = clange_("1", k, n, &a[*m - *k + 1 + a_dim1], lda, &rwork[1]);
resid = clange_("1", k, m, &r__[*m - *k + 1 + (*n - *m + 1) * r_dim1],
lda, &rwork[1]);
if (anorm > 0.f) {
result[1] = resid / (real) max(1,*n) / anorm / eps;
} else {
result[1] = 0.f;
}
/* Compute I - Q*Q' */
claset_("Full", m, m, &c_b9, &c_b15, &r__[r_offset], lda);
cherk_("Upper", "No transpose", m, n, &c_b23, &q[q_offset], lda, &c_b24, &
r__[r_offset], lda);
/* Compute norm( I - Q*Q' ) / ( N * EPS ) . */
resid = clansy_("1", "Upper", m, &r__[r_offset], lda, &rwork[1]);
result[2] = resid / (real) max(1,*n) / eps;
return 0;
/* End of CRQT02 */
} /* crqt02_ */
/* Subroutine */ int cgrqts_(integer *m, integer *p, integer *n, complex *a,
complex *af, complex *q, complex *r__, integer *lda, complex *taua,
complex *b, complex *bf, complex *z__, complex *t, complex *bwk,
integer *ldb, complex *taub, complex *work, integer *lwork, real *
rwork, real *result)
{
/* System generated locals */
integer a_dim1, a_offset, af_dim1, af_offset, r_dim1, r_offset, q_dim1,
q_offset, b_dim1, b_offset, bf_dim1, bf_offset, t_dim1, t_offset,
z_dim1, z_offset, bwk_dim1, bwk_offset, i__1, i__2;
real r__1;
complex q__1;
/* Local variables */
static integer info;
static real unfl;
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, bnorm;
extern doublereal clange_(char *, integer *, integer *, complex *,
integer *, real *), clanhe_(char *, char *, integer *,
complex *, integer *, real *), slamch_(char *);
extern /* Subroutine */ int cggrqf_(integer *, integer *, integer *,
complex *, integer *, complex *, complex *, integer *, complex *,
complex *, integer *, integer *), clacpy_(char *, integer *,
integer *, complex *, integer *, complex *, integer *),
claset_(char *, integer *, integer *, complex *, complex *,
complex *, integer *), cungqr_(integer *, integer *,
integer *, complex *, integer *, complex *, complex *, integer *,
integer *), cungrq_(integer *, integer *, integer *, complex *,
integer *, complex *, complex *, integer *, integer *);
static real ulp;
#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 r___subscr(a_1,a_2) (a_2)*r_dim1 + a_1
#define r___ref(a_1,a_2) r__[r___subscr(a_1,a_2)]
#define z___subscr(a_1,a_2) (a_2)*z_dim1 + a_1
#define z___ref(a_1,a_2) z__[z___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)]
#define bf_subscr(a_1,a_2) (a_2)*bf_dim1 + a_1
#define bf_ref(a_1,a_2) bf[bf_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
=======
CGRQTS tests CGGRQF, which computes the GRQ factorization of an
M-by-N matrix A and a P-by-N matrix B: A = R*Q and B = Z*T*Q.
Arguments
=========
M (input) INTEGER
The number of rows of the matrix A. M >= 0.
P (input) INTEGER
The number of rows of the matrix B. P >= 0.
N (input) INTEGER
The number of columns of the matrices A and B. 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 GRQ factorization of A and B, as returned
by CGGRQF, see CGGRQF for further details.
Q (output) COMPLEX array, dimension (LDA,N)
The N-by-N unitary matrix Q.
R (workspace) COMPLEX array, dimension (LDA,MAX(M,N))
LDA (input) INTEGER
The leading dimension of the arrays A, AF, R and Q.
LDA >= max(M,N).
TAUA (output) COMPLEX array, dimension (min(M,N))
The scalar factors of the elementary reflectors, as returned
by SGGQRC.
B (input) COMPLEX array, dimension (LDB,N)
On entry, the P-by-N matrix A.
BF (output) COMPLEX array, dimension (LDB,N)
Details of the GQR factorization of A and B, as returned
by CGGRQF, see CGGRQF for further details.
Z (output) REAL array, dimension (LDB,P)
The P-by-P unitary matrix Z.
T (workspace) COMPLEX array, dimension (LDB,max(P,N))
BWK (workspace) COMPLEX array, dimension (LDB,N)
LDB (input) INTEGER
The leading dimension of the arrays B, BF, Z and T.
LDB >= max(P,N).
TAUB (output) COMPLEX array, dimension (min(P,N))
The scalar factors of the elementary reflectors, as returned
by SGGRQF.
WORK (workspace) COMPLEX array, dimension (LWORK)
LWORK (input) INTEGER
The dimension of the array WORK, LWORK >= max(M,P,N)**2.
RWORK (workspace) REAL array, dimension (M)
RESULT (output) REAL array, dimension (4)
The test ratios:
RESULT(1) = norm( R - A*Q' ) / ( MAX(M,N)*norm(A)*ULP)
RESULT(2) = norm( T*Q - Z'*B ) / (MAX(P,N)*norm(B)*ULP)
RESULT(3) = norm( I - Q'*Q ) / ( N*ULP )
RESULT(4) = norm( I - Z'*Z ) / ( P*ULP )
=====================================================================
Parameter adjustments */
r_dim1 = *lda;
r_offset = 1 + r_dim1 * 1;
r__ -= r_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;
--taua;
bwk_dim1 = *ldb;
bwk_offset = 1 + bwk_dim1 * 1;
bwk -= bwk_offset;
t_dim1 = *ldb;
t_offset = 1 + t_dim1 * 1;
t -= t_offset;
z_dim1 = *ldb;
z_offset = 1 + z_dim1 * 1;
z__ -= z_offset;
bf_dim1 = *ldb;
bf_offset = 1 + bf_dim1 * 1;
bf -= bf_offset;
b_dim1 = *ldb;
b_offset = 1 + b_dim1 * 1;
b -= b_offset;
--taub;
--work;
--rwork;
--result;
/* Function Body */
ulp = slamch_("Precision");
unfl = slamch_("Safe minimum");
/* Copy the matrix A to the array AF. */
clacpy_("Full", m, n, &a[a_offset], lda, &af[af_offset], lda);
clacpy_("Full", p, n, &b[b_offset], ldb, &bf[bf_offset], ldb);
/* Computing MAX */
r__1 = clange_("1", m, n, &a[a_offset], lda, &rwork[1]);
anorm = dmax(r__1,unfl);
/* Computing MAX */
r__1 = clange_("1", p, n, &b[b_offset], ldb, &rwork[1]);
bnorm = dmax(r__1,unfl);
/* Factorize the matrices A and B in the arrays AF and BF. */
cggrqf_(m, p, n, &af[af_offset], lda, &taua[1], &bf[bf_offset], ldb, &
taub[1], &work[1], lwork, &info);
/* Generate the N-by-N matrix Q */
claset_("Full", n, n, &c_b3, &c_b3, &q[q_offset], lda);
if (*m <= *n) {
if (*m > 0 && *m < *n) {
i__1 = *n - *m;
clacpy_("Full", m, &i__1, &af[af_offset], lda, &q_ref(*n - *m + 1,
1), lda);
}
if (*m > 1) {
i__1 = *m - 1;
i__2 = *m - 1;
clacpy_("Lower", &i__1, &i__2, &af_ref(2, *n - *m + 1), lda, &
q_ref(*n - *m + 2, *n - *m + 1), lda);
}
} else {
if (*n > 1) {
i__1 = *n - 1;
i__2 = *n - 1;
clacpy_("Lower", &i__1, &i__2, &af_ref(*m - *n + 2, 1), lda, &
q_ref(2, 1), lda);
}
}
i__1 = min(*m,*n);
cungrq_(n, n, &i__1, &q[q_offset], lda, &taua[1], &work[1], lwork, &info);
/* Generate the P-by-P matrix Z */
claset_("Full", p, p, &c_b3, &c_b3, &z__[z_offset], ldb);
if (*p > 1) {
i__1 = *p - 1;
clacpy_("Lower", &i__1, n, &bf_ref(2, 1), ldb, &z___ref(2, 1), ldb);
}
i__1 = min(*p,*n);
cungqr_(p, p, &i__1, &z__[z_offset], ldb, &taub[1], &work[1], lwork, &
info);
/* Copy R */
claset_("Full", m, n, &c_b1, &c_b1, &r__[r_offset], lda);
if (*m <= *n) {
clacpy_("Upper", m, m, &af_ref(1, *n - *m + 1), lda, &r___ref(1, *n -
*m + 1), lda);
} else {
i__1 = *m - *n;
clacpy_("Full", &i__1, n, &af[af_offset], lda, &r__[r_offset], lda);
clacpy_("Upper", n, n, &af_ref(*m - *n + 1, 1), lda, &r___ref(*m - *n
+ 1, 1), lda);
}
/* Copy T */
claset_("Full", p, n, &c_b1, &c_b1, &t[t_offset], ldb);
clacpy_("Upper", p, n, &bf[bf_offset], ldb, &t[t_offset], ldb);
/* Compute R - A*Q' */
q__1.r = -1.f, q__1.i = 0.f;
cgemm_("No transpose", "Conjugate transpose", m, n, n, &q__1, &a[a_offset]
, lda, &q[q_offset], lda, &c_b2, &r__[r_offset], lda);
/* Compute norm( R - A*Q' ) / ( MAX(M,N)*norm(A)*ULP ) . */
resid = clange_("1", m, n, &r__[r_offset], lda, &rwork[1]);
if (anorm > 0.f) {
/* Computing MAX */
i__1 = max(1,*m);
result[1] = resid / (real) max(i__1,*n) / anorm / ulp;
} else {
result[1] = 0.f;
}
/* Compute T*Q - Z'*B */
cgemm_("Conjugate transpose", "No transpose", p, n, p, &c_b2, &z__[
z_offset], ldb, &b[b_offset], ldb, &c_b1, &bwk[bwk_offset], ldb);
q__1.r = -1.f, q__1.i = 0.f;
cgemm_("No transpose", "No transpose", p, n, n, &c_b2, &t[t_offset], ldb,
&q[q_offset], lda, &q__1, &bwk[bwk_offset], ldb);
/* Compute norm( T*Q - Z'*B ) / ( MAX(P,N)*norm(A)*ULP ) . */
resid = clange_("1", p, n, &bwk[bwk_offset], ldb, &rwork[1]);
if (bnorm > 0.f) {
/* Computing MAX */
i__1 = max(1,*p);
result[2] = resid / (real) max(i__1,*m) / bnorm / ulp;
} else {
result[2] = 0.f;
}
/* Compute I - Q*Q' */
claset_("Full", n, n, &c_b1, &c_b2, &r__[r_offset], lda);
cherk_("Upper", "No Transpose", n, n, &c_b34, &q[q_offset], lda, &c_b35, &
r__[r_offset], lda);
/* Compute norm( I - Q'*Q ) / ( N * ULP ) . */
resid = clanhe_("1", "Upper", n, &r__[r_offset], lda, &rwork[1]);
result[3] = resid / (real) max(1,*n) / ulp;
/* Compute I - Z'*Z */
claset_("Full", p, p, &c_b1, &c_b2, &t[t_offset], ldb);
cherk_("Upper", "Conjugate transpose", p, p, &c_b34, &z__[z_offset], ldb,
&c_b35, &t[t_offset], ldb);
/* Compute norm( I - Z'*Z ) / ( P*ULP ) . */
resid = clanhe_("1", "Upper", p, &t[t_offset], ldb, &rwork[1]);
result[4] = resid / (real) max(1,*p) / ulp;
return 0;
/* End of CGRQTS */
} /* cgrqts_ */
/* Subroutine */ int crqt01_(integer *m, integer *n, complex *a, complex *af,
complex *q, complex *r__, integer *lda, complex *tau, complex *work,
integer *lwork, real *rwork, real *result)
{
/* System generated locals */
integer a_dim1, a_offset, af_dim1, af_offset, q_dim1, q_offset, r_dim1,
r_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 *), slamch_(char *);
extern /* Subroutine */ int cgerqf_(integer *, integer *, complex *,
integer *, complex *, complex *, integer *, integer *), 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 cungrq_(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 */
/* ======= */
/* CRQT01 tests CGERQF, which computes the RQ factorization of an m-by-n */
/* matrix A, and partially tests CUNGRQ which forms the n-by-n */
/* orthogonal matrix Q. */
/* CRQT01 compares R with A*Q', and checks that Q is orthogonal. */
/* Arguments */
/* ========= */
/* M (input) INTEGER */
/* The number of rows of the matrix A. M >= 0. */
/* N (input) INTEGER */
/* The number of columns of the matrix A. N >= 0. */
/* A (input) COMPLEX array, dimension (LDA,N) */
/* The m-by-n matrix A. */
/* AF (output) COMPLEX array, dimension (LDA,N) */
/* Details of the RQ factorization of A, as returned by CGERQF. */
/* See CGERQF for further details. */
/* Q (output) COMPLEX array, dimension (LDA,N) */
/* The n-by-n orthogonal matrix Q. */
/* R (workspace) COMPLEX array, dimension (LDA,max(M,N)) */
/* LDA (input) INTEGER */
/* The leading dimension of the arrays A, AF, Q and L. */
/* LDA >= max(M,N). */
/* TAU (output) COMPLEX array, dimension (min(M,N)) */
/* The scalar factors of the elementary reflectors, as returned */
/* by CGERQF. */
/* WORK (workspace) COMPLEX array, dimension (LWORK) */
/* LWORK (input) INTEGER */
/* The dimension of the array WORK. */
/* RWORK (workspace) REAL array, dimension (max(M,N)) */
/* RESULT (output) REAL array, dimension (2) */
/* The test ratios: */
/* RESULT(1) = norm( R - A*Q' ) / ( N * norm(A) * EPS ) */
/* RESULT(2) = norm( I - Q*Q' ) / ( N * EPS ) */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Scalars in Common .. */
/* .. */
/* .. Common blocks .. */
/* .. */
/* .. Executable Statements .. */
/* Parameter adjustments */
r_dim1 = *lda;
r_offset = 1 + r_dim1;
r__ -= r_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, "CGERQF", (ftnlen)32, (ftnlen)6);
cgerqf_(m, n, &af[af_offset], lda, &tau[1], &work[1], lwork, &info);
/* Copy details of Q */
claset_("Full", n, n, &c_b1, &c_b1, &q[q_offset], lda);
if (*m <= *n) {
if (*m > 0 && *m < *n) {
i__1 = *n - *m;
clacpy_("Full", m, &i__1, &af[af_offset], lda, &q[*n - *m + 1 +
q_dim1], lda);
}
if (*m > 1) {
i__1 = *m - 1;
i__2 = *m - 1;
clacpy_("Lower", &i__1, &i__2, &af[(*n - *m + 1) * af_dim1 + 2],
lda, &q[*n - *m + 2 + (*n - *m + 1) * q_dim1], lda);
}
} else {
if (*n > 1) {
i__1 = *n - 1;
i__2 = *n - 1;
clacpy_("Lower", &i__1, &i__2, &af[*m - *n + 2 + af_dim1], lda, &
q[q_dim1 + 2], lda);
}
}
/* Generate the n-by-n matrix Q */
s_copy(srnamc_1.srnamt, "CUNGRQ", (ftnlen)32, (ftnlen)6);
cungrq_(n, n, &minmn, &q[q_offset], lda, &tau[1], &work[1], lwork, &info);
/* Copy R */
claset_("Full", m, n, &c_b12, &c_b12, &r__[r_offset], lda);
if (*m <= *n) {
if (*m > 0) {
clacpy_("Upper", m, m, &af[(*n - *m + 1) * af_dim1 + 1], lda, &
r__[(*n - *m + 1) * r_dim1 + 1], lda);
}
} else {
if (*m > *n && *n > 0) {
i__1 = *m - *n;
clacpy_("Full", &i__1, n, &af[af_offset], lda, &r__[r_offset],
lda);
}
if (*n > 0) {
clacpy_("Upper", n, n, &af[*m - *n + 1 + af_dim1], lda, &r__[*m -
*n + 1 + r_dim1], lda);
}
}
/* Compute R - A*Q' */
cgemm_("No transpose", "Conjugate transpose", m, n, n, &c_b19, &a[
a_offset], lda, &q[q_offset], lda, &c_b20, &r__[r_offset], lda);
/* Compute norm( R - Q'*A ) / ( N * norm(A) * EPS ) . */
anorm = clange_("1", m, n, &a[a_offset], lda, &rwork[1]);
resid = clange_("1", m, n, &r__[r_offset], lda, &rwork[1]);
if (anorm > 0.f) {
result[1] = resid / (real) max(1,*n) / anorm / eps;
} else {
result[1] = 0.f;
}
/* Compute I - Q*Q' */
claset_("Full", n, n, &c_b12, &c_b20, &r__[r_offset], lda);
cherk_("Upper", "No transpose", n, n, &c_b28, &q[q_offset], lda, &c_b29, &
r__[r_offset], lda);
/* Compute norm( I - Q*Q' ) / ( N * EPS ) . */
resid = clansy_("1", "Upper", n, &r__[r_offset], lda, &rwork[1]);
result[2] = resid / (real) max(1,*n) / eps;
return 0;
/* End of CRQT01 */
} /* crqt01_ */
/* Subroutine */ int ctimrq_(char *line, integer *nm, integer *mval, integer *
nval, integer *nk, integer *kval, integer *nnb, integer *nbval,
integer *nxval, integer *nlda, integer *ldaval, real *timmin, complex
*a, complex *tau, complex *b, complex *work, real *rwork, real *
reslts, integer *ldr1, integer *ldr2, integer *ldr3, integer *nout,
ftnlen line_len)
{
/* Initialized data */
static char subnam[6*3] = "CGERQF" "CUNGRQ" "CUNMRQ";
static char sides[1*2] = "L" "R";
static char transs[1*2] = "N" "C";
static integer iseed[4] = { 0,0,0,1 };
/* Format strings */
static char fmt_9999[] = "(1x,a6,\002 timing run not attempted\002,/)";
static char fmt_9998[] = "(/\002 *** Speed of \002,a6,\002 in megaflops "
"***\002)";
static char fmt_9997[] = "(5x,\002line \002,i2,\002 with LDA = \002,i5)";
static char fmt_9996[] = "(5x,\002K = min(M,N)\002,/)";
static char fmt_9995[] = "(/5x,a6,\002 with SIDE = '\002,a1,\002', TRANS"
" = '\002,a1,\002', \002,a1,\002 =\002,i6,/)";
static char fmt_9994[] = "(\002 *** No pairs (M,N) found with M <= N: "
" \002,a6,\002 not timed\002)";
/* System generated locals */
integer reslts_dim1, reslts_dim2, reslts_dim3, reslts_offset, i__1, i__2,
i__3, i__4, i__5, i__6;
/* Builtin functions
Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen);
integer s_wsfe(cilist *), do_fio(integer *, char *, ftnlen), e_wsfe(void),
s_wsle(cilist *), e_wsle(void);
/* Local variables */
static integer ilda;
static char labm[1], side[1];
static integer info;
static char path[3];
static real time;
static integer isub, muse[12], nuse[12], i__, k, m, n;
static char cname[6];
static integer iside, itoff, itran, minmn;
extern doublereal sopla_(char *, integer *, integer *, integer *, integer
*, integer *);
extern /* Subroutine */ int icopy_(integer *, integer *, integer *,
integer *, integer *);
static char trans[1];
static integer k1, i4, m1, n1;
static real s1, s2;
static integer ic;
extern /* Subroutine */ int sprtb4_(char *, char *, char *, integer *,
integer *, integer *, integer *, integer *, integer *, integer *,
real *, integer *, integer *, integer *, ftnlen, ftnlen, ftnlen),
sprtb5_(char *, char *, char *, integer *, integer *, integer *,
integer *, integer *, integer *, real *, integer *, integer *,
integer *, ftnlen, ftnlen, ftnlen);
static integer nb, ik, im, lw, nx, reseed[4];
extern /* Subroutine */ int atimck_(integer *, char *, integer *, integer
*, integer *, integer *, integer *, integer *, ftnlen), cgerqf_(
integer *, integer *, complex *, integer *, complex *, complex *,
integer *, integer *);
extern doublereal second_(void);
extern /* Subroutine */ int clacpy_(char *, integer *, integer *, complex
*, integer *, complex *, integer *), ctimmg_(integer *,
integer *, integer *, complex *, integer *, integer *, integer *),
atimin_(char *, char *, integer *, char *, logical *, integer *,
integer *, ftnlen, ftnlen, ftnlen), clatms_(integer *, integer *,
char *, integer *, char *, real *, integer *, real *, real *,
integer *, integer *, char *, complex *, integer *, complex *,
integer *), xlaenv_(integer *, integer *);
extern doublereal smflop_(real *, real *, integer *);
static real untime;
extern /* Subroutine */ int cungrq_(integer *, integer *, integer *,
complex *, integer *, complex *, complex *, integer *, integer *);
static logical timsub[3];
extern /* Subroutine */ int cunmrq_(char *, char *, integer *, integer *,
integer *, complex *, integer *, complex *, complex *, integer *,
complex *, integer *, integer *);
static integer lda, icl, inb, imx;
static real ops;
/* Fortran I/O blocks */
static cilist io___9 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___29 = { 0, 0, 0, fmt_9998, 0 };
static cilist io___31 = { 0, 0, 0, fmt_9997, 0 };
static cilist io___32 = { 0, 0, 0, 0, 0 };
static cilist io___33 = { 0, 0, 0, fmt_9996, 0 };
static cilist io___34 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___49 = { 0, 0, 0, fmt_9998, 0 };
static cilist io___50 = { 0, 0, 0, fmt_9997, 0 };
static cilist io___51 = { 0, 0, 0, fmt_9995, 0 };
static cilist io___53 = { 0, 0, 0, fmt_9995, 0 };
static cilist io___54 = { 0, 0, 0, fmt_9994, 0 };
#define subnam_ref(a_0,a_1) &subnam[(a_1)*6 + a_0 - 6]
#define reslts_ref(a_1,a_2,a_3,a_4) reslts[(((a_4)*reslts_dim3 + (a_3))*\
reslts_dim2 + (a_2))*reslts_dim1 + a_1]
/* -- LAPACK timing routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
March 31, 1993
Purpose
=======
CTIMRQ times the LAPACK routines to perform the RQ factorization of
a COMPLEX general matrix.
Arguments
=========
LINE (input) CHARACTER*80
The input line that requested this routine. The first six
characters contain either the name of a subroutine or a
generic path name. The remaining characters may be used to
specify the individual routines to be timed. See ATIMIN for
a full description of the format of the input line.
NM (input) INTEGER
The number of values of M and N contained in the vectors
MVAL and NVAL. The matrix sizes are used in pairs (M,N).
MVAL (input) INTEGER array, dimension (NM)
The values of the matrix row dimension M.
NVAL (input) INTEGER array, dimension (NM)
The values of the matrix column dimension N.
NK (input) INTEGER
The number of values of K in the vector KVAL.
KVAL (input) INTEGER array, dimension (NK)
The values of the matrix dimension K, used in CUNMRQ.
NNB (input) INTEGER
The number of values of NB and NX contained in the
vectors NBVAL and NXVAL. The blocking parameters are used
in pairs (NB,NX).
NBVAL (input) INTEGER array, dimension (NNB)
The values of the blocksize NB.
NXVAL (input) INTEGER array, dimension (NNB)
The values of the crossover point NX.
NLDA (input) INTEGER
The number of values of LDA contained in the vector LDAVAL.
LDAVAL (input) INTEGER array, dimension (NLDA)
The values of the leading dimension of the array A.
TIMMIN (input) REAL
The minimum time a subroutine will be timed.
A (workspace) COMPLEX array, dimension (LDAMAX*NMAX)
where LDAMAX and NMAX are the maximum values of LDA and N.
TAU (workspace) COMPLEX array, dimension (min(M,N))
B (workspace) COMPLEX array, dimension (LDAMAX*NMAX)
WORK (workspace) COMPLEX array, dimension (LDAMAX*NBMAX)
where NBMAX is the maximum value of NB.
RWORK (workspace) REAL array, dimension
(min(MMAX,NMAX))
RESLTS (workspace) REAL array, dimension
(LDR1,LDR2,LDR3,2*NK)
The timing results for each subroutine over the relevant
values of (M,N), (NB,NX), and LDA.
LDR1 (input) INTEGER
The first dimension of RESLTS. LDR1 >= max(1,NNB).
LDR2 (input) INTEGER
The second dimension of RESLTS. LDR2 >= max(1,NM).
LDR3 (input) INTEGER
The third dimension of RESLTS. LDR3 >= max(1,NLDA).
NOUT (input) INTEGER
The unit number for output.
Internal Parameters
===================
MODE INTEGER
The matrix type. MODE = 3 is a geometric distribution of
eigenvalues. See CLATMS for further details.
COND REAL
The condition number of the matrix. The singular values are
set to values from DMAX to DMAX/COND.
DMAX REAL
The magnitude of the largest singular value.
=====================================================================
Parameter adjustments */
--mval;
--nval;
--kval;
--nbval;
--nxval;
--ldaval;
--a;
--tau;
--b;
--work;
--rwork;
reslts_dim1 = *ldr1;
reslts_dim2 = *ldr2;
reslts_dim3 = *ldr3;
reslts_offset = 1 + reslts_dim1 * (1 + reslts_dim2 * (1 + reslts_dim3 * 1)
);
reslts -= reslts_offset;
/* Function Body
Extract the timing request from the input line. */
s_copy(path, "Complex precision", (ftnlen)1, (ftnlen)17);
s_copy(path + 1, "RQ", (ftnlen)2, (ftnlen)2);
atimin_(path, line, &c__3, subnam, timsub, nout, &info, (ftnlen)3, (
ftnlen)80, (ftnlen)6);
if (info != 0) {
goto L230;
}
/* Check that M <= LDA for the input values. */
s_copy(cname, line, (ftnlen)6, (ftnlen)6);
atimck_(&c__1, cname, nm, &mval[1], nlda, &ldaval[1], nout, &info, (
ftnlen)6);
if (info > 0) {
io___9.ciunit = *nout;
s_wsfe(&io___9);
do_fio(&c__1, cname, (ftnlen)6);
e_wsfe();
goto L230;
}
/* Do for each pair of values (M,N): */
i__1 = *nm;
for (im = 1; im <= i__1; ++im) {
m = mval[im];
n = nval[im];
minmn = min(m,n);
icopy_(&c__4, iseed, &c__1, reseed, &c__1);
/* Do for each value of LDA: */
i__2 = *nlda;
for (ilda = 1; ilda <= i__2; ++ilda) {
lda = ldaval[ilda];
/* Do for each pair of values (NB, NX) in NBVAL and NXVAL. */
i__3 = *nnb;
for (inb = 1; inb <= i__3; ++inb) {
nb = nbval[inb];
xlaenv_(&c__1, &nb);
nx = nxval[inb];
xlaenv_(&c__3, &nx);
/* Computing MAX */
i__4 = 1, i__5 = m * max(1,nb);
lw = max(i__4,i__5);
/* Generate a test matrix of size M by N. */
icopy_(&c__4, reseed, &c__1, iseed, &c__1);
clatms_(&m, &n, "Uniform", iseed, "Nonsymm", &rwork[1], &c__3,
&c_b24, &c_b25, &m, &n, "No packing", &b[1], &lda, &
work[1], &info);
if (timsub[0]) {
/* CGERQF: RQ factorization */
clacpy_("Full", &m, &n, &b[1], &lda, &a[1], &lda);
ic = 0;
s1 = second_();
L10:
cgerqf_(&m, &n, &a[1], &lda, &tau[1], &work[1], &lw, &
info);
s2 = second_();
time = s2 - s1;
++ic;
if (time < *timmin) {
clacpy_("Full", &m, &n, &b[1], &lda, &a[1], &lda);
goto L10;
}
/* Subtract the time used in CLACPY. */
icl = 1;
s1 = second_();
L20:
s2 = second_();
untime = s2 - s1;
++icl;
if (icl <= ic) {
clacpy_("Full", &m, &n, &a[1], &lda, &b[1], &lda);
goto L20;
}
time = (time - untime) / (real) ic;
ops = sopla_("CGERQF", &m, &n, &c__0, &c__0, &nb);
reslts_ref(inb, im, ilda, 1) = smflop_(&ops, &time, &info)
;
} else {
/* If CGERQF was not timed, generate a matrix and factor
it using CGERQF anyway so that the factored form of
the matrix can be used in timing the other routines. */
clacpy_("Full", &m, &n, &b[1], &lda, &a[1], &lda);
cgerqf_(&m, &n, &a[1], &lda, &tau[1], &work[1], &lw, &
info);
}
if (timsub[1]) {
/* CUNGRQ: Generate orthogonal matrix Q from the RQ
factorization */
clacpy_("Full", &minmn, &n, &a[1], &lda, &b[1], &lda);
ic = 0;
s1 = second_();
L30:
cungrq_(&minmn, &n, &minmn, &b[1], &lda, &tau[1], &work[1]
, &lw, &info);
s2 = second_();
time = s2 - s1;
++ic;
if (time < *timmin) {
clacpy_("Full", &minmn, &n, &a[1], &lda, &b[1], &lda);
goto L30;
}
/* Subtract the time used in CLACPY. */
icl = 1;
s1 = second_();
L40:
s2 = second_();
untime = s2 - s1;
++icl;
if (icl <= ic) {
clacpy_("Full", &minmn, &n, &a[1], &lda, &b[1], &lda);
goto L40;
}
time = (time - untime) / (real) ic;
ops = sopla_("CUNGRQ", &minmn, &n, &minmn, &c__0, &nb);
reslts_ref(inb, im, ilda, 2) = smflop_(&ops, &time, &info)
;
}
/* L50: */
}
/* L60: */
}
/* L70: */
}
/* Print tables of results */
for (isub = 1; isub <= 2; ++isub) {
if (! timsub[isub - 1]) {
goto L90;
}
io___29.ciunit = *nout;
s_wsfe(&io___29);
do_fio(&c__1, subnam_ref(0, isub), (ftnlen)6);
e_wsfe();
if (*nlda > 1) {
i__1 = *nlda;
for (i__ = 1; i__ <= i__1; ++i__) {
io___31.ciunit = *nout;
s_wsfe(&io___31);
do_fio(&c__1, (char *)&i__, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&ldaval[i__], (ftnlen)sizeof(integer));
e_wsfe();
/* L80: */
}
}
io___32.ciunit = *nout;
s_wsle(&io___32);
e_wsle();
if (isub == 2) {
io___33.ciunit = *nout;
s_wsfe(&io___33);
e_wsfe();
}
sprtb4_("( NB, NX)", "M", "N", nnb, &nbval[1], &nxval[1], nm, &mval[
1], &nval[1], nlda, &reslts_ref(1, 1, 1, isub), ldr1, ldr2,
nout, (ftnlen)11, (ftnlen)1, (ftnlen)1);
L90:
;
}
/* Time CUNMRQ separately. Here the starting matrix is M by N, and
K is the free dimension of the matrix multiplied by Q. */
if (timsub[2]) {
/* Check that K <= LDA for the input values. */
atimck_(&c__3, cname, nk, &kval[1], nlda, &ldaval[1], nout, &info, (
ftnlen)6);
if (info > 0) {
io___34.ciunit = *nout;
s_wsfe(&io___34);
do_fio(&c__1, subnam_ref(0, 3), (ftnlen)6);
e_wsfe();
goto L230;
}
/* Use only the pairs (M,N) where M <= N. */
imx = 0;
i__1 = *nm;
for (im = 1; im <= i__1; ++im) {
if (mval[im] <= nval[im]) {
++imx;
muse[imx - 1] = mval[im];
nuse[imx - 1] = nval[im];
}
/* L100: */
}
/* CUNMRQ: Multiply by Q stored as a product of elementary
transformations
Do for each pair of values (M,N): */
i__1 = imx;
for (im = 1; im <= i__1; ++im) {
m = muse[im - 1];
n = nuse[im - 1];
/* Do for each value of LDA: */
i__2 = *nlda;
for (ilda = 1; ilda <= i__2; ++ilda) {
lda = ldaval[ilda];
/* Generate an M by N matrix and form its RQ decomposition. */
clatms_(&m, &n, "Uniform", iseed, "Nonsymm", &rwork[1], &c__3,
&c_b24, &c_b25, &m, &n, "No packing", &a[1], &lda, &
work[1], &info);
/* Computing MAX */
i__3 = 1, i__4 = m * max(1,nb);
lw = max(i__3,i__4);
cgerqf_(&m, &n, &a[1], &lda, &tau[1], &work[1], &lw, &info);
/* Do first for SIDE = 'L', then for SIDE = 'R' */
i4 = 0;
for (iside = 1; iside <= 2; ++iside) {
*(unsigned char *)side = *(unsigned char *)&sides[iside -
1];
/* Do for each pair of values (NB, NX) in NBVAL and
NXVAL. */
i__3 = *nnb;
for (inb = 1; inb <= i__3; ++inb) {
nb = nbval[inb];
xlaenv_(&c__1, &nb);
nx = nxval[inb];
xlaenv_(&c__3, &nx);
/* Do for each value of K in KVAL */
i__4 = *nk;
for (ik = 1; ik <= i__4; ++ik) {
k = kval[ik];
/* Sort out which variable is which */
if (iside == 1) {
k1 = m;
m1 = n;
n1 = k;
/* Computing MAX */
i__5 = 1, i__6 = n1 * max(1,nb);
lw = max(i__5,i__6);
} else {
k1 = m;
n1 = n;
m1 = k;
/* Computing MAX */
i__5 = 1, i__6 = m1 * max(1,nb);
lw = max(i__5,i__6);
}
/* Do first for TRANS = 'N', then for TRANS = 'T' */
itoff = 0;
for (itran = 1; itran <= 2; ++itran) {
*(unsigned char *)trans = *(unsigned char *)&
transs[itran - 1];
ctimmg_(&c__0, &m1, &n1, &b[1], &lda, &c__0, &
c__0);
ic = 0;
s1 = second_();
L110:
cunmrq_(side, trans, &m1, &n1, &k1, &a[1], &
lda, &tau[1], &b[1], &lda, &work[1], &
lw, &info);
s2 = second_();
time = s2 - s1;
++ic;
if (time < *timmin) {
ctimmg_(&c__0, &m1, &n1, &b[1], &lda, &
c__0, &c__0);
goto L110;
}
/* Subtract the time used in CTIMMG. */
icl = 1;
s1 = second_();
L120:
s2 = second_();
untime = s2 - s1;
++icl;
if (icl <= ic) {
ctimmg_(&c__0, &m1, &n1, &b[1], &lda, &
c__0, &c__0);
goto L120;
}
time = (time - untime) / (real) ic;
i__5 = iside - 1;
ops = sopla_("CUNMRQ", &m1, &n1, &k1, &i__5, &
nb);
reslts_ref(inb, im, ilda, i4 + itoff + ik) =
smflop_(&ops, &time, &info);
itoff = *nk;
/* L130: */
}
/* L140: */
}
/* L150: */
}
i4 = *nk << 1;
/* L160: */
}
/* L170: */
}
/* L180: */
}
/* Print tables of results */
isub = 3;
i4 = 1;
if (imx >= 1) {
for (iside = 1; iside <= 2; ++iside) {
*(unsigned char *)side = *(unsigned char *)&sides[iside - 1];
if (iside == 1) {
io___49.ciunit = *nout;
s_wsfe(&io___49);
do_fio(&c__1, subnam_ref(0, isub), (ftnlen)6);
e_wsfe();
if (*nlda > 1) {
i__1 = *nlda;
for (i__ = 1; i__ <= i__1; ++i__) {
io___50.ciunit = *nout;
s_wsfe(&io___50);
do_fio(&c__1, (char *)&i__, (ftnlen)sizeof(
integer));
do_fio(&c__1, (char *)&ldaval[i__], (ftnlen)
sizeof(integer));
e_wsfe();
/* L190: */
}
}
}
for (itran = 1; itran <= 2; ++itran) {
*(unsigned char *)trans = *(unsigned char *)&transs[itran
- 1];
i__1 = *nk;
for (ik = 1; ik <= i__1; ++ik) {
if (iside == 1) {
n = kval[ik];
io___51.ciunit = *nout;
s_wsfe(&io___51);
do_fio(&c__1, subnam_ref(0, isub), (ftnlen)6);
do_fio(&c__1, side, (ftnlen)1);
do_fio(&c__1, trans, (ftnlen)1);
do_fio(&c__1, "N", (ftnlen)1);
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer))
;
e_wsfe();
*(unsigned char *)labm = 'M';
} else {
m = kval[ik];
io___53.ciunit = *nout;
s_wsfe(&io___53);
do_fio(&c__1, subnam_ref(0, isub), (ftnlen)6);
do_fio(&c__1, side, (ftnlen)1);
do_fio(&c__1, trans, (ftnlen)1);
do_fio(&c__1, "M", (ftnlen)1);
do_fio(&c__1, (char *)&m, (ftnlen)sizeof(integer))
;
e_wsfe();
*(unsigned char *)labm = 'N';
}
sprtb5_("NB", "K", labm, nnb, &nbval[1], &imx, muse,
nuse, nlda, &reslts_ref(1, 1, 1, i4), ldr1,
ldr2, nout, (ftnlen)2, (ftnlen)1, (ftnlen)1);
++i4;
/* L200: */
}
/* L210: */
}
/* L220: */
}
} else {
io___54.ciunit = *nout;
s_wsfe(&io___54);
do_fio(&c__1, subnam_ref(0, isub), (ftnlen)6);
e_wsfe();
}
}
L230:
return 0;
/* End of CTIMRQ */
} /* ctimrq_ */
/* Subroutine */ int cgqrts_(integer *n, integer *m, integer *p, complex *a,
complex *af, complex *q, complex *r__, integer *lda, complex *taua,
complex *b, complex *bf, complex *z__, complex *t, complex *bwk,
integer *ldb, complex *taub, complex *work, integer *lwork, real *
rwork, real *result)
{
/* System generated locals */
integer a_dim1, a_offset, af_dim1, af_offset, r_dim1, r_offset, q_dim1,
q_offset, b_dim1, b_offset, bf_dim1, bf_offset, t_dim1, t_offset,
z_dim1, z_offset, bwk_dim1, bwk_offset, i__1, i__2;
real r__1;
complex q__1;
/* Local variables */
real ulp;
integer info;
real unfl;
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, bnorm;
extern doublereal clange_(char *, integer *, integer *, complex *,
integer *, real *), clanhe_(char *, char *, integer *,
complex *, integer *, real *), slamch_(char *);
extern /* Subroutine */ int cggqrf_(integer *, integer *, integer *,
complex *, integer *, complex *, complex *, integer *, complex *,
complex *, integer *, integer *), clacpy_(char *, integer *,
integer *, complex *, integer *, complex *, integer *),
claset_(char *, integer *, integer *, complex *, complex *,
complex *, integer *), cungqr_(integer *, integer *,
integer *, complex *, integer *, complex *, complex *, integer *,
integer *), cungrq_(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 */
/* ======= */
/* CGQRTS tests CGGQRF, which computes the GQR factorization of an */
/* N-by-M matrix A and a N-by-P matrix B: A = Q*R and B = Q*T*Z. */
/* Arguments */
/* ========= */
/* N (input) INTEGER */
/* The number of rows of the matrices A and B. N >= 0. */
/* M (input) INTEGER */
/* The number of columns of the matrix A. M >= 0. */
/* P (input) INTEGER */
/* The number of columns of the matrix B. P >= 0. */
/* A (input) COMPLEX array, dimension (LDA,M) */
/* The N-by-M matrix A. */
/* AF (output) COMPLEX array, dimension (LDA,N) */
/* Details of the GQR factorization of A and B, as returned */
/* by CGGQRF, see CGGQRF for further details. */
/* Q (output) COMPLEX array, dimension (LDA,N) */
/* The M-by-M unitary matrix Q. */
/* R (workspace) COMPLEX array, dimension (LDA,MAX(M,N)) */
/* LDA (input) INTEGER */
/* The leading dimension of the arrays A, AF, R and Q. */
/* LDA >= max(M,N). */
/* TAUA (output) COMPLEX array, dimension (min(M,N)) */
/* The scalar factors of the elementary reflectors, as returned */
/* by CGGQRF. */
/* B (input) COMPLEX array, dimension (LDB,P) */
/* On entry, the N-by-P matrix A. */
/* BF (output) COMPLEX array, dimension (LDB,N) */
/* Details of the GQR factorization of A and B, as returned */
/* by CGGQRF, see CGGQRF for further details. */
/* Z (output) COMPLEX array, dimension (LDB,P) */
/* The P-by-P unitary matrix Z. */
/* T (workspace) COMPLEX array, dimension (LDB,max(P,N)) */
/* BWK (workspace) COMPLEX array, dimension (LDB,N) */
/* LDB (input) INTEGER */
/* The leading dimension of the arrays B, BF, Z and T. */
/* LDB >= max(P,N). */
/* TAUB (output) COMPLEX array, dimension (min(P,N)) */
/* The scalar factors of the elementary reflectors, as returned */
/* by SGGRQF. */
/* WORK (workspace) COMPLEX array, dimension (LWORK) */
/* LWORK (input) INTEGER */
/* The dimension of the array WORK, LWORK >= max(N,M,P)**2. */
/* RWORK (workspace) REAL array, dimension (max(N,M,P)) */
/* RESULT (output) REAL array, dimension (4) */
/* The test ratios: */
/* RESULT(1) = norm( R - Q'*A ) / ( MAX(M,N)*norm(A)*ULP) */
/* RESULT(2) = norm( T*Z - Q'*B ) / (MAX(P,N)*norm(B)*ULP) */
/* RESULT(3) = norm( I - Q'*Q ) / ( M*ULP ) */
/* RESULT(4) = norm( I - Z'*Z ) / ( P*ULP ) */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Parameter adjustments */
r_dim1 = *lda;
r_offset = 1 + r_dim1;
r__ -= r_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;
--taua;
bwk_dim1 = *ldb;
bwk_offset = 1 + bwk_dim1;
bwk -= bwk_offset;
t_dim1 = *ldb;
t_offset = 1 + t_dim1;
t -= t_offset;
z_dim1 = *ldb;
z_offset = 1 + z_dim1;
z__ -= z_offset;
bf_dim1 = *ldb;
bf_offset = 1 + bf_dim1;
bf -= bf_offset;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
--taub;
--work;
--rwork;
--result;
/* Function Body */
ulp = slamch_("Precision");
unfl = slamch_("Safe minimum");
/* Copy the matrix A to the array AF. */
clacpy_("Full", n, m, &a[a_offset], lda, &af[af_offset], lda);
clacpy_("Full", n, p, &b[b_offset], ldb, &bf[bf_offset], ldb);
/* Computing MAX */
r__1 = clange_("1", n, m, &a[a_offset], lda, &rwork[1]);
anorm = dmax(r__1,unfl);
/* Computing MAX */
r__1 = clange_("1", n, p, &b[b_offset], ldb, &rwork[1]);
bnorm = dmax(r__1,unfl);
/* Factorize the matrices A and B in the arrays AF and BF. */
cggqrf_(n, m, p, &af[af_offset], lda, &taua[1], &bf[bf_offset], ldb, &
taub[1], &work[1], lwork, &info);
/* Generate the N-by-N matrix Q */
claset_("Full", n, n, &c_b3, &c_b3, &q[q_offset], lda);
i__1 = *n - 1;
clacpy_("Lower", &i__1, m, &af[af_dim1 + 2], lda, &q[q_dim1 + 2], lda);
i__1 = min(*n,*m);
cungqr_(n, n, &i__1, &q[q_offset], lda, &taua[1], &work[1], lwork, &info);
/* Generate the P-by-P matrix Z */
claset_("Full", p, p, &c_b3, &c_b3, &z__[z_offset], ldb);
if (*n <= *p) {
if (*n > 0 && *n < *p) {
i__1 = *p - *n;
clacpy_("Full", n, &i__1, &bf[bf_offset], ldb, &z__[*p - *n + 1 +
z_dim1], ldb);
}
if (*n > 1) {
i__1 = *n - 1;
i__2 = *n - 1;
clacpy_("Lower", &i__1, &i__2, &bf[(*p - *n + 1) * bf_dim1 + 2],
ldb, &z__[*p - *n + 2 + (*p - *n + 1) * z_dim1], ldb);
}
} else {
if (*p > 1) {
i__1 = *p - 1;
i__2 = *p - 1;
clacpy_("Lower", &i__1, &i__2, &bf[*n - *p + 2 + bf_dim1], ldb, &
z__[z_dim1 + 2], ldb);
}
}
i__1 = min(*n,*p);
cungrq_(p, p, &i__1, &z__[z_offset], ldb, &taub[1], &work[1], lwork, &
info);
/* Copy R */
claset_("Full", n, m, &c_b1, &c_b1, &r__[r_offset], lda);
clacpy_("Upper", n, m, &af[af_offset], lda, &r__[r_offset], lda);
/* Copy T */
claset_("Full", n, p, &c_b1, &c_b1, &t[t_offset], ldb);
if (*n <= *p) {
clacpy_("Upper", n, n, &bf[(*p - *n + 1) * bf_dim1 + 1], ldb, &t[(*p
- *n + 1) * t_dim1 + 1], ldb);
} else {
i__1 = *n - *p;
clacpy_("Full", &i__1, p, &bf[bf_offset], ldb, &t[t_offset], ldb);
clacpy_("Upper", p, p, &bf[*n - *p + 1 + bf_dim1], ldb, &t[*n - *p +
1 + t_dim1], ldb);
}
/* Compute R - Q'*A */
q__1.r = -1.f, q__1.i = -0.f;
cgemm_("Conjugate transpose", "No transpose", n, m, n, &q__1, &q[q_offset]
, lda, &a[a_offset], lda, &c_b2, &r__[r_offset], lda);
/* Compute norm( R - Q'*A ) / ( MAX(M,N)*norm(A)*ULP ) . */
resid = clange_("1", n, m, &r__[r_offset], lda, &rwork[1]);
if (anorm > 0.f) {
/* Computing MAX */
i__1 = max(1,*m);
result[1] = resid / (real) max(i__1,*n) / anorm / ulp;
} else {
result[1] = 0.f;
}
/* Compute T*Z - Q'*B */
cgemm_("No Transpose", "No transpose", n, p, p, &c_b2, &t[t_offset], ldb,
&z__[z_offset], ldb, &c_b1, &bwk[bwk_offset], ldb);
q__1.r = -1.f, q__1.i = -0.f;
cgemm_("Conjugate transpose", "No transpose", n, p, n, &q__1, &q[q_offset]
, lda, &b[b_offset], ldb, &c_b2, &bwk[bwk_offset], ldb);
/* Compute norm( T*Z - Q'*B ) / ( MAX(P,N)*norm(A)*ULP ) . */
resid = clange_("1", n, p, &bwk[bwk_offset], ldb, &rwork[1]);
if (bnorm > 0.f) {
/* Computing MAX */
i__1 = max(1,*p);
result[2] = resid / (real) max(i__1,*n) / bnorm / ulp;
} else {
result[2] = 0.f;
}
/* Compute I - Q'*Q */
claset_("Full", n, n, &c_b1, &c_b2, &r__[r_offset], lda);
cherk_("Upper", "Conjugate transpose", n, n, &c_b34, &q[q_offset], lda, &
c_b35, &r__[r_offset], lda);
/* Compute norm( I - Q'*Q ) / ( N * ULP ) . */
resid = clanhe_("1", "Upper", n, &r__[r_offset], lda, &rwork[1]);
result[3] = resid / (real) max(1,*n) / ulp;
/* Compute I - Z'*Z */
claset_("Full", p, p, &c_b1, &c_b2, &t[t_offset], ldb);
cherk_("Upper", "Conjugate transpose", p, p, &c_b34, &z__[z_offset], ldb,
&c_b35, &t[t_offset], ldb);
/* Compute norm( I - Z'*Z ) / ( P*ULP ) . */
resid = clanhe_("1", "Upper", p, &t[t_offset], ldb, &rwork[1]);
result[4] = resid / (real) max(1,*p) / ulp;
return 0;
/* End of CGQRTS */
} /* cgqrts_ */
/* Subroutine */ int crqt01_(integer *m, integer *n, complex *a, complex *af,
complex *q, complex *r__, integer *lda, complex *tau, complex *work,
integer *lwork, real *rwork, real *result)
{
/* System generated locals */
integer a_dim1, a_offset, af_dim1, af_offset, q_dim1, q_offset, r_dim1,
r_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 *), slamch_(char *);
extern /* Subroutine */ int cgerqf_(integer *, integer *, complex *,
integer *, complex *, complex *, integer *, integer *), 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 cungrq_(integer *, integer *, integer *,
complex *, integer *, complex *, complex *, integer *, integer *);
static real eps;
#define q_subscr(a_1,a_2) (a_2)*q_dim1 + a_1
#define q_ref(a_1,a_2) q[q_subscr(a_1,a_2)]
#define r___subscr(a_1,a_2) (a_2)*r_dim1 + a_1
#define r___ref(a_1,a_2) r__[r___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
=======
CRQT01 tests CGERQF, which computes the RQ factorization of an m-by-n
matrix A, and partially tests CUNGRQ which forms the n-by-n
orthogonal matrix Q.
CRQT01 compares R with A*Q', and checks that Q is orthogonal.
Arguments
=========
M (input) INTEGER
The number of rows of the matrix A. M >= 0.
N (input) INTEGER
The number of columns of the matrix A. N >= 0.
A (input) COMPLEX array, dimension (LDA,N)
The m-by-n matrix A.
AF (output) COMPLEX array, dimension (LDA,N)
Details of the RQ factorization of A, as returned by CGERQF.
See CGERQF for further details.
Q (output) COMPLEX array, dimension (LDA,N)
The n-by-n orthogonal matrix Q.
R (workspace) COMPLEX array, dimension (LDA,max(M,N))
LDA (input) INTEGER
The leading dimension of the arrays A, AF, Q and L.
LDA >= max(M,N).
TAU (output) COMPLEX array, dimension (min(M,N))
The scalar factors of the elementary reflectors, as returned
by CGERQF.
WORK (workspace) COMPLEX array, dimension (LWORK)
LWORK (input) INTEGER
The dimension of the array WORK.
RWORK (workspace) REAL array, dimension (max(M,N))
RESULT (output) REAL array, dimension (2)
The test ratios:
RESULT(1) = norm( R - A*Q' ) / ( N * norm(A) * EPS )
RESULT(2) = norm( I - Q*Q' ) / ( N * EPS )
=====================================================================
Parameter adjustments */
r_dim1 = *lda;
r_offset = 1 + r_dim1 * 1;
r__ -= r_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, "CGERQF", (ftnlen)6, (ftnlen)6);
cgerqf_(m, n, &af[af_offset], lda, &tau[1], &work[1], lwork, &info);
/* Copy details of Q */
claset_("Full", n, n, &c_b1, &c_b1, &q[q_offset], lda);
if (*m <= *n) {
if (*m > 0 && *m < *n) {
i__1 = *n - *m;
clacpy_("Full", m, &i__1, &af[af_offset], lda, &q_ref(*n - *m + 1,
1), lda);
}
if (*m > 1) {
i__1 = *m - 1;
i__2 = *m - 1;
clacpy_("Lower", &i__1, &i__2, &af_ref(2, *n - *m + 1), lda, &
q_ref(*n - *m + 2, *n - *m + 1), lda);
}
} else {
if (*n > 1) {
i__1 = *n - 1;
i__2 = *n - 1;
clacpy_("Lower", &i__1, &i__2, &af_ref(*m - *n + 2, 1), lda, &
q_ref(2, 1), lda);
}
}
/* Generate the n-by-n matrix Q */
s_copy(srnamc_1.srnamt, "CUNGRQ", (ftnlen)6, (ftnlen)6);
cungrq_(n, n, &minmn, &q[q_offset], lda, &tau[1], &work[1], lwork, &info);
/* Copy R */
claset_("Full", m, n, &c_b12, &c_b12, &r__[r_offset], lda);
if (*m <= *n) {
if (*m > 0) {
clacpy_("Upper", m, m, &af_ref(1, *n - *m + 1), lda, &r___ref(1, *
n - *m + 1), lda);
}
} else {
if (*m > *n && *n > 0) {
i__1 = *m - *n;
clacpy_("Full", &i__1, n, &af[af_offset], lda, &r__[r_offset],
lda);
}
if (*n > 0) {
clacpy_("Upper", n, n, &af_ref(*m - *n + 1, 1), lda, &r___ref(*m
- *n + 1, 1), lda);
}
}
/* Compute R - A*Q' */
cgemm_("No transpose", "Conjugate transpose", m, n, n, &c_b19, &a[
a_offset], lda, &q[q_offset], lda, &c_b20, &r__[r_offset], lda);
/* Compute norm( R - Q'*A ) / ( N * norm(A) * EPS ) . */
anorm = clange_("1", m, n, &a[a_offset], lda, &rwork[1]);
resid = clange_("1", m, n, &r__[r_offset], lda, &rwork[1]);
if (anorm > 0.f) {
result[1] = resid / (real) max(1,*n) / anorm / eps;
} else {
result[1] = 0.f;
}
/* Compute I - Q*Q' */
claset_("Full", n, n, &c_b12, &c_b20, &r__[r_offset], lda);
cherk_("Upper", "No transpose", n, n, &c_b28, &q[q_offset], lda, &c_b29, &
r__[r_offset], lda);
/* Compute norm( I - Q*Q' ) / ( N * EPS ) . */
resid = clansy_("1", "Upper", n, &r__[r_offset], lda, &rwork[1]);
result[2] = resid / (real) max(1,*n) / eps;
return 0;
/* End of CRQT01 */
} /* crqt01_ */
/* Subroutine */ int cerrrq_(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 cgerq2_(integer *, integer *, complex *,
integer *, complex *, complex *, integer *), cungr2_(integer *,
integer *, integer *, complex *, integer *, complex *, complex *,
integer *), cunmr2_(char *, char *, integer *, integer *, integer
*, complex *, integer *, complex *, complex *, integer *, complex
*, integer *), alaesm_(char *, logical *, integer
*), cgerqf_(integer *, integer *, complex *, integer *,
complex *, complex *, integer *, integer *), cgerqs_(integer *,
integer *, integer *, complex *, integer *, complex *, complex *,
integer *, complex *, integer *, integer *), chkxer_(char *,
integer *, integer *, logical *, logical *), cungrq_(
integer *, integer *, integer *, complex *, integer *, complex *,
complex *, integer *, integer *), cunmrq_(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 */
/* ======= */
/* CERRRQ tests the error exits for the COMPLEX routines */
/* that use the RQ 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 RQ factorization */
/* CGERQF */
s_copy(srnamc_1.srnamt, "CGERQF", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
cgerqf_(&c_n1, &c__0, a, &c__1, b, w, &c__1, &info);
chkxer_("CGERQF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
cgerqf_(&c__0, &c_n1, a, &c__1, b, w, &c__1, &info);
chkxer_("CGERQF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
cgerqf_(&c__2, &c__1, a, &c__1, b, w, &c__2, &info);
chkxer_("CGERQF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
cgerqf_(&c__2, &c__1, a, &c__2, b, w, &c__1, &info);
chkxer_("CGERQF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* CGERQ2 */
s_copy(srnamc_1.srnamt, "CGERQ2", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
cgerq2_(&c_n1, &c__0, a, &c__1, b, w, &info);
chkxer_("CGERQ2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
cgerq2_(&c__0, &c_n1, a, &c__1, b, w, &info);
chkxer_("CGERQ2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
cgerq2_(&c__2, &c__1, a, &c__1, b, w, &info);
chkxer_("CGERQ2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* CGERQS */
s_copy(srnamc_1.srnamt, "CGERQS", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
cgerqs_(&c_n1, &c__0, &c__0, a, &c__1, x, b, &c__1, w, &c__1, &info);
chkxer_("CGERQS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
cgerqs_(&c__0, &c_n1, &c__0, a, &c__1, x, b, &c__1, w, &c__1, &info);
chkxer_("CGERQS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
cgerqs_(&c__2, &c__1, &c__0, a, &c__2, x, b, &c__1, w, &c__1, &info);
chkxer_("CGERQS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
cgerqs_(&c__0, &c__0, &c_n1, a, &c__1, x, b, &c__1, w, &c__1, &info);
chkxer_("CGERQS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
cgerqs_(&c__2, &c__2, &c__0, a, &c__1, x, b, &c__2, w, &c__1, &info);
chkxer_("CGERQS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 8;
cgerqs_(&c__2, &c__2, &c__0, a, &c__2, x, b, &c__1, w, &c__1, &info);
chkxer_("CGERQS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 10;
cgerqs_(&c__1, &c__1, &c__2, a, &c__1, x, b, &c__1, w, &c__1, &info);
chkxer_("CGERQS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* CUNGRQ */
s_copy(srnamc_1.srnamt, "CUNGRQ", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
cungrq_(&c_n1, &c__0, &c__0, a, &c__1, x, w, &c__1, &info);
chkxer_("CUNGRQ", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
cungrq_(&c__0, &c_n1, &c__0, a, &c__1, x, w, &c__1, &info);
chkxer_("CUNGRQ", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
cungrq_(&c__2, &c__1, &c__0, a, &c__2, x, w, &c__2, &info);
chkxer_("CUNGRQ", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
cungrq_(&c__0, &c__0, &c_n1, a, &c__1, x, w, &c__1, &info);
chkxer_("CUNGRQ", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
cungrq_(&c__1, &c__2, &c__2, a, &c__1, x, w, &c__1, &info);
chkxer_("CUNGRQ", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
cungrq_(&c__2, &c__2, &c__0, a, &c__1, x, w, &c__2, &info);
chkxer_("CUNGRQ", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 8;
cungrq_(&c__2, &c__2, &c__0, a, &c__2, x, w, &c__1, &info);
chkxer_("CUNGRQ", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* CUNGR2 */
s_copy(srnamc_1.srnamt, "CUNGR2", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
cungr2_(&c_n1, &c__0, &c__0, a, &c__1, x, w, &info);
chkxer_("CUNGR2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
cungr2_(&c__0, &c_n1, &c__0, a, &c__1, x, w, &info);
chkxer_("CUNGR2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
cungr2_(&c__2, &c__1, &c__0, a, &c__2, x, w, &info);
chkxer_("CUNGR2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
cungr2_(&c__0, &c__0, &c_n1, a, &c__1, x, w, &info);
chkxer_("CUNGR2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
cungr2_(&c__1, &c__2, &c__2, a, &c__2, x, w, &info);
chkxer_("CUNGR2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
cungr2_(&c__2, &c__2, &c__0, a, &c__1, x, w, &info);
chkxer_("CUNGR2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* CUNMRQ */
s_copy(srnamc_1.srnamt, "CUNMRQ", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
cunmrq_("/", "N", &c__0, &c__0, &c__0, a, &c__1, x, af, &c__1, w, &c__1, &
info);
chkxer_("CUNMRQ", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
cunmrq_("L", "/", &c__0, &c__0, &c__0, a, &c__1, x, af, &c__1, w, &c__1, &
info);
chkxer_("CUNMRQ", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
cunmrq_("L", "N", &c_n1, &c__0, &c__0, a, &c__1, x, af, &c__1, w, &c__1, &
info);
chkxer_("CUNMRQ", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
cunmrq_("L", "N", &c__0, &c_n1, &c__0, a, &c__1, x, af, &c__1, w, &c__1, &
info);
chkxer_("CUNMRQ", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
cunmrq_("L", "N", &c__0, &c__0, &c_n1, a, &c__1, x, af, &c__1, w, &c__1, &
info);
chkxer_("CUNMRQ", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
cunmrq_("L", "N", &c__0, &c__1, &c__1, a, &c__1, x, af, &c__1, w, &c__1, &
info);
chkxer_("CUNMRQ", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
cunmrq_("R", "N", &c__1, &c__0, &c__1, a, &c__1, x, af, &c__1, w, &c__1, &
info);
chkxer_("CUNMRQ", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
cunmrq_("L", "N", &c__2, &c__1, &c__2, a, &c__1, x, af, &c__2, w, &c__1, &
info);
chkxer_("CUNMRQ", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
cunmrq_("R", "N", &c__1, &c__2, &c__2, a, &c__1, x, af, &c__1, w, &c__1, &
info);
chkxer_("CUNMRQ", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 10;
cunmrq_("L", "N", &c__2, &c__1, &c__0, a, &c__1, x, af, &c__1, w, &c__1, &
info);
chkxer_("CUNMRQ", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 12;
cunmrq_("L", "N", &c__1, &c__2, &c__0, a, &c__1, x, af, &c__1, w, &c__1, &
info);
chkxer_("CUNMRQ", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 12;
cunmrq_("R", "N", &c__2, &c__1, &c__0, a, &c__1, x, af, &c__2, w, &c__1, &
info);
chkxer_("CUNMRQ", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* CUNMR2 */
s_copy(srnamc_1.srnamt, "CUNMR2", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
cunmr2_("/", "N", &c__0, &c__0, &c__0, a, &c__1, x, af, &c__1, w, &info);
chkxer_("CUNMR2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
cunmr2_("L", "/", &c__0, &c__0, &c__0, a, &c__1, x, af, &c__1, w, &info);
chkxer_("CUNMR2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
cunmr2_("L", "N", &c_n1, &c__0, &c__0, a, &c__1, x, af, &c__1, w, &info);
chkxer_("CUNMR2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
cunmr2_("L", "N", &c__0, &c_n1, &c__0, a, &c__1, x, af, &c__1, w, &info);
chkxer_("CUNMR2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
cunmr2_("L", "N", &c__0, &c__0, &c_n1, a, &c__1, x, af, &c__1, w, &info);
chkxer_("CUNMR2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
cunmr2_("L", "N", &c__0, &c__1, &c__1, a, &c__1, x, af, &c__1, w, &info);
chkxer_("CUNMR2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
cunmr2_("R", "N", &c__1, &c__0, &c__1, a, &c__1, x, af, &c__1, w, &info);
chkxer_("CUNMR2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
cunmr2_("L", "N", &c__2, &c__1, &c__2, a, &c__1, x, af, &c__2, w, &info);
chkxer_("CUNMR2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
cunmr2_("R", "N", &c__1, &c__2, &c__2, a, &c__1, x, af, &c__1, w, &info);
chkxer_("CUNMR2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 10;
cunmr2_("L", "N", &c__2, &c__1, &c__0, a, &c__1, x, af, &c__1, w, &info);
chkxer_("CUNMR2", &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 CERRRQ */
} /* cerrrq_ */
/* Subroutine */ int crqt03_(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;
/* Builtin functions
Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen);
/* Local variables */
static char side[1];
static integer info, j;
extern /* Subroutine */ int cgemm_(char *, char *, integer *, integer *,
integer *, complex *, complex *, integer *, complex *, integer *,
complex *, complex *, integer *);
static integer iside;
extern logical lsame_(char *, char *);
static real resid;
static integer minmn;
static real cnorm;
static char trans[1];
static integer mc, nc;
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 *), clarnv_(integer *, integer *, integer *, complex *),
cungrq_(integer *, integer *, integer *, complex *, integer *,
complex *, complex *, integer *, integer *);
static integer itrans;
extern /* Subroutine */ int cunmrq_(char *, char *, integer *, integer *,
integer *, complex *, integer *, complex *, complex *, integer *,
complex *, integer *, integer *);
static real eps;
#define c___subscr(a_1,a_2) (a_2)*c_dim1 + a_1
#define c___ref(a_1,a_2) c__[c___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
=======
CRQT03 tests CUNMRQ, which computes Q*C, Q'*C, C*Q or C*Q'.
CRQT03 compares the results of a call to CUNMRQ with the results of
forming Q explicitly by a call to CUNGRQ and then performing matrix
multiplication by a call to CGEMM.
Arguments
=========
M (input) INTEGER
The number of rows or columns of the matrix C; C is n-by-m if
Q is applied from the left, or m-by-n if Q is applied from
the right. M >= 0.
N (input) INTEGER
The order of the orthogonal matrix Q. N >= 0.
K (input) INTEGER
The number of elementary reflectors whose product defines the
orthogonal matrix Q. N >= K >= 0.
AF (input) COMPLEX array, dimension (LDA,N)
Details of the RQ factorization of an m-by-n matrix, as
returned by CGERQF. See CGERQF for further details.
C (workspace) COMPLEX array, dimension (LDA,N)
CC (workspace) COMPLEX array, dimension (LDA,N)
Q (workspace) COMPLEX array, dimension (LDA,N)
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 RQ 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 n-by-n orthogonal matrix Q.
RESULT(1) = norm( Q*C - Q*C ) / ( N * norm(C) * EPS )
RESULT(2) = norm( C*Q - C*Q ) / ( N * norm(C) * EPS )
RESULT(3) = norm( Q'*C - Q'*C )/ ( N * norm(C) * EPS )
RESULT(4) = norm( C*Q' - C*Q' )/ ( N * norm(C) * EPS )
=====================================================================
Parameter adjustments */
q_dim1 = *lda;
q_offset = 1 + q_dim1 * 1;
q -= q_offset;
cc_dim1 = *lda;
cc_offset = 1 + cc_dim1 * 1;
cc -= cc_offset;
c_dim1 = *lda;
c_offset = 1 + c_dim1 * 1;
c__ -= c_offset;
af_dim1 = *lda;
af_offset = 1 + af_dim1 * 1;
af -= af_offset;
--tau;
--work;
--rwork;
--result;
/* Function Body */
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 rows of the factorization to the array Q */
claset_("Full", n, n, &c_b1, &c_b1, &q[q_offset], lda);
if (*k > 0 && *n > *k) {
i__1 = *n - *k;
clacpy_("Full", k, &i__1, &af_ref(*m - *k + 1, 1), lda, &q_ref(*n - *
k + 1, 1), lda);
}
if (*k > 1) {
i__1 = *k - 1;
i__2 = *k - 1;
clacpy_("Lower", &i__1, &i__2, &af_ref(*m - *k + 2, *n - *k + 1), lda,
&q_ref(*n - *k + 2, *n - *k + 1), lda);
}
/* Generate the n-by-n matrix Q */
s_copy(srnamc_1.srnamt, "CUNGRQ", (ftnlen)6, (ftnlen)6);
cungrq_(n, n, 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 = *n;
nc = *m;
} else {
*(unsigned char *)side = 'R';
mc = *m;
nc = *n;
}
/* Generate MC by NC matrix C */
i__1 = nc;
for (j = 1; j <= i__1; ++j) {
clarnv_(&c__2, iseed, &mc, &c___ref(1, j));
/* 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, "CUNMRQ", (ftnlen)6, (ftnlen)6);
if (*k > 0) {
cunmrq_(side, trans, &mc, &nc, k, &af_ref(*m - *k + 1, 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,*n) *
cnorm * eps);
/* L20: */
}
/* L30: */
}
return 0;
/* End of CRQT03 */
} /* crqt03_ */
/* Subroutine */ int crqt03_(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 */
/* ======= */
/* CRQT03 tests CUNMRQ, which computes Q*C, Q'*C, C*Q or C*Q'. */
/* CRQT03 compares the results of a call to CUNMRQ with the results of */
/* forming Q explicitly by a call to CUNGRQ and then performing matrix */
/* multiplication by a call to CGEMM. */
/* Arguments */
/* ========= */
/* M (input) INTEGER */
/* The number of rows or columns of the matrix C; C is n-by-m if */
/* Q is applied from the left, or m-by-n if Q is applied from */
/* the right. M >= 0. */
/* N (input) INTEGER */
/* The order of the orthogonal matrix Q. N >= 0. */
/* K (input) INTEGER */
/* The number of elementary reflectors whose product defines the */
/* orthogonal matrix Q. N >= K >= 0. */
/* AF (input) COMPLEX array, dimension (LDA,N) */
/* Details of the RQ factorization of an m-by-n matrix, as */
/* returned by CGERQF. See CGERQF for further details. */
/* C (workspace) COMPLEX array, dimension (LDA,N) */
/* CC (workspace) COMPLEX array, dimension (LDA,N) */
/* Q (workspace) COMPLEX array, dimension (LDA,N) */
/* 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 RQ 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 n-by-n orthogonal matrix Q. */
/* RESULT(1) = norm( Q*C - Q*C ) / ( N * norm(C) * EPS ) */
/* RESULT(2) = norm( C*Q - C*Q ) / ( N * norm(C) * EPS ) */
/* RESULT(3) = norm( Q'*C - Q'*C )/ ( N * norm(C) * EPS ) */
/* RESULT(4) = norm( C*Q' - C*Q' )/ ( N * 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 rows of the factorization to the array Q */
claset_("Full", n, n, &c_b1, &c_b1, &q[q_offset], lda);
if (*k > 0 && *n > *k) {
i__1 = *n - *k;
clacpy_("Full", k, &i__1, &af[*m - *k + 1 + af_dim1], lda, &q[*n - *k
+ 1 + q_dim1], lda);
}
if (*k > 1) {
i__1 = *k - 1;
i__2 = *k - 1;
clacpy_("Lower", &i__1, &i__2, &af[*m - *k + 2 + (*n - *k + 1) *
af_dim1], lda, &q[*n - *k + 2 + (*n - *k + 1) * q_dim1], lda);
}
/* Generate the n-by-n matrix Q */
s_copy(srnamc_1.srnamt, "CUNGRQ", (ftnlen)32, (ftnlen)6);
cungrq_(n, n, 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 = *n;
nc = *m;
} else {
*(unsigned char *)side = 'R';
mc = *m;
nc = *n;
}
/* 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, "CUNMRQ", (ftnlen)32, (ftnlen)6);
if (*k > 0) {
cunmrq_(side, trans, &mc, &nc, k, &af[*m - *k + 1 + af_dim1],
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,*n) *
cnorm * eps);
/* L20: */
}
/* L30: */
}
return 0;
/* End of CRQT03 */
} /* crqt03_ */
