/* Subroutine */ int clqt03_(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;
/* 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, 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 *),
cunglq_(integer *, integer *, integer *, complex *, integer *,
complex *, complex *, integer *, integer *), cunmlq_(char *, char
*, integer *, integer *, integer *, complex *, integer *, complex
*, complex *, integer *, complex *, integer *, integer *);
static integer itrans;
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
=======
CLQT03 tests CUNMLQ, which computes Q*C, Q'*C, C*Q or C*Q'.
CLQT03 compares the results of a call to CUNMLQ with the results of
forming Q explicitly by a call to CUNGLQ 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 LQ factorization of an m-by-n matrix, as
returned by CGELQF. See CGELQF 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 LQ 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");
/* Copy the first k rows of the factorization to the array Q */
claset_("Full", n, n, &c_b1, &c_b1, &q[q_offset], lda);
i__1 = *n - 1;
clacpy_("Upper", k, &i__1, &af_ref(1, 2), lda, &q_ref(1, 2), lda);
/* Generate the n-by-n matrix Q */
s_copy(srnamc_1.srnamt, "CUNGLQ", (ftnlen)6, (ftnlen)6);
cunglq_(n, n, k, &q[q_offset], lda, &tau[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, "CUNMLQ", (ftnlen)6, (ftnlen)6);
cunmlq_(side, trans, &mc, &nc, k, &af[af_offset], lda, &tau[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_b20, &q[
q_offset], lda, &c__[c_offset], lda, &c_b21, &cc[
cc_offset], lda);
} else {
cgemm_("No transpose", trans, &mc, &nc, &nc, &c_b20, &c__[
c_offset], lda, &q[q_offset], lda, &c_b21, &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 CLQT03 */
} /* clqt03_ */
/* Subroutine */ int cungbr_(char *vect, integer *m, integer *n, integer *k,
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;
/* Local variables */
integer i__, j, nb, mn;
extern logical lsame_(char *, char *);
integer iinfo;
logical wantq;
extern /* Subroutine */ int xerbla_(char *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *);
extern /* Subroutine */ int cunglq_(integer *, integer *, integer *,
complex *, integer *, complex *, complex *, integer *, integer *),
cungqr_(integer *, integer *, integer *, complex *, integer *,
complex *, complex *, integer *, integer *);
integer lwkopt;
logical lquery;
/* -- LAPACK routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* CUNGBR generates one of the complex unitary matrices Q or P**H */
/* determined by CGEBRD when reducing a complex matrix A to bidiagonal */
/* form: A = Q * B * P**H. Q and P**H are defined as products of */
/* elementary reflectors H(i) or G(i) respectively. */
/* If VECT = 'Q', A is assumed to have been an M-by-K matrix, and Q */
/* is of order M: */
/* if m >= k, Q = H(1) H(2) . . . H(k) and CUNGBR returns the first n */
/* columns of Q, where m >= n >= k; */
/* if m < k, Q = H(1) H(2) . . . H(m-1) and CUNGBR returns Q as an */
/* M-by-M matrix. */
/* If VECT = 'P', A is assumed to have been a K-by-N matrix, and P**H */
/* is of order N: */
/* if k < n, P**H = G(k) . . . G(2) G(1) and CUNGBR returns the first m */
/* rows of P**H, where n >= m >= k; */
/* if k >= n, P**H = G(n-1) . . . G(2) G(1) and CUNGBR returns P**H as */
/* an N-by-N matrix. */
/* Arguments */
/* ========= */
/* VECT (input) CHARACTER*1 */
/* Specifies whether the matrix Q or the matrix P**H is */
/* required, as defined in the transformation applied by CGEBRD: */
/* = 'Q': generate Q; */
/* = 'P': generate P**H. */
/* M (input) INTEGER */
/* The number of rows of the matrix Q or P**H to be returned. */
/* M >= 0. */
/* N (input) INTEGER */
/* The number of columns of the matrix Q or P**H to be returned. */
/* N >= 0. */
/* If VECT = 'Q', M >= N >= min(M,K); */
/* if VECT = 'P', N >= M >= min(N,K). */
/* K (input) INTEGER */
/* If VECT = 'Q', the number of columns in the original M-by-K */
/* matrix reduced by CGEBRD. */
/* If VECT = 'P', the number of rows in the original K-by-N */
/* matrix reduced by CGEBRD. */
/* K >= 0. */
/* A (input/output) COMPLEX array, dimension (LDA,N) */
/* On entry, the vectors which define the elementary reflectors, */
/* as returned by CGEBRD. */
/* On exit, the M-by-N matrix Q or P**H. */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= M. */
/* TAU (input) COMPLEX array, dimension */
/* (min(M,K)) if VECT = 'Q' */
/* (min(N,K)) if VECT = 'P' */
/* TAU(i) must contain the scalar factor of the elementary */
/* reflector H(i) or G(i), which determines Q or P**H, as */
/* returned by CGEBRD in its array argument TAUQ or TAUP. */
/* 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 >= max(1,min(M,N)). */
/* For optimum performance LWORK >= min(M,N)*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 */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input arguments */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--tau;
--work;
/* Function Body */
*info = 0;
wantq = lsame_(vect, "Q");
mn = min(*m,*n);
lquery = *lwork == -1;
if (! wantq && ! lsame_(vect, "P")) {
*info = -1;
} else if (*m < 0) {
*info = -2;
} else if (*n < 0 || wantq && (*n > *m || *n < min(*m,*k)) || ! wantq && (
*m > *n || *m < min(*n,*k))) {
*info = -3;
} else if (*k < 0) {
*info = -4;
} else if (*lda < max(1,*m)) {
*info = -6;
} else if (*lwork < max(1,mn) && ! lquery) {
*info = -9;
}
if (*info == 0) {
if (wantq) {
nb = ilaenv_(&c__1, "CUNGQR", " ", m, n, k, &c_n1);
} else {
nb = ilaenv_(&c__1, "CUNGLQ", " ", m, n, k, &c_n1);
}
lwkopt = max(1,mn) * nb;
work[1].r = (real) lwkopt, work[1].i = 0.f;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("CUNGBR", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible */
if (*m == 0 || *n == 0) {
work[1].r = 1.f, work[1].i = 0.f;
return 0;
}
if (wantq) {
/* Form Q, determined by a call to CGEBRD to reduce an m-by-k */
/* matrix */
if (*m >= *k) {
/* If m >= k, assume m >= n >= k */
cungqr_(m, n, k, &a[a_offset], lda, &tau[1], &work[1], lwork, &
iinfo);
} else {
/* If m < k, assume m = n */
/* 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 = *m; j >= 2; --j) {
i__1 = j * a_dim1 + 1;
a[i__1].r = 0.f, a[i__1].i = 0.f;
i__1 = *m;
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;
/* L10: */
}
/* L20: */
}
i__1 = a_dim1 + 1;
a[i__1].r = 1.f, a[i__1].i = 0.f;
i__1 = *m;
for (i__ = 2; i__ <= i__1; ++i__) {
i__2 = i__ + a_dim1;
a[i__2].r = 0.f, a[i__2].i = 0.f;
/* L30: */
}
if (*m > 1) {
/* Form Q(2:m,2:m) */
i__1 = *m - 1;
i__2 = *m - 1;
i__3 = *m - 1;
cungqr_(&i__1, &i__2, &i__3, &a[(a_dim1 << 1) + 2], lda, &tau[
1], &work[1], lwork, &iinfo);
}
}
} else {
/* Form P', determined by a call to CGEBRD to reduce a k-by-n */
/* matrix */
if (*k < *n) {
/* If k < n, assume k <= m <= n */
cunglq_(m, n, k, &a[a_offset], lda, &tau[1], &work[1], lwork, &
iinfo);
} else {
/* If k >= n, assume m = n */
/* Shift the vectors which define the elementary reflectors one */
/* row downward, and set the first row and column of P' to */
/* those of the unit matrix */
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;
/* L40: */
}
i__1 = *n;
for (j = 2; j <= i__1; ++j) {
for (i__ = j - 1; i__ >= 2; --i__) {
i__2 = i__ + j * a_dim1;
i__3 = i__ - 1 + j * a_dim1;
a[i__2].r = a[i__3].r, a[i__2].i = a[i__3].i;
/* L50: */
}
i__2 = j * a_dim1 + 1;
a[i__2].r = 0.f, a[i__2].i = 0.f;
/* L60: */
}
if (*n > 1) {
/* Form P'(2:n,2:n) */
i__1 = *n - 1;
i__2 = *n - 1;
i__3 = *n - 1;
cunglq_(&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 CUNGBR */
} /* cungbr_ */
/* Subroutine */ int clqt01_(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;
/* 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 cgelqf_(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 cunglq_(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 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
=======
CLQT01 tests CGELQF, which computes the LQ factorization of an m-by-n
matrix A, and partially tests CUNGLQ which forms the n-by-n
orthogonal matrix Q.
CLQT01 compares L 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 LQ factorization of A, as returned by CGELQF.
See CGELQF for further details.
Q (output) COMPLEX array, dimension (LDA,N)
The n-by-n 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 L.
LDA >= max(M,N).
TAU (output) COMPLEX array, dimension (min(M,N))
The scalar factors of the elementary reflectors, as returned
by CGELQF.
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( L - A*Q' ) / ( N * norm(A) * EPS )
RESULT(2) = norm( I - Q*Q' ) / ( N * 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, "CGELQF", (ftnlen)6, (ftnlen)6);
cgelqf_(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 (*n > 1) {
i__1 = *n - 1;
clacpy_("Upper", m, &i__1, &af_ref(1, 2), lda, &q_ref(1, 2), lda);
}
/* Generate the n-by-n matrix Q */
s_copy(srnamc_1.srnamt, "CUNGLQ", (ftnlen)6, (ftnlen)6);
cunglq_(n, n, &minmn, &q[q_offset], lda, &tau[1], &work[1], lwork, &info);
/* Copy L */
claset_("Full", m, n, &c_b10, &c_b10, &l[l_offset], lda);
clacpy_("Lower", m, n, &af[af_offset], lda, &l[l_offset], lda);
/* Compute L - A*Q' */
cgemm_("No transpose", "Conjugate transpose", m, n, n, &c_b15, &a[
a_offset], lda, &q[q_offset], lda, &c_b16, &l[l_offset], lda);
/* Compute norm( L - Q'*A ) / ( N * 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,*n) / anorm / eps;
} else {
result[1] = 0.f;
}
/* Compute I - Q*Q' */
claset_("Full", n, n, &c_b10, &c_b16, &l[l_offset], lda);
cherk_("Upper", "No transpose", n, n, &c_b24, &q[q_offset], lda, &c_b25, &
l[l_offset], lda);
/* Compute norm( I - Q*Q' ) / ( N * EPS ) . */
resid = clansy_("1", "Upper", n, &l[l_offset], lda, &rwork[1]);
result[2] = resid / (real) max(1,*n) / eps;
return 0;
/* End of CLQT01 */
} /* clqt01_ */
/* Subroutine */ int ctimlq_(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] = "CGELQF" "CUNGLQ" "CUNMLQ";
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;
extern /* Subroutine */ int cgelqf_(integer *, integer *, complex *,
integer *, complex *, complex *, integer *, integer *);
static integer lw, nx, reseed[4];
extern /* Subroutine */ int atimck_(integer *, char *, integer *, integer
*, integer *, integer *, integer *, integer *, ftnlen);
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 *), cunglq_(integer *, integer *,
integer *, complex *, integer *, complex *, complex *, integer *,
integer *), xlaenv_(integer *, integer *), cunmlq_(char *, char *,
integer *, integer *, integer *, complex *, integer *, complex *,
complex *, integer *, complex *, integer *, integer *);
extern doublereal smflop_(real *, real *, integer *);
static real untime;
static logical timsub[3];
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
=======
CTIMLQ times the LAPACK routines to perform the LQ 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 CUNMLQ.
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, "LQ", (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]) {
/* CGELQF: LQ factorization */
clacpy_("Full", &m, &n, &b[1], &lda, &a[1], &lda);
ic = 0;
s1 = second_();
L10:
cgelqf_(&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_("CGELQF", &m, &n, &c__0, &c__0, &nb);
reslts_ref(inb, im, ilda, 1) = smflop_(&ops, &time, &info)
;
} else {
/* If CGELQF was not timed, generate a matrix and factor
it using CGELQF 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);
cgelqf_(&m, &n, &a[1], &lda, &tau[1], &work[1], &lw, &
info);
}
if (timsub[1]) {
/* CUNGLQ: Generate orthogonal matrix Q from the LQ
factorization */
clacpy_("Full", &minmn, &n, &a[1], &lda, &b[1], &lda);
ic = 0;
s1 = second_();
L30:
cunglq_(&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_("CUNGLQ", &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 CUNMLQ 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: */
}
/* CUNMLQ: 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 LQ 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);
cgelqf_(&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:
cunmlq_(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_("CUNMLQ", &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 CTIMLQ */
} /* ctimlq_ */
/* Subroutine */ int cungbr_(char *vect, integer *m, integer *n, integer *k,
complex *a, integer *lda, complex *tau, complex *work, integer *lwork,
integer *info)
{
/* -- LAPACK routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
June 30, 1999
Purpose
=======
CUNGBR generates one of the complex unitary matrices Q or P**H
determined by CGEBRD when reducing a complex matrix A to bidiagonal
form: A = Q * B * P**H. Q and P**H are defined as products of
elementary reflectors H(i) or G(i) respectively.
If VECT = 'Q', A is assumed to have been an M-by-K matrix, and Q
is of order M:
if m >= k, Q = H(1) H(2) . . . H(k) and CUNGBR returns the first n
columns of Q, where m >= n >= k;
if m < k, Q = H(1) H(2) . . . H(m-1) and CUNGBR returns Q as an
M-by-M matrix.
If VECT = 'P', A is assumed to have been a K-by-N matrix, and P**H
is of order N:
if k < n, P**H = G(k) . . . G(2) G(1) and CUNGBR returns the first m
rows of P**H, where n >= m >= k;
if k >= n, P**H = G(n-1) . . . G(2) G(1) and CUNGBR returns P**H as
an N-by-N matrix.
Arguments
=========
VECT (input) CHARACTER*1
Specifies whether the matrix Q or the matrix P**H is
required, as defined in the transformation applied by CGEBRD:
= 'Q': generate Q;
= 'P': generate P**H.
M (input) INTEGER
The number of rows of the matrix Q or P**H to be returned.
M >= 0.
N (input) INTEGER
The number of columns of the matrix Q or P**H to be returned.
N >= 0.
If VECT = 'Q', M >= N >= min(M,K);
if VECT = 'P', N >= M >= min(N,K).
K (input) INTEGER
If VECT = 'Q', the number of columns in the original M-by-K
matrix reduced by CGEBRD.
If VECT = 'P', the number of rows in the original K-by-N
matrix reduced by CGEBRD.
K >= 0.
A (input/output) COMPLEX array, dimension (LDA,N)
On entry, the vectors which define the elementary reflectors,
as returned by CGEBRD.
On exit, the M-by-N matrix Q or P**H.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= M.
TAU (input) COMPLEX array, dimension
(min(M,K)) if VECT = 'Q'
(min(N,K)) if VECT = 'P'
TAU(i) must contain the scalar factor of the elementary
reflector H(i) or G(i), which determines Q or P**H, as
returned by CGEBRD in its array argument TAUQ or TAUP.
WORK (workspace/output) COMPLEX array, dimension (LWORK)
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input) INTEGER
The dimension of the array WORK. LWORK >= max(1,min(M,N)).
For optimum performance LWORK >= min(M,N)*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 */
/* Table of constant values */
static integer c__1 = 1;
static integer c_n1 = -1;
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3;
/* Local variables */
static integer i__, j;
extern logical lsame_(char *, char *);
static integer iinfo;
static logical wantq;
static integer nb, mn;
extern /* Subroutine */ int xerbla_(char *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *, ftnlen, ftnlen);
extern /* Subroutine */ int cunglq_(integer *, integer *, integer *,
complex *, integer *, complex *, complex *, integer *, integer *),
cungqr_(integer *, integer *, integer *, complex *, integer *,
complex *, complex *, integer *, integer *);
static integer lwkopt;
static logical lquery;
#define a_subscr(a_1,a_2) (a_2)*a_dim1 + a_1
#define a_ref(a_1,a_2) a[a_subscr(a_1,a_2)]
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
--tau;
--work;
/* Function Body */
*info = 0;
wantq = lsame_(vect, "Q");
mn = min(*m,*n);
lquery = *lwork == -1;
if (! wantq && ! lsame_(vect, "P")) {
*info = -1;
} else if (*m < 0) {
*info = -2;
} else if (*n < 0 || wantq && (*n > *m || *n < min(*m,*k)) || ! wantq && (
*m > *n || *m < min(*n,*k))) {
*info = -3;
} else if (*k < 0) {
*info = -4;
} else if (*lda < max(1,*m)) {
*info = -6;
} else if (*lwork < max(1,mn) && ! lquery) {
*info = -9;
}
if (*info == 0) {
if (wantq) {
nb = ilaenv_(&c__1, "CUNGQR", " ", m, n, k, &c_n1, (ftnlen)6, (
ftnlen)1);
} else {
nb = ilaenv_(&c__1, "CUNGLQ", " ", m, n, k, &c_n1, (ftnlen)6, (
ftnlen)1);
}
lwkopt = max(1,mn) * nb;
work[1].r = (real) lwkopt, work[1].i = 0.f;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("CUNGBR", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible */
if (*m == 0 || *n == 0) {
work[1].r = 1.f, work[1].i = 0.f;
return 0;
}
if (wantq) {
/* Form Q, determined by a call to CGEBRD to reduce an m-by-k
matrix */
if (*m >= *k) {
/* If m >= k, assume m >= n >= k */
cungqr_(m, n, k, &a[a_offset], lda, &tau[1], &work[1], lwork, &
iinfo);
} else {
/* If m < k, assume m = n
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 = *m; j >= 2; --j) {
i__1 = a_subscr(1, j);
a[i__1].r = 0.f, a[i__1].i = 0.f;
i__1 = *m;
for (i__ = j + 1; i__ <= i__1; ++i__) {
i__2 = a_subscr(i__, j);
i__3 = a_subscr(i__, j - 1);
a[i__2].r = a[i__3].r, a[i__2].i = a[i__3].i;
/* L10: */
}
/* L20: */
}
i__1 = a_subscr(1, 1);
a[i__1].r = 1.f, a[i__1].i = 0.f;
i__1 = *m;
for (i__ = 2; i__ <= i__1; ++i__) {
i__2 = a_subscr(i__, 1);
a[i__2].r = 0.f, a[i__2].i = 0.f;
/* L30: */
}
if (*m > 1) {
/* Form Q(2:m,2:m) */
i__1 = *m - 1;
i__2 = *m - 1;
i__3 = *m - 1;
cungqr_(&i__1, &i__2, &i__3, &a_ref(2, 2), lda, &tau[1], &
work[1], lwork, &iinfo);
}
}
} else {
/* Form P', determined by a call to CGEBRD to reduce a k-by-n
matrix */
if (*k < *n) {
/* If k < n, assume k <= m <= n */
cunglq_(m, n, k, &a[a_offset], lda, &tau[1], &work[1], lwork, &
iinfo);
} else {
/* If k >= n, assume m = n
Shift the vectors which define the elementary reflectors one
row downward, and set the first row and column of P' to
those of the unit matrix */
i__1 = a_subscr(1, 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 = a_subscr(i__, 1);
a[i__2].r = 0.f, a[i__2].i = 0.f;
/* L40: */
}
i__1 = *n;
for (j = 2; j <= i__1; ++j) {
for (i__ = j - 1; i__ >= 2; --i__) {
i__2 = a_subscr(i__, j);
i__3 = a_subscr(i__ - 1, j);
a[i__2].r = a[i__3].r, a[i__2].i = a[i__3].i;
/* L50: */
}
i__2 = a_subscr(1, j);
a[i__2].r = 0.f, a[i__2].i = 0.f;
/* L60: */
}
if (*n > 1) {
/* Form P'(2:n,2:n) */
i__1 = *n - 1;
i__2 = *n - 1;
i__3 = *n - 1;
cunglq_(&i__1, &i__2, &i__3, &a_ref(2, 2), lda, &tau[1], &
work[1], lwork, &iinfo);
}
}
}
work[1].r = (real) lwkopt, work[1].i = 0.f;
return 0;
/* End of CUNGBR */
} /* cungbr_ */
/* Subroutine */ int clqt01_(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;
/* 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 cgelqf_(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 cunglq_(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 */
/* ======= */
/* CLQT01 tests CGELQF, which computes the LQ factorization of an m-by-n */
/* matrix A, and partially tests CUNGLQ which forms the n-by-n */
/* orthogonal matrix Q. */
/* CLQT01 compares L 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 LQ factorization of A, as returned by CGELQF. */
/* See CGELQF for further details. */
/* Q (output) COMPLEX array, dimension (LDA,N) */
/* The n-by-n 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 L. */
/* LDA >= max(M,N). */
/* TAU (output) COMPLEX array, dimension (min(M,N)) */
/* The scalar factors of the elementary reflectors, as returned */
/* by CGELQF. */
/* 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( L - 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 */
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, "CGELQF", (ftnlen)6, (ftnlen)6);
cgelqf_(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 (*n > 1) {
i__1 = *n - 1;
clacpy_("Upper", m, &i__1, &af[(af_dim1 << 1) + 1], lda, &q[(q_dim1 <<
1) + 1], lda);
}
/* Generate the n-by-n matrix Q */
s_copy(srnamc_1.srnamt, "CUNGLQ", (ftnlen)6, (ftnlen)6);
cunglq_(n, n, &minmn, &q[q_offset], lda, &tau[1], &work[1], lwork, &info);
/* Copy L */
claset_("Full", m, n, &c_b10, &c_b10, &l[l_offset], lda);
clacpy_("Lower", m, n, &af[af_offset], lda, &l[l_offset], lda);
/* Compute L - A*Q' */
cgemm_("No transpose", "Conjugate transpose", m, n, n, &c_b15, &a[
a_offset], lda, &q[q_offset], lda, &c_b16, &l[l_offset], lda);
/* Compute norm( L - Q'*A ) / ( N * 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,*n) / anorm / eps;
} else {
result[1] = 0.f;
}
/* Compute I - Q*Q' */
claset_("Full", n, n, &c_b10, &c_b16, &l[l_offset], lda);
cherk_("Upper", "No transpose", n, n, &c_b24, &q[q_offset], lda, &c_b25, &
l[l_offset], lda);
/* Compute norm( I - Q*Q' ) / ( N * EPS ) . */
resid = clansy_("1", "Upper", n, &l[l_offset], lda, &rwork[1]);
result[2] = resid / (real) max(1,*n) / eps;
return 0;
/* End of CLQT01 */
} /* clqt01_ */
/* Subroutine */ int clqt03_(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;
/* Local variables */
integer j, mc, nc;
real eps;
char side[1];
integer info;
integer iside;
real resid, 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 */
/* ======= */
/* CLQT03 tests CUNMLQ, which computes Q*C, Q'*C, C*Q or C*Q'. */
/* CLQT03 compares the results of a call to CUNMLQ with the results of */
/* forming Q explicitly by a call to CUNGLQ 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 LQ factorization of an m-by-n matrix, as */
/* returned by CGELQF. See CGELQF 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 LQ 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");
/* Copy the first k rows of the factorization to the array Q */
claset_("Full", n, n, &c_b1, &c_b1, &q[q_offset], lda);
i__1 = *n - 1;
clacpy_("Upper", k, &i__1, &af[(af_dim1 << 1) + 1], lda, &q[(q_dim1 << 1)
+ 1], lda);
/* Generate the n-by-n matrix Q */
s_copy(srnamc_1.srnamt, "CUNGLQ", (ftnlen)32, (ftnlen)6);
cunglq_(n, n, k, &q[q_offset], lda, &tau[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, "CUNMLQ", (ftnlen)32, (ftnlen)6);
cunmlq_(side, trans, &mc, &nc, k, &af[af_offset], lda, &tau[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_b20, &q[
q_offset], lda, &c__[c_offset], lda, &c_b21, &cc[
cc_offset], lda);
} else {
cgemm_("No transpose", trans, &mc, &nc, &nc, &c_b20, &c__[
c_offset], lda, &q[q_offset], lda, &c_b21, &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 CLQT03 */
} /* clqt03_ */
