/* Subroutine */ int cgeqls_(integer *m, integer *n, integer *nrhs, complex *
a, integer *lda, complex *tau, complex *b, integer *ldb, complex *
work, integer *lwork, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, i__1;
/* Local variables */
/* -- LAPACK routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* Solve the least squares problem */
/* min || A*X - B || */
/* using the QL factorization */
/* A = Q*L */
/* computed by CGEQLF. */
/* 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. M >= N >= 0. */
/* NRHS (input) INTEGER */
/* The number of columns of B. NRHS >= 0. */
/* A (input) COMPLEX array, dimension (LDA,N) */
/* Details of the QL factorization of the original matrix A as */
/* returned by CGEQLF. */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= M. */
/* TAU (input) COMPLEX array, dimension (N) */
/* Details of the orthogonal matrix Q. */
/* B (input/output) COMPLEX array, dimension (LDB,NRHS) */
/* On entry, the m-by-nrhs right hand side matrix B. */
/* On exit, the n-by-nrhs solution matrix X, stored in rows */
/* m-n+1:m. */
/* LDB (input) INTEGER */
/* The leading dimension of the array B. LDB >= M. */
/* WORK (workspace) COMPLEX array, dimension (LWORK) */
/* LWORK (input) INTEGER */
/* The length of the array WORK. LWORK must be at least NRHS, */
/* and should be at least NRHS*NB, where NB is the block size */
/* for this environment. */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input arguments. */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--tau;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
--work;
/* Function Body */
*info = 0;
if (*m < 0) {
*info = -1;
} else if (*n < 0 || *n > *m) {
*info = -2;
} else if (*nrhs < 0) {
*info = -3;
} else if (*lda < max(1,*m)) {
*info = -5;
} else if (*ldb < max(1,*m)) {
*info = -8;
} else if (*lwork < 1 || *lwork < *nrhs && *m > 0 && *n > 0) {
*info = -10;
}
if (*info != 0) {
i__1 = -(*info);
this_xerbla_("CGEQLS", &i__1);
return 0;
}
/* Quick return if possible */
if (*n == 0 || *nrhs == 0 || *m == 0) {
return 0;
}
/* B := Q' * B */
cunmql_("Left", "Conjugate transpose", m, nrhs, n, &a[a_offset], lda, &
tau[1], &b[b_offset], ldb, &work[1], lwork, info);
/* Solve L*X = B(m-n+1:m,:) */
ctrsm_("Left", "Lower", "No transpose", "Non-unit", n, nrhs, &c_b1, &a[*m
- *n + 1 + a_dim1], lda, &b[*m - *n + 1 + b_dim1], ldb);
return 0;
/* End of CGEQLS */
} /* cgeqls_ */
/* Subroutine */ int cunmtr_(char *side, char *uplo, char *trans, integer *m,
integer *n, complex *a, integer *lda, complex *tau, complex *c__,
integer *ldc, complex *work, integer *lwork, integer *info)
{
/* System generated locals */
address a__1[2];
integer a_dim1, a_offset, c_dim1, c_offset, i__1[2], i__2, i__3;
char ch__1[2];
/* Builtin functions */
/* Subroutine */ int s_cat(char *, char **, integer *, integer *, ftnlen);
/* Local variables */
integer i1, i2, nb, mi, ni, nq, nw;
logical left;
extern logical lsame_(char *, char *);
integer iinfo;
logical upper;
extern /* Subroutine */ int xerbla_(char *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *);
extern /* Subroutine */ int cunmql_(char *, char *, integer *, integer *,
integer *, complex *, integer *, complex *, complex *, integer *,
complex *, integer *, integer *), cunmqr_(char *,
char *, integer *, integer *, integer *, complex *, integer *,
complex *, complex *, integer *, 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 */
/* ======= */
/* CUNMTR overwrites the general complex M-by-N matrix C with */
/* SIDE = 'L' SIDE = 'R' */
/* TRANS = 'N': Q * C C * Q */
/* TRANS = 'C': Q**H * C C * Q**H */
/* where Q is a complex unitary matrix of order nq, with nq = m if */
/* SIDE = 'L' and nq = n if SIDE = 'R'. Q is defined as the product of */
/* nq-1 elementary reflectors, as returned by CHETRD: */
/* if UPLO = 'U', Q = H(nq-1) . . . H(2) H(1); */
/* if UPLO = 'L', Q = H(1) H(2) . . . H(nq-1). */
/* Arguments */
/* ========= */
/* SIDE (input) CHARACTER*1 */
/* = 'L': apply Q or Q**H from the Left; */
/* = 'R': apply Q or Q**H from the Right. */
/* UPLO (input) CHARACTER*1 */
/* = 'U': Upper triangle of A contains elementary reflectors */
/* from CHETRD; */
/* = 'L': Lower triangle of A contains elementary reflectors */
/* from CHETRD. */
/* TRANS (input) CHARACTER*1 */
/* = 'N': No transpose, apply Q; */
/* = 'C': Conjugate transpose, apply Q**H. */
/* M (input) INTEGER */
/* The number of rows of the matrix C. M >= 0. */
/* N (input) INTEGER */
/* The number of columns of the matrix C. N >= 0. */
/* A (input) COMPLEX array, dimension */
/* (LDA,M) if SIDE = 'L' */
/* (LDA,N) if SIDE = 'R' */
/* The vectors which define the elementary reflectors, as */
/* returned by CHETRD. */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. */
/* LDA >= max(1,M) if SIDE = 'L'; LDA >= max(1,N) if SIDE = 'R'. */
/* TAU (input) COMPLEX array, dimension */
/* (M-1) if SIDE = 'L' */
/* (N-1) if SIDE = 'R' */
/* TAU(i) must contain the scalar factor of the elementary */
/* reflector H(i), as returned by CHETRD. */
/* C (input/output) COMPLEX array, dimension (LDC,N) */
/* On entry, the M-by-N matrix C. */
/* On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q. */
/* LDC (input) INTEGER */
/* The leading dimension of the array C. LDC >= max(1,M). */
/* 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. */
/* If SIDE = 'L', LWORK >= max(1,N); */
/* if SIDE = 'R', LWORK >= max(1,M). */
/* For optimum performance LWORK >= N*NB if SIDE = 'L', and */
/* LWORK >=M*NB if SIDE = 'R', 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 */
/* ===================================================================== */
/* .. 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;
c_dim1 = *ldc;
c_offset = 1 + c_dim1;
c__ -= c_offset;
--work;
/* Function Body */
*info = 0;
left = lsame_(side, "L");
upper = lsame_(uplo, "U");
lquery = *lwork == -1;
/* NQ is the order of Q and NW is the minimum dimension of WORK */
if (left) {
nq = *m;
nw = *n;
} else {
nq = *n;
nw = *m;
}
if (! left && ! lsame_(side, "R")) {
*info = -1;
} else if (! upper && ! lsame_(uplo, "L")) {
*info = -2;
} else if (! lsame_(trans, "N") && ! lsame_(trans,
"C")) {
*info = -3;
} else if (*m < 0) {
*info = -4;
} else if (*n < 0) {
*info = -5;
} else if (*lda < max(1,nq)) {
*info = -7;
} else if (*ldc < max(1,*m)) {
*info = -10;
} else if (*lwork < max(1,nw) && ! lquery) {
*info = -12;
}
if (*info == 0) {
if (upper) {
if (left) {
/* Writing concatenation */
i__1[0] = 1, a__1[0] = side;
i__1[1] = 1, a__1[1] = trans;
s_cat(ch__1, a__1, i__1, &c__2, (ftnlen)2);
i__2 = *m - 1;
i__3 = *m - 1;
nb = ilaenv_(&c__1, "CUNMQL", ch__1, &i__2, n, &i__3, &c_n1);
} else {
/* Writing concatenation */
i__1[0] = 1, a__1[0] = side;
i__1[1] = 1, a__1[1] = trans;
s_cat(ch__1, a__1, i__1, &c__2, (ftnlen)2);
i__2 = *n - 1;
i__3 = *n - 1;
nb = ilaenv_(&c__1, "CUNMQL", ch__1, m, &i__2, &i__3, &c_n1);
}
} else {
if (left) {
/* Writing concatenation */
i__1[0] = 1, a__1[0] = side;
i__1[1] = 1, a__1[1] = trans;
s_cat(ch__1, a__1, i__1, &c__2, (ftnlen)2);
i__2 = *m - 1;
i__3 = *m - 1;
nb = ilaenv_(&c__1, "CUNMQR", ch__1, &i__2, n, &i__3, &c_n1);
} else {
/* Writing concatenation */
i__1[0] = 1, a__1[0] = side;
i__1[1] = 1, a__1[1] = trans;
s_cat(ch__1, a__1, i__1, &c__2, (ftnlen)2);
i__2 = *n - 1;
i__3 = *n - 1;
nb = ilaenv_(&c__1, "CUNMQR", ch__1, m, &i__2, &i__3, &c_n1);
}
}
lwkopt = max(1,nw) * nb;
work[1].r = (real) lwkopt, work[1].i = 0.f;
}
if (*info != 0) {
i__2 = -(*info);
xerbla_("CUNMTR", &i__2);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible */
if (*m == 0 || *n == 0 || nq == 1) {
work[1].r = 1.f, work[1].i = 0.f;
return 0;
}
if (left) {
mi = *m - 1;
ni = *n;
} else {
mi = *m;
ni = *n - 1;
}
if (upper) {
/* Q was determined by a call to CHETRD with UPLO = 'U' */
i__2 = nq - 1;
cunmql_(side, trans, &mi, &ni, &i__2, &a[(a_dim1 << 1) + 1], lda, &
tau[1], &c__[c_offset], ldc, &work[1], lwork, &iinfo);
} else {
/* Q was determined by a call to CHETRD with UPLO = 'L' */
if (left) {
i1 = 2;
i2 = 1;
} else {
i1 = 1;
i2 = 2;
}
i__2 = nq - 1;
cunmqr_(side, trans, &mi, &ni, &i__2, &a[a_dim1 + 2], lda, &tau[1], &
c__[i1 + i2 * c_dim1], ldc, &work[1], lwork, &iinfo);
}
work[1].r = (real) lwkopt, work[1].i = 0.f;
return 0;
/* End of CUNMTR */
} /* cunmtr_ */
/* Subroutine */
int cunmtr_(char *side, char *uplo, char *trans, integer *m, integer *n, complex *a, integer *lda, complex *tau, complex *c__, integer *ldc, complex *work, integer *lwork, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, c_dim1, c_offset, i__2, i__3;
char ch__1[2];
/* Builtin functions */
/* Subroutine */
/* Local variables */
integer i1, i2, nb, mi, ni, nq, nw;
logical left;
extern logical lsame_(char *, char *);
integer iinfo;
logical upper;
extern /* Subroutine */
int xerbla_(char *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *);
extern /* Subroutine */
int cunmql_(char *, char *, integer *, integer *, integer *, complex *, integer *, complex *, complex *, integer *, complex *, integer *, integer *), cunmqr_(char *, char *, integer *, integer *, integer *, complex *, integer *, complex *, complex *, integer *, complex *, integer *, integer *);
integer lwkopt;
logical lquery;
/* -- LAPACK computational routine (version 3.4.0) -- */
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
/* November 2011 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* ===================================================================== */
/* .. 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;
c_dim1 = *ldc;
c_offset = 1 + c_dim1;
c__ -= c_offset;
--work;
/* Function Body */
*info = 0;
left = lsame_(side, "L");
upper = lsame_(uplo, "U");
lquery = *lwork == -1;
/* NQ is the order of Q and NW is the minimum dimension of WORK */
if (left)
{
nq = *m;
nw = *n;
}
else
{
nq = *n;
nw = *m;
}
if (! left && ! lsame_(side, "R"))
{
*info = -1;
}
else if (! upper && ! lsame_(uplo, "L"))
{
*info = -2;
}
else if (! lsame_(trans, "N") && ! lsame_(trans, "C"))
{
*info = -3;
}
else if (*m < 0)
{
*info = -4;
}
else if (*n < 0)
{
*info = -5;
}
else if (*lda < max(1,nq))
{
*info = -7;
}
else if (*ldc < max(1,*m))
{
*info = -10;
}
else if (*lwork < max(1,nw) && ! lquery)
{
*info = -12;
}
if (*info == 0)
{
if (upper)
{
if (left)
{
i__2 = *m - 1;
i__3 = *m - 1;
nb = ilaenv_(&c__1, "CUNMQL", ch__1, &i__2, n, &i__3, &c_n1);
}
else
{
i__2 = *n - 1;
i__3 = *n - 1;
nb = ilaenv_(&c__1, "CUNMQL", ch__1, m, &i__2, &i__3, &c_n1);
}
}
else
{
if (left)
{
i__2 = *m - 1;
i__3 = *m - 1;
nb = ilaenv_(&c__1, "CUNMQR", ch__1, &i__2, n, &i__3, &c_n1);
}
else
{
i__2 = *n - 1;
i__3 = *n - 1;
nb = ilaenv_(&c__1, "CUNMQR", ch__1, m, &i__2, &i__3, &c_n1);
}
}
lwkopt = max(1,nw) * nb;
work[1].r = (real) lwkopt;
work[1].i = 0.f; // , expr subst
}
if (*info != 0)
{
i__2 = -(*info);
xerbla_("CUNMTR", &i__2);
return 0;
}
else if (lquery)
{
return 0;
}
/* Quick return if possible */
if (*m == 0 || *n == 0 || nq == 1)
{
work[1].r = 1.f;
work[1].i = 0.f; // , expr subst
return 0;
}
if (left)
{
mi = *m - 1;
ni = *n;
}
else
{
mi = *m;
ni = *n - 1;
}
if (upper)
{
/* Q was determined by a call to CHETRD with UPLO = 'U' */
i__2 = nq - 1;
cunmql_(side, trans, &mi, &ni, &i__2, &a[(a_dim1 << 1) + 1], lda, & tau[1], &c__[c_offset], ldc, &work[1], lwork, &iinfo);
}
else
{
/* Q was determined by a call to CHETRD with UPLO = 'L' */
if (left)
{
i1 = 2;
i2 = 1;
}
else
{
i1 = 1;
i2 = 2;
}
i__2 = nq - 1;
cunmqr_(side, trans, &mi, &ni, &i__2, &a[a_dim1 + 2], lda, &tau[1], & c__[i1 + i2 * c_dim1], ldc, &work[1], lwork, &iinfo);
}
work[1].r = (real) lwkopt;
work[1].i = 0.f; // , expr subst
return 0;
/* End of CUNMTR */
}
/* Subroutine */ int cerrql_(char *path, integer *nunit)
{
/* System generated locals */
integer i__1;
real r__1, r__2;
complex q__1;
/* Builtin functions */
integer s_wsle(cilist *), e_wsle(void);
/* Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen);
/* Local variables */
complex a[4] /* was [2][2] */, b[2];
integer i__, j;
complex w[2], x[2], af[4] /* was [2][2] */;
integer info;
extern /* Subroutine */ int cgeql2_(integer *, integer *, complex *,
integer *, complex *, complex *, integer *), cung2l_(integer *,
integer *, integer *, complex *, integer *, complex *, complex *,
integer *), cunm2l_(char *, char *, integer *, integer *, integer
*, complex *, integer *, complex *, complex *, integer *, complex
*, integer *), cgeqlf_(integer *, integer *,
complex *, integer *, complex *, complex *, integer *, integer *),
alaesm_(char *, logical *, integer *), cgeqls_(integer *,
integer *, integer *, complex *, integer *, complex *, complex *,
integer *, complex *, integer *, integer *), chkxer_(char *,
integer *, integer *, logical *, logical *), cungql_(
integer *, integer *, integer *, complex *, integer *, complex *,
complex *, integer *, integer *), cunmql_(char *, char *, integer
*, integer *, integer *, complex *, integer *, complex *, complex
*, integer *, complex *, integer *, integer *);
/* Fortran I/O blocks */
static cilist io___1 = { 0, 0, 0, 0, 0 };
/* -- LAPACK test routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* CERRQL tests the error exits for the COMPLEX routines */
/* that use the QL decomposition of a general matrix. */
/* Arguments */
/* ========= */
/* PATH (input) CHARACTER*3 */
/* The LAPACK path name for the routines to be tested. */
/* NUNIT (input) INTEGER */
/* The unit number for output. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Scalars in Common .. */
/* .. */
/* .. Common blocks .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
infoc_1.nout = *nunit;
io___1.ciunit = infoc_1.nout;
s_wsle(&io___1);
e_wsle();
/* Set the variables to innocuous values. */
for (j = 1; j <= 2; ++j) {
for (i__ = 1; i__ <= 2; ++i__) {
i__1 = i__ + (j << 1) - 3;
r__1 = 1.f / (real) (i__ + j);
r__2 = -1.f / (real) (i__ + j);
q__1.r = r__1, q__1.i = r__2;
a[i__1].r = q__1.r, a[i__1].i = q__1.i;
i__1 = i__ + (j << 1) - 3;
r__1 = 1.f / (real) (i__ + j);
r__2 = -1.f / (real) (i__ + j);
q__1.r = r__1, q__1.i = r__2;
af[i__1].r = q__1.r, af[i__1].i = q__1.i;
/* L10: */
}
i__1 = j - 1;
b[i__1].r = 0.f, b[i__1].i = 0.f;
i__1 = j - 1;
w[i__1].r = 0.f, w[i__1].i = 0.f;
i__1 = j - 1;
x[i__1].r = 0.f, x[i__1].i = 0.f;
/* L20: */
}
infoc_1.ok = TRUE_;
/* Error exits for QL factorization */
/* CGEQLF */
s_copy(srnamc_1.srnamt, "CGEQLF", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
cgeqlf_(&c_n1, &c__0, a, &c__1, b, w, &c__1, &info);
chkxer_("CGEQLF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
cgeqlf_(&c__0, &c_n1, a, &c__1, b, w, &c__1, &info);
chkxer_("CGEQLF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
cgeqlf_(&c__2, &c__1, a, &c__1, b, w, &c__1, &info);
chkxer_("CGEQLF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
cgeqlf_(&c__1, &c__2, a, &c__1, b, w, &c__1, &info);
chkxer_("CGEQLF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* CGEQL2 */
s_copy(srnamc_1.srnamt, "CGEQL2", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
cgeql2_(&c_n1, &c__0, a, &c__1, b, w, &info);
chkxer_("CGEQL2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
cgeql2_(&c__0, &c_n1, a, &c__1, b, w, &info);
chkxer_("CGEQL2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
cgeql2_(&c__2, &c__1, a, &c__1, b, w, &info);
chkxer_("CGEQL2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* CGEQLS */
s_copy(srnamc_1.srnamt, "CGEQLS", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
cgeqls_(&c_n1, &c__0, &c__0, a, &c__1, x, b, &c__1, w, &c__1, &info);
chkxer_("CGEQLS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
cgeqls_(&c__0, &c_n1, &c__0, a, &c__1, x, b, &c__1, w, &c__1, &info);
chkxer_("CGEQLS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
cgeqls_(&c__1, &c__2, &c__0, a, &c__1, x, b, &c__1, w, &c__1, &info);
chkxer_("CGEQLS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
cgeqls_(&c__0, &c__0, &c_n1, a, &c__1, x, b, &c__1, w, &c__1, &info);
chkxer_("CGEQLS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
cgeqls_(&c__2, &c__1, &c__0, a, &c__1, x, b, &c__2, w, &c__1, &info);
chkxer_("CGEQLS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 8;
cgeqls_(&c__2, &c__1, &c__0, a, &c__2, x, b, &c__1, w, &c__1, &info);
chkxer_("CGEQLS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 10;
cgeqls_(&c__1, &c__1, &c__2, a, &c__1, x, b, &c__1, w, &c__1, &info);
chkxer_("CGEQLS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* CUNGQL */
s_copy(srnamc_1.srnamt, "CUNGQL", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
cungql_(&c_n1, &c__0, &c__0, a, &c__1, x, w, &c__1, &info);
chkxer_("CUNGQL", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
cungql_(&c__0, &c_n1, &c__0, a, &c__1, x, w, &c__1, &info);
chkxer_("CUNGQL", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
cungql_(&c__1, &c__2, &c__0, a, &c__1, x, w, &c__2, &info);
chkxer_("CUNGQL", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
cungql_(&c__0, &c__0, &c_n1, a, &c__1, x, w, &c__1, &info);
chkxer_("CUNGQL", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
cungql_(&c__1, &c__1, &c__2, a, &c__1, x, w, &c__1, &info);
chkxer_("CUNGQL", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
cungql_(&c__2, &c__1, &c__0, a, &c__1, x, w, &c__1, &info);
chkxer_("CUNGQL", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 8;
cungql_(&c__2, &c__2, &c__0, a, &c__2, x, w, &c__1, &info);
chkxer_("CUNGQL", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* CUNG2L */
s_copy(srnamc_1.srnamt, "CUNG2L", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
cung2l_(&c_n1, &c__0, &c__0, a, &c__1, x, w, &info);
chkxer_("CUNG2L", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
cung2l_(&c__0, &c_n1, &c__0, a, &c__1, x, w, &info);
chkxer_("CUNG2L", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
cung2l_(&c__1, &c__2, &c__0, a, &c__1, x, w, &info);
chkxer_("CUNG2L", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
cung2l_(&c__0, &c__0, &c_n1, a, &c__1, x, w, &info);
chkxer_("CUNG2L", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
cung2l_(&c__2, &c__1, &c__2, a, &c__2, x, w, &info);
chkxer_("CUNG2L", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
cung2l_(&c__2, &c__1, &c__0, a, &c__1, x, w, &info);
chkxer_("CUNG2L", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* CUNMQL */
s_copy(srnamc_1.srnamt, "CUNMQL", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
cunmql_("/", "N", &c__0, &c__0, &c__0, a, &c__1, x, af, &c__1, w, &c__1, &
info);
chkxer_("CUNMQL", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
cunmql_("L", "/", &c__0, &c__0, &c__0, a, &c__1, x, af, &c__1, w, &c__1, &
info);
chkxer_("CUNMQL", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
cunmql_("L", "N", &c_n1, &c__0, &c__0, a, &c__1, x, af, &c__1, w, &c__1, &
info);
chkxer_("CUNMQL", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
cunmql_("L", "N", &c__0, &c_n1, &c__0, a, &c__1, x, af, &c__1, w, &c__1, &
info);
chkxer_("CUNMQL", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
cunmql_("L", "N", &c__0, &c__0, &c_n1, a, &c__1, x, af, &c__1, w, &c__1, &
info);
chkxer_("CUNMQL", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
cunmql_("L", "N", &c__0, &c__1, &c__1, a, &c__1, x, af, &c__1, w, &c__1, &
info);
chkxer_("CUNMQL", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
cunmql_("R", "N", &c__1, &c__0, &c__1, a, &c__1, x, af, &c__1, w, &c__1, &
info);
chkxer_("CUNMQL", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
cunmql_("L", "N", &c__2, &c__1, &c__0, a, &c__1, x, af, &c__2, w, &c__1, &
info);
chkxer_("CUNMQL", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
cunmql_("R", "N", &c__1, &c__2, &c__0, a, &c__1, x, af, &c__1, w, &c__1, &
info);
chkxer_("CUNMQL", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 10;
cunmql_("L", "N", &c__2, &c__1, &c__0, a, &c__2, x, af, &c__1, w, &c__1, &
info);
chkxer_("CUNMQL", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 12;
cunmql_("L", "N", &c__1, &c__2, &c__0, a, &c__1, x, af, &c__1, w, &c__1, &
info);
chkxer_("CUNMQL", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 12;
cunmql_("R", "N", &c__2, &c__1, &c__0, a, &c__1, x, af, &c__2, w, &c__1, &
info);
chkxer_("CUNMQL", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* CUNM2L */
s_copy(srnamc_1.srnamt, "CUNM2L", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
cunm2l_("/", "N", &c__0, &c__0, &c__0, a, &c__1, x, af, &c__1, w, &info);
chkxer_("CUNM2L", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
cunm2l_("L", "/", &c__0, &c__0, &c__0, a, &c__1, x, af, &c__1, w, &info);
chkxer_("CUNM2L", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
cunm2l_("L", "N", &c_n1, &c__0, &c__0, a, &c__1, x, af, &c__1, w, &info);
chkxer_("CUNM2L", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
cunm2l_("L", "N", &c__0, &c_n1, &c__0, a, &c__1, x, af, &c__1, w, &info);
chkxer_("CUNM2L", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
cunm2l_("L", "N", &c__0, &c__0, &c_n1, a, &c__1, x, af, &c__1, w, &info);
chkxer_("CUNM2L", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
cunm2l_("L", "N", &c__0, &c__1, &c__1, a, &c__1, x, af, &c__1, w, &info);
chkxer_("CUNM2L", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
cunm2l_("R", "N", &c__1, &c__0, &c__1, a, &c__1, x, af, &c__1, w, &info);
chkxer_("CUNM2L", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
cunm2l_("L", "N", &c__2, &c__1, &c__0, a, &c__1, x, af, &c__2, w, &info);
chkxer_("CUNM2L", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
cunm2l_("R", "N", &c__1, &c__2, &c__0, a, &c__1, x, af, &c__1, w, &info);
chkxer_("CUNM2L", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 10;
cunm2l_("L", "N", &c__2, &c__1, &c__0, a, &c__2, x, af, &c__1, w, &info);
chkxer_("CUNM2L", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* Print a summary line. */
alaesm_(path, &infoc_1.ok, &infoc_1.nout);
return 0;
/* End of CERRQL */
} /* cerrql_ */
/* Subroutine */ int cqlt03_(integer *m, integer *n, integer *k, complex *af,
complex *c__, complex *cc, complex *q, integer *lda, complex *tau,
complex *work, integer *lwork, real *rwork, real *result)
{
/* Initialized data */
static integer iseed[4] = { 1988,1989,1990,1991 };
/* System generated locals */
integer af_dim1, af_offset, c_dim1, c_offset, cc_dim1, cc_offset, q_dim1,
q_offset, i__1, i__2;
/* Local variables */
integer j, mc, nc;
real eps;
char side[1];
integer info;
integer iside;
real resid;
integer minmn;
real cnorm;
char trans[1];
integer itrans;
/* -- LAPACK test routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* CQLT03 tests CUNMQL, which computes Q*C, Q'*C, C*Q or C*Q'. */
/* CQLT03 compares the results of a call to CUNMQL with the results of */
/* forming Q explicitly by a call to CUNGQL and then performing matrix */
/* multiplication by a call to CGEMM. */
/* Arguments */
/* ========= */
/* M (input) INTEGER */
/* The order of the orthogonal matrix Q. M >= 0. */
/* N (input) INTEGER */
/* The number of rows or columns of the matrix C; C is m-by-n if */
/* Q is applied from the left, or n-by-m if Q is applied from */
/* the right. N >= 0. */
/* K (input) INTEGER */
/* The number of elementary reflectors whose product defines the */
/* orthogonal matrix Q. M >= K >= 0. */
/* AF (input) COMPLEX array, dimension (LDA,N) */
/* Details of the QL factorization of an m-by-n matrix, as */
/* returned by CGEQLF. See CGEQLF for further details. */
/* C (workspace) COMPLEX array, dimension (LDA,N) */
/* CC (workspace) COMPLEX array, dimension (LDA,N) */
/* Q (workspace) COMPLEX array, dimension (LDA,M) */
/* LDA (input) INTEGER */
/* The leading dimension of the arrays AF, C, CC, and Q. */
/* TAU (input) COMPLEX array, dimension (min(M,N)) */
/* The scalar factors of the elementary reflectors corresponding */
/* to the QL factorization in AF. */
/* WORK (workspace) COMPLEX array, dimension (LWORK) */
/* LWORK (input) INTEGER */
/* The length of WORK. LWORK must be at least M, and should be */
/* M*NB, where NB is the blocksize for this environment. */
/* RWORK (workspace) REAL array, dimension (M) */
/* RESULT (output) REAL array, dimension (4) */
/* The test ratios compare two techniques for multiplying a */
/* random matrix C by an m-by-m orthogonal matrix Q. */
/* RESULT(1) = norm( Q*C - Q*C ) / ( M * norm(C) * EPS ) */
/* RESULT(2) = norm( C*Q - C*Q ) / ( M * norm(C) * EPS ) */
/* RESULT(3) = norm( Q'*C - Q'*C )/ ( M * norm(C) * EPS ) */
/* RESULT(4) = norm( C*Q' - C*Q' )/ ( M * norm(C) * EPS ) */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Scalars in Common .. */
/* .. */
/* .. Common blocks .. */
/* .. */
/* .. Data statements .. */
/* Parameter adjustments */
q_dim1 = *lda;
q_offset = 1 + q_dim1;
q -= q_offset;
cc_dim1 = *lda;
cc_offset = 1 + cc_dim1;
cc -= cc_offset;
c_dim1 = *lda;
c_offset = 1 + c_dim1;
c__ -= c_offset;
af_dim1 = *lda;
af_offset = 1 + af_dim1;
af -= af_offset;
--tau;
--work;
--rwork;
--result;
/* Function Body */
/* .. */
/* .. Executable Statements .. */
eps = slamch_("Epsilon");
minmn = min(*m,*n);
/* Quick return if possible */
if (minmn == 0) {
result[1] = 0.f;
result[2] = 0.f;
result[3] = 0.f;
result[4] = 0.f;
return 0;
}
/* Copy the last k columns of the factorization to the array Q */
claset_("Full", m, m, &c_b1, &c_b1, &q[q_offset], lda);
if (*k > 0 && *m > *k) {
i__1 = *m - *k;
clacpy_("Full", &i__1, k, &af[(*n - *k + 1) * af_dim1 + 1], lda, &q[(*
m - *k + 1) * q_dim1 + 1], lda);
}
if (*k > 1) {
i__1 = *k - 1;
i__2 = *k - 1;
clacpy_("Upper", &i__1, &i__2, &af[*m - *k + 1 + (*n - *k + 2) *
af_dim1], lda, &q[*m - *k + 1 + (*m - *k + 2) * q_dim1], lda);
}
/* Generate the m-by-m matrix Q */
s_copy(srnamc_1.srnamt, "CUNGQL", (ftnlen)32, (ftnlen)6);
cungql_(m, m, k, &q[q_offset], lda, &tau[minmn - *k + 1], &work[1], lwork,
&info);
for (iside = 1; iside <= 2; ++iside) {
if (iside == 1) {
*(unsigned char *)side = 'L';
mc = *m;
nc = *n;
} else {
*(unsigned char *)side = 'R';
mc = *n;
nc = *m;
}
/* Generate MC by NC matrix C */
i__1 = nc;
for (j = 1; j <= i__1; ++j) {
clarnv_(&c__2, iseed, &mc, &c__[j * c_dim1 + 1]);
/* L10: */
}
cnorm = clange_("1", &mc, &nc, &c__[c_offset], lda, &rwork[1]);
if (cnorm == 0.f) {
cnorm = 1.f;
}
for (itrans = 1; itrans <= 2; ++itrans) {
if (itrans == 1) {
*(unsigned char *)trans = 'N';
} else {
*(unsigned char *)trans = 'C';
}
/* Copy C */
clacpy_("Full", &mc, &nc, &c__[c_offset], lda, &cc[cc_offset],
lda);
/* Apply Q or Q' to C */
s_copy(srnamc_1.srnamt, "CUNMQL", (ftnlen)32, (ftnlen)6);
if (*k > 0) {
cunmql_(side, trans, &mc, &nc, k, &af[(*n - *k + 1) * af_dim1
+ 1], lda, &tau[minmn - *k + 1], &cc[cc_offset], lda,
&work[1], lwork, &info);
}
/* Form explicit product and subtract */
if (lsame_(side, "L")) {
cgemm_(trans, "No transpose", &mc, &nc, &mc, &c_b21, &q[
q_offset], lda, &c__[c_offset], lda, &c_b22, &cc[
cc_offset], lda);
} else {
cgemm_("No transpose", trans, &mc, &nc, &nc, &c_b21, &c__[
c_offset], lda, &q[q_offset], lda, &c_b22, &cc[
cc_offset], lda);
}
/* Compute error in the difference */
resid = clange_("1", &mc, &nc, &cc[cc_offset], lda, &rwork[1]);
result[(iside - 1 << 1) + itrans] = resid / ((real) max(1,*m) *
cnorm * eps);
/* L20: */
}
/* L30: */
}
return 0;
/* End of CQLT03 */
} /* cqlt03_ */
