int main(void)
{
/* Local scalars */
lapack_int m, m_i;
lapack_int n, n_i;
lapack_int k, k_i;
lapack_int lda, lda_i;
lapack_int lda_r;
lapack_int lwork, lwork_i;
lapack_int info, info_i;
lapack_int i;
int failed;
/* Local arrays */
double *a = NULL, *a_i = NULL;
double *tau = NULL, *tau_i = NULL;
double *work = NULL, *work_i = NULL;
double *a_save = NULL;
double *a_r = NULL;
/* Iniitialize the scalar parameters */
init_scalars_dorglq( &m, &n, &k, &lda, &lwork );
lda_r = n+2;
m_i = m;
n_i = n;
k_i = k;
lda_i = lda;
lwork_i = lwork;
/* Allocate memory for the LAPACK routine arrays */
a = (double *)LAPACKE_malloc( lda*n * sizeof(double) );
tau = (double *)LAPACKE_malloc( k * sizeof(double) );
work = (double *)LAPACKE_malloc( lwork * sizeof(double) );
/* Allocate memory for the C interface function arrays */
a_i = (double *)LAPACKE_malloc( lda*n * sizeof(double) );
tau_i = (double *)LAPACKE_malloc( k * sizeof(double) );
work_i = (double *)LAPACKE_malloc( lwork * sizeof(double) );
/* Allocate memory for the backup arrays */
a_save = (double *)LAPACKE_malloc( lda*n * sizeof(double) );
/* Allocate memory for the row-major arrays */
a_r = (double *)LAPACKE_malloc( m*(n+2) * sizeof(double) );
/* Initialize input arrays */
init_a( lda*n, a );
init_tau( k, tau );
init_work( lwork, work );
/* Backup the ouptut arrays */
for( i = 0; i < lda*n; i++ ) {
a_save[i] = a[i];
}
/* Call the LAPACK routine */
dorglq_( &m, &n, &k, a, &lda, tau, work, &lwork, &info );
/* Initialize input data, call the column-major middle-level
* interface to LAPACK routine and check the results */
for( i = 0; i < lda*n; i++ ) {
a_i[i] = a_save[i];
}
for( i = 0; i < k; i++ ) {
tau_i[i] = tau[i];
}
for( i = 0; i < lwork; i++ ) {
work_i[i] = work[i];
}
info_i = LAPACKE_dorglq_work( LAPACK_COL_MAJOR, m_i, n_i, k_i, a_i, lda_i,
tau_i, work_i, lwork_i );
failed = compare_dorglq( a, a_i, info, info_i, lda, n );
if( failed == 0 ) {
printf( "PASSED: column-major middle-level interface to dorglq\n" );
} else {
printf( "FAILED: column-major middle-level interface to dorglq\n" );
}
/* Initialize input data, call the column-major high-level
* interface to LAPACK routine and check the results */
for( i = 0; i < lda*n; i++ ) {
a_i[i] = a_save[i];
}
for( i = 0; i < k; i++ ) {
tau_i[i] = tau[i];
}
for( i = 0; i < lwork; i++ ) {
work_i[i] = work[i];
}
info_i = LAPACKE_dorglq( LAPACK_COL_MAJOR, m_i, n_i, k_i, a_i, lda_i,
tau_i );
failed = compare_dorglq( a, a_i, info, info_i, lda, n );
if( failed == 0 ) {
printf( "PASSED: column-major high-level interface to dorglq\n" );
} else {
printf( "FAILED: column-major high-level interface to dorglq\n" );
}
/* Initialize input data, call the row-major middle-level
* interface to LAPACK routine and check the results */
for( i = 0; i < lda*n; i++ ) {
a_i[i] = a_save[i];
}
for( i = 0; i < k; i++ ) {
tau_i[i] = tau[i];
}
for( i = 0; i < lwork; i++ ) {
work_i[i] = work[i];
}
LAPACKE_dge_trans( LAPACK_COL_MAJOR, m, n, a_i, lda, a_r, n+2 );
info_i = LAPACKE_dorglq_work( LAPACK_ROW_MAJOR, m_i, n_i, k_i, a_r, lda_r,
tau_i, work_i, lwork_i );
LAPACKE_dge_trans( LAPACK_ROW_MAJOR, m, n, a_r, n+2, a_i, lda );
failed = compare_dorglq( a, a_i, info, info_i, lda, n );
if( failed == 0 ) {
printf( "PASSED: row-major middle-level interface to dorglq\n" );
} else {
printf( "FAILED: row-major middle-level interface to dorglq\n" );
}
/* Initialize input data, call the row-major high-level
* interface to LAPACK routine and check the results */
for( i = 0; i < lda*n; i++ ) {
a_i[i] = a_save[i];
}
for( i = 0; i < k; i++ ) {
tau_i[i] = tau[i];
}
for( i = 0; i < lwork; i++ ) {
work_i[i] = work[i];
}
/* Init row_major arrays */
LAPACKE_dge_trans( LAPACK_COL_MAJOR, m, n, a_i, lda, a_r, n+2 );
info_i = LAPACKE_dorglq( LAPACK_ROW_MAJOR, m_i, n_i, k_i, a_r, lda_r,
tau_i );
LAPACKE_dge_trans( LAPACK_ROW_MAJOR, m, n, a_r, n+2, a_i, lda );
failed = compare_dorglq( a, a_i, info, info_i, lda, n );
if( failed == 0 ) {
printf( "PASSED: row-major high-level interface to dorglq\n" );
} else {
printf( "FAILED: row-major high-level interface to dorglq\n" );
}
/* Release memory */
if( a != NULL ) {
LAPACKE_free( a );
}
if( a_i != NULL ) {
LAPACKE_free( a_i );
}
if( a_r != NULL ) {
LAPACKE_free( a_r );
}
if( a_save != NULL ) {
LAPACKE_free( a_save );
}
if( tau != NULL ) {
LAPACKE_free( tau );
}
if( tau_i != NULL ) {
LAPACKE_free( tau_i );
}
if( work != NULL ) {
LAPACKE_free( work );
}
if( work_i != NULL ) {
LAPACKE_free( work_i );
}
return 0;
}
/* Subroutine */ int dlqt03_(integer *m, integer *n, integer *k, doublereal *
af, doublereal *c__, doublereal *cc, doublereal *q, integer *lda,
doublereal *tau, doublereal *work, integer *lwork, doublereal *rwork,
doublereal *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 */
integer j, mc, nc;
doublereal eps;
char side[1];
integer info;
extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *,
integer *, doublereal *, doublereal *, integer *, doublereal *,
integer *, doublereal *, doublereal *, integer *);
integer iside;
extern logical lsame_(char *, char *);
doublereal resid, cnorm;
char trans[1];
extern doublereal dlamch_(char *), dlange_(char *, integer *,
integer *, doublereal *, integer *, doublereal *);
extern /* Subroutine */ int dlacpy_(char *, integer *, integer *,
doublereal *, integer *, doublereal *, integer *),
dlaset_(char *, integer *, integer *, doublereal *, doublereal *,
doublereal *, integer *), dlarnv_(integer *, integer *,
integer *, doublereal *), dorglq_(integer *, integer *, integer *,
doublereal *, integer *, doublereal *, doublereal *, integer *,
integer *), dormlq_(char *, char *, integer *, integer *, integer
*, doublereal *, integer *, doublereal *, doublereal *, integer *,
doublereal *, integer *, integer *);
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 */
/* ======= */
/* DLQT03 tests DORMLQ, which computes Q*C, Q'*C, C*Q or C*Q'. */
/* DLQT03 compares the results of a call to DORMLQ with the results of */
/* forming Q explicitly by a call to DORGLQ and then performing matrix */
/* multiplication by a call to DGEMM. */
/* 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) DOUBLE PRECISION array, dimension (LDA,N) */
/* Details of the LQ factorization of an m-by-n matrix, as */
/* returned by DGELQF. See SGELQF for further details. */
/* C (workspace) DOUBLE PRECISION array, dimension (LDA,N) */
/* CC (workspace) DOUBLE PRECISION array, dimension (LDA,N) */
/* Q (workspace) DOUBLE PRECISION array, dimension (LDA,N) */
/* LDA (input) INTEGER */
/* The leading dimension of the arrays AF, C, CC, and Q. */
/* TAU (input) DOUBLE PRECISION array, dimension (min(M,N)) */
/* The scalar factors of the elementary reflectors corresponding */
/* to the LQ factorization in AF. */
/* WORK (workspace) DOUBLE PRECISION 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) DOUBLE PRECISION array, dimension (M) */
/* RESULT (output) DOUBLE PRECISION 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 = dlamch_("Epsilon");
/* Copy the first k rows of the factorization to the array Q */
dlaset_("Full", n, n, &c_b4, &c_b4, &q[q_offset], lda);
i__1 = *n - 1;
dlacpy_("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, "DORGLQ", (ftnlen)6, (ftnlen)6);
dorglq_(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) {
dlarnv_(&c__2, iseed, &mc, &c__[j * c_dim1 + 1]);
/* L10: */
}
cnorm = dlange_("1", &mc, &nc, &c__[c_offset], lda, &rwork[1]);
if (cnorm == 0.) {
cnorm = 1.;
}
for (itrans = 1; itrans <= 2; ++itrans) {
if (itrans == 1) {
*(unsigned char *)trans = 'N';
} else {
*(unsigned char *)trans = 'T';
}
/* Copy C */
dlacpy_("Full", &mc, &nc, &c__[c_offset], lda, &cc[cc_offset],
lda);
/* Apply Q or Q' to C */
s_copy(srnamc_1.srnamt, "DORMLQ", (ftnlen)6, (ftnlen)6);
dormlq_(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")) {
dgemm_(trans, "No transpose", &mc, &nc, &mc, &c_b21, &q[
q_offset], lda, &c__[c_offset], lda, &c_b22, &cc[
cc_offset], lda);
} else {
dgemm_("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 = dlange_("1", &mc, &nc, &cc[cc_offset], lda, &rwork[1]);
result[(iside - 1 << 1) + itrans] = resid / ((doublereal) max(1,*
n) * cnorm * eps);
/* L20: */
}
/* L30: */
}
return 0;
/* End of DLQT03 */
} /* dlqt03_ */
/* Subroutine */ int dorgbr_(char *vect, integer *m, integer *n, integer *k,
doublereal *a, integer *lda, doublereal *tau, doublereal *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 dorglq_(integer *, integer *, integer *,
doublereal *, integer *, doublereal *, doublereal *, integer *,
integer *), dorgqr_(integer *, integer *, integer *, doublereal *,
integer *, doublereal *, doublereal *, 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 */
/* ======= */
/* DORGBR generates one of the real orthogonal matrices Q or P**T */
/* determined by DGEBRD when reducing a real matrix A to bidiagonal */
/* form: A = Q * B * P**T. Q and P**T 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 DORGBR returns the first n */
/* columns of Q, where m >= n >= k; */
/* if m < k, Q = H(1) H(2) . . . H(m-1) and DORGBR returns Q as an */
/* M-by-M matrix. */
/* If VECT = 'P', A is assumed to have been a K-by-N matrix, and P**T */
/* is of order N: */
/* if k < n, P**T = G(k) . . . G(2) G(1) and DORGBR returns the first m */
/* rows of P**T, where n >= m >= k; */
/* if k >= n, P**T = G(n-1) . . . G(2) G(1) and DORGBR returns P**T as */
/* an N-by-N matrix. */
/* Arguments */
/* ========= */
/* VECT (input) CHARACTER*1 */
/* Specifies whether the matrix Q or the matrix P**T is */
/* required, as defined in the transformation applied by DGEBRD: */
/* = 'Q': generate Q; */
/* = 'P': generate P**T. */
/* M (input) INTEGER */
/* The number of rows of the matrix Q or P**T to be returned. */
/* M >= 0. */
/* N (input) INTEGER */
/* The number of columns of the matrix Q or P**T 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 DGEBRD. */
/* If VECT = 'P', the number of rows in the original K-by-N */
/* matrix reduced by DGEBRD. */
/* K >= 0. */
/* A (input/output) DOUBLE PRECISION array, dimension (LDA,N) */
/* On entry, the vectors which define the elementary reflectors, */
/* as returned by DGEBRD. */
/* On exit, the M-by-N matrix Q or P**T. */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= max(1,M). */
/* TAU (input) DOUBLE PRECISION 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**T, as */
/* returned by DGEBRD in its array argument TAUQ or TAUP. */
/* WORK (workspace/output) DOUBLE PRECISION 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, "DORGQR", " ", m, n, k, &c_n1);
} else {
nb = ilaenv_(&c__1, "DORGLQ", " ", m, n, k, &c_n1);
}
lwkopt = max(1,mn) * nb;
work[1] = (doublereal) lwkopt;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("DORGBR", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible */
if (*m == 0 || *n == 0) {
work[1] = 1.;
return 0;
}
if (wantq) {
/* Form Q, determined by a call to DGEBRD to reduce an m-by-k */
/* matrix */
if (*m >= *k) {
/* If m >= k, assume m >= n >= k */
dorgqr_(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) {
a[j * a_dim1 + 1] = 0.;
i__1 = *m;
for (i__ = j + 1; i__ <= i__1; ++i__) {
a[i__ + j * a_dim1] = a[i__ + (j - 1) * a_dim1];
/* L10: */
}
/* L20: */
}
a[a_dim1 + 1] = 1.;
i__1 = *m;
for (i__ = 2; i__ <= i__1; ++i__) {
a[i__ + a_dim1] = 0.;
/* L30: */
}
if (*m > 1) {
/* Form Q(2:m,2:m) */
i__1 = *m - 1;
i__2 = *m - 1;
i__3 = *m - 1;
dorgqr_(&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 DGEBRD to reduce a k-by-n */
/* matrix */
if (*k < *n) {
/* If k < n, assume k <= m <= n */
dorglq_(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 */
a[a_dim1 + 1] = 1.;
i__1 = *n;
for (i__ = 2; i__ <= i__1; ++i__) {
a[i__ + a_dim1] = 0.;
/* L40: */
}
i__1 = *n;
for (j = 2; j <= i__1; ++j) {
for (i__ = j - 1; i__ >= 2; --i__) {
a[i__ + j * a_dim1] = a[i__ - 1 + j * a_dim1];
/* L50: */
}
a[j * a_dim1 + 1] = 0.;
/* L60: */
}
if (*n > 1) {
/* Form P'(2:n,2:n) */
i__1 = *n - 1;
i__2 = *n - 1;
i__3 = *n - 1;
dorglq_(&i__1, &i__2, &i__3, &a[(a_dim1 << 1) + 2], lda, &tau[
1], &work[1], lwork, &iinfo);
}
}
}
work[1] = (doublereal) lwkopt;
return 0;
/* End of DORGBR */
} /* dorgbr_ */
/* Subroutine */ int dtimlq_(char *line, integer *nm, integer *mval, integer *
nval, integer *nk, integer *kval, integer *nnb, integer *nbval,
integer *nxval, integer *nlda, integer *ldaval, doublereal *timmin,
doublereal *a, doublereal *tau, doublereal *b, doublereal *work,
doublereal *reslts, integer *ldr1, integer *ldr2, integer *ldr3,
integer *nout, ftnlen line_len)
{
/* Initialized data */
static char subnam[6*3] = "DGELQF" "DORGLQ" "DORMLQ";
static char sides[1*2] = "L" "R";
static char transs[1*2] = "N" "T";
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 doublereal time;
static integer isub, muse[12], nuse[12], i__, k, m, n;
static char cname[6];
static integer iside;
extern doublereal dopla_(char *, integer *, integer *, integer *, integer
*, integer *);
static integer itoff, itran, minmn;
extern /* Subroutine */ int icopy_(integer *, integer *, integer *,
integer *, integer *);
static char trans[1];
static integer k1, i4, m1, n1;
static doublereal s1, s2;
extern /* Subroutine */ int dprtb4_(char *, char *, char *, integer *,
integer *, integer *, integer *, integer *, integer *, integer *,
doublereal *, integer *, integer *, integer *, ftnlen, ftnlen,
ftnlen), dprtb5_(char *, char *, char *, integer *, integer *,
integer *, integer *, integer *, integer *, doublereal *, integer
*, integer *, integer *, ftnlen, ftnlen, ftnlen);
static integer ic, nb, ik, im;
extern doublereal dsecnd_(void);
extern /* Subroutine */ int dgelqf_(integer *, integer *, doublereal *,
integer *, doublereal *, doublereal *, integer *, integer *);
static integer lw, nx, reseed[4];
extern /* Subroutine */ int atimck_(integer *, char *, integer *, integer
*, integer *, integer *, integer *, integer *, ftnlen), dlacpy_(
char *, integer *, integer *, doublereal *, integer *, doublereal
*, integer *);
extern doublereal dmflop_(doublereal *, doublereal *, integer *);
extern /* Subroutine */ int atimin_(char *, char *, integer *, char *,
logical *, integer *, integer *, ftnlen, ftnlen, ftnlen), dtimmg_(
integer *, integer *, integer *, doublereal *, integer *, integer
*, integer *), dlatms_(integer *, integer *, char *, integer *,
char *, doublereal *, integer *, doublereal *, doublereal *,
integer *, integer *, char *, doublereal *, integer *, doublereal
*, integer *), dorglq_(integer *, integer
*, integer *, doublereal *, integer *, doublereal *, doublereal *,
integer *, integer *), dormlq_(char *, char *, integer *,
integer *, integer *, doublereal *, integer *, doublereal *,
doublereal *, integer *, doublereal *, integer *, integer *), xlaenv_(integer *, integer *);
static doublereal untime;
static logical timsub[3];
static integer lda, icl, inb, imx;
static doublereal 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
=======
DTIMLQ times the LAPACK routines to perform the LQ factorization of
a DOUBLE PRECISION 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 DORMLQ.
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) DOUBLE PRECISION
The minimum time a subroutine will be timed.
A (workspace) DOUBLE PRECISION array, dimension (LDAMAX*NMAX)
where LDAMAX and NMAX are the maximum values of LDA and N.
TAU (workspace) DOUBLE PRECISION array, dimension (min(M,N))
B (workspace) DOUBLE PRECISION array, dimension (LDAMAX*NMAX)
WORK (workspace) DOUBLE PRECISION array, dimension (LDAMAX*NBMAX)
where NBMAX is the maximum value of NB.
RESLTS (workspace) DOUBLE PRECISION 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 DLATMS for further details.
COND DOUBLE PRECISION
The condition number of the matrix. The singular values are
set to values from DMAX to DMAX/COND.
DMAX DOUBLE PRECISION
The magnitude of the largest singular value.
=====================================================================
Parameter adjustments */
--mval;
--nval;
--kval;
--nbval;
--nxval;
--ldaval;
--a;
--tau;
--b;
--work;
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, "Double precision", (ftnlen)1, (ftnlen)16);
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);
dlatms_(&m, &n, "Uniform", iseed, "Nonsym", &tau[1], &c__3, &
c_b24, &c_b25, &m, &n, "No packing", &b[1], &lda, &
work[1], &info);
if (timsub[0]) {
/* DGELQF: LQ factorization */
dlacpy_("Full", &m, &n, &b[1], &lda, &a[1], &lda);
ic = 0;
s1 = dsecnd_();
L10:
dgelqf_(&m, &n, &a[1], &lda, &tau[1], &work[1], &lw, &
info);
s2 = dsecnd_();
time = s2 - s1;
++ic;
if (time < *timmin) {
dlacpy_("Full", &m, &n, &b[1], &lda, &a[1], &lda);
goto L10;
}
/* Subtract the time used in DLACPY. */
icl = 1;
s1 = dsecnd_();
L20:
s2 = dsecnd_();
untime = s2 - s1;
++icl;
if (icl <= ic) {
dlacpy_("Full", &m, &n, &a[1], &lda, &b[1], &lda);
goto L20;
}
time = (time - untime) / (doublereal) ic;
ops = dopla_("DGELQF", &m, &n, &c__0, &c__0, &nb);
reslts_ref(inb, im, ilda, 1) = dmflop_(&ops, &time, &info)
;
} else {
/* If DGELQF was not timed, generate a matrix and factor
it using DGELQF anyway so that the factored form of
the matrix can be used in timing the other routines. */
dlacpy_("Full", &m, &n, &b[1], &lda, &a[1], &lda);
dgelqf_(&m, &n, &a[1], &lda, &tau[1], &work[1], &lw, &
info);
}
if (timsub[1]) {
/* DORGLQ: Generate orthogonal matrix Q from the LQ
factorization */
dlacpy_("Full", &minmn, &n, &a[1], &lda, &b[1], &lda);
ic = 0;
s1 = dsecnd_();
L30:
dorglq_(&minmn, &n, &minmn, &b[1], &lda, &tau[1], &work[1]
, &lw, &info);
s2 = dsecnd_();
time = s2 - s1;
++ic;
if (time < *timmin) {
dlacpy_("Full", &minmn, &n, &a[1], &lda, &b[1], &lda);
goto L30;
}
/* Subtract the time used in DLACPY. */
icl = 1;
s1 = dsecnd_();
L40:
s2 = dsecnd_();
untime = s2 - s1;
++icl;
if (icl <= ic) {
dlacpy_("Full", &minmn, &n, &a[1], &lda, &b[1], &lda);
goto L40;
}
time = (time - untime) / (doublereal) ic;
ops = dopla_("DORGLQ", &minmn, &n, &minmn, &c__0, &nb);
reslts_ref(inb, im, ilda, 2) = dmflop_(&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();
}
dprtb4_("( 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 DORMLQ 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: */
}
/* DORMLQ: 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. */
dlatms_(&m, &n, "Uniform", iseed, "Nonsymm", &tau[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);
dgelqf_(&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];
dtimmg_(&c__0, &m1, &n1, &b[1], &lda, &c__0, &
c__0);
ic = 0;
s1 = dsecnd_();
L110:
dormlq_(side, trans, &m1, &n1, &k1, &a[1], &
lda, &tau[1], &b[1], &lda, &work[1], &
lw, &info);
s2 = dsecnd_();
time = s2 - s1;
++ic;
if (time < *timmin) {
dtimmg_(&c__0, &m1, &n1, &b[1], &lda, &
c__0, &c__0);
goto L110;
}
/* Subtract the time used in DTIMMG. */
icl = 1;
s1 = dsecnd_();
L120:
s2 = dsecnd_();
untime = s2 - s1;
++icl;
if (icl <= ic) {
dtimmg_(&c__0, &m1, &n1, &b[1], &lda, &
c__0, &c__0);
goto L120;
}
time = (time - untime) / (doublereal) ic;
i__5 = iside - 1;
ops = dopla_("DORMLQ", &m1, &n1, &k1, &i__5, &
nb);
reslts_ref(inb, im, ilda, i4 + itoff + ik) =
dmflop_(&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';
}
dprtb5_("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 DTIMLQ */
} /* dtimlq_ */
/* Subroutine */ int derrlq_(char *path, integer *nunit)
{
/* Builtin functions */
integer s_wsle(cilist *), e_wsle(void);
/* Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen);
/* Local variables */
static integer info;
static doublereal a[4] /* was [2][2] */, b[2];
static integer i__, j;
static doublereal w[2], x[2];
extern /* Subroutine */ int dgelq2_(integer *, integer *, doublereal *,
integer *, doublereal *, doublereal *, integer *), dorgl2_(
integer *, integer *, integer *, doublereal *, integer *,
doublereal *, doublereal *, integer *), dorml2_(char *, char *,
integer *, integer *, integer *, doublereal *, integer *,
doublereal *, doublereal *, integer *, doublereal *, integer *);
static doublereal af[4] /* was [2][2] */;
extern /* Subroutine */ int alaesm_(char *, logical *, integer *),
dgelqf_(integer *, integer *, doublereal *, integer *,
doublereal *, doublereal *, integer *, integer *), dgelqs_(
integer *, integer *, integer *, doublereal *, integer *,
doublereal *, doublereal *, integer *, doublereal *, integer *,
integer *), chkxer_(char *, integer *, integer *, logical *,
logical *), dorglq_(integer *, integer *, integer *,
doublereal *, integer *, doublereal *, doublereal *, integer *,
integer *), dormlq_(char *, char *, integer *, integer *, integer
*, doublereal *, integer *, doublereal *, doublereal *, integer *,
doublereal *, integer *, integer *);
/* Fortran I/O blocks */
static cilist io___1 = { 0, 0, 0, 0, 0 };
#define a_ref(a_1,a_2) a[(a_2)*2 + a_1 - 3]
#define af_ref(a_1,a_2) af[(a_2)*2 + a_1 - 3]
/* -- LAPACK test routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
February 29, 1992
Purpose
=======
DERRLQ tests the error exits for the DOUBLE PRECISION routines
that use the LQ decomposition of a general matrix.
Arguments
=========
PATH (input) CHARACTER*3
The LAPACK path name for the routines to be tested.
NUNIT (input) INTEGER
The unit number for output.
===================================================================== */
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__) {
a_ref(i__, j) = 1. / (doublereal) (i__ + j);
af_ref(i__, j) = 1. / (doublereal) (i__ + j);
/* L10: */
}
b[j - 1] = 0.;
w[j - 1] = 0.;
x[j - 1] = 0.;
/* L20: */
}
infoc_1.ok = TRUE_;
/* Error exits for LQ factorization
DGELQF */
s_copy(srnamc_1.srnamt, "DGELQF", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
dgelqf_(&c_n1, &c__0, a, &c__1, b, w, &c__1, &info);
chkxer_("DGELQF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
dgelqf_(&c__0, &c_n1, a, &c__1, b, w, &c__1, &info);
chkxer_("DGELQF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
dgelqf_(&c__2, &c__1, a, &c__1, b, w, &c__2, &info);
chkxer_("DGELQF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
dgelqf_(&c__2, &c__1, a, &c__2, b, w, &c__1, &info);
chkxer_("DGELQF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* DGELQ2 */
s_copy(srnamc_1.srnamt, "DGELQ2", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
dgelq2_(&c_n1, &c__0, a, &c__1, b, w, &info);
chkxer_("DGELQ2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
dgelq2_(&c__0, &c_n1, a, &c__1, b, w, &info);
chkxer_("DGELQ2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
dgelq2_(&c__2, &c__1, a, &c__1, b, w, &info);
chkxer_("DGELQ2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* DGELQS */
s_copy(srnamc_1.srnamt, "DGELQS", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
dgelqs_(&c_n1, &c__0, &c__0, a, &c__1, x, b, &c__1, w, &c__1, &info);
chkxer_("DGELQS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
dgelqs_(&c__0, &c_n1, &c__0, a, &c__1, x, b, &c__1, w, &c__1, &info);
chkxer_("DGELQS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
dgelqs_(&c__2, &c__1, &c__0, a, &c__2, x, b, &c__1, w, &c__1, &info);
chkxer_("DGELQS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
dgelqs_(&c__0, &c__0, &c_n1, a, &c__1, x, b, &c__1, w, &c__1, &info);
chkxer_("DGELQS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
dgelqs_(&c__2, &c__2, &c__0, a, &c__1, x, b, &c__2, w, &c__1, &info);
chkxer_("DGELQS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 8;
dgelqs_(&c__1, &c__2, &c__0, a, &c__1, x, b, &c__1, w, &c__1, &info);
chkxer_("DGELQS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 10;
dgelqs_(&c__1, &c__1, &c__2, a, &c__1, x, b, &c__1, w, &c__1, &info);
chkxer_("DGELQS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* DORGLQ */
s_copy(srnamc_1.srnamt, "DORGLQ", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
dorglq_(&c_n1, &c__0, &c__0, a, &c__1, x, w, &c__1, &info);
chkxer_("DORGLQ", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
dorglq_(&c__0, &c_n1, &c__0, a, &c__1, x, w, &c__1, &info);
chkxer_("DORGLQ", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
dorglq_(&c__2, &c__1, &c__0, a, &c__2, x, w, &c__2, &info);
chkxer_("DORGLQ", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
dorglq_(&c__0, &c__0, &c_n1, a, &c__1, x, w, &c__1, &info);
chkxer_("DORGLQ", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
dorglq_(&c__1, &c__1, &c__2, a, &c__1, x, w, &c__1, &info);
chkxer_("DORGLQ", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
dorglq_(&c__2, &c__2, &c__0, a, &c__1, x, w, &c__2, &info);
chkxer_("DORGLQ", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 8;
dorglq_(&c__2, &c__2, &c__0, a, &c__2, x, w, &c__1, &info);
chkxer_("DORGLQ", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* DORGL2 */
s_copy(srnamc_1.srnamt, "DORGL2", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
dorgl2_(&c_n1, &c__0, &c__0, a, &c__1, x, w, &info);
chkxer_("DORGL2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
dorgl2_(&c__0, &c_n1, &c__0, a, &c__1, x, w, &info);
chkxer_("DORGL2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
dorgl2_(&c__2, &c__1, &c__0, a, &c__2, x, w, &info);
chkxer_("DORGL2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
dorgl2_(&c__0, &c__0, &c_n1, a, &c__1, x, w, &info);
chkxer_("DORGL2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
dorgl2_(&c__1, &c__1, &c__2, a, &c__1, x, w, &info);
chkxer_("DORGL2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
dorgl2_(&c__2, &c__2, &c__0, a, &c__1, x, w, &info);
chkxer_("DORGL2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* DORMLQ */
s_copy(srnamc_1.srnamt, "DORMLQ", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
dormlq_("/", "N", &c__0, &c__0, &c__0, a, &c__1, x, af, &c__1, w, &c__1, &
info);
chkxer_("DORMLQ", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
dormlq_("L", "/", &c__0, &c__0, &c__0, a, &c__1, x, af, &c__1, w, &c__1, &
info);
chkxer_("DORMLQ", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
dormlq_("L", "N", &c_n1, &c__0, &c__0, a, &c__1, x, af, &c__1, w, &c__1, &
info);
chkxer_("DORMLQ", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
dormlq_("L", "N", &c__0, &c_n1, &c__0, a, &c__1, x, af, &c__1, w, &c__1, &
info);
chkxer_("DORMLQ", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
dormlq_("L", "N", &c__0, &c__0, &c_n1, a, &c__1, x, af, &c__1, w, &c__1, &
info);
chkxer_("DORMLQ", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
dormlq_("L", "N", &c__0, &c__1, &c__1, a, &c__1, x, af, &c__1, w, &c__1, &
info);
chkxer_("DORMLQ", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
dormlq_("R", "N", &c__1, &c__0, &c__1, a, &c__1, x, af, &c__1, w, &c__1, &
info);
chkxer_("DORMLQ", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
dormlq_("L", "N", &c__2, &c__0, &c__2, a, &c__1, x, af, &c__2, w, &c__1, &
info);
chkxer_("DORMLQ", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
dormlq_("R", "N", &c__0, &c__2, &c__2, a, &c__1, x, af, &c__1, w, &c__1, &
info);
chkxer_("DORMLQ", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 10;
dormlq_("L", "N", &c__2, &c__1, &c__0, a, &c__2, x, af, &c__1, w, &c__1, &
info);
chkxer_("DORMLQ", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 12;
dormlq_("L", "N", &c__1, &c__2, &c__0, a, &c__1, x, af, &c__1, w, &c__1, &
info);
chkxer_("DORMLQ", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 12;
dormlq_("R", "N", &c__2, &c__1, &c__0, a, &c__1, x, af, &c__2, w, &c__1, &
info);
chkxer_("DORMLQ", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* DORML2 */
s_copy(srnamc_1.srnamt, "DORML2", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
dorml2_("/", "N", &c__0, &c__0, &c__0, a, &c__1, x, af, &c__1, w, &info);
chkxer_("DORML2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
dorml2_("L", "/", &c__0, &c__0, &c__0, a, &c__1, x, af, &c__1, w, &info);
chkxer_("DORML2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
dorml2_("L", "N", &c_n1, &c__0, &c__0, a, &c__1, x, af, &c__1, w, &info);
chkxer_("DORML2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
dorml2_("L", "N", &c__0, &c_n1, &c__0, a, &c__1, x, af, &c__1, w, &info);
chkxer_("DORML2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
dorml2_("L", "N", &c__0, &c__0, &c_n1, a, &c__1, x, af, &c__1, w, &info);
chkxer_("DORML2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
dorml2_("L", "N", &c__0, &c__1, &c__1, a, &c__1, x, af, &c__1, w, &info);
chkxer_("DORML2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
dorml2_("R", "N", &c__1, &c__0, &c__1, a, &c__1, x, af, &c__1, w, &info);
chkxer_("DORML2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
dorml2_("L", "N", &c__2, &c__1, &c__2, a, &c__1, x, af, &c__2, w, &info);
chkxer_("DORML2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
dorml2_("R", "N", &c__1, &c__2, &c__2, a, &c__1, x, af, &c__1, w, &info);
chkxer_("DORML2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 10;
dorml2_("L", "N", &c__2, &c__1, &c__0, a, &c__2, x, af, &c__1, w, &info);
chkxer_("DORML2", &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 DERRLQ */
} /* derrlq_ */
/* Subroutine */ int dlqt02_(integer *m, integer *n, integer *k, doublereal *
a, doublereal *af, doublereal *q, doublereal *l, integer *lda,
doublereal *tau, doublereal *work, integer *lwork, doublereal *rwork,
doublereal *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 dgemm_(char *, char *, integer *, integer *,
integer *, doublereal *, doublereal *, integer *, doublereal *,
integer *, doublereal *, doublereal *, integer *);
static doublereal resid, anorm;
extern /* Subroutine */ int dsyrk_(char *, char *, integer *, integer *,
doublereal *, doublereal *, integer *, doublereal *, doublereal *,
integer *);
extern doublereal dlamch_(char *), dlange_(char *, integer *,
integer *, doublereal *, integer *, doublereal *);
extern /* Subroutine */ int dlacpy_(char *, integer *, integer *,
doublereal *, integer *, doublereal *, integer *),
dlaset_(char *, integer *, integer *, doublereal *, doublereal *,
doublereal *, integer *), dorglq_(integer *, integer *,
integer *, doublereal *, integer *, doublereal *, doublereal *,
integer *, integer *);
extern doublereal dlansy_(char *, char *, integer *, doublereal *,
integer *, doublereal *);
static doublereal eps;
#define q_ref(a_1,a_2) q[(a_2)*q_dim1 + a_1]
#define af_ref(a_1,a_2) af[(a_2)*af_dim1 + a_1]
/* -- 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
=======
DLQT02 tests DORGLQ, which generates an m-by-n matrix Q with
orthonornmal rows that is defined as the product of k elementary
reflectors.
Given the LQ factorization of an m-by-n matrix A, DLQT02 generates
the orthogonal matrix Q defined by the factorization of the first k
rows of A; it compares L(1:k,1:m) with A(1:k,1:n)*Q(1:m,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) DOUBLE PRECISION array, dimension (LDA,N)
The m-by-n matrix A which was factorized by DLQT01.
AF (input) DOUBLE PRECISION array, dimension (LDA,N)
Details of the LQ factorization of A, as returned by DGELQF.
See DGELQF for further details.
Q (workspace) DOUBLE PRECISION array, dimension (LDA,N)
L (workspace) DOUBLE PRECISION array, dimension (LDA,M)
LDA (input) INTEGER
The leading dimension of the arrays A, AF, Q and L. LDA >= N.
TAU (input) DOUBLE PRECISION array, dimension (M)
The scalar factors of the elementary reflectors corresponding
to the LQ factorization in AF.
WORK (workspace) DOUBLE PRECISION array, dimension (LWORK)
LWORK (input) INTEGER
The dimension of the array WORK.
RWORK (workspace) DOUBLE PRECISION array, dimension (M)
RESULT (output) DOUBLE PRECISION 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 */
eps = dlamch_("Epsilon");
/* Copy the first k rows of the factorization to the array Q */
dlaset_("Full", m, n, &c_b4, &c_b4, &q[q_offset], lda);
i__1 = *n - 1;
dlacpy_("Upper", k, &i__1, &af_ref(1, 2), lda, &q_ref(1, 2), lda);
/* Generate the first n columns of the matrix Q */
s_copy(srnamc_1.srnamt, "DORGLQ", (ftnlen)6, (ftnlen)6);
dorglq_(m, n, k, &q[q_offset], lda, &tau[1], &work[1], lwork, &info);
/* Copy L(1:k,1:m) */
dlaset_("Full", k, m, &c_b9, &c_b9, &l[l_offset], lda);
dlacpy_("Lower", k, m, &af[af_offset], lda, &l[l_offset], lda);
/* Compute L(1:k,1:m) - A(1:k,1:n) * Q(1:m,1:n)' */
dgemm_("No transpose", "Transpose", k, m, n, &c_b14, &a[a_offset], lda, &
q[q_offset], lda, &c_b15, &l[l_offset], lda);
/* Compute norm( L - A*Q' ) / ( N * norm(A) * EPS ) . */
anorm = dlange_("1", k, n, &a[a_offset], lda, &rwork[1]);
resid = dlange_("1", k, m, &l[l_offset], lda, &rwork[1]);
if (anorm > 0.) {
result[1] = resid / (doublereal) max(1,*n) / anorm / eps;
} else {
result[1] = 0.;
}
/* Compute I - Q*Q' */
dlaset_("Full", m, m, &c_b9, &c_b15, &l[l_offset], lda);
dsyrk_("Upper", "No transpose", m, n, &c_b14, &q[q_offset], lda, &c_b15, &
l[l_offset], lda);
/* Compute norm( I - Q*Q' ) / ( N * EPS ) . */
resid = dlansy_("1", "Upper", m, &l[l_offset], lda, &rwork[1]);
result[2] = resid / (doublereal) max(1,*n) / eps;
return 0;
/* End of DLQT02 */
} /* dlqt02_ */
/* Subroutine */ int dorgbr_(char *vect, integer *m, integer *n, integer *k,
doublereal *a, integer *lda, doublereal *tau, doublereal *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
=======
DORGBR generates one of the real orthogonal matrices Q or P**T
determined by DGEBRD when reducing a real matrix A to bidiagonal
form: A = Q * B * P**T. Q and P**T 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 DORGBR returns the first n
columns of Q, where m >= n >= k;
if m < k, Q = H(1) H(2) . . . H(m-1) and DORGBR returns Q as an
M-by-M matrix.
If VECT = 'P', A is assumed to have been a K-by-N matrix, and P**T
is of order N:
if k < n, P**T = G(k) . . . G(2) G(1) and DORGBR returns the first m
rows of P**T, where n >= m >= k;
if k >= n, P**T = G(n-1) . . . G(2) G(1) and DORGBR returns P**T as
an N-by-N matrix.
Arguments
=========
VECT (input) CHARACTER*1
Specifies whether the matrix Q or the matrix P**T is
required, as defined in the transformation applied by DGEBRD:
= 'Q': generate Q;
= 'P': generate P**T.
M (input) INTEGER
The number of rows of the matrix Q or P**T to be returned.
M >= 0.
N (input) INTEGER
The number of columns of the matrix Q or P**T 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 DGEBRD.
If VECT = 'P', the number of rows in the original K-by-N
matrix reduced by DGEBRD.
K >= 0.
A (input/output) DOUBLE PRECISION array, dimension (LDA,N)
On entry, the vectors which define the elementary reflectors,
as returned by DGEBRD.
On exit, the M-by-N matrix Q or P**T.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,M).
TAU (input) DOUBLE PRECISION 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**T, as
returned by DGEBRD in its array argument TAUQ or TAUP.
WORK (workspace/output) DOUBLE PRECISION 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 dorglq_(integer *, integer *, integer *,
doublereal *, integer *, doublereal *, doublereal *, integer *,
integer *), dorgqr_(integer *, integer *, integer *, doublereal *,
integer *, doublereal *, doublereal *, integer *, integer *);
static integer lwkopt;
static logical lquery;
#define a_ref(a_1,a_2) a[(a_2)*a_dim1 + a_1]
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, "DORGQR", " ", m, n, k, &c_n1, (ftnlen)6, (
ftnlen)1);
} else {
nb = ilaenv_(&c__1, "DORGLQ", " ", m, n, k, &c_n1, (ftnlen)6, (
ftnlen)1);
}
lwkopt = max(1,mn) * nb;
work[1] = (doublereal) lwkopt;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("DORGBR", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible */
if (*m == 0 || *n == 0) {
work[1] = 1.;
return 0;
}
if (wantq) {
/* Form Q, determined by a call to DGEBRD to reduce an m-by-k
matrix */
if (*m >= *k) {
/* If m >= k, assume m >= n >= k */
dorgqr_(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) {
a_ref(1, j) = 0.;
i__1 = *m;
for (i__ = j + 1; i__ <= i__1; ++i__) {
a_ref(i__, j) = a_ref(i__, j - 1);
/* L10: */
}
/* L20: */
}
a_ref(1, 1) = 1.;
i__1 = *m;
for (i__ = 2; i__ <= i__1; ++i__) {
a_ref(i__, 1) = 0.;
/* L30: */
}
if (*m > 1) {
/* Form Q(2:m,2:m) */
i__1 = *m - 1;
i__2 = *m - 1;
i__3 = *m - 1;
dorgqr_(&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 DGEBRD to reduce a k-by-n
matrix */
if (*k < *n) {
/* If k < n, assume k <= m <= n */
dorglq_(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 */
a_ref(1, 1) = 1.;
i__1 = *n;
for (i__ = 2; i__ <= i__1; ++i__) {
a_ref(i__, 1) = 0.;
/* L40: */
}
i__1 = *n;
for (j = 2; j <= i__1; ++j) {
for (i__ = j - 1; i__ >= 2; --i__) {
a_ref(i__, j) = a_ref(i__ - 1, j);
/* L50: */
}
a_ref(1, j) = 0.;
/* L60: */
}
if (*n > 1) {
/* Form P'(2:n,2:n) */
i__1 = *n - 1;
i__2 = *n - 1;
i__3 = *n - 1;
dorglq_(&i__1, &i__2, &i__3, &a_ref(2, 2), lda, &tau[1], &
work[1], lwork, &iinfo);
}
}
}
work[1] = (doublereal) lwkopt;
return 0;
/* End of DORGBR */
} /* dorgbr_ */
