377 lines
11 KiB
C++
377 lines
11 KiB
C++
/* fortran/dorgql.f -- translated by f2c (version 20200916).
|
|
You must link the resulting object file with libf2c:
|
|
on Microsoft Windows system, link with libf2c.lib;
|
|
on Linux or Unix systems, link with .../path/to/libf2c.a -lm
|
|
or, if you install libf2c.a in a standard place, with -lf2c -lm
|
|
-- in that order, at the end of the command line, as in
|
|
cc *.o -lf2c -lm
|
|
Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
|
|
|
|
http://www.netlib.org/f2c/libf2c.zip
|
|
*/
|
|
|
|
#ifdef __cplusplus
|
|
extern "C" {
|
|
#endif
|
|
#include "lmp_f2c.h"
|
|
|
|
/* Table of constant values */
|
|
|
|
static integer c__1 = 1;
|
|
static integer c_n1 = -1;
|
|
static integer c__3 = 3;
|
|
static integer c__2 = 2;
|
|
|
|
/* > \brief \b DORGQL */
|
|
|
|
/* =========== DOCUMENTATION =========== */
|
|
|
|
/* Online html documentation available at */
|
|
/* http://www.netlib.org/lapack/explore-html/ */
|
|
|
|
/* > \htmlonly */
|
|
/* > Download DORGQL + dependencies */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dorgql.
|
|
f"> */
|
|
/* > [TGZ]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dorgql.
|
|
f"> */
|
|
/* > [ZIP]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dorgql.
|
|
f"> */
|
|
/* > [TXT]</a> */
|
|
/* > \endhtmlonly */
|
|
|
|
/* Definition: */
|
|
/* =========== */
|
|
|
|
/* SUBROUTINE DORGQL( M, N, K, A, LDA, TAU, WORK, LWORK, INFO ) */
|
|
|
|
/* .. Scalar Arguments .. */
|
|
/* INTEGER INFO, K, LDA, LWORK, M, N */
|
|
/* .. */
|
|
/* .. Array Arguments .. */
|
|
/* DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) */
|
|
/* .. */
|
|
|
|
|
|
/* > \par Purpose: */
|
|
/* ============= */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > DORGQL generates an M-by-N real matrix Q with orthonormal columns, */
|
|
/* > which is defined as the last N columns of a product of K elementary */
|
|
/* > reflectors of order M */
|
|
/* > */
|
|
/* > Q = H(k) . . . H(2) H(1) */
|
|
/* > */
|
|
/* > as returned by DGEQLF. */
|
|
/* > \endverbatim */
|
|
|
|
/* Arguments: */
|
|
/* ========== */
|
|
|
|
/* > \param[in] M */
|
|
/* > \verbatim */
|
|
/* > M is INTEGER */
|
|
/* > The number of rows of the matrix Q. M >= 0. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] N */
|
|
/* > \verbatim */
|
|
/* > N is INTEGER */
|
|
/* > The number of columns of the matrix Q. M >= N >= 0. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] K */
|
|
/* > \verbatim */
|
|
/* > K is INTEGER */
|
|
/* > The number of elementary reflectors whose product defines the */
|
|
/* > matrix Q. N >= K >= 0. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] A */
|
|
/* > \verbatim */
|
|
/* > A is DOUBLE PRECISION array, dimension (LDA,N) */
|
|
/* > On entry, the (n-k+i)-th column must contain the vector which */
|
|
/* > defines the elementary reflector H(i), for i = 1,2,...,k, as */
|
|
/* > returned by DGEQLF in the last k columns of its array */
|
|
/* > argument A. */
|
|
/* > On exit, the M-by-N matrix Q. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDA */
|
|
/* > \verbatim */
|
|
/* > LDA is INTEGER */
|
|
/* > The first dimension of the array A. LDA >= max(1,M). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] TAU */
|
|
/* > \verbatim */
|
|
/* > TAU is DOUBLE PRECISION array, dimension (K) */
|
|
/* > TAU(i) must contain the scalar factor of the elementary */
|
|
/* > reflector H(i), as returned by DGEQLF. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] WORK */
|
|
/* > \verbatim */
|
|
/* > WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) */
|
|
/* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LWORK */
|
|
/* > \verbatim */
|
|
/* > LWORK is INTEGER */
|
|
/* > The dimension of the array WORK. LWORK >= max(1,N). */
|
|
/* > For optimum performance LWORK >= 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. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] INFO */
|
|
/* > \verbatim */
|
|
/* > INFO is INTEGER */
|
|
/* > = 0: successful exit */
|
|
/* > < 0: if INFO = -i, the i-th argument has an illegal value */
|
|
/* > \endverbatim */
|
|
|
|
/* Authors: */
|
|
/* ======== */
|
|
|
|
/* > \author Univ. of Tennessee */
|
|
/* > \author Univ. of California Berkeley */
|
|
/* > \author Univ. of Colorado Denver */
|
|
/* > \author NAG Ltd. */
|
|
|
|
/* > \ingroup doubleOTHERcomputational */
|
|
|
|
/* ===================================================================== */
|
|
/* Subroutine */ int dorgql_(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, i__4;
|
|
|
|
/* Local variables */
|
|
integer i__, j, l, ib, nb, kk, nx, iws, nbmin, iinfo;
|
|
extern /* Subroutine */ int dorg2l_(integer *, integer *, integer *,
|
|
doublereal *, integer *, doublereal *, doublereal *, integer *),
|
|
dlarfb_(char *, char *, char *, char *, integer *, integer *,
|
|
integer *, doublereal *, integer *, doublereal *, integer *,
|
|
doublereal *, integer *, doublereal *, integer *, ftnlen, ftnlen,
|
|
ftnlen, ftnlen), dlarft_(char *, char *, integer *, integer *,
|
|
doublereal *, integer *, doublereal *, doublereal *, integer *,
|
|
ftnlen, ftnlen), xerbla_(char *, integer *, ftnlen);
|
|
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
|
|
integer *, integer *, ftnlen, ftnlen);
|
|
integer ldwork, lwkopt;
|
|
logical lquery;
|
|
|
|
|
|
/* -- LAPACK computational routine -- */
|
|
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
|
|
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
|
|
|
|
/* .. Scalar Arguments .. */
|
|
/* .. */
|
|
/* .. Array Arguments .. */
|
|
/* .. */
|
|
|
|
/* ===================================================================== */
|
|
|
|
/* .. Parameters .. */
|
|
/* .. */
|
|
/* .. Local Scalars .. */
|
|
/* .. */
|
|
/* .. External Subroutines .. */
|
|
/* .. */
|
|
/* .. Intrinsic Functions .. */
|
|
/* .. */
|
|
/* .. External 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;
|
|
lquery = *lwork == -1;
|
|
if (*m < 0) {
|
|
*info = -1;
|
|
} else if (*n < 0 || *n > *m) {
|
|
*info = -2;
|
|
} else if (*k < 0 || *k > *n) {
|
|
*info = -3;
|
|
} else if (*lda < max(1,*m)) {
|
|
*info = -5;
|
|
}
|
|
|
|
if (*info == 0) {
|
|
if (*n == 0) {
|
|
lwkopt = 1;
|
|
} else {
|
|
nb = ilaenv_(&c__1, (char *)"DORGQL", (char *)" ", m, n, k, &c_n1, (ftnlen)6, (
|
|
ftnlen)1);
|
|
lwkopt = *n * nb;
|
|
}
|
|
work[1] = (doublereal) lwkopt;
|
|
|
|
if (*lwork < max(1,*n) && ! lquery) {
|
|
*info = -8;
|
|
}
|
|
}
|
|
|
|
if (*info != 0) {
|
|
i__1 = -(*info);
|
|
xerbla_((char *)"DORGQL", &i__1, (ftnlen)6);
|
|
return 0;
|
|
} else if (lquery) {
|
|
return 0;
|
|
}
|
|
|
|
/* Quick return if possible */
|
|
|
|
if (*n <= 0) {
|
|
return 0;
|
|
}
|
|
|
|
nbmin = 2;
|
|
nx = 0;
|
|
iws = *n;
|
|
if (nb > 1 && nb < *k) {
|
|
|
|
/* Determine when to cross over from blocked to unblocked code. */
|
|
|
|
/* Computing MAX */
|
|
i__1 = 0, i__2 = ilaenv_(&c__3, (char *)"DORGQL", (char *)" ", m, n, k, &c_n1, (
|
|
ftnlen)6, (ftnlen)1);
|
|
nx = max(i__1,i__2);
|
|
if (nx < *k) {
|
|
|
|
/* Determine if workspace is large enough for blocked code. */
|
|
|
|
ldwork = *n;
|
|
iws = ldwork * nb;
|
|
if (*lwork < iws) {
|
|
|
|
/* Not enough workspace to use optimal NB: reduce NB and */
|
|
/* determine the minimum value of NB. */
|
|
|
|
nb = *lwork / ldwork;
|
|
/* Computing MAX */
|
|
i__1 = 2, i__2 = ilaenv_(&c__2, (char *)"DORGQL", (char *)" ", m, n, k, &c_n1,
|
|
(ftnlen)6, (ftnlen)1);
|
|
nbmin = max(i__1,i__2);
|
|
}
|
|
}
|
|
}
|
|
|
|
if (nb >= nbmin && nb < *k && nx < *k) {
|
|
|
|
/* Use blocked code after the first block. */
|
|
/* The last kk columns are handled by the block method. */
|
|
|
|
/* Computing MIN */
|
|
i__1 = *k, i__2 = (*k - nx + nb - 1) / nb * nb;
|
|
kk = min(i__1,i__2);
|
|
|
|
/* Set A(m-kk+1:m,1:n-kk) to zero. */
|
|
|
|
i__1 = *n - kk;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
i__2 = *m;
|
|
for (i__ = *m - kk + 1; i__ <= i__2; ++i__) {
|
|
a[i__ + j * a_dim1] = 0.;
|
|
/* L10: */
|
|
}
|
|
/* L20: */
|
|
}
|
|
} else {
|
|
kk = 0;
|
|
}
|
|
|
|
/* Use unblocked code for the first or only block. */
|
|
|
|
i__1 = *m - kk;
|
|
i__2 = *n - kk;
|
|
i__3 = *k - kk;
|
|
dorg2l_(&i__1, &i__2, &i__3, &a[a_offset], lda, &tau[1], &work[1], &iinfo)
|
|
;
|
|
|
|
if (kk > 0) {
|
|
|
|
/* Use blocked code */
|
|
|
|
i__1 = *k;
|
|
i__2 = nb;
|
|
for (i__ = *k - kk + 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ +=
|
|
i__2) {
|
|
/* Computing MIN */
|
|
i__3 = nb, i__4 = *k - i__ + 1;
|
|
ib = min(i__3,i__4);
|
|
if (*n - *k + i__ > 1) {
|
|
|
|
/* Form the triangular factor of the block reflector */
|
|
/* H = H(i+ib-1) . . . H(i+1) H(i) */
|
|
|
|
i__3 = *m - *k + i__ + ib - 1;
|
|
dlarft_((char *)"Backward", (char *)"Columnwise", &i__3, &ib, &a[(*n - *k +
|
|
i__) * a_dim1 + 1], lda, &tau[i__], &work[1], &ldwork,
|
|
(ftnlen)8, (ftnlen)10);
|
|
|
|
/* Apply H to A(1:m-k+i+ib-1,1:n-k+i-1) from the left */
|
|
|
|
i__3 = *m - *k + i__ + ib - 1;
|
|
i__4 = *n - *k + i__ - 1;
|
|
dlarfb_((char *)"Left", (char *)"No transpose", (char *)"Backward", (char *)"Columnwise", &
|
|
i__3, &i__4, &ib, &a[(*n - *k + i__) * a_dim1 + 1],
|
|
lda, &work[1], &ldwork, &a[a_offset], lda, &work[ib +
|
|
1], &ldwork, (ftnlen)4, (ftnlen)12, (ftnlen)8, (
|
|
ftnlen)10);
|
|
}
|
|
|
|
/* Apply H to rows 1:m-k+i+ib-1 of current block */
|
|
|
|
i__3 = *m - *k + i__ + ib - 1;
|
|
dorg2l_(&i__3, &ib, &ib, &a[(*n - *k + i__) * a_dim1 + 1], lda, &
|
|
tau[i__], &work[1], &iinfo);
|
|
|
|
/* Set rows m-k+i+ib:m of current block to zero */
|
|
|
|
i__3 = *n - *k + i__ + ib - 1;
|
|
for (j = *n - *k + i__; j <= i__3; ++j) {
|
|
i__4 = *m;
|
|
for (l = *m - *k + i__ + ib; l <= i__4; ++l) {
|
|
a[l + j * a_dim1] = 0.;
|
|
/* L30: */
|
|
}
|
|
/* L40: */
|
|
}
|
|
/* L50: */
|
|
}
|
|
}
|
|
|
|
work[1] = (doublereal) iws;
|
|
return 0;
|
|
|
|
/* End of DORGQL */
|
|
|
|
} /* dorgql_ */
|
|
|
|
#ifdef __cplusplus
|
|
}
|
|
#endif
|