397 lines
12 KiB
C++
397 lines
12 KiB
C++
/* fortran/dormtr.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__2 = 2;
|
|
|
|
/* > \brief \b DORMTR */
|
|
|
|
/* =========== DOCUMENTATION =========== */
|
|
|
|
/* Online html documentation available at */
|
|
/* http://www.netlib.org/lapack/explore-html/ */
|
|
|
|
/* > \htmlonly */
|
|
/* > Download DORMTR + dependencies */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dormtr.
|
|
f"> */
|
|
/* > [TGZ]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dormtr.
|
|
f"> */
|
|
/* > [ZIP]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dormtr.
|
|
f"> */
|
|
/* > [TXT]</a> */
|
|
/* > \endhtmlonly */
|
|
|
|
/* Definition: */
|
|
/* =========== */
|
|
|
|
/* SUBROUTINE DORMTR( SIDE, UPLO, TRANS, M, N, A, LDA, TAU, C, LDC, */
|
|
/* WORK, LWORK, INFO ) */
|
|
|
|
/* .. Scalar Arguments .. */
|
|
/* CHARACTER SIDE, TRANS, UPLO */
|
|
/* INTEGER INFO, LDA, LDC, LWORK, M, N */
|
|
/* .. */
|
|
/* .. Array Arguments .. */
|
|
/* DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) */
|
|
/* .. */
|
|
|
|
|
|
/* > \par Purpose: */
|
|
/* ============= */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > DORMTR overwrites the general real M-by-N matrix C with */
|
|
/* > */
|
|
/* > SIDE = 'L' SIDE = 'R' */
|
|
/* > TRANS = 'N': Q * C C * Q */
|
|
/* > TRANS = 'T': Q**T * C C * Q**T */
|
|
/* > */
|
|
/* > where Q is a real orthogonal 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 DSYTRD: */
|
|
/* > */
|
|
/* > if UPLO = 'U', Q = H(nq-1) . . . H(2) H(1); */
|
|
/* > */
|
|
/* > if UPLO = 'L', Q = H(1) H(2) . . . H(nq-1). */
|
|
/* > \endverbatim */
|
|
|
|
/* Arguments: */
|
|
/* ========== */
|
|
|
|
/* > \param[in] SIDE */
|
|
/* > \verbatim */
|
|
/* > SIDE is CHARACTER*1 */
|
|
/* > = 'L': apply Q or Q**T from the Left; */
|
|
/* > = 'R': apply Q or Q**T from the Right. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] UPLO */
|
|
/* > \verbatim */
|
|
/* > UPLO is CHARACTER*1 */
|
|
/* > = 'U': Upper triangle of A contains elementary reflectors */
|
|
/* > from DSYTRD; */
|
|
/* > = 'L': Lower triangle of A contains elementary reflectors */
|
|
/* > from DSYTRD. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] TRANS */
|
|
/* > \verbatim */
|
|
/* > TRANS is CHARACTER*1 */
|
|
/* > = 'N': No transpose, apply Q; */
|
|
/* > = 'T': Transpose, apply Q**T. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] M */
|
|
/* > \verbatim */
|
|
/* > M is INTEGER */
|
|
/* > The number of rows of the matrix C. M >= 0. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] N */
|
|
/* > \verbatim */
|
|
/* > N is INTEGER */
|
|
/* > The number of columns of the matrix C. N >= 0. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] A */
|
|
/* > \verbatim */
|
|
/* > A is DOUBLE PRECISION array, dimension */
|
|
/* > (LDA,M) if SIDE = 'L' */
|
|
/* > (LDA,N) if SIDE = 'R' */
|
|
/* > The vectors which define the elementary reflectors, as */
|
|
/* > returned by DSYTRD. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDA */
|
|
/* > \verbatim */
|
|
/* > LDA is INTEGER */
|
|
/* > The leading dimension of the array A. */
|
|
/* > LDA >= max(1,M) if SIDE = 'L'; LDA >= max(1,N) if SIDE = 'R'. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] TAU */
|
|
/* > \verbatim */
|
|
/* > TAU is DOUBLE PRECISION 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 DSYTRD. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] C */
|
|
/* > \verbatim */
|
|
/* > C is DOUBLE PRECISION array, dimension (LDC,N) */
|
|
/* > On entry, the M-by-N matrix C. */
|
|
/* > On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDC */
|
|
/* > \verbatim */
|
|
/* > LDC is INTEGER */
|
|
/* > The leading dimension of the array C. LDC >= max(1,M). */
|
|
/* > \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. */
|
|
/* > 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. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] INFO */
|
|
/* > \verbatim */
|
|
/* > INFO is INTEGER */
|
|
/* > = 0: successful exit */
|
|
/* > < 0: if INFO = -i, the i-th argument had 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 dormtr_(char *side, char *uplo, char *trans, integer *m,
|
|
integer *n, doublereal *a, integer *lda, doublereal *tau, doublereal *
|
|
c__, integer *ldc, doublereal *work, integer *lwork, integer *info,
|
|
ftnlen side_len, ftnlen uplo_len, ftnlen trans_len)
|
|
{
|
|
/* 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 *, ftnlen, ftnlen);
|
|
integer iinfo;
|
|
logical upper;
|
|
extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
|
|
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
|
|
integer *, integer *, ftnlen, ftnlen);
|
|
extern /* Subroutine */ int dormql_(char *, char *, integer *, integer *,
|
|
integer *, doublereal *, integer *, doublereal *, doublereal *,
|
|
integer *, doublereal *, integer *, integer *, ftnlen, ftnlen),
|
|
dormqr_(char *, char *, integer *, integer *, integer *,
|
|
doublereal *, integer *, doublereal *, doublereal *, integer *,
|
|
doublereal *, integer *, integer *, ftnlen, ftnlen);
|
|
integer 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 .. */
|
|
/* .. */
|
|
|
|
/* ===================================================================== */
|
|
|
|
/* .. 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, (char *)"L", (ftnlen)1, (ftnlen)1);
|
|
upper = lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1);
|
|
lquery = *lwork == -1;
|
|
|
|
/* NQ is the order of Q and NW is the minimum dimension of WORK */
|
|
|
|
if (left) {
|
|
nq = *m;
|
|
nw = max(1,*n);
|
|
} else {
|
|
nq = *n;
|
|
nw = max(1,*m);
|
|
}
|
|
if (! left && ! lsame_(side, (char *)"R", (ftnlen)1, (ftnlen)1)) {
|
|
*info = -1;
|
|
} else if (! upper && ! lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) {
|
|
*info = -2;
|
|
} else if (! lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1) && ! lsame_(trans,
|
|
(char *)"T", (ftnlen)1, (ftnlen)1)) {
|
|
*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 < 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, (char *)"DORMQL", ch__1, &i__2, n, &i__3, &c_n1, (
|
|
ftnlen)6, (ftnlen)2);
|
|
} 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, (char *)"DORMQL", ch__1, m, &i__2, &i__3, &c_n1, (
|
|
ftnlen)6, (ftnlen)2);
|
|
}
|
|
} 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, (char *)"DORMQR", ch__1, &i__2, n, &i__3, &c_n1, (
|
|
ftnlen)6, (ftnlen)2);
|
|
} 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, (char *)"DORMQR", ch__1, m, &i__2, &i__3, &c_n1, (
|
|
ftnlen)6, (ftnlen)2);
|
|
}
|
|
}
|
|
lwkopt = nw * nb;
|
|
work[1] = (doublereal) lwkopt;
|
|
}
|
|
|
|
if (*info != 0) {
|
|
i__2 = -(*info);
|
|
xerbla_((char *)"DORMTR", &i__2, (ftnlen)6);
|
|
return 0;
|
|
} else if (lquery) {
|
|
return 0;
|
|
}
|
|
|
|
/* Quick return if possible */
|
|
|
|
if (*m == 0 || *n == 0 || nq == 1) {
|
|
work[1] = 1.;
|
|
return 0;
|
|
}
|
|
|
|
if (left) {
|
|
mi = *m - 1;
|
|
ni = *n;
|
|
} else {
|
|
mi = *m;
|
|
ni = *n - 1;
|
|
}
|
|
|
|
if (upper) {
|
|
|
|
/* Q was determined by a call to DSYTRD with UPLO = 'U' */
|
|
|
|
i__2 = nq - 1;
|
|
dormql_(side, trans, &mi, &ni, &i__2, &a[(a_dim1 << 1) + 1], lda, &
|
|
tau[1], &c__[c_offset], ldc, &work[1], lwork, &iinfo, (ftnlen)
|
|
1, (ftnlen)1);
|
|
} else {
|
|
|
|
/* Q was determined by a call to DSYTRD with UPLO = 'L' */
|
|
|
|
if (left) {
|
|
i1 = 2;
|
|
i2 = 1;
|
|
} else {
|
|
i1 = 1;
|
|
i2 = 2;
|
|
}
|
|
i__2 = nq - 1;
|
|
dormqr_(side, trans, &mi, &ni, &i__2, &a[a_dim1 + 2], lda, &tau[1], &
|
|
c__[i1 + i2 * c_dim1], ldc, &work[1], lwork, &iinfo, (ftnlen)
|
|
1, (ftnlen)1);
|
|
}
|
|
work[1] = (doublereal) lwkopt;
|
|
return 0;
|
|
|
|
/* End of DORMTR */
|
|
|
|
} /* dormtr_ */
|
|
|
|
#ifdef __cplusplus
|
|
}
|
|
#endif
|