/* -- translated by f2c (version 20100827).
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*/
#include "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 DORGQR
=========== DOCUMENTATION ===========
Online html documentation available at
http://www.netlib.org/lapack/explore-html/
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Definition:
===========
SUBROUTINE DORGQR( M, N, K, A, LDA, TAU, WORK, LWORK, INFO )
INTEGER INFO, K, LDA, LWORK, M, N
DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
> \par Purpose:
=============
>
> \verbatim
>
> DORGQR generates an M-by-N real matrix Q with orthonormal columns,
> which is defined as the first N columns of a product of K elementary
> reflectors of order M
>
> Q = H(1) H(2) . . . H(k)
>
> as returned by DGEQRF.
> \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 i-th column must contain the vector which
> defines the elementary reflector H(i), for i = 1,2,...,k, as
> returned by DGEQRF in the first 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 DGEQRF.
> \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.
> \date November 2011
> \ingroup doubleOTHERcomputational
=====================================================================
Subroutine */ int igraphdorgqr_(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, l, ib, nb, ki, kk, nx, iws, nbmin, iinfo;
extern /* Subroutine */ int igraphdorg2r_(integer *, integer *, integer *,
doublereal *, integer *, doublereal *, doublereal *, integer *),
igraphdlarfb_(char *, char *, char *, char *, integer *, integer *,
integer *, doublereal *, integer *, doublereal *, integer *,
doublereal *, integer *, doublereal *, integer *), igraphdlarft_(char *, char *, integer *, integer *,
doublereal *, integer *, doublereal *, doublereal *, integer *), igraphxerbla_(char *, integer *, ftnlen);
extern integer igraphilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *, ftnlen, ftnlen);
integer ldwork, 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
=====================================================================
Test the input arguments
Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--tau;
--work;
/* Function Body */
*info = 0;
nb = igraphilaenv_(&c__1, "DORGQR", " ", m, n, k, &c_n1, (ftnlen)6, (ftnlen)1);
lwkopt = max(1,*n) * nb;
work[1] = (doublereal) lwkopt;
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;
} else if (*lwork < max(1,*n) && ! lquery) {
*info = -8;
}
if (*info != 0) {
i__1 = -(*info);
igraphxerbla_("DORGQR", &i__1, (ftnlen)6);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible */
if (*n <= 0) {
work[1] = 1.;
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 = igraphilaenv_(&c__3, "DORGQR", " ", 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 = igraphilaenv_(&c__2, "DORGQR", " ", 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 last block.
The first kk columns are handled by the block method. */
ki = (*k - nx - 1) / nb * nb;
/* Computing MIN */
i__1 = *k, i__2 = ki + nb;
kk = min(i__1,i__2);
/* Set A(1:kk,kk+1:n) to zero. */
i__1 = *n;
for (j = kk + 1; j <= i__1; ++j) {
i__2 = kk;
for (i__ = 1; i__ <= i__2; ++i__) {
a[i__ + j * a_dim1] = 0.;
/* L10: */
}
/* L20: */
}
} else {
kk = 0;
}
/* Use unblocked code for the last or only block. */
if (kk < *n) {
i__1 = *m - kk;
i__2 = *n - kk;
i__3 = *k - kk;
igraphdorg2r_(&i__1, &i__2, &i__3, &a[kk + 1 + (kk + 1) * a_dim1], lda, &
tau[kk + 1], &work[1], &iinfo);
}
if (kk > 0) {
/* Use blocked code */
i__1 = -nb;
for (i__ = ki + 1; i__1 < 0 ? i__ >= 1 : i__ <= 1; i__ += i__1) {
/* Computing MIN */
i__2 = nb, i__3 = *k - i__ + 1;
ib = min(i__2,i__3);
if (i__ + ib <= *n) {
/* Form the triangular factor of the block reflector
H = H(i) H(i+1) . . . H(i+ib-1) */
i__2 = *m - i__ + 1;
igraphdlarft_("Forward", "Columnwise", &i__2, &ib, &a[i__ + i__ *
a_dim1], lda, &tau[i__], &work[1], &ldwork);
/* Apply H to A(i:m,i+ib:n) from the left */
i__2 = *m - i__ + 1;
i__3 = *n - i__ - ib + 1;
igraphdlarfb_("Left", "No transpose", "Forward", "Columnwise", &
i__2, &i__3, &ib, &a[i__ + i__ * a_dim1], lda, &work[
1], &ldwork, &a[i__ + (i__ + ib) * a_dim1], lda, &
work[ib + 1], &ldwork);
}
/* Apply H to rows i:m of current block */
i__2 = *m - i__ + 1;
igraphdorg2r_(&i__2, &ib, &ib, &a[i__ + i__ * a_dim1], lda, &tau[i__], &
work[1], &iinfo);
/* Set rows 1:i-1 of current block to zero */
i__2 = i__ + ib - 1;
for (j = i__; j <= i__2; ++j) {
i__3 = i__ - 1;
for (l = 1; l <= i__3; ++l) {
a[l + j * a_dim1] = 0.;
/* L30: */
}
/* L40: */
}
/* L50: */
}
}
work[1] = (doublereal) iws;
return 0;
/* End of DORGQR */
} /* igraphdorgqr_ */