405 lines
11 KiB
C++
405 lines
11 KiB
C++
/* fortran/dorgbr.f -- translated by f2c (version 20200916).
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You must link the resulting object file with libf2c:
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on Microsoft Windows system, link with libf2c.lib;
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on Linux or Unix systems, link with .../path/to/libf2c.a -lm
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or, if you install libf2c.a in a standard place, with -lf2c -lm
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-- in that order, at the end of the command line, as in
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cc *.o -lf2c -lm
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Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
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http://www.netlib.org/f2c/libf2c.zip
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*/
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#ifdef __cplusplus
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extern "C" {
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#endif
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#include "lmp_f2c.h"
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/* Table of constant values */
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static integer c_n1 = -1;
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/* > \brief \b DORGBR */
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/* =========== DOCUMENTATION =========== */
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/* Online html documentation available at */
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/* http://www.netlib.org/lapack/explore-html/ */
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/* > \htmlonly */
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/* > Download DORGBR + dependencies */
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/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dorgbr.
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f"> */
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/* > [TGZ]</a> */
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/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dorgbr.
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f"> */
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/* > [ZIP]</a> */
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/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dorgbr.
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f"> */
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/* > [TXT]</a> */
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/* > \endhtmlonly */
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/* Definition: */
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/* =========== */
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/* SUBROUTINE DORGBR( VECT, M, N, K, A, LDA, TAU, WORK, LWORK, INFO ) */
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/* .. Scalar Arguments .. */
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/* CHARACTER VECT */
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/* INTEGER INFO, K, LDA, LWORK, M, N */
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/* .. */
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/* .. Array Arguments .. */
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/* DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) */
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/* .. */
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/* > \par Purpose: */
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/* ============= */
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/* > */
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/* > \verbatim */
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/* > */
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/* > DORGBR generates one of the real orthogonal matrices Q or P**T */
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/* > determined by DGEBRD when reducing a real matrix A to bidiagonal */
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/* > form: A = Q * B * P**T. Q and P**T are defined as products of */
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/* > elementary reflectors H(i) or G(i) respectively. */
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/* > */
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/* > If VECT = 'Q', A is assumed to have been an M-by-K matrix, and Q */
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/* > is of order M: */
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/* > if m >= k, Q = H(1) H(2) . . . H(k) and DORGBR returns the first n */
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/* > columns of Q, where m >= n >= k; */
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/* > if m < k, Q = H(1) H(2) . . . H(m-1) and DORGBR returns Q as an */
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/* > M-by-M matrix. */
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/* > */
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/* > If VECT = 'P', A is assumed to have been a K-by-N matrix, and P**T */
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/* > is of order N: */
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/* > if k < n, P**T = G(k) . . . G(2) G(1) and DORGBR returns the first m */
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/* > rows of P**T, where n >= m >= k; */
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/* > if k >= n, P**T = G(n-1) . . . G(2) G(1) and DORGBR returns P**T as */
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/* > an N-by-N matrix. */
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/* > \endverbatim */
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/* Arguments: */
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/* ========== */
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/* > \param[in] VECT */
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/* > \verbatim */
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/* > VECT is CHARACTER*1 */
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/* > Specifies whether the matrix Q or the matrix P**T is */
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/* > required, as defined in the transformation applied by DGEBRD: */
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/* > = 'Q': generate Q; */
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/* > = 'P': generate P**T. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] M */
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/* > \verbatim */
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/* > M is INTEGER */
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/* > The number of rows of the matrix Q or P**T to be returned. */
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/* > M >= 0. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] N */
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/* > \verbatim */
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/* > N is INTEGER */
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/* > The number of columns of the matrix Q or P**T to be returned. */
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/* > N >= 0. */
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/* > If VECT = 'Q', M >= N >= min(M,K); */
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/* > if VECT = 'P', N >= M >= min(N,K). */
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/* > \endverbatim */
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/* > */
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/* > \param[in] K */
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/* > \verbatim */
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/* > K is INTEGER */
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/* > If VECT = 'Q', the number of columns in the original M-by-K */
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/* > matrix reduced by DGEBRD. */
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/* > If VECT = 'P', the number of rows in the original K-by-N */
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/* > matrix reduced by DGEBRD. */
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/* > K >= 0. */
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/* > \endverbatim */
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/* > */
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/* > \param[in,out] A */
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/* > \verbatim */
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/* > A is DOUBLE PRECISION array, dimension (LDA,N) */
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/* > On entry, the vectors which define the elementary reflectors, */
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/* > as returned by DGEBRD. */
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/* > On exit, the M-by-N matrix Q or P**T. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] LDA */
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/* > \verbatim */
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/* > LDA is INTEGER */
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/* > The leading dimension of the array A. LDA >= max(1,M). */
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/* > \endverbatim */
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/* > */
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/* > \param[in] TAU */
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/* > \verbatim */
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/* > TAU is DOUBLE PRECISION array, dimension */
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/* > (min(M,K)) if VECT = 'Q' */
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/* > (min(N,K)) if VECT = 'P' */
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/* > TAU(i) must contain the scalar factor of the elementary */
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/* > reflector H(i) or G(i), which determines Q or P**T, as */
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/* > returned by DGEBRD in its array argument TAUQ or TAUP. */
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/* > \endverbatim */
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/* > */
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/* > \param[out] WORK */
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/* > \verbatim */
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/* > WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) */
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/* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] LWORK */
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/* > \verbatim */
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/* > LWORK is INTEGER */
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/* > The dimension of the array WORK. LWORK >= max(1,min(M,N)). */
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/* > For optimum performance LWORK >= min(M,N)*NB, where NB */
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/* > is the optimal blocksize. */
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/* > */
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/* > If LWORK = -1, then a workspace query is assumed; the routine */
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/* > only calculates the optimal size of the WORK array, returns */
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/* > this value as the first entry of the WORK array, and no error */
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/* > message related to LWORK is issued by XERBLA. */
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/* > \endverbatim */
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/* > */
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/* > \param[out] INFO */
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/* > \verbatim */
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/* > INFO is INTEGER */
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/* > = 0: successful exit */
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/* > < 0: if INFO = -i, the i-th argument had an illegal value */
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/* > \endverbatim */
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/* Authors: */
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/* ======== */
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/* > \author Univ. of Tennessee */
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/* > \author Univ. of California Berkeley */
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/* > \author Univ. of Colorado Denver */
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/* > \author NAG Ltd. */
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/* > \ingroup doubleGBcomputational */
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/* ===================================================================== */
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/* Subroutine */ int dorgbr_(char *vect, integer *m, integer *n, integer *k,
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doublereal *a, integer *lda, doublereal *tau, doublereal *work,
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integer *lwork, integer *info, ftnlen vect_len)
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{
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/* System generated locals */
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integer a_dim1, a_offset, i__1, i__2, i__3;
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/* Local variables */
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integer i__, j, mn;
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extern logical lsame_(char *, char *, ftnlen, ftnlen);
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integer iinfo;
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logical wantq;
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extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen), dorglq_(
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integer *, integer *, integer *, doublereal *, integer *,
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doublereal *, doublereal *, integer *, integer *), dorgqr_(
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integer *, integer *, integer *, doublereal *, integer *,
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doublereal *, doublereal *, integer *, integer *);
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integer lwkopt;
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logical lquery;
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/* -- LAPACK computational routine -- */
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/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
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/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
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/* .. Scalar Arguments .. */
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/* .. */
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/* .. Array Arguments .. */
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/* .. */
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/* ===================================================================== */
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/* .. Parameters .. */
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/* .. */
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/* .. Local Scalars .. */
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/* .. */
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/* .. External Functions .. */
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/* .. */
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/* .. External Subroutines .. */
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/* .. */
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/* .. Intrinsic Functions .. */
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/* .. */
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/* .. Executable Statements .. */
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/* Test the input arguments */
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/* Parameter adjustments */
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a_dim1 = *lda;
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a_offset = 1 + a_dim1;
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a -= a_offset;
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--tau;
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--work;
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/* Function Body */
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*info = 0;
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wantq = lsame_(vect, (char *)"Q", (ftnlen)1, (ftnlen)1);
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mn = min(*m,*n);
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lquery = *lwork == -1;
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if (! wantq && ! lsame_(vect, (char *)"P", (ftnlen)1, (ftnlen)1)) {
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*info = -1;
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} else if (*m < 0) {
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*info = -2;
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} else if (*n < 0 || wantq && (*n > *m || *n < min(*m,*k)) || ! wantq && (
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*m > *n || *m < min(*n,*k))) {
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*info = -3;
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} else if (*k < 0) {
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*info = -4;
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} else if (*lda < max(1,*m)) {
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*info = -6;
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} else if (*lwork < max(1,mn) && ! lquery) {
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*info = -9;
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}
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if (*info == 0) {
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work[1] = 1.;
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if (wantq) {
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if (*m >= *k) {
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dorgqr_(m, n, k, &a[a_offset], lda, &tau[1], &work[1], &c_n1,
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&iinfo);
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} else {
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if (*m > 1) {
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i__1 = *m - 1;
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i__2 = *m - 1;
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i__3 = *m - 1;
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dorgqr_(&i__1, &i__2, &i__3, &a[a_offset], lda, &tau[1], &
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work[1], &c_n1, &iinfo);
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}
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}
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} else {
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if (*k < *n) {
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dorglq_(m, n, k, &a[a_offset], lda, &tau[1], &work[1], &c_n1,
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&iinfo);
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} else {
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if (*n > 1) {
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i__1 = *n - 1;
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i__2 = *n - 1;
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i__3 = *n - 1;
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dorglq_(&i__1, &i__2, &i__3, &a[a_offset], lda, &tau[1], &
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work[1], &c_n1, &iinfo);
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}
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}
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}
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lwkopt = (integer) work[1];
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lwkopt = max(lwkopt,mn);
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}
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if (*info != 0) {
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i__1 = -(*info);
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xerbla_((char *)"DORGBR", &i__1, (ftnlen)6);
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return 0;
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} else if (lquery) {
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work[1] = (doublereal) lwkopt;
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return 0;
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}
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/* Quick return if possible */
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if (*m == 0 || *n == 0) {
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work[1] = 1.;
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return 0;
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}
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if (wantq) {
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/* Form Q, determined by a call to DGEBRD to reduce an m-by-k */
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/* matrix */
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if (*m >= *k) {
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/* If m >= k, assume m >= n >= k */
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dorgqr_(m, n, k, &a[a_offset], lda, &tau[1], &work[1], lwork, &
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iinfo);
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} else {
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/* If m < k, assume m = n */
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/* Shift the vectors which define the elementary reflectors one */
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/* column to the right, and set the first row and column of Q */
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/* to those of the unit matrix */
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for (j = *m; j >= 2; --j) {
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a[j * a_dim1 + 1] = 0.;
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i__1 = *m;
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for (i__ = j + 1; i__ <= i__1; ++i__) {
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a[i__ + j * a_dim1] = a[i__ + (j - 1) * a_dim1];
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/* L10: */
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}
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/* L20: */
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}
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a[a_dim1 + 1] = 1.;
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i__1 = *m;
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for (i__ = 2; i__ <= i__1; ++i__) {
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a[i__ + a_dim1] = 0.;
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/* L30: */
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}
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if (*m > 1) {
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/* Form Q(2:m,2:m) */
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i__1 = *m - 1;
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i__2 = *m - 1;
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i__3 = *m - 1;
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dorgqr_(&i__1, &i__2, &i__3, &a[(a_dim1 << 1) + 2], lda, &tau[
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1], &work[1], lwork, &iinfo);
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}
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}
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} else {
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/* Form P**T, determined by a call to DGEBRD to reduce a k-by-n */
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/* matrix */
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if (*k < *n) {
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/* If k < n, assume k <= m <= n */
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dorglq_(m, n, k, &a[a_offset], lda, &tau[1], &work[1], lwork, &
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iinfo);
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} else {
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/* If k >= n, assume m = n */
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/* Shift the vectors which define the elementary reflectors one */
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/* row downward, and set the first row and column of P**T to */
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/* those of the unit matrix */
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a[a_dim1 + 1] = 1.;
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i__1 = *n;
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for (i__ = 2; i__ <= i__1; ++i__) {
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a[i__ + a_dim1] = 0.;
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/* L40: */
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}
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i__1 = *n;
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for (j = 2; j <= i__1; ++j) {
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for (i__ = j - 1; i__ >= 2; --i__) {
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a[i__ + j * a_dim1] = a[i__ - 1 + j * a_dim1];
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/* L50: */
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}
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a[j * a_dim1 + 1] = 0.;
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/* L60: */
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}
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if (*n > 1) {
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/* Form P**T(2:n,2:n) */
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i__1 = *n - 1;
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i__2 = *n - 1;
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i__3 = *n - 1;
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dorglq_(&i__1, &i__2, &i__3, &a[(a_dim1 << 1) + 2], lda, &tau[
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1], &work[1], lwork, &iinfo);
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}
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}
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}
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work[1] = (doublereal) lwkopt;
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return 0;
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/* End of DORGBR */
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} /* dorgbr_ */
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#ifdef __cplusplus
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}
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#endif
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