Add graph references
This commit is contained in:
Abdelrahman Said
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/* -- translated by f2c (version 20240504).
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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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#include "f2c.h"
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/* Table of constant values */
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static integer c__1 = 1;
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static integer c_n1 = -1;
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static integer c__3 = 3;
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static integer c__2 = 2;
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static integer c__65 = 65;
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static doublereal c_b25 = -1.;
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static doublereal c_b26 = 1.;
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/* > \brief \b DGEHRD
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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 DGEHRD + dependencies
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> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dgehrd.
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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/dgehrd.
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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/dgehrd.
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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 DGEHRD( N, ILO, IHI, A, LDA, TAU, WORK, LWORK, INFO )
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INTEGER IHI, ILO, INFO, LDA, LWORK, N
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DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
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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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> DGEHRD reduces a real general matrix A to upper Hessenberg form H by
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> an orthogonal similarity transformation: Q**T * A * Q = H .
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> \endverbatim
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Arguments:
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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 order of the matrix A. N >= 0.
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> \endverbatim
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>
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> \param[in] ILO
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> \verbatim
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> ILO is INTEGER
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> \endverbatim
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>
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> \param[in] IHI
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> \verbatim
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> IHI is INTEGER
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>
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> It is assumed that A is already upper triangular in rows
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> and columns 1:ILO-1 and IHI+1:N. ILO and IHI are normally
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> set by a previous call to DGEBAL; otherwise they should be
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> set to 1 and N respectively. See Further Details.
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> 1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=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 N-by-N general matrix to be reduced.
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> On exit, the upper triangle and the first subdiagonal of A
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> are overwritten with the upper Hessenberg matrix H, and the
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> elements below the first subdiagonal, with the array TAU,
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> represent the orthogonal matrix Q as a product of elementary
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> reflectors. See Further Details.
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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,N).
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> \endverbatim
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>
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> \param[out] TAU
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> \verbatim
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> TAU is DOUBLE PRECISION array, dimension (N-1)
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> The scalar factors of the elementary reflectors (see Further
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> Details). Elements 1:ILO-1 and IHI:N-1 of TAU are set to
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> zero.
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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 (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 length of the array WORK. LWORK >= max(1,N).
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> For optimum performance LWORK >= N*NB, where NB is the
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> 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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> \date November 2011
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> \ingroup doubleGEcomputational
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> \par Further Details:
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=====================
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>
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> \verbatim
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>
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> The matrix Q is represented as a product of (ihi-ilo) elementary
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> reflectors
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>
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> Q = H(ilo) H(ilo+1) . . . H(ihi-1).
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>
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> Each H(i) has the form
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>
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> H(i) = I - tau * v * v**T
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>
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> where tau is a real scalar, and v is a real vector with
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> v(1:i) = 0, v(i+1) = 1 and v(ihi+1:n) = 0; v(i+2:ihi) is stored on
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> exit in A(i+2:ihi,i), and tau in TAU(i).
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>
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> The contents of A are illustrated by the following example, with
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> n = 7, ilo = 2 and ihi = 6:
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>
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> on entry, on exit,
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>
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> ( a a a a a a a ) ( a a h h h h a )
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> ( a a a a a a ) ( a h h h h a )
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> ( a a a a a a ) ( h h h h h h )
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> ( a a a a a a ) ( v2 h h h h h )
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> ( a a a a a a ) ( v2 v3 h h h h )
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> ( a a a a a a ) ( v2 v3 v4 h h h )
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> ( a ) ( a )
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>
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> where a denotes an element of the original matrix A, h denotes a
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> modified element of the upper Hessenberg matrix H, and vi denotes an
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> element of the vector defining H(i).
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>
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> This file is a slight modification of LAPACK-3.0's DGEHRD
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> subroutine incorporating improvements proposed by Quintana-Orti and
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> Van de Geijn (2006). (See DLAHR2.)
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> \endverbatim
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>
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=====================================================================
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Subroutine */ int igraphdgehrd_(integer *n, integer *ilo, integer *ihi,
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doublereal *a, integer *lda, doublereal *tau, doublereal *work,
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integer *lwork, integer *info)
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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, i__4;
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/* Local variables */
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integer i__, j;
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doublereal t[4160] /* was [65][64] */;
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integer ib;
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doublereal ei;
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integer nb, nh, nx, iws;
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extern /* Subroutine */ int igraphdgemm_(char *, char *, integer *, integer *,
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integer *, doublereal *, doublereal *, integer *, doublereal *,
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integer *, doublereal *, doublereal *, integer *);
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integer nbmin, iinfo;
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extern /* Subroutine */ int igraphdtrmm_(char *, char *, char *, char *,
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integer *, integer *, doublereal *, doublereal *, integer *,
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doublereal *, integer *), igraphdaxpy_(
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integer *, doublereal *, doublereal *, integer *, doublereal *,
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integer *), igraphdgehd2_(integer *, integer *, integer *, doublereal *,
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integer *, doublereal *, doublereal *, integer *), igraphdlahr2_(
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integer *, integer *, integer *, doublereal *, integer *,
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doublereal *, doublereal *, integer *, doublereal *, integer *),
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igraphdlarfb_(char *, char *, char *, char *, integer *, integer *,
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integer *, doublereal *, integer *, doublereal *, integer *,
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doublereal *, integer *, doublereal *, integer *), igraphxerbla_(char *, integer *, ftnlen);
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extern integer igraphilaenv_(integer *, char *, char *, integer *, integer *,
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integer *, integer *, ftnlen, ftnlen);
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integer ldwork, lwkopt;
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logical lquery;
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/* -- LAPACK computational routine (version 3.4.0) --
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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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November 2011
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=====================================================================
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Test the input parameters
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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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/* Computing MIN */
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i__1 = 64, i__2 = igraphilaenv_(&c__1, "DGEHRD", " ", n, ilo, ihi, &c_n1, (
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ftnlen)6, (ftnlen)1);
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nb = min(i__1,i__2);
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lwkopt = *n * nb;
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work[1] = (doublereal) lwkopt;
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lquery = *lwork == -1;
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if (*n < 0) {
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*info = -1;
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} else if (*ilo < 1 || *ilo > max(1,*n)) {
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*info = -2;
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} else if (*ihi < min(*ilo,*n) || *ihi > *n) {
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*info = -3;
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} else if (*lda < max(1,*n)) {
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*info = -5;
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} else if (*lwork < max(1,*n) && ! lquery) {
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*info = -8;
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}
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if (*info != 0) {
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i__1 = -(*info);
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igraphxerbla_("DGEHRD", &i__1, (ftnlen)6);
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return 0;
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} else if (lquery) {
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return 0;
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}
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/* Set elements 1:ILO-1 and IHI:N-1 of TAU to zero */
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i__1 = *ilo - 1;
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for (i__ = 1; i__ <= i__1; ++i__) {
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tau[i__] = 0.;
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/* L10: */
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}
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i__1 = *n - 1;
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for (i__ = max(1,*ihi); i__ <= i__1; ++i__) {
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tau[i__] = 0.;
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/* L20: */
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}
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/* Quick return if possible */
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nh = *ihi - *ilo + 1;
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if (nh <= 1) {
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work[1] = 1.;
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return 0;
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}
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/* Determine the block size
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Computing MIN */
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i__1 = 64, i__2 = igraphilaenv_(&c__1, "DGEHRD", " ", n, ilo, ihi, &c_n1, (
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ftnlen)6, (ftnlen)1);
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nb = min(i__1,i__2);
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nbmin = 2;
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iws = 1;
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if (nb > 1 && nb < nh) {
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/* Determine when to cross over from blocked to unblocked code
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(last block is always handled by unblocked code)
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Computing MAX */
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i__1 = nb, i__2 = igraphilaenv_(&c__3, "DGEHRD", " ", n, ilo, ihi, &c_n1, (
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ftnlen)6, (ftnlen)1);
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nx = max(i__1,i__2);
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if (nx < nh) {
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/* Determine if workspace is large enough for blocked code */
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iws = *n * nb;
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if (*lwork < iws) {
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/* Not enough workspace to use optimal NB: determine the
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minimum value of NB, and reduce NB or force use of
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unblocked code
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Computing MAX */
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i__1 = 2, i__2 = igraphilaenv_(&c__2, "DGEHRD", " ", n, ilo, ihi, &
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c_n1, (ftnlen)6, (ftnlen)1);
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nbmin = max(i__1,i__2);
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if (*lwork >= *n * nbmin) {
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nb = *lwork / *n;
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} else {
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nb = 1;
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}
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}
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}
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}
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ldwork = *n;
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if (nb < nbmin || nb >= nh) {
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/* Use unblocked code below */
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i__ = *ilo;
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} else {
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/* Use blocked code */
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i__1 = *ihi - 1 - nx;
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i__2 = nb;
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for (i__ = *ilo; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) {
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/* Computing MIN */
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i__3 = nb, i__4 = *ihi - i__;
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ib = min(i__3,i__4);
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/* Reduce columns i:i+ib-1 to Hessenberg form, returning the
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matrices V and T of the block reflector H = I - V*T*V**T
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which performs the reduction, and also the matrix Y = A*V*T */
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igraphdlahr2_(ihi, &i__, &ib, &a[i__ * a_dim1 + 1], lda, &tau[i__], t, &
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c__65, &work[1], &ldwork);
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/* Apply the block reflector H to A(1:ihi,i+ib:ihi) from the
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right, computing A := A - Y * V**T. V(i+ib,ib-1) must be set
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to 1 */
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ei = a[i__ + ib + (i__ + ib - 1) * a_dim1];
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a[i__ + ib + (i__ + ib - 1) * a_dim1] = 1.;
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i__3 = *ihi - i__ - ib + 1;
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igraphdgemm_("No transpose", "Transpose", ihi, &i__3, &ib, &c_b25, &
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work[1], &ldwork, &a[i__ + ib + i__ * a_dim1], lda, &
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c_b26, &a[(i__ + ib) * a_dim1 + 1], lda);
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a[i__ + ib + (i__ + ib - 1) * a_dim1] = ei;
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/* Apply the block reflector H to A(1:i,i+1:i+ib-1) from the
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right */
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i__3 = ib - 1;
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igraphdtrmm_("Right", "Lower", "Transpose", "Unit", &i__, &i__3, &c_b26,
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&a[i__ + 1 + i__ * a_dim1], lda, &work[1], &ldwork);
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i__3 = ib - 2;
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for (j = 0; j <= i__3; ++j) {
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igraphdaxpy_(&i__, &c_b25, &work[ldwork * j + 1], &c__1, &a[(i__ +
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j + 1) * a_dim1 + 1], &c__1);
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/* L30: */
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}
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/* Apply the block reflector H to A(i+1:ihi,i+ib:n) from the
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left */
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i__3 = *ihi - i__;
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i__4 = *n - i__ - ib + 1;
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igraphdlarfb_("Left", "Transpose", "Forward", "Columnwise", &i__3, &
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i__4, &ib, &a[i__ + 1 + i__ * a_dim1], lda, t, &c__65, &a[
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i__ + 1 + (i__ + ib) * a_dim1], lda, &work[1], &ldwork);
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/* L40: */
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}
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}
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/* Use unblocked code to reduce the rest of the matrix */
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igraphdgehd2_(n, &i__, ihi, &a[a_offset], lda, &tau[1], &work[1], &iinfo);
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work[1] = (doublereal) iws;
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return 0;
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/* End of DGEHRD */
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} /* igraphdgehrd_ */
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