Abdelrahman Said
256 lines
7.8 KiB
C
256 lines
7.8 KiB
C
/* -- 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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/* > \brief \b DGEHD2 reduces a general square matrix to upper Hessenberg form using an unblocked algorithm.
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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 DGEHD2 + dependencies
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> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dgehd2.
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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/dgehd2.
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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/dgehd2.
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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 DGEHD2( N, ILO, IHI, A, LDA, TAU, WORK, INFO )
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INTEGER IHI, ILO, INFO, LDA, 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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> DGEHD2 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 <= max(1,N).
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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).
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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 (N)
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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 September 2012
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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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> \endverbatim
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>
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=====================================================================
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Subroutine */ int igraphdgehd2_(integer *n, integer *ilo, integer *ihi,
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doublereal *a, integer *lda, doublereal *tau, doublereal *work,
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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;
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/* Local variables */
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integer i__;
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doublereal aii;
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extern /* Subroutine */ int igraphdlarf_(char *, integer *, integer *,
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doublereal *, integer *, doublereal *, doublereal *, integer *,
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doublereal *), igraphdlarfg_(integer *, doublereal *,
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doublereal *, integer *, doublereal *), igraphxerbla_(char *, integer *,
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ftnlen);
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/* -- LAPACK computational routine (version 3.4.2) --
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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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September 2012
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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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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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}
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if (*info != 0) {
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i__1 = -(*info);
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igraphxerbla_("DGEHD2", &i__1, (ftnlen)6);
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return 0;
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}
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i__1 = *ihi - 1;
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for (i__ = *ilo; i__ <= i__1; ++i__) {
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/* Compute elementary reflector H(i) to annihilate A(i+2:ihi,i) */
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i__2 = *ihi - i__;
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/* Computing MIN */
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i__3 = i__ + 2;
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igraphdlarfg_(&i__2, &a[i__ + 1 + i__ * a_dim1], &a[min(i__3,*n) + i__ *
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a_dim1], &c__1, &tau[i__]);
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aii = a[i__ + 1 + i__ * a_dim1];
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a[i__ + 1 + i__ * a_dim1] = 1.;
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/* Apply H(i) to A(1:ihi,i+1:ihi) from the right */
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i__2 = *ihi - i__;
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igraphdlarf_("Right", ihi, &i__2, &a[i__ + 1 + i__ * a_dim1], &c__1, &tau[
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i__], &a[(i__ + 1) * a_dim1 + 1], lda, &work[1]);
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/* Apply H(i) to A(i+1:ihi,i+1:n) from the left */
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i__2 = *ihi - i__;
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i__3 = *n - i__;
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igraphdlarf_("Left", &i__2, &i__3, &a[i__ + 1 + i__ * a_dim1], &c__1, &tau[
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i__], &a[i__ + 1 + (i__ + 1) * a_dim1], lda, &work[1]);
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a[i__ + 1 + i__ * a_dim1] = aii;
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/* L10: */
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}
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return 0;
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/* End of DGEHD2 */
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} /* igraphdgehd2_ */
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