Abdelrahman Said
429 lines
13 KiB
C
429 lines
13 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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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 doublereal c_b22 = -1.;
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static doublereal c_b23 = 1.;
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/* > \brief \b DSYTRD
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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 DSYTRD + dependencies
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> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dsytrd.
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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/dsytrd.
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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/dsytrd.
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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 DSYTRD( UPLO, N, A, LDA, D, E, TAU, WORK, LWORK, INFO )
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CHARACTER UPLO
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INTEGER INFO, LDA, LWORK, N
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DOUBLE PRECISION A( LDA, * ), D( * ), E( * ), TAU( * ),
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$ 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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> DSYTRD reduces a real symmetric matrix A to real symmetric
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> tridiagonal form T by an orthogonal similarity transformation:
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> Q**T * A * Q = T.
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> \endverbatim
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Arguments:
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==========
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> \param[in] UPLO
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> \verbatim
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> UPLO is CHARACTER*1
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> = 'U': Upper triangle of A is stored;
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> = 'L': Lower triangle of A is stored.
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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 order of the matrix A. 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 symmetric matrix A. If UPLO = 'U', the leading
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> N-by-N upper triangular part of A contains the upper
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> triangular part of the matrix A, and the strictly lower
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> triangular part of A is not referenced. If UPLO = 'L', the
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> leading N-by-N lower triangular part of A contains the lower
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> triangular part of the matrix A, and the strictly upper
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> triangular part of A is not referenced.
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> On exit, if UPLO = 'U', the diagonal and first superdiagonal
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> of A are overwritten by the corresponding elements of the
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> tridiagonal matrix T, and the elements above the first
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> superdiagonal, with the array TAU, represent the orthogonal
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> matrix Q as a product of elementary reflectors; if UPLO
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> = 'L', the diagonal and first subdiagonal of A are over-
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> written by the corresponding elements of the tridiagonal
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> matrix T, and the elements below the first subdiagonal, with
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> the array TAU, represent the orthogonal matrix Q as a product
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> of elementary 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] D
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> \verbatim
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> D is DOUBLE PRECISION array, dimension (N)
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> The diagonal elements of the tridiagonal matrix T:
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> D(i) = A(i,i).
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> \endverbatim
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>
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> \param[out] E
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> \verbatim
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> E is DOUBLE PRECISION array, dimension (N-1)
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> The off-diagonal elements of the tridiagonal matrix T:
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> E(i) = A(i,i+1) if UPLO = 'U', E(i) = A(i+1,i) if UPLO = 'L'.
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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 (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 >= 1.
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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 doubleSYcomputational
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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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> If UPLO = 'U', the matrix Q is represented as a product of elementary
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> reflectors
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>
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> Q = H(n-1) . . . H(2) H(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(i+1:n) = 0 and v(i) = 1; v(1:i-1) is stored on exit in
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> A(1:i-1,i+1), and tau in TAU(i).
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>
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> If UPLO = 'L', the matrix Q is represented as a product of elementary
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> reflectors
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>
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> Q = H(1) H(2) . . . H(n-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 and v(i+1) = 1; v(i+2:n) is stored on exit in A(i+2:n,i),
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> and tau in TAU(i).
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>
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> The contents of A on exit are illustrated by the following examples
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> with n = 5:
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>
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> if UPLO = 'U': if UPLO = 'L':
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>
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> ( d e v2 v3 v4 ) ( d )
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> ( d e v3 v4 ) ( e d )
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> ( d e v4 ) ( v1 e d )
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> ( d e ) ( v1 v2 e d )
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> ( d ) ( v1 v2 v3 e d )
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>
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> where d and e denote diagonal and off-diagonal elements of T, and vi
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> denotes an 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 igraphdsytrd_(char *uplo, integer *n, doublereal *a, integer *
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lda, doublereal *d__, doublereal *e, doublereal *tau, doublereal *
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work, 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;
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/* Local variables */
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integer i__, j, nb, kk, nx, iws;
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extern logical igraphlsame_(char *, char *);
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integer nbmin, iinfo;
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logical upper;
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extern /* Subroutine */ int igraphdsytd2_(char *, integer *, doublereal *,
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integer *, doublereal *, doublereal *, doublereal *, integer *), igraphdsyr2k_(char *, char *, integer *, integer *, doublereal
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*, doublereal *, integer *, doublereal *, integer *, doublereal *,
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doublereal *, integer *), igraphdlatrd_(char *,
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integer *, integer *, doublereal *, integer *, doublereal *,
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doublereal *, doublereal *, integer *), igraphxerbla_(char *,
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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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--d__;
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--e;
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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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upper = igraphlsame_(uplo, "U");
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lquery = *lwork == -1;
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if (! upper && ! igraphlsame_(uplo, "L")) {
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*info = -1;
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} else if (*n < 0) {
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*info = -2;
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} else if (*lda < max(1,*n)) {
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*info = -4;
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} else if (*lwork < 1 && ! lquery) {
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*info = -9;
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}
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if (*info == 0) {
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/* Determine the block size. */
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nb = igraphilaenv_(&c__1, "DSYTRD", uplo, n, &c_n1, &c_n1, &c_n1, (ftnlen)6,
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(ftnlen)1);
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lwkopt = *n * nb;
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work[1] = (doublereal) lwkopt;
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}
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if (*info != 0) {
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i__1 = -(*info);
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igraphxerbla_("DSYTRD", &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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/* Quick return if possible */
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if (*n == 0) {
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work[1] = 1.;
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return 0;
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}
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nx = *n;
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iws = 1;
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if (nb > 1 && nb < *n) {
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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, "DSYTRD", uplo, n, &c_n1, &c_n1, &
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c_n1, (ftnlen)6, (ftnlen)1);
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nx = max(i__1,i__2);
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if (nx < *n) {
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/* Determine if workspace is large enough for blocked code. */
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ldwork = *n;
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iws = ldwork * 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 by setting NX = N.
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Computing MAX */
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i__1 = *lwork / ldwork;
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nb = max(i__1,1);
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nbmin = igraphilaenv_(&c__2, "DSYTRD", uplo, n, &c_n1, &c_n1, &c_n1,
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(ftnlen)6, (ftnlen)1);
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if (nb < nbmin) {
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nx = *n;
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}
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}
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} else {
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nx = *n;
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}
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} else {
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nb = 1;
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}
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if (upper) {
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/* Reduce the upper triangle of A.
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Columns 1:kk are handled by the unblocked method. */
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kk = *n - (*n - nx + nb - 1) / nb * nb;
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i__1 = kk + 1;
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i__2 = -nb;
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for (i__ = *n - nb + 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ +=
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i__2) {
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/* Reduce columns i:i+nb-1 to tridiagonal form and form the
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matrix W which is needed to update the unreduced part of
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the matrix */
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i__3 = i__ + nb - 1;
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igraphdlatrd_(uplo, &i__3, &nb, &a[a_offset], lda, &e[1], &tau[1], &
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work[1], &ldwork);
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/* Update the unreduced submatrix A(1:i-1,1:i-1), using an
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update of the form: A := A - V*W**T - W*V**T */
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i__3 = i__ - 1;
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igraphdsyr2k_(uplo, "No transpose", &i__3, &nb, &c_b22, &a[i__ * a_dim1
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+ 1], lda, &work[1], &ldwork, &c_b23, &a[a_offset], lda);
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/* Copy superdiagonal elements back into A, and diagonal
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elements into D */
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i__3 = i__ + nb - 1;
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for (j = i__; j <= i__3; ++j) {
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a[j - 1 + j * a_dim1] = e[j - 1];
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d__[j] = a[j + j * a_dim1];
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/* L10: */
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}
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/* L20: */
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}
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/* Use unblocked code to reduce the last or only block */
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igraphdsytd2_(uplo, &kk, &a[a_offset], lda, &d__[1], &e[1], &tau[1], &iinfo);
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} else {
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/* Reduce the lower triangle of A */
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i__2 = *n - nx;
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i__1 = nb;
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for (i__ = 1; i__1 < 0 ? i__ >= i__2 : i__ <= i__2; i__ += i__1) {
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/* Reduce columns i:i+nb-1 to tridiagonal form and form the
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matrix W which is needed to update the unreduced part of
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the matrix */
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i__3 = *n - i__ + 1;
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igraphdlatrd_(uplo, &i__3, &nb, &a[i__ + i__ * a_dim1], lda, &e[i__], &
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tau[i__], &work[1], &ldwork);
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/* Update the unreduced submatrix A(i+ib:n,i+ib:n), using
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an update of the form: A := A - V*W**T - W*V**T */
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i__3 = *n - i__ - nb + 1;
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igraphdsyr2k_(uplo, "No transpose", &i__3, &nb, &c_b22, &a[i__ + nb +
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i__ * a_dim1], lda, &work[nb + 1], &ldwork, &c_b23, &a[
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i__ + nb + (i__ + nb) * a_dim1], lda);
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/* Copy subdiagonal elements back into A, and diagonal
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elements into D */
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i__3 = i__ + nb - 1;
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for (j = i__; j <= i__3; ++j) {
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a[j + 1 + j * a_dim1] = e[j];
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d__[j] = a[j + j * a_dim1];
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/* L30: */
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}
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/* L40: */
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}
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/* Use unblocked code to reduce the last or only block */
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i__1 = *n - i__ + 1;
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igraphdsytd2_(uplo, &i__1, &a[i__ + i__ * a_dim1], lda, &d__[i__], &e[i__],
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&tau[i__], &iinfo);
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}
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work[1] = (doublereal) lwkopt;
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return 0;
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/* End of DSYTRD */
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} /* igraphdsytrd_ */
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