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334 lines
11 KiB
334 lines
11 KiB
2 years ago
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*> \brief \b SSYTRD_2STAGE
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*
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* @generated from zhetrd_2stage.f, fortran z -> s, Sun Nov 6 19:34:06 2016
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*
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* =========== DOCUMENTATION ===========
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*
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* Online html documentation available at
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* http://www.netlib.org/lapack/explore-html/
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*
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*> \htmlonly
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*> Download SSYTRD_2STAGE + dependencies
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/ssytrd_2stage.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/ssytrd_2stage.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/ssytrd_2stage.f">
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*> [TXT]</a>
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*> \endhtmlonly
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*
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* Definition:
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* ===========
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*
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* SUBROUTINE SSYTRD_2STAGE( VECT, UPLO, N, A, LDA, D, E, TAU,
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* HOUS2, LHOUS2, WORK, LWORK, INFO )
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*
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* IMPLICIT NONE
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*
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* .. Scalar Arguments ..
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* CHARACTER VECT, UPLO
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* INTEGER N, LDA, LWORK, LHOUS2, INFO
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* ..
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* .. Array Arguments ..
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* REAL D( * ), E( * )
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* REAL A( LDA, * ), TAU( * ),
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* HOUS2( * ), WORK( * )
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* ..
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*
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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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*> SSYTRD_2STAGE reduces a real symmetric matrix A to real symmetric
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*> tridiagonal form T by a orthogonal similarity transformation:
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*> Q1**T Q2**T* A * Q2 * Q1 = T.
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*> \endverbatim
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*
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* Arguments:
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* ==========
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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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*> = 'N': No need for the Housholder representation,
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*> in particular for the second stage (Band to
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*> tridiagonal) and thus LHOUS2 is of size max(1, 4*N);
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*> = 'V': the Householder representation is needed to
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*> either generate Q1 Q2 or to apply Q1 Q2,
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*> then LHOUS2 is to be queried and computed.
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*> (NOT AVAILABLE IN THIS RELEASE).
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*> \endverbatim
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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 REAL 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 band superdiagonal
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*> of A are overwritten by the corresponding elements of the
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*> internal band-diagonal matrix AB, and the elements above
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*> the KD superdiagonal, with the array TAU, represent the orthogonal
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*> matrix Q1 as a product of elementary reflectors; if UPLO
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*> = 'L', the diagonal and band subdiagonal of A are over-
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*> written by the corresponding elements of the internal band-diagonal
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*> matrix AB, and the elements below the KD subdiagonal, with
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*> the array TAU, represent the orthogonal matrix Q1 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 REAL array, dimension (N)
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*> The diagonal elements of the tridiagonal matrix T.
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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 REAL array, dimension (N-1)
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*> The off-diagonal elements of the tridiagonal matrix T.
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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 REAL array, dimension (N-KD)
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*> The scalar factors of the elementary reflectors of
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*> the first stage (see Further Details).
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*> \endverbatim
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*>
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*> \param[out] HOUS2
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*> \verbatim
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*> HOUS2 is REAL array, dimension (LHOUS2)
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*> Stores the Householder representation of the stage2
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*> band to tridiagonal.
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*> \endverbatim
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*>
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*> \param[in] LHOUS2
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*> \verbatim
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*> LHOUS2 is INTEGER
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*> The dimension of the array HOUS2.
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*> If LWORK = -1, or LHOUS2 = -1,
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*> then a query is assumed; the routine
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*> only calculates the optimal size of the HOUS2 array, returns
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*> this value as the first entry of the HOUS2 array, and no error
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*> message related to LHOUS2 is issued by XERBLA.
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*> If VECT='N', LHOUS2 = max(1, 4*n);
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*> if VECT='V', option not yet available.
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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 REAL array, dimension (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, dimension)
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*> If LWORK = -1, or LHOUS2=-1,
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*> 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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*> LWORK = MAX(1, dimension) where
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*> dimension = max(stage1,stage2) + (KD+1)*N
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*> = N*KD + N*max(KD+1,FACTOPTNB)
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*> + max(2*KD*KD, KD*NTHREADS)
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*> + (KD+1)*N
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*> where KD is the blocking size of the reduction,
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*> FACTOPTNB is the blocking used by the QR or LQ
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*> algorithm, usually FACTOPTNB=128 is a good choice
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*> NTHREADS is the number of threads used when
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*> openMP compilation is enabled, otherwise =1.
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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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*
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* Authors:
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* ========
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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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*
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*> \ingroup realSYcomputational
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*
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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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*> Implemented by Azzam Haidar.
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*>
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*> All details are available on technical report, SC11, SC13 papers.
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*>
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*> Azzam Haidar, Hatem Ltaief, and Jack Dongarra.
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*> Parallel reduction to condensed forms for symmetric eigenvalue problems
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*> using aggregated fine-grained and memory-aware kernels. In Proceedings
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*> of 2011 International Conference for High Performance Computing,
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*> Networking, Storage and Analysis (SC '11), New York, NY, USA,
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*> Article 8 , 11 pages.
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*> http://doi.acm.org/10.1145/2063384.2063394
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*>
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*> A. Haidar, J. Kurzak, P. Luszczek, 2013.
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*> An improved parallel singular value algorithm and its implementation
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*> for multicore hardware, In Proceedings of 2013 International Conference
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*> for High Performance Computing, Networking, Storage and Analysis (SC '13).
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*> Denver, Colorado, USA, 2013.
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*> Article 90, 12 pages.
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*> http://doi.acm.org/10.1145/2503210.2503292
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*>
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*> A. Haidar, R. Solca, S. Tomov, T. Schulthess and J. Dongarra.
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*> A novel hybrid CPU-GPU generalized eigensolver for electronic structure
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*> calculations based on fine-grained memory aware tasks.
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*> International Journal of High Performance Computing Applications.
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*> Volume 28 Issue 2, Pages 196-209, May 2014.
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*> http://hpc.sagepub.com/content/28/2/196
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*>
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*> \endverbatim
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*>
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* =====================================================================
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SUBROUTINE SSYTRD_2STAGE( VECT, UPLO, N, A, LDA, D, E, TAU,
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$ HOUS2, LHOUS2, WORK, LWORK, INFO )
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*
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IMPLICIT NONE
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*
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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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*
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* .. Scalar Arguments ..
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CHARACTER VECT, UPLO
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INTEGER N, LDA, LWORK, LHOUS2, INFO
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* ..
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* .. Array Arguments ..
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REAL D( * ), E( * )
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REAL A( LDA, * ), TAU( * ),
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$ HOUS2( * ), WORK( * )
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* ..
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*
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* =====================================================================
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* ..
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* .. Local Scalars ..
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LOGICAL LQUERY, UPPER, WANTQ
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INTEGER KD, IB, LWMIN, LHMIN, LWRK, LDAB, WPOS, ABPOS
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* ..
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* .. External Subroutines ..
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EXTERNAL XERBLA, SSYTRD_SY2SB, SSYTRD_SB2ST
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* ..
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* .. External Functions ..
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LOGICAL LSAME
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INTEGER ILAENV2STAGE
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EXTERNAL LSAME, ILAENV2STAGE
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* ..
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* .. Executable Statements ..
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*
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* Test the input parameters
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*
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INFO = 0
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WANTQ = LSAME( VECT, 'V' )
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UPPER = LSAME( UPLO, 'U' )
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LQUERY = ( LWORK.EQ.-1 ) .OR. ( LHOUS2.EQ.-1 )
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*
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* Determine the block size, the workspace size and the hous size.
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*
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KD = ILAENV2STAGE( 1, 'SSYTRD_2STAGE', VECT, N, -1, -1, -1 )
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IB = ILAENV2STAGE( 2, 'SSYTRD_2STAGE', VECT, N, KD, -1, -1 )
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LHMIN = ILAENV2STAGE( 3, 'SSYTRD_2STAGE', VECT, N, KD, IB, -1 )
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LWMIN = ILAENV2STAGE( 4, 'SSYTRD_2STAGE', VECT, N, KD, IB, -1 )
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* WRITE(*,*),'SSYTRD_2STAGE N KD UPLO LHMIN LWMIN ',N, KD, UPLO,
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* $ LHMIN, LWMIN
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*
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IF( .NOT.LSAME( VECT, 'N' ) ) THEN
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INFO = -1
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ELSE IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
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INFO = -2
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ELSE IF( N.LT.0 ) THEN
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INFO = -3
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ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
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INFO = -5
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ELSE IF( LHOUS2.LT.LHMIN .AND. .NOT.LQUERY ) THEN
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INFO = -10
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ELSE IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN
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INFO = -12
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END IF
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*
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IF( INFO.EQ.0 ) THEN
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HOUS2( 1 ) = LHMIN
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WORK( 1 ) = LWMIN
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END IF
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*
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IF( INFO.NE.0 ) THEN
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CALL XERBLA( 'SSYTRD_2STAGE', -INFO )
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RETURN
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ELSE IF( LQUERY ) THEN
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RETURN
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END IF
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*
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* Quick return if possible
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*
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IF( N.EQ.0 ) THEN
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WORK( 1 ) = 1
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RETURN
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END IF
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*
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* Determine pointer position
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*
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LDAB = KD+1
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LWRK = LWORK-LDAB*N
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ABPOS = 1
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WPOS = ABPOS + LDAB*N
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CALL SSYTRD_SY2SB( UPLO, N, KD, A, LDA, WORK( ABPOS ), LDAB,
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$ TAU, WORK( WPOS ), LWRK, INFO )
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IF( INFO.NE.0 ) THEN
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CALL XERBLA( 'SSYTRD_SY2SB', -INFO )
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RETURN
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END IF
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CALL SSYTRD_SB2ST( 'Y', VECT, UPLO, N, KD,
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$ WORK( ABPOS ), LDAB, D, E,
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$ HOUS2, LHOUS2, WORK( WPOS ), LWRK, INFO )
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IF( INFO.NE.0 ) THEN
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CALL XERBLA( 'SSYTRD_SB2ST', -INFO )
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RETURN
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END IF
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*
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*
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HOUS2( 1 ) = LHMIN
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WORK( 1 ) = LWMIN
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RETURN
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*
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* End of SSYTRD_2STAGE
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*
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END
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