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542 lines
17 KiB
542 lines
17 KiB
2 years ago
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*> \brief \b DSFRK performs a symmetric rank-k operation for matrix in RFP format.
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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 DSFRK + dependencies
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dsfrk.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/dsfrk.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/dsfrk.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 DSFRK( TRANSR, UPLO, TRANS, N, K, ALPHA, A, LDA, BETA,
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* C )
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*
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* .. Scalar Arguments ..
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* DOUBLE PRECISION ALPHA, BETA
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* INTEGER K, LDA, N
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* CHARACTER TRANS, TRANSR, UPLO
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* ..
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* .. Array Arguments ..
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* DOUBLE PRECISION A( LDA, * ), C( * )
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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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*> Level 3 BLAS like routine for C in RFP Format.
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*>
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*> DSFRK performs one of the symmetric rank--k operations
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*>
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*> C := alpha*A*A**T + beta*C,
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*>
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*> or
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*>
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*> C := alpha*A**T*A + beta*C,
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*>
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*> where alpha and beta are real scalars, C is an n--by--n symmetric
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*> matrix and A is an n--by--k matrix in the first case and a k--by--n
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*> matrix in the second case.
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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] TRANSR
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*> \verbatim
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*> TRANSR is CHARACTER*1
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*> = 'N': The Normal Form of RFP A is stored;
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*> = 'T': The Transpose Form of RFP A is stored.
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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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*> On entry, UPLO specifies whether the upper or lower
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*> triangular part of the array C is to be referenced as
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*> follows:
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*>
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*> UPLO = 'U' or 'u' Only the upper triangular part of C
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*> is to be referenced.
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*>
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*> UPLO = 'L' or 'l' Only the lower triangular part of C
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*> is to be referenced.
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*>
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*> Unchanged on exit.
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*> \endverbatim
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*>
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*> \param[in] TRANS
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*> \verbatim
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*> TRANS is CHARACTER*1
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*> On entry, TRANS specifies the operation to be performed as
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*> follows:
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*>
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*> TRANS = 'N' or 'n' C := alpha*A*A**T + beta*C.
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*>
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*> TRANS = 'T' or 't' C := alpha*A**T*A + beta*C.
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*>
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*> Unchanged on exit.
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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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*> On entry, N specifies the order of the matrix C. N must be
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*> at least zero.
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*> Unchanged on exit.
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*> \endverbatim
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*>
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*> \param[in] K
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*> \verbatim
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*> K is INTEGER
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*> On entry with TRANS = 'N' or 'n', K specifies the number
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*> of columns of the matrix A, and on entry with TRANS = 'T'
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*> or 't', K specifies the number of rows of the matrix A. K
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*> must be at least zero.
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*> Unchanged on exit.
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*> \endverbatim
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*>
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*> \param[in] ALPHA
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*> \verbatim
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*> ALPHA is DOUBLE PRECISION
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*> On entry, ALPHA specifies the scalar alpha.
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*> Unchanged on exit.
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*> \endverbatim
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*>
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*> \param[in] A
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*> \verbatim
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*> A is DOUBLE PRECISION array, dimension (LDA,ka)
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*> where KA
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*> is K when TRANS = 'N' or 'n', and is N otherwise. Before
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*> entry with TRANS = 'N' or 'n', the leading N--by--K part of
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*> the array A must contain the matrix A, otherwise the leading
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*> K--by--N part of the array A must contain the matrix A.
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*> Unchanged on exit.
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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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*> On entry, LDA specifies the first dimension of A as declared
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*> in the calling (sub) program. When TRANS = 'N' or 'n'
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*> then LDA must be at least max( 1, n ), otherwise LDA must
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*> be at least max( 1, k ).
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*> Unchanged on exit.
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*> \endverbatim
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*>
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*> \param[in] BETA
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*> \verbatim
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*> BETA is DOUBLE PRECISION
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*> On entry, BETA specifies the scalar beta.
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*> Unchanged on exit.
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*> \endverbatim
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*>
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*> \param[in,out] C
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*> \verbatim
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*> C is DOUBLE PRECISION array, dimension (NT)
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*> NT = N*(N+1)/2. On entry, the symmetric matrix C in RFP
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*> Format. RFP Format is described by TRANSR, UPLO and N.
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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 doubleOTHERcomputational
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*
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* =====================================================================
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SUBROUTINE DSFRK( TRANSR, UPLO, TRANS, N, K, ALPHA, A, LDA, BETA,
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$ C )
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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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DOUBLE PRECISION ALPHA, BETA
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INTEGER K, LDA, N
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CHARACTER TRANS, TRANSR, UPLO
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* ..
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* .. Array Arguments ..
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DOUBLE PRECISION A( LDA, * ), C( * )
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* ..
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*
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* =====================================================================
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*
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* ..
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* .. Parameters ..
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DOUBLE PRECISION ONE, ZERO
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PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
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* ..
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* .. Local Scalars ..
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LOGICAL LOWER, NORMALTRANSR, NISODD, NOTRANS
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INTEGER INFO, NROWA, J, NK, N1, N2
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* ..
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* .. External Functions ..
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LOGICAL LSAME
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EXTERNAL LSAME
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* ..
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* .. External Subroutines ..
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EXTERNAL XERBLA, DGEMM, DSYRK
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC MAX
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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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NORMALTRANSR = LSAME( TRANSR, 'N' )
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LOWER = LSAME( UPLO, 'L' )
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NOTRANS = LSAME( TRANS, 'N' )
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*
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IF( NOTRANS ) THEN
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NROWA = N
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ELSE
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NROWA = K
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END IF
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*
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IF( .NOT.NORMALTRANSR .AND. .NOT.LSAME( TRANSR, 'T' ) ) THEN
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INFO = -1
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ELSE IF( .NOT.LOWER .AND. .NOT.LSAME( UPLO, 'U' ) ) THEN
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INFO = -2
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ELSE IF( .NOT.NOTRANS .AND. .NOT.LSAME( TRANS, 'T' ) ) THEN
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INFO = -3
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ELSE IF( N.LT.0 ) THEN
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INFO = -4
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ELSE IF( K.LT.0 ) THEN
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INFO = -5
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ELSE IF( LDA.LT.MAX( 1, NROWA ) ) THEN
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INFO = -8
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END IF
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IF( INFO.NE.0 ) THEN
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CALL XERBLA( 'DSFRK ', -INFO )
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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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* The quick return case: ((ALPHA.EQ.0).AND.(BETA.NE.ZERO)) is not
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* done (it is in DSYRK for example) and left in the general case.
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*
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IF( ( N.EQ.0 ) .OR. ( ( ( ALPHA.EQ.ZERO ) .OR. ( K.EQ.0 ) ) .AND.
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$ ( BETA.EQ.ONE ) ) )RETURN
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*
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IF( ( ALPHA.EQ.ZERO ) .AND. ( BETA.EQ.ZERO ) ) THEN
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DO J = 1, ( ( N*( N+1 ) ) / 2 )
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C( J ) = ZERO
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END DO
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RETURN
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END IF
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*
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* C is N-by-N.
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* If N is odd, set NISODD = .TRUE., and N1 and N2.
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* If N is even, NISODD = .FALSE., and NK.
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*
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IF( MOD( N, 2 ).EQ.0 ) THEN
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NISODD = .FALSE.
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NK = N / 2
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ELSE
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NISODD = .TRUE.
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IF( LOWER ) THEN
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N2 = N / 2
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N1 = N - N2
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ELSE
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N1 = N / 2
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N2 = N - N1
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END IF
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END IF
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*
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IF( NISODD ) THEN
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*
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* N is odd
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*
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IF( NORMALTRANSR ) THEN
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*
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* N is odd and TRANSR = 'N'
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*
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IF( LOWER ) THEN
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*
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* N is odd, TRANSR = 'N', and UPLO = 'L'
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*
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IF( NOTRANS ) THEN
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*
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* N is odd, TRANSR = 'N', UPLO = 'L', and TRANS = 'N'
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*
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CALL DSYRK( 'L', 'N', N1, K, ALPHA, A( 1, 1 ), LDA,
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$ BETA, C( 1 ), N )
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CALL DSYRK( 'U', 'N', N2, K, ALPHA, A( N1+1, 1 ), LDA,
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$ BETA, C( N+1 ), N )
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CALL DGEMM( 'N', 'T', N2, N1, K, ALPHA, A( N1+1, 1 ),
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$ LDA, A( 1, 1 ), LDA, BETA, C( N1+1 ), N )
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*
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ELSE
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*
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* N is odd, TRANSR = 'N', UPLO = 'L', and TRANS = 'T'
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*
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CALL DSYRK( 'L', 'T', N1, K, ALPHA, A( 1, 1 ), LDA,
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$ BETA, C( 1 ), N )
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CALL DSYRK( 'U', 'T', N2, K, ALPHA, A( 1, N1+1 ), LDA,
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$ BETA, C( N+1 ), N )
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CALL DGEMM( 'T', 'N', N2, N1, K, ALPHA, A( 1, N1+1 ),
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$ LDA, A( 1, 1 ), LDA, BETA, C( N1+1 ), N )
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*
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END IF
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*
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ELSE
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*
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* N is odd, TRANSR = 'N', and UPLO = 'U'
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*
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IF( NOTRANS ) THEN
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*
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* N is odd, TRANSR = 'N', UPLO = 'U', and TRANS = 'N'
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*
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CALL DSYRK( 'L', 'N', N1, K, ALPHA, A( 1, 1 ), LDA,
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$ BETA, C( N2+1 ), N )
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CALL DSYRK( 'U', 'N', N2, K, ALPHA, A( N2, 1 ), LDA,
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$ BETA, C( N1+1 ), N )
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CALL DGEMM( 'N', 'T', N1, N2, K, ALPHA, A( 1, 1 ),
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$ LDA, A( N2, 1 ), LDA, BETA, C( 1 ), N )
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*
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ELSE
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*
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* N is odd, TRANSR = 'N', UPLO = 'U', and TRANS = 'T'
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*
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CALL DSYRK( 'L', 'T', N1, K, ALPHA, A( 1, 1 ), LDA,
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$ BETA, C( N2+1 ), N )
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CALL DSYRK( 'U', 'T', N2, K, ALPHA, A( 1, N2 ), LDA,
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$ BETA, C( N1+1 ), N )
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CALL DGEMM( 'T', 'N', N1, N2, K, ALPHA, A( 1, 1 ),
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$ LDA, A( 1, N2 ), LDA, BETA, C( 1 ), N )
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*
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END IF
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*
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END IF
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*
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ELSE
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*
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* N is odd, and TRANSR = 'T'
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*
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IF( LOWER ) THEN
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*
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* N is odd, TRANSR = 'T', and UPLO = 'L'
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*
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IF( NOTRANS ) THEN
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*
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* N is odd, TRANSR = 'T', UPLO = 'L', and TRANS = 'N'
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*
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CALL DSYRK( 'U', 'N', N1, K, ALPHA, A( 1, 1 ), LDA,
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$ BETA, C( 1 ), N1 )
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CALL DSYRK( 'L', 'N', N2, K, ALPHA, A( N1+1, 1 ), LDA,
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$ BETA, C( 2 ), N1 )
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CALL DGEMM( 'N', 'T', N1, N2, K, ALPHA, A( 1, 1 ),
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$ LDA, A( N1+1, 1 ), LDA, BETA,
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$ C( N1*N1+1 ), N1 )
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*
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ELSE
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*
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* N is odd, TRANSR = 'T', UPLO = 'L', and TRANS = 'T'
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|
*
|
||
|
|
CALL DSYRK( 'U', 'T', N1, K, ALPHA, A( 1, 1 ), LDA,
|
||
|
|
$ BETA, C( 1 ), N1 )
|
||
|
|
CALL DSYRK( 'L', 'T', N2, K, ALPHA, A( 1, N1+1 ), LDA,
|
||
|
|
$ BETA, C( 2 ), N1 )
|
||
|
|
CALL DGEMM( 'T', 'N', N1, N2, K, ALPHA, A( 1, 1 ),
|
||
|
|
$ LDA, A( 1, N1+1 ), LDA, BETA,
|
||
|
|
$ C( N1*N1+1 ), N1 )
|
||
|
|
*
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
ELSE
|
||
|
|
*
|
||
|
|
* N is odd, TRANSR = 'T', and UPLO = 'U'
|
||
|
|
*
|
||
|
|
IF( NOTRANS ) THEN
|
||
|
|
*
|
||
|
|
* N is odd, TRANSR = 'T', UPLO = 'U', and TRANS = 'N'
|
||
|
|
*
|
||
|
|
CALL DSYRK( 'U', 'N', N1, K, ALPHA, A( 1, 1 ), LDA,
|
||
|
|
$ BETA, C( N2*N2+1 ), N2 )
|
||
|
|
CALL DSYRK( 'L', 'N', N2, K, ALPHA, A( N1+1, 1 ), LDA,
|
||
|
|
$ BETA, C( N1*N2+1 ), N2 )
|
||
|
|
CALL DGEMM( 'N', 'T', N2, N1, K, ALPHA, A( N1+1, 1 ),
|
||
|
|
$ LDA, A( 1, 1 ), LDA, BETA, C( 1 ), N2 )
|
||
|
|
*
|
||
|
|
ELSE
|
||
|
|
*
|
||
|
|
* N is odd, TRANSR = 'T', UPLO = 'U', and TRANS = 'T'
|
||
|
|
*
|
||
|
|
CALL DSYRK( 'U', 'T', N1, K, ALPHA, A( 1, 1 ), LDA,
|
||
|
|
$ BETA, C( N2*N2+1 ), N2 )
|
||
|
|
CALL DSYRK( 'L', 'T', N2, K, ALPHA, A( 1, N1+1 ), LDA,
|
||
|
|
$ BETA, C( N1*N2+1 ), N2 )
|
||
|
|
CALL DGEMM( 'T', 'N', N2, N1, K, ALPHA, A( 1, N1+1 ),
|
||
|
|
$ LDA, A( 1, 1 ), LDA, BETA, C( 1 ), N2 )
|
||
|
|
*
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
ELSE
|
||
|
|
*
|
||
|
|
* N is even
|
||
|
|
*
|
||
|
|
IF( NORMALTRANSR ) THEN
|
||
|
|
*
|
||
|
|
* N is even and TRANSR = 'N'
|
||
|
|
*
|
||
|
|
IF( LOWER ) THEN
|
||
|
|
*
|
||
|
|
* N is even, TRANSR = 'N', and UPLO = 'L'
|
||
|
|
*
|
||
|
|
IF( NOTRANS ) THEN
|
||
|
|
*
|
||
|
|
* N is even, TRANSR = 'N', UPLO = 'L', and TRANS = 'N'
|
||
|
|
*
|
||
|
|
CALL DSYRK( 'L', 'N', NK, K, ALPHA, A( 1, 1 ), LDA,
|
||
|
|
$ BETA, C( 2 ), N+1 )
|
||
|
|
CALL DSYRK( 'U', 'N', NK, K, ALPHA, A( NK+1, 1 ), LDA,
|
||
|
|
$ BETA, C( 1 ), N+1 )
|
||
|
|
CALL DGEMM( 'N', 'T', NK, NK, K, ALPHA, A( NK+1, 1 ),
|
||
|
|
$ LDA, A( 1, 1 ), LDA, BETA, C( NK+2 ),
|
||
|
|
$ N+1 )
|
||
|
|
*
|
||
|
|
ELSE
|
||
|
|
*
|
||
|
|
* N is even, TRANSR = 'N', UPLO = 'L', and TRANS = 'T'
|
||
|
|
*
|
||
|
|
CALL DSYRK( 'L', 'T', NK, K, ALPHA, A( 1, 1 ), LDA,
|
||
|
|
$ BETA, C( 2 ), N+1 )
|
||
|
|
CALL DSYRK( 'U', 'T', NK, K, ALPHA, A( 1, NK+1 ), LDA,
|
||
|
|
$ BETA, C( 1 ), N+1 )
|
||
|
|
CALL DGEMM( 'T', 'N', NK, NK, K, ALPHA, A( 1, NK+1 ),
|
||
|
|
$ LDA, A( 1, 1 ), LDA, BETA, C( NK+2 ),
|
||
|
|
$ N+1 )
|
||
|
|
*
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
ELSE
|
||
|
|
*
|
||
|
|
* N is even, TRANSR = 'N', and UPLO = 'U'
|
||
|
|
*
|
||
|
|
IF( NOTRANS ) THEN
|
||
|
|
*
|
||
|
|
* N is even, TRANSR = 'N', UPLO = 'U', and TRANS = 'N'
|
||
|
|
*
|
||
|
|
CALL DSYRK( 'L', 'N', NK, K, ALPHA, A( 1, 1 ), LDA,
|
||
|
|
$ BETA, C( NK+2 ), N+1 )
|
||
|
|
CALL DSYRK( 'U', 'N', NK, K, ALPHA, A( NK+1, 1 ), LDA,
|
||
|
|
$ BETA, C( NK+1 ), N+1 )
|
||
|
|
CALL DGEMM( 'N', 'T', NK, NK, K, ALPHA, A( 1, 1 ),
|
||
|
|
$ LDA, A( NK+1, 1 ), LDA, BETA, C( 1 ),
|
||
|
|
$ N+1 )
|
||
|
|
*
|
||
|
|
ELSE
|
||
|
|
*
|
||
|
|
* N is even, TRANSR = 'N', UPLO = 'U', and TRANS = 'T'
|
||
|
|
*
|
||
|
|
CALL DSYRK( 'L', 'T', NK, K, ALPHA, A( 1, 1 ), LDA,
|
||
|
|
$ BETA, C( NK+2 ), N+1 )
|
||
|
|
CALL DSYRK( 'U', 'T', NK, K, ALPHA, A( 1, NK+1 ), LDA,
|
||
|
|
$ BETA, C( NK+1 ), N+1 )
|
||
|
|
CALL DGEMM( 'T', 'N', NK, NK, K, ALPHA, A( 1, 1 ),
|
||
|
|
$ LDA, A( 1, NK+1 ), LDA, BETA, C( 1 ),
|
||
|
|
$ N+1 )
|
||
|
|
*
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
ELSE
|
||
|
|
*
|
||
|
|
* N is even, and TRANSR = 'T'
|
||
|
|
*
|
||
|
|
IF( LOWER ) THEN
|
||
|
|
*
|
||
|
|
* N is even, TRANSR = 'T', and UPLO = 'L'
|
||
|
|
*
|
||
|
|
IF( NOTRANS ) THEN
|
||
|
|
*
|
||
|
|
* N is even, TRANSR = 'T', UPLO = 'L', and TRANS = 'N'
|
||
|
|
*
|
||
|
|
CALL DSYRK( 'U', 'N', NK, K, ALPHA, A( 1, 1 ), LDA,
|
||
|
|
$ BETA, C( NK+1 ), NK )
|
||
|
|
CALL DSYRK( 'L', 'N', NK, K, ALPHA, A( NK+1, 1 ), LDA,
|
||
|
|
$ BETA, C( 1 ), NK )
|
||
|
|
CALL DGEMM( 'N', 'T', NK, NK, K, ALPHA, A( 1, 1 ),
|
||
|
|
$ LDA, A( NK+1, 1 ), LDA, BETA,
|
||
|
|
$ C( ( ( NK+1 )*NK )+1 ), NK )
|
||
|
|
*
|
||
|
|
ELSE
|
||
|
|
*
|
||
|
|
* N is even, TRANSR = 'T', UPLO = 'L', and TRANS = 'T'
|
||
|
|
*
|
||
|
|
CALL DSYRK( 'U', 'T', NK, K, ALPHA, A( 1, 1 ), LDA,
|
||
|
|
$ BETA, C( NK+1 ), NK )
|
||
|
|
CALL DSYRK( 'L', 'T', NK, K, ALPHA, A( 1, NK+1 ), LDA,
|
||
|
|
$ BETA, C( 1 ), NK )
|
||
|
|
CALL DGEMM( 'T', 'N', NK, NK, K, ALPHA, A( 1, 1 ),
|
||
|
|
$ LDA, A( 1, NK+1 ), LDA, BETA,
|
||
|
|
$ C( ( ( NK+1 )*NK )+1 ), NK )
|
||
|
|
*
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
ELSE
|
||
|
|
*
|
||
|
|
* N is even, TRANSR = 'T', and UPLO = 'U'
|
||
|
|
*
|
||
|
|
IF( NOTRANS ) THEN
|
||
|
|
*
|
||
|
|
* N is even, TRANSR = 'T', UPLO = 'U', and TRANS = 'N'
|
||
|
|
*
|
||
|
|
CALL DSYRK( 'U', 'N', NK, K, ALPHA, A( 1, 1 ), LDA,
|
||
|
|
$ BETA, C( NK*( NK+1 )+1 ), NK )
|
||
|
|
CALL DSYRK( 'L', 'N', NK, K, ALPHA, A( NK+1, 1 ), LDA,
|
||
|
|
$ BETA, C( NK*NK+1 ), NK )
|
||
|
|
CALL DGEMM( 'N', 'T', NK, NK, K, ALPHA, A( NK+1, 1 ),
|
||
|
|
$ LDA, A( 1, 1 ), LDA, BETA, C( 1 ), NK )
|
||
|
|
*
|
||
|
|
ELSE
|
||
|
|
*
|
||
|
|
* N is even, TRANSR = 'T', UPLO = 'U', and TRANS = 'T'
|
||
|
|
*
|
||
|
|
CALL DSYRK( 'U', 'T', NK, K, ALPHA, A( 1, 1 ), LDA,
|
||
|
|
$ BETA, C( NK*( NK+1 )+1 ), NK )
|
||
|
|
CALL DSYRK( 'L', 'T', NK, K, ALPHA, A( 1, NK+1 ), LDA,
|
||
|
|
$ BETA, C( NK*NK+1 ), NK )
|
||
|
|
CALL DGEMM( 'T', 'N', NK, NK, K, ALPHA, A( 1, NK+1 ),
|
||
|
|
$ LDA, A( 1, 1 ), LDA, BETA, C( 1 ), NK )
|
||
|
|
*
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
RETURN
|
||
|
|
*
|
||
|
|
* End of DSFRK
|
||
|
|
*
|
||
|
|
END
|