400 lines
12 KiB
Fortran
400 lines
12 KiB
Fortran
*> \brief \b DSYR2K
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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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* Definition:
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* ===========
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*
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* SUBROUTINE DSYR2K(UPLO,TRANS,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
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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,LDB,LDC,N
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* CHARACTER TRANS,UPLO
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* ..
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* .. Array Arguments ..
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* DOUBLE PRECISION A(LDA,*),B(LDB,*),C(LDC,*)
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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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*> DSYR2K performs one of the symmetric rank 2k operations
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*>
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*> C := alpha*A*B**T + alpha*B*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*B + alpha*B**T*A + beta*C,
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*>
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*> where alpha and beta are scalars, C is an n by n symmetric matrix
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*> and A and B are n by k matrices in the first case and k by n
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*> matrices 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] 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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*> \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*B**T + alpha*B*A**T +
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*> beta*C.
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*>
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*> TRANS = 'T' or 't' C := alpha*A**T*B + alpha*B**T*A +
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*> beta*C.
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*>
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*> TRANS = 'C' or 'c' C := alpha*A**T*B + alpha*B**T*A +
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*> beta*C.
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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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*> \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 matrices A and B, and on entry with
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*> TRANS = 'T' or 't' or 'C' or 'c', K specifies the number
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*> of rows of the matrices A and B. K must be at least zero.
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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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*> \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 of DIMENSION ( LDA, ka ), where ka is
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*> k when TRANS = 'N' or 'n', and is n otherwise.
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*> Before entry with TRANS = 'N' or 'n', the leading n by k
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*> part of the array A must contain the matrix A, otherwise
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*> the leading k by n part of the array A must contain the
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*> matrix A.
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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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*> \endverbatim
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*>
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*> \param[in] B
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*> \verbatim
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*> B is DOUBLE PRECISION array of DIMENSION ( LDB, kb ), where kb is
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*> k when TRANS = 'N' or 'n', and is n otherwise.
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*> Before entry with TRANS = 'N' or 'n', the leading n by k
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*> part of the array B must contain the matrix B, otherwise
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*> the leading k by n part of the array B must contain the
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*> matrix B.
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*> \endverbatim
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*>
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*> \param[in] LDB
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*> \verbatim
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*> LDB is INTEGER
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*> On entry, LDB specifies the first dimension of B as declared
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*> in the calling (sub) program. When TRANS = 'N' or 'n'
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*> then LDB must be at least max( 1, n ), otherwise LDB must
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*> be at least max( 1, k ).
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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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*> \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 of DIMENSION ( LDC, n ).
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*> Before entry with UPLO = 'U' or 'u', the leading n by n
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*> upper triangular part of the array C must contain the upper
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*> triangular part of the symmetric matrix and the strictly
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*> lower triangular part of C is not referenced. On exit, the
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*> upper triangular part of the array C is overwritten by the
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*> upper triangular part of the updated matrix.
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*> Before entry with UPLO = 'L' or 'l', the leading n by n
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*> lower triangular part of the array C must contain the lower
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*> triangular part of the symmetric matrix and the strictly
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*> upper triangular part of C is not referenced. On exit, the
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*> lower triangular part of the array C is overwritten by the
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*> lower triangular part of the updated matrix.
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*> \endverbatim
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*>
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*> \param[in] LDC
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*> \verbatim
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*> LDC is INTEGER
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*> On entry, LDC specifies the first dimension of C as declared
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*> in the calling (sub) program. LDC must be at least
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*> max( 1, 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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*> \date November 2011
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*
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*> \ingroup double_blas_level3
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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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*> Level 3 Blas routine.
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*>
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*>
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*> -- Written on 8-February-1989.
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*> Jack Dongarra, Argonne National Laboratory.
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*> Iain Duff, AERE Harwell.
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*> Jeremy Du Croz, Numerical Algorithms Group Ltd.
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*> Sven Hammarling, Numerical Algorithms Group Ltd.
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*> \endverbatim
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*>
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* =====================================================================
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SUBROUTINE DSYR2K(UPLO,TRANS,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
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*
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* -- Reference BLAS level3 routine (version 3.4.0) --
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* -- Reference BLAS 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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* .. Scalar Arguments ..
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DOUBLE PRECISION ALPHA,BETA
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INTEGER K,LDA,LDB,LDC,N
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CHARACTER TRANS,UPLO
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* ..
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* .. Array Arguments ..
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DOUBLE PRECISION A(LDA,*),B(LDB,*),C(LDC,*)
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* ..
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*
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* =====================================================================
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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
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC MAX
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* ..
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* .. Local Scalars ..
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DOUBLE PRECISION TEMP1,TEMP2
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INTEGER I,INFO,J,L,NROWA
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LOGICAL UPPER
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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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*
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* Test the input parameters.
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*
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IF (LSAME(TRANS,'N')) 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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UPPER = LSAME(UPLO,'U')
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*
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INFO = 0
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IF ((.NOT.UPPER) .AND. (.NOT.LSAME(UPLO,'L'))) THEN
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INFO = 1
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ELSE IF ((.NOT.LSAME(TRANS,'N')) .AND.
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+ (.NOT.LSAME(TRANS,'T')) .AND.
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+ (.NOT.LSAME(TRANS,'C'))) 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 (K.LT.0) THEN
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INFO = 4
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ELSE IF (LDA.LT.MAX(1,NROWA)) THEN
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INFO = 7
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ELSE IF (LDB.LT.MAX(1,NROWA)) THEN
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INFO = 9
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ELSE IF (LDC.LT.MAX(1,N)) THEN
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INFO = 12
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END IF
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IF (INFO.NE.0) THEN
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CALL XERBLA('DSYR2K',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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IF ((N.EQ.0) .OR. (((ALPHA.EQ.ZERO).OR.
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+ (K.EQ.0)).AND. (BETA.EQ.ONE))) RETURN
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*
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* And when alpha.eq.zero.
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*
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IF (ALPHA.EQ.ZERO) THEN
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IF (UPPER) THEN
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IF (BETA.EQ.ZERO) THEN
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DO 20 J = 1,N
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DO 10 I = 1,J
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C(I,J) = ZERO
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10 CONTINUE
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20 CONTINUE
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ELSE
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DO 40 J = 1,N
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DO 30 I = 1,J
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C(I,J) = BETA*C(I,J)
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30 CONTINUE
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40 CONTINUE
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END IF
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ELSE
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IF (BETA.EQ.ZERO) THEN
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DO 60 J = 1,N
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DO 50 I = J,N
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C(I,J) = ZERO
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50 CONTINUE
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60 CONTINUE
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ELSE
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DO 80 J = 1,N
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DO 70 I = J,N
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C(I,J) = BETA*C(I,J)
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70 CONTINUE
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80 CONTINUE
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END IF
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END IF
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RETURN
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END IF
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*
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* Start the operations.
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*
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IF (LSAME(TRANS,'N')) THEN
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*
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* Form C := alpha*A*B**T + alpha*B*A**T + C.
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*
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IF (UPPER) THEN
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DO 130 J = 1,N
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IF (BETA.EQ.ZERO) THEN
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DO 90 I = 1,J
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C(I,J) = ZERO
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90 CONTINUE
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ELSE IF (BETA.NE.ONE) THEN
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DO 100 I = 1,J
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C(I,J) = BETA*C(I,J)
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100 CONTINUE
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END IF
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DO 120 L = 1,K
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IF ((A(J,L).NE.ZERO) .OR. (B(J,L).NE.ZERO)) THEN
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TEMP1 = ALPHA*B(J,L)
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TEMP2 = ALPHA*A(J,L)
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DO 110 I = 1,J
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C(I,J) = C(I,J) + A(I,L)*TEMP1 +
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+ B(I,L)*TEMP2
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110 CONTINUE
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END IF
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120 CONTINUE
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130 CONTINUE
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ELSE
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DO 180 J = 1,N
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IF (BETA.EQ.ZERO) THEN
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DO 140 I = J,N
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C(I,J) = ZERO
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140 CONTINUE
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ELSE IF (BETA.NE.ONE) THEN
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DO 150 I = J,N
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C(I,J) = BETA*C(I,J)
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150 CONTINUE
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END IF
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DO 170 L = 1,K
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IF ((A(J,L).NE.ZERO) .OR. (B(J,L).NE.ZERO)) THEN
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TEMP1 = ALPHA*B(J,L)
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TEMP2 = ALPHA*A(J,L)
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DO 160 I = J,N
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C(I,J) = C(I,J) + A(I,L)*TEMP1 +
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+ B(I,L)*TEMP2
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160 CONTINUE
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END IF
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170 CONTINUE
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180 CONTINUE
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END IF
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ELSE
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*
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* Form C := alpha*A**T*B + alpha*B**T*A + C.
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*
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IF (UPPER) THEN
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DO 210 J = 1,N
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DO 200 I = 1,J
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TEMP1 = ZERO
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TEMP2 = ZERO
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DO 190 L = 1,K
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TEMP1 = TEMP1 + A(L,I)*B(L,J)
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TEMP2 = TEMP2 + B(L,I)*A(L,J)
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190 CONTINUE
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IF (BETA.EQ.ZERO) THEN
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C(I,J) = ALPHA*TEMP1 + ALPHA*TEMP2
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ELSE
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C(I,J) = BETA*C(I,J) + ALPHA*TEMP1 +
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+ ALPHA*TEMP2
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END IF
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200 CONTINUE
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210 CONTINUE
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ELSE
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DO 240 J = 1,N
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DO 230 I = J,N
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TEMP1 = ZERO
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TEMP2 = ZERO
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DO 220 L = 1,K
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TEMP1 = TEMP1 + A(L,I)*B(L,J)
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TEMP2 = TEMP2 + B(L,I)*A(L,J)
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220 CONTINUE
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IF (BETA.EQ.ZERO) THEN
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C(I,J) = ALPHA*TEMP1 + ALPHA*TEMP2
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ELSE
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C(I,J) = BETA*C(I,J) + ALPHA*TEMP1 +
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+ ALPHA*TEMP2
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END IF
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230 CONTINUE
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240 CONTINUE
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END IF
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END IF
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*
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RETURN
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*
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* End of DSYR2K.
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*
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END
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