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version 1.6, 2011/07/22 07:38:10 version 1.7, 2011/11/21 20:43:03
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       SUBROUTINE DSFRK( TRANSR, UPLO, TRANS, N, K, ALPHA, A, LDA, BETA,  *> \brief \b DSFRK
      $                  C )  *
   *  =========== DOCUMENTATION ===========
   *
   * Online html documentation available at 
   *            http://www.netlib.org/lapack/explore-html/ 
   *
   *> \htmlonly
   *> Download DSFRK + dependencies 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dsfrk.f"> 
   *> [TGZ]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dsfrk.f"> 
   *> [ZIP]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dsfrk.f"> 
   *> [TXT]</a>
   *> \endhtmlonly 
   *
   *  Definition:
   *  ===========
   *
   *       SUBROUTINE DSFRK( TRANSR, UPLO, TRANS, N, K, ALPHA, A, LDA, BETA,
   *                         C )
   * 
   *       .. Scalar Arguments ..
   *       DOUBLE PRECISION   ALPHA, BETA
   *       INTEGER            K, LDA, N
   *       CHARACTER          TRANS, TRANSR, UPLO
   *       ..
   *       .. Array Arguments ..
   *       DOUBLE PRECISION   A( LDA, * ), C( * )
   *       ..
   *  
   *
   *> \par Purpose:
   *  =============
   *>
   *> \verbatim
   *>
   *> Level 3 BLAS like routine for C in RFP Format.
   *>
   *> DSFRK performs one of the symmetric rank--k operations
   *>
   *>    C := alpha*A*A**T + beta*C,
   *>
   *> or
   *>
   *>    C := alpha*A**T*A + beta*C,
   *>
   *> where alpha and beta are real scalars, C is an n--by--n symmetric
   *> matrix and A is an n--by--k matrix in the first case and a k--by--n
   *> matrix in the second case.
   *> \endverbatim
   *
   *  Arguments:
   *  ==========
   *
   *> \param[in] TRANSR
   *> \verbatim
   *>          TRANSR is CHARACTER*1
   *>          = 'N':  The Normal Form of RFP A is stored;
   *>          = 'T':  The Transpose Form of RFP A is stored.
   *> \endverbatim
   *>
   *> \param[in] UPLO
   *> \verbatim
   *>          UPLO is CHARACTER*1
   *>           On  entry, UPLO specifies whether the upper or lower
   *>           triangular part of the array C is to be referenced as
   *>           follows:
   *>
   *>              UPLO = 'U' or 'u'   Only the upper triangular part of C
   *>                                  is to be referenced.
   *>
   *>              UPLO = 'L' or 'l'   Only the lower triangular part of C
   *>                                  is to be referenced.
   *>
   *>           Unchanged on exit.
   *> \endverbatim
   *>
   *> \param[in] TRANS
   *> \verbatim
   *>          TRANS is CHARACTER*1
   *>           On entry, TRANS specifies the operation to be performed as
   *>           follows:
   *>
   *>              TRANS = 'N' or 'n'   C := alpha*A*A**T + beta*C.
   *>
   *>              TRANS = 'T' or 't'   C := alpha*A**T*A + beta*C.
   *>
   *>           Unchanged on exit.
   *> \endverbatim
   *>
   *> \param[in] N
   *> \verbatim
   *>          N is INTEGER
   *>           On entry, N specifies the order of the matrix C. N must be
   *>           at least zero.
   *>           Unchanged on exit.
   *> \endverbatim
   *>
   *> \param[in] K
   *> \verbatim
   *>          K is INTEGER
   *>           On entry with TRANS = 'N' or 'n', K specifies the number
   *>           of  columns of the matrix A, and on entry with TRANS = 'T'
   *>           or 't', K specifies the number of rows of the matrix A. K
   *>           must be at least zero.
   *>           Unchanged on exit.
   *> \endverbatim
   *>
   *> \param[in] ALPHA
   *> \verbatim
   *>          ALPHA is DOUBLE PRECISION
   *>           On entry, ALPHA specifies the scalar alpha.
   *>           Unchanged on exit.
   *> \endverbatim
   *>
   *> \param[in] A
   *> \verbatim
   *>          A is DOUBLE PRECISION array, dimension (LDA,ka)
   *>           where KA
   *>           is K  when TRANS = 'N' or 'n', and is N otherwise. Before
   *>           entry with TRANS = 'N' or 'n', the leading N--by--K part of
   *>           the array A must contain the matrix A, otherwise the leading
   *>           K--by--N part of the array A must contain the matrix A.
   *>           Unchanged on exit.
   *> \endverbatim
   *>
   *> \param[in] LDA
   *> \verbatim
   *>          LDA is INTEGER
   *>           On entry, LDA specifies the first dimension of A as declared
   *>           in  the  calling  (sub)  program.   When  TRANS = 'N' or 'n'
   *>           then  LDA must be at least  max( 1, n ), otherwise  LDA must
   *>           be at least  max( 1, k ).
   *>           Unchanged on exit.
   *> \endverbatim
   *>
   *> \param[in] BETA
   *> \verbatim
   *>          BETA is DOUBLE PRECISION
   *>           On entry, BETA specifies the scalar beta.
   *>           Unchanged on exit.
   *> \endverbatim
   *>
   *> \param[in,out] C
   *> \verbatim
   *>          C is DOUBLE PRECISION array, dimension (NT)
   *>           NT = N*(N+1)/2. On entry, the symmetric matrix C in RFP
   *>           Format. RFP Format is described by TRANSR, UPLO and N.
   *> \endverbatim
   *
   *  Authors:
   *  ========
   *
   *> \author Univ. of Tennessee 
   *> \author Univ. of California Berkeley 
   *> \author Univ. of Colorado Denver 
   *> \author NAG Ltd. 
   *
   *> \date November 2011
 *  *
 *  -- LAPACK routine (version 3.3.1)                                    --  *> \ingroup doubleOTHERcomputational
 *  *
 *  -- Contributed by Julien Langou of the Univ. of Colorado Denver    --  *  =====================================================================
 *  -- April 2011                                                      --        SUBROUTINE DSFRK( TRANSR, UPLO, TRANS, N, K, ALPHA, A, LDA, BETA,
        $                  C )
 *  *
   *  -- LAPACK computational routine (version 3.4.0) --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --  *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--  *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
   *     November 2011
 *  *
 *     ..  
 *     .. Scalar Arguments ..  *     .. Scalar Arguments ..
       DOUBLE PRECISION   ALPHA, BETA        DOUBLE PRECISION   ALPHA, BETA
       INTEGER            K, LDA, N        INTEGER            K, LDA, N
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       DOUBLE PRECISION   A( LDA, * ), C( * )        DOUBLE PRECISION   A( LDA, * ), C( * )
 *     ..  *     ..
 *  *
 *  Purpose  
 *  =======  
 *  
 *  Level 3 BLAS like routine for C in RFP Format.  
 *  
 *  DSFRK performs one of the symmetric rank--k operations  
 *  
 *     C := alpha*A*A**T + beta*C,  
 *  
 *  or  
 *  
 *     C := alpha*A**T*A + beta*C,  
 *  
 *  where alpha and beta are real scalars, C is an n--by--n symmetric  
 *  matrix and A is an n--by--k matrix in the first case and a k--by--n  
 *  matrix in the second case.  
 *  
 *  Arguments  
 *  ==========  
 *  
 *  TRANSR  (input) CHARACTER*1  
 *          = 'N':  The Normal Form of RFP A is stored;  
 *          = 'T':  The Transpose Form of RFP A is stored.  
 *  
 *  UPLO    (input) CHARACTER*1  
 *           On  entry, UPLO specifies whether the upper or lower  
 *           triangular part of the array C is to be referenced as  
 *           follows:  
 *  
 *              UPLO = 'U' or 'u'   Only the upper triangular part of C  
 *                                  is to be referenced.  
 *  
 *              UPLO = 'L' or 'l'   Only the lower triangular part of C  
 *                                  is to be referenced.  
 *  
 *           Unchanged on exit.  
 *  
 *  TRANS   (input) CHARACTER*1  
 *           On entry, TRANS specifies the operation to be performed as  
 *           follows:  
 *  
 *              TRANS = 'N' or 'n'   C := alpha*A*A**T + beta*C.  
 *  
 *              TRANS = 'T' or 't'   C := alpha*A**T*A + beta*C.  
 *  
 *           Unchanged on exit.  
 *  
 *  N       (input) INTEGER  
 *           On entry, N specifies the order of the matrix C. N must be  
 *           at least zero.  
 *           Unchanged on exit.  
 *  
 *  K       (input) INTEGER  
 *           On entry with TRANS = 'N' or 'n', K specifies the number  
 *           of  columns of the matrix A, and on entry with TRANS = 'T'  
 *           or 't', K specifies the number of rows of the matrix A. K  
 *           must be at least zero.  
 *           Unchanged on exit.  
 *  
 *  ALPHA   (input) DOUBLE PRECISION  
 *           On entry, ALPHA specifies the scalar alpha.  
 *           Unchanged on exit.  
 *  
 *  A       (input) DOUBLE PRECISION array, dimension (LDA,ka)  
 *           where KA  
 *           is K  when TRANS = 'N' or 'n', and is N otherwise. Before  
 *           entry with TRANS = 'N' or 'n', the leading N--by--K part of  
 *           the array A must contain the matrix A, otherwise the leading  
 *           K--by--N part of the array A must contain the matrix A.  
 *           Unchanged on exit.  
 *  
 *  LDA     (input) INTEGER  
 *           On entry, LDA specifies the first dimension of A as declared  
 *           in  the  calling  (sub)  program.   When  TRANS = 'N' or 'n'  
 *           then  LDA must be at least  max( 1, n ), otherwise  LDA must  
 *           be at least  max( 1, k ).  
 *           Unchanged on exit.  
 *  
 *  BETA    (input) DOUBLE PRECISION  
 *           On entry, BETA specifies the scalar beta.  
 *           Unchanged on exit.  
 *  
 *  
 *  C       (input/output) DOUBLE PRECISION array, dimension (NT)  
 *           NT = N*(N+1)/2. On entry, the symmetric matrix C in RFP  
 *           Format. RFP Format is described by TRANSR, UPLO and N.  
 *  
 *  =====================================================================  *  =====================================================================
 *  *
 *     ..  *     ..
Removed from v.1.6  
changed lines
  Added in v.1.7

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