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version 1.7, 2011/07/22 07:38:02 version 1.8, 2011/11/21 20:37:08
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   *> \brief \b DSYRK
   *
   *  =========== DOCUMENTATION ===========
   *
   * Online html documentation available at 
   *            http://www.netlib.org/lapack/explore-html/ 
   *
   *  Definition:
   *  ===========
   *
   *       SUBROUTINE DSYRK(UPLO,TRANS,N,K,ALPHA,A,LDA,BETA,C,LDC)
   * 
   *       .. Scalar Arguments ..
   *       DOUBLE PRECISION ALPHA,BETA
   *       INTEGER K,LDA,LDC,N
   *       CHARACTER TRANS,UPLO
   *       ..
   *       .. Array Arguments ..
   *       DOUBLE PRECISION A(LDA,*),C(LDC,*)
   *       ..
   *  
   *
   *> \par Purpose:
   *  =============
   *>
   *> \verbatim
   *>
   *> DSYRK  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 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] 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.
   *> \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.
   *>
   *>              TRANS = 'C' or 'c'   C := alpha*A**T*A + beta*C.
   *> \endverbatim
   *>
   *> \param[in] N
   *> \verbatim
   *>          N is INTEGER
   *>           On entry,  N specifies the order of the matrix C.  N must be
   *>           at least zero.
   *> \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' or 'C' or 'c',  K  specifies  the  number
   *>           of rows of the matrix  A.  K must be at least zero.
   *> \endverbatim
   *>
   *> \param[in] ALPHA
   *> \verbatim
   *>          ALPHA is DOUBLE PRECISION.
   *>           On entry, ALPHA specifies the scalar alpha.
   *> \endverbatim
   *>
   *> \param[in] A
   *> \verbatim
   *>          A is DOUBLE PRECISION array of 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.
   *> \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 ).
   *> \endverbatim
   *>
   *> \param[in] BETA
   *> \verbatim
   *>          BETA is DOUBLE PRECISION.
   *>           On entry, BETA specifies the scalar beta.
   *> \endverbatim
   *>
   *> \param[in,out] C
   *> \verbatim
   *>          C is DOUBLE PRECISION array of DIMENSION ( LDC, n ).
   *>           Before entry  with  UPLO = 'U' or 'u',  the leading  n by n
   *>           upper triangular part of the array C must contain the upper
   *>           triangular part  of the  symmetric matrix  and the strictly
   *>           lower triangular part of C is not referenced.  On exit, the
   *>           upper triangular part of the array  C is overwritten by the
   *>           upper triangular part of the updated matrix.
   *>           Before entry  with  UPLO = 'L' or 'l',  the leading  n by n
   *>           lower triangular part of the array C must contain the lower
   *>           triangular part  of the  symmetric matrix  and the strictly
   *>           upper triangular part of C is not referenced.  On exit, the
   *>           lower triangular part of the array  C is overwritten by the
   *>           lower triangular part of the updated matrix.
   *> \endverbatim
   *>
   *> \param[in] LDC
   *> \verbatim
   *>          LDC is INTEGER
   *>           On entry, LDC specifies the first dimension of C as declared
   *>           in  the  calling  (sub)  program.   LDC  must  be  at  least
   *>           max( 1, n ).
   *> \endverbatim
   *
   *  Authors:
   *  ========
   *
   *> \author Univ. of Tennessee 
   *> \author Univ. of California Berkeley 
   *> \author Univ. of Colorado Denver 
   *> \author NAG Ltd. 
   *
   *> \date November 2011
   *
   *> \ingroup double_blas_level3
   *
   *> \par Further Details:
   *  =====================
   *>
   *> \verbatim
   *>
   *>  Level 3 Blas routine.
   *>
   *>  -- Written on 8-February-1989.
   *>     Jack Dongarra, Argonne National Laboratory.
   *>     Iain Duff, AERE Harwell.
   *>     Jeremy Du Croz, Numerical Algorithms Group Ltd.
   *>     Sven Hammarling, Numerical Algorithms Group Ltd.
   *> \endverbatim
   *>
   *  =====================================================================
       SUBROUTINE DSYRK(UPLO,TRANS,N,K,ALPHA,A,LDA,BETA,C,LDC)        SUBROUTINE DSYRK(UPLO,TRANS,N,K,ALPHA,A,LDA,BETA,C,LDC)
   *
   *  -- Reference BLAS level3 routine (version 3.4.0) --
   *  -- Reference BLAS is a software package provided by Univ. of Tennessee,    --
   *  -- 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,LDC,N        INTEGER K,LDA,LDC,N
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       DOUBLE PRECISION A(LDA,*),C(LDC,*)        DOUBLE PRECISION A(LDA,*),C(LDC,*)
 *     ..  *     ..
 *  *
 *  Purpose  
 *  =======  
 *  
 *  DSYRK  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 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  
 *  ==========  
 *  
 *  UPLO   - 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  - 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.  
 *  
 *              TRANS = 'C' or 'c'   C := alpha*A**T*A + beta*C.  
 *  
 *           Unchanged on exit.  
 *  
 *  N      - INTEGER.  
 *           On entry,  N specifies the order of the matrix C.  N must be  
 *           at least zero.  
 *           Unchanged on exit.  
 *  
 *  K      - 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' or 'C' or 'c',  K  specifies  the  number  
 *           of rows of the matrix  A.  K must be at least zero.  
 *           Unchanged on exit.  
 *  
 *  ALPHA  - DOUBLE PRECISION.  
 *           On entry, ALPHA specifies the scalar alpha.  
 *           Unchanged on exit.  
 *  
 *  A      - DOUBLE PRECISION array of 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    - 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   - DOUBLE PRECISION.  
 *           On entry, BETA specifies the scalar beta.  
 *           Unchanged on exit.  
 *  
 *  C      - DOUBLE PRECISION array of DIMENSION ( LDC, n ).  
 *           Before entry  with  UPLO = 'U' or 'u',  the leading  n by n  
 *           upper triangular part of the array C must contain the upper  
 *           triangular part  of the  symmetric matrix  and the strictly  
 *           lower triangular part of C is not referenced.  On exit, the  
 *           upper triangular part of the array  C is overwritten by the  
 *           upper triangular part of the updated matrix.  
 *           Before entry  with  UPLO = 'L' or 'l',  the leading  n by n  
 *           lower triangular part of the array C must contain the lower  
 *           triangular part  of the  symmetric matrix  and the strictly  
 *           upper triangular part of C is not referenced.  On exit, the  
 *           lower triangular part of the array  C is overwritten by the  
 *           lower triangular part of the updated matrix.  
 *  
 *  LDC    - INTEGER.  
 *           On entry, LDC specifies the first dimension of C as declared  
 *           in  the  calling  (sub)  program.   LDC  must  be  at  least  
 *           max( 1, n ).  
 *           Unchanged on exit.  
 *  
 *  Further Details  
 *  ===============  
 *  
 *  Level 3 Blas routine.  
 *  
 *  -- Written on 8-February-1989.  
 *     Jack Dongarra, Argonne National Laboratory.  
 *     Iain Duff, AERE Harwell.  
 *     Jeremy Du Croz, Numerical Algorithms Group Ltd.  
 *     Sven Hammarling, Numerical Algorithms Group Ltd.  
 *  
 *  =====================================================================  *  =====================================================================
 *  *
 *     .. External Functions ..  *     .. External Functions ..
Removed from v.1.7  
changed lines
  Added in v.1.8

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