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version 1.6, 2010/12/21 13:51:25 version 1.7, 2011/11/21 20:37:07
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   *> \brief \b DSYMM
   *
   *  =========== DOCUMENTATION ===========
   *
   * Online html documentation available at 
   *            http://www.netlib.org/lapack/explore-html/ 
   *
   *  Definition:
   *  ===========
   *
   *       SUBROUTINE DSYMM(SIDE,UPLO,M,N,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
   * 
   *       .. Scalar Arguments ..
   *       DOUBLE PRECISION ALPHA,BETA
   *       INTEGER LDA,LDB,LDC,M,N
   *       CHARACTER SIDE,UPLO
   *       ..
   *       .. Array Arguments ..
   *       DOUBLE PRECISION A(LDA,*),B(LDB,*),C(LDC,*)
   *       ..
   *  
   *
   *> \par Purpose:
   *  =============
   *>
   *> \verbatim
   *>
   *> DSYMM  performs one of the matrix-matrix operations
   *>
   *>    C := alpha*A*B + beta*C,
   *>
   *> or
   *>
   *>    C := alpha*B*A + beta*C,
   *>
   *> where alpha and beta are scalars,  A is a symmetric matrix and  B and
   *> C are  m by n matrices.
   *> \endverbatim
   *
   *  Arguments:
   *  ==========
   *
   *> \param[in] SIDE
   *> \verbatim
   *>          SIDE is CHARACTER*1
   *>           On entry,  SIDE  specifies whether  the  symmetric matrix  A
   *>           appears on the  left or right  in the  operation as follows:
   *>
   *>              SIDE = 'L' or 'l'   C := alpha*A*B + beta*C,
   *>
   *>              SIDE = 'R' or 'r'   C := alpha*B*A + beta*C,
   *> \endverbatim
   *>
   *> \param[in] UPLO
   *> \verbatim
   *>          UPLO is CHARACTER*1
   *>           On  entry,   UPLO  specifies  whether  the  upper  or  lower
   *>           triangular  part  of  the  symmetric  matrix   A  is  to  be
   *>           referenced as follows:
   *>
   *>              UPLO = 'U' or 'u'   Only the upper triangular part of the
   *>                                  symmetric matrix is to be referenced.
   *>
   *>              UPLO = 'L' or 'l'   Only the lower triangular part of the
   *>                                  symmetric matrix is to be referenced.
   *> \endverbatim
   *>
   *> \param[in] M
   *> \verbatim
   *>          M is INTEGER
   *>           On entry,  M  specifies the number of rows of the matrix  C.
   *>           M  must be at least zero.
   *> \endverbatim
   *>
   *> \param[in] N
   *> \verbatim
   *>          N is INTEGER
   *>           On entry, N specifies the number of columns of the matrix C.
   *>           N  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
   *>           m  when  SIDE = 'L' or 'l'  and is  n otherwise.
   *>           Before entry  with  SIDE = 'L' or 'l',  the  m by m  part of
   *>           the array  A  must contain the  symmetric matrix,  such that
   *>           when  UPLO = 'U' or 'u', the leading m by m upper triangular
   *>           part of the array  A  must contain the upper triangular part
   *>           of the  symmetric matrix and the  strictly  lower triangular
   *>           part of  A  is not referenced,  and when  UPLO = 'L' or 'l',
   *>           the leading  m by m  lower triangular part  of the  array  A
   *>           must  contain  the  lower triangular part  of the  symmetric
   *>           matrix and the  strictly upper triangular part of  A  is not
   *>           referenced.
   *>           Before entry  with  SIDE = 'R' or 'r',  the  n by n  part of
   *>           the array  A  must contain the  symmetric matrix,  such that
   *>           when  UPLO = 'U' or 'u', the leading n by n upper triangular
   *>           part of the array  A  must contain the upper triangular part
   *>           of the  symmetric matrix and the  strictly  lower triangular
   *>           part of  A  is not referenced,  and when  UPLO = 'L' or 'l',
   *>           the leading  n by n  lower triangular part  of the  array  A
   *>           must  contain  the  lower triangular part  of the  symmetric
   *>           matrix and the  strictly upper triangular part of  A  is not
   *>           referenced.
   *> \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  SIDE = 'L' or 'l'  then
   *>           LDA must be at least  max( 1, m ), otherwise  LDA must be at
   *>           least  max( 1, n ).
   *> \endverbatim
   *>
   *> \param[in] B
   *> \verbatim
   *>          B is DOUBLE PRECISION array of DIMENSION ( LDB, n ).
   *>           Before entry, the leading  m by n part of the array  B  must
   *>           contain the matrix B.
   *> \endverbatim
   *>
   *> \param[in] LDB
   *> \verbatim
   *>          LDB is INTEGER
   *>           On entry, LDB specifies the first dimension of B as declared
   *>           in  the  calling  (sub)  program.   LDB  must  be  at  least
   *>           max( 1, m ).
   *> \endverbatim
   *>
   *> \param[in] BETA
   *> \verbatim
   *>          BETA is DOUBLE PRECISION.
   *>           On entry,  BETA  specifies the scalar  beta.  When  BETA  is
   *>           supplied as zero then C need not be set on input.
   *> \endverbatim
   *>
   *> \param[in,out] C
   *> \verbatim
   *>          C is DOUBLE PRECISION array of DIMENSION ( LDC, n ).
   *>           Before entry, the leading  m by n  part of the array  C must
   *>           contain the matrix  C,  except when  beta  is zero, in which
   *>           case C need not be set on entry.
   *>           On exit, the array  C  is overwritten by the  m by n 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, m ).
   *> \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 DSYMM(SIDE,UPLO,M,N,ALPHA,A,LDA,B,LDB,BETA,C,LDC)        SUBROUTINE DSYMM(SIDE,UPLO,M,N,ALPHA,A,LDA,B,LDB,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 LDA,LDB,LDC,M,N        INTEGER LDA,LDB,LDC,M,N
Line 8 Line 203
       DOUBLE PRECISION A(LDA,*),B(LDB,*),C(LDC,*)        DOUBLE PRECISION A(LDA,*),B(LDB,*),C(LDC,*)
 *     ..  *     ..
 *  *
 *  Purpose  
 *  =======  
 *  
 *  DSYMM  performs one of the matrix-matrix operations  
 *  
 *     C := alpha*A*B + beta*C,  
 *  
 *  or  
 *  
 *     C := alpha*B*A + beta*C,  
 *  
 *  where alpha and beta are scalars,  A is a symmetric matrix and  B and  
 *  C are  m by n matrices.  
 *  
 *  Arguments  
 *  ==========  
 *  
 *  SIDE   - CHARACTER*1.  
 *           On entry,  SIDE  specifies whether  the  symmetric matrix  A  
 *           appears on the  left or right  in the  operation as follows:  
 *  
 *              SIDE = 'L' or 'l'   C := alpha*A*B + beta*C,  
 *  
 *              SIDE = 'R' or 'r'   C := alpha*B*A + beta*C,  
 *  
 *           Unchanged on exit.  
 *  
 *  UPLO   - CHARACTER*1.  
 *           On  entry,   UPLO  specifies  whether  the  upper  or  lower  
 *           triangular  part  of  the  symmetric  matrix   A  is  to  be  
 *           referenced as follows:  
 *  
 *              UPLO = 'U' or 'u'   Only the upper triangular part of the  
 *                                  symmetric matrix is to be referenced.  
 *  
 *              UPLO = 'L' or 'l'   Only the lower triangular part of the  
 *                                  symmetric matrix is to be referenced.  
 *  
 *           Unchanged on exit.  
 *  
 *  M      - INTEGER.  
 *           On entry,  M  specifies the number of rows of the matrix  C.  
 *           M  must be at least zero.  
 *           Unchanged on exit.  
 *  
 *  N      - INTEGER.  
 *           On entry, N specifies the number of columns of the matrix C.  
 *           N  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  
 *           m  when  SIDE = 'L' or 'l'  and is  n otherwise.  
 *           Before entry  with  SIDE = 'L' or 'l',  the  m by m  part of  
 *           the array  A  must contain the  symmetric matrix,  such that  
 *           when  UPLO = 'U' or 'u', the leading m by m upper triangular  
 *           part of the array  A  must contain the upper triangular part  
 *           of the  symmetric matrix and the  strictly  lower triangular  
 *           part of  A  is not referenced,  and when  UPLO = 'L' or 'l',  
 *           the leading  m by m  lower triangular part  of the  array  A  
 *           must  contain  the  lower triangular part  of the  symmetric  
 *           matrix and the  strictly upper triangular part of  A  is not  
 *           referenced.  
 *           Before entry  with  SIDE = 'R' or 'r',  the  n by n  part of  
 *           the array  A  must contain the  symmetric matrix,  such that  
 *           when  UPLO = 'U' or 'u', the leading n by n upper triangular  
 *           part of the array  A  must contain the upper triangular part  
 *           of the  symmetric matrix and the  strictly  lower triangular  
 *           part of  A  is not referenced,  and when  UPLO = 'L' or 'l',  
 *           the leading  n by n  lower triangular part  of the  array  A  
 *           must  contain  the  lower triangular part  of the  symmetric  
 *           matrix and the  strictly upper triangular part of  A  is not  
 *           referenced.  
 *           Unchanged on exit.  
 *  
 *  LDA    - INTEGER.  
 *           On entry, LDA specifies the first dimension of A as declared  
 *           in the calling (sub) program.  When  SIDE = 'L' or 'l'  then  
 *           LDA must be at least  max( 1, m ), otherwise  LDA must be at  
 *           least  max( 1, n ).  
 *           Unchanged on exit.  
 *  
 *  B      - DOUBLE PRECISION array of DIMENSION ( LDB, n ).  
 *           Before entry, the leading  m by n part of the array  B  must  
 *           contain the matrix B.  
 *           Unchanged on exit.  
 *  
 *  LDB    - INTEGER.  
 *           On entry, LDB specifies the first dimension of B as declared  
 *           in  the  calling  (sub)  program.   LDB  must  be  at  least  
 *           max( 1, m ).  
 *           Unchanged on exit.  
 *  
 *  BETA   - DOUBLE PRECISION.  
 *           On entry,  BETA  specifies the scalar  beta.  When  BETA  is  
 *           supplied as zero then C need not be set on input.  
 *           Unchanged on exit.  
 *  
 *  C      - DOUBLE PRECISION array of DIMENSION ( LDC, n ).  
 *           Before entry, the leading  m by n  part of the array  C must  
 *           contain the matrix  C,  except when  beta  is zero, in which  
 *           case C need not be set on entry.  
 *           On exit, the array  C  is overwritten by the  m by n 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, m ).  
 *           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.1.6  
changed lines
  Added in v.1.7

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