dgemm.f

Go to the documentation of this file.

*> \brief \b DGEMM
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at
*            http://www.netlib.org/lapack/explore-html/
*
*  Definition:
*  ===========
*
*       SUBROUTINE DGEMM(TRANSA,TRANSB,M,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
*
*       .. Scalar Arguments ..
*       DOUBLE PRECISION ALPHA,BETA
*       INTEGER K,LDA,LDB,LDC,M,N
*       CHARACTER TRANSA,TRANSB
*       ..
*       .. Array Arguments ..
*       DOUBLE PRECISION A(LDA,*),B(LDB,*),C(LDC,*)
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> DGEMM  performs one of the matrix-matrix operations
*>
*>    C := alpha*op( A )*op( B ) + beta*C,
*>
*> where  op( X ) is one of
*>
*>    op( X ) = X   or   op( X ) = X**T,
*>
*> alpha and beta are scalars, and A, B and C are matrices, with op( A )
*> an m by k matrix,  op( B )  a  k by n matrix and  C an m by n matrix.
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] TRANSA
*> \verbatim
*>          TRANSA is CHARACTER*1
*>           On entry, TRANSA specifies the form of op( A ) to be used in
*>           the matrix multiplication as follows:
*>
*>              TRANSA = 'N' or 'n',  op( A ) = A.
*>
*>              TRANSA = 'T' or 't',  op( A ) = A**T.
*>
*>              TRANSA = 'C' or 'c',  op( A ) = A**T.
*> \endverbatim
*>
*> \param[in] TRANSB
*> \verbatim
*>          TRANSB is CHARACTER*1
*>           On entry, TRANSB specifies the form of op( B ) to be used in
*>           the matrix multiplication as follows:
*>
*>              TRANSB = 'N' or 'n',  op( B ) = B.
*>
*>              TRANSB = 'T' or 't',  op( B ) = B**T.
*>
*>              TRANSB = 'C' or 'c',  op( B ) = B**T.
*> \endverbatim
*>
*> \param[in] M
*> \verbatim
*>          M is INTEGER
*>           On entry,  M  specifies  the number  of rows  of the  matrix
*>           op( A )  and 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
*>           op( B ) and the number of columns of the matrix C. N must be
*>           at least zero.
*> \endverbatim
*>
*> \param[in] K
*> \verbatim
*>          K is INTEGER
*>           On entry,  K  specifies  the number of columns of the matrix
*>           op( A ) and the number of rows of the matrix op( B ). 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, dimension ( LDA, ka ), where ka is
*>           k  when  TRANSA = 'N' or 'n',  and is  m  otherwise.
*>           Before entry with  TRANSA = 'N' or 'n',  the leading  m by k
*>           part of the array  A  must contain the matrix  A,  otherwise
*>           the leading  k by m  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  TRANSA = 'N' or 'n' then
*>           LDA must be at least  max( 1, m ), otherwise  LDA must be at
*>           least  max( 1, k ).
*> \endverbatim
*>
*> \param[in] B
*> \verbatim
*>          B is DOUBLE PRECISION array, dimension ( LDB, kb ), where kb is
*>           n  when  TRANSB = 'N' or 'n',  and is  k  otherwise.
*>           Before entry with  TRANSB = 'N' or 'n',  the leading  k by n
*>           part of the array  B  must contain the matrix  B,  otherwise
*>           the leading  n by k  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. When  TRANSB = 'N' or 'n' then
*>           LDB must be at least  max( 1, k ), otherwise  LDB must be at
*>           least  max( 1, n ).
*> \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, 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  matrix
*>           ( alpha*op( A )*op( B ) + beta*C ).
*> \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.
*
*> \ingroup gemm
*
*> \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 dgemm(TRANSA,TRANSB,M,N,K,ALPHA,A,LDA,B,LDB,
     +         BETA,C,LDC)
*
*  -- Reference BLAS level3 routine --
*  -- Reference BLAS is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
*     .. Scalar Arguments ..
      DOUBLE PRECISION ALPHA,BETA
      INTEGER K,LDA,LDB,LDC,M,N
      CHARACTER TRANSA,TRANSB
*     ..
*     .. Array Arguments ..
      DOUBLE PRECISION A(LDA,*),B(LDB,*),C(LDC,*)
*     ..
*
*  =====================================================================
*
*     .. External Functions ..
      LOGICAL LSAME
      EXTERNAL lsame
*     ..
*     .. External Subroutines ..
      EXTERNAL xerbla
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC max
*     ..
*     .. Local Scalars ..
      DOUBLE PRECISION TEMP
      INTEGER I,INFO,J,L,NROWA,NROWB
      LOGICAL NOTA,NOTB
*     ..
*     .. Parameters ..
      DOUBLE PRECISION ONE,ZERO
      parameter(one=1.0d+0,zero=0.0d+0)
*     ..
*
*     Set  NOTA  and  NOTB  as  true if  A  and  B  respectively are not
*     transposed and set  NROWA and NROWB  as the number of rows of  A
*     and  B  respectively.
*
      nota = lsame(transa,'N')
      notb = lsame(transb,'N')
      IF (nota) THEN
          nrowa = m
      ELSE
          nrowa = k
      END IF
      IF (notb) THEN
          nrowb = k
      ELSE
          nrowb = n
      END IF
*
*     Test the input parameters.
*
      info = 0
      IF ((.NOT.nota) .AND. (.NOT.lsame(transa,'C')) .AND.
     +    (.NOT.lsame(transa,'T'))) THEN
          info = 1
      ELSE IF ((.NOT.notb) .AND. (.NOT.lsame(transb,'C')) .AND.
     +         (.NOT.lsame(transb,'T'))) THEN
          info = 2
      ELSE IF (m.LT.0) THEN
          info = 3
      ELSE IF (n.LT.0) THEN
          info = 4
      ELSE IF (k.LT.0) THEN
          info = 5
      ELSE IF (lda.LT.max(1,nrowa)) THEN
          info = 8
      ELSE IF (ldb.LT.max(1,nrowb)) THEN
          info = 10
      ELSE IF (ldc.LT.max(1,m)) THEN
          info = 13
      END IF
      IF (info.NE.0) THEN
          CALL xerbla('DGEMM ',info)
          RETURN
      END IF
*
*     Quick return if possible.
*
      IF ((m.EQ.0) .OR. (n.EQ.0) .OR.
     +    (((alpha.EQ.zero).OR. (k.EQ.0)).AND. (beta.EQ.one))) RETURN
*
*     And if  alpha.eq.zero.
*
      IF (alpha.EQ.zero) THEN
          IF (beta.EQ.zero) THEN
              DO 20 j = 1,n
                  DO 10 i = 1,m
                      c(i,j) = zero
   10             CONTINUE
   20         CONTINUE
          ELSE
              DO 40 j = 1,n
                  DO 30 i = 1,m
                      c(i,j) = beta*c(i,j)
   30             CONTINUE
   40         CONTINUE
          END IF
          RETURN
      END IF
*
*     Start the operations.
*
      IF (notb) THEN
          IF (nota) THEN
*
*           Form  C := alpha*A*B + beta*C.
*
              DO 90 j = 1,n
                  IF (beta.EQ.zero) THEN
                      DO 50 i = 1,m
                          c(i,j) = zero
   50                 CONTINUE
                  ELSE IF (beta.NE.one) THEN
                      DO 60 i = 1,m
                          c(i,j) = beta*c(i,j)
   60                 CONTINUE
                  END IF
                  DO 80 l = 1,k
                      temp = alpha*b(l,j)
                      DO 70 i = 1,m
                          c(i,j) = c(i,j) + temp*a(i,l)
   70                 CONTINUE
   80             CONTINUE
   90         CONTINUE
          ELSE
*
*           Form  C := alpha*A**T*B + beta*C
*
              DO 120 j = 1,n
                  DO 110 i = 1,m
                      temp = zero
                      DO 100 l = 1,k
                          temp = temp + a(l,i)*b(l,j)
  100                 CONTINUE
                      IF (beta.EQ.zero) THEN
                          c(i,j) = alpha*temp
                      ELSE
                          c(i,j) = alpha*temp + beta*c(i,j)
                      END IF
  110             CONTINUE
  120         CONTINUE
          END IF
      ELSE
          IF (nota) THEN
*
*           Form  C := alpha*A*B**T + beta*C
*
              DO 170 j = 1,n
                  IF (beta.EQ.zero) THEN
                      DO 130 i = 1,m
                          c(i,j) = zero
  130                 CONTINUE
                  ELSE IF (beta.NE.one) THEN
                      DO 140 i = 1,m
                          c(i,j) = beta*c(i,j)
  140                 CONTINUE
                  END IF
                  DO 160 l = 1,k
                      temp = alpha*b(j,l)
                      DO 150 i = 1,m
                          c(i,j) = c(i,j) + temp*a(i,l)
  150                 CONTINUE
  160             CONTINUE
  170         CONTINUE
          ELSE
*
*           Form  C := alpha*A**T*B**T + beta*C
*
              DO 200 j = 1,n
                  DO 190 i = 1,m
                      temp = zero
                      DO 180 l = 1,k
                          temp = temp + a(l,i)*b(j,l)
  180                 CONTINUE
                      IF (beta.EQ.zero) THEN
                          c(i,j) = alpha*temp
                      ELSE
                          c(i,j) = alpha*temp + beta*c(i,j)
                      END IF
  190             CONTINUE
  200         CONTINUE
          END IF
      END IF
*
      RETURN
*
*     End of DGEMM
*
      END