# dgemm.f

          SUBROUTINE DGEMM (TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB,
         $   BETA, C, LDC)
    C***BEGIN PROLOGUE  DGEMM
    C***PURPOSE  Perform one of the matrix-matrix operations.
    C***LIBRARY   SLATEC (BLAS)
    C***CATEGORY  D1B6
    C***TYPE      DOUBLE PRECISION (SGEMM-S, DGEMM-D, CGEMM-C)
    C***KEYWORDS  LEVEL 3 BLAS, LINEAR ALGEBRA
    C***AUTHOR  Dongarra, J., (ANL)
    C           Duff, I., (AERE)
    C           Du Croz, J., (NAG)
    C           Hammarling, S. (NAG)
    C***DESCRIPTION
    C
    C  DGEMM  performs one of the matrix-matrix operations
    C
    C     C := alpha*op( A )*op( B ) + beta*C,
    C
    C  where  op( X ) is one of
    C
    C     op( X ) = X   or   op( X ) = X',
    C
    C  alpha and beta are scalars, and A, B and C are matrices, with op( A )
    C  an m by k matrix,  op( B )  a  k by n matrix and  C an m by n matrix.
    C
    C  Parameters
    C  ==========
    C
    C  TRANSA - CHARACTER*1.
    C           On entry, TRANSA specifies the form of op( A ) to be used in
    C           the matrix multiplication as follows:
    C
    C              TRANSA = 'N' or 'n',  op( A ) = A.
    C
    C              TRANSA = 'T' or 't',  op( A ) = A'.
    C
    C              TRANSA = 'C' or 'c',  op( A ) = A'.
    C
    C           Unchanged on exit.
    C
    C  TRANSB - CHARACTER*1.
    C           On entry, TRANSB specifies the form of op( B ) to be used in
    C           the matrix multiplication as follows:
    C
    C              TRANSB = 'N' or 'n',  op( B ) = B.
    C
    C              TRANSB = 'T' or 't',  op( B ) = B'.
    C
    C              TRANSB = 'C' or 'c',  op( B ) = B'.
    C
    C           Unchanged on exit.
    C
    C  M      - INTEGER.
    C           On entry,  M  specifies  the number  of rows  of the  matrix
    C           op( A )  and of the  matrix  C.  M  must  be at least  zero.
    C           Unchanged on exit.
    C
    C  N      - INTEGER.
    C           On entry,  N  specifies the number  of columns of the matrix
    C           op( B ) and the number of columns of the matrix C. N must be
    C           at least zero.
    C           Unchanged on exit.
    C
    C  K      - INTEGER.
    C           On entry,  K  specifies  the number of columns of the matrix
    C           op( A ) and the number of rows of the matrix op( B ). K must
    C           be at least  zero.
    C           Unchanged on exit.
    C
    C  ALPHA  - DOUBLE PRECISION.
    C           On entry, ALPHA specifies the scalar alpha.
    C           Unchanged on exit.
    C
    C  A      - DOUBLE PRECISION array of DIMENSION ( LDA, ka ), where ka is
    C           k  when  TRANSA = 'N' or 'n',  and is  m  otherwise.
    C           Before entry with  TRANSA = 'N' or 'n',  the leading  m by k
    C           part of the array  A  must contain the matrix  A,  otherwise
    C           the leading  k by m  part of the array  A  must contain  the
    C           matrix A.
    C           Unchanged on exit.
    C
    C  LDA    - INTEGER.
    C           On entry, LDA specifies the first dimension of A as declared
    C           in the calling (sub) program. When  TRANSA = 'N' or 'n' then
    C           LDA must be at least  max( 1, m ), otherwise  LDA must be at
    C           least  max( 1, k ).
    C           Unchanged on exit.
    C
    C  B      - DOUBLE PRECISION array of DIMENSION ( LDB, kb ), where kb is
    C           n  when  TRANSB = 'N' or 'n',  and is  k  otherwise.
    C           Before entry with  TRANSB = 'N' or 'n',  the leading  k by n
    C           part of the array  B  must contain the matrix  B,  otherwise
    C           the leading  n by k  part of the array  B  must contain  the
    C           matrix B.
    C           Unchanged on exit.
    C
    C  LDB    - INTEGER.
    C           On entry, LDB specifies the first dimension of B as declared
    C           in the calling (sub) program. When  TRANSB = 'N' or 'n' then
    C           LDB must be at least  max( 1, k ), otherwise  LDB must be at
    C           least  max( 1, n ).
    C           Unchanged on exit.
    C
    C  BETA   - DOUBLE PRECISION.
    C           On entry,  BETA  specifies the scalar  beta.  When  BETA  is
    C           supplied as zero then C need not be set on input.
    C           Unchanged on exit.
    C
    C  C      - DOUBLE PRECISION array of DIMENSION ( LDC, n ).
    C           Before entry, the leading  m by n  part of the array  C must
    C           contain the matrix  C,  except when  beta  is zero, in which
    C           case C need not be set on entry.
    C           On exit, the array  C  is overwritten by the  m by n  matrix
    C           ( alpha*op( A )*op( B ) + beta*C ).
    C
    C  LDC    - INTEGER.
    C           On entry, LDC specifies the first dimension of C as declared
    C           in  the  calling  (sub)  program.   LDC  must  be  at  least
    C           max( 1, m ).
    C           Unchanged on exit.
    C
    C***REFERENCES  Dongarra, J., Du Croz, J., Duff, I., and Hammarling, S.
    C                 A set of level 3 basic linear algebra subprograms.
    C                 ACM TOMS, Vol. 16, No. 1, pp. 1-17, March 1990.
    C***ROUTINES CALLED  LSAME, XERBLA
    C***REVISION HISTORY  (YYMMDD)
    C   890208  DATE WRITTEN
    C   910605  Modified to meet SLATEC prologue standards.  Only comment
    C           lines were modified.  (BKS)
    C***END PROLOGUE  DGEMM