SYNOPSIS
 SUBROUTINE DGEMM
 ( TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC )
 CHARACTER*1 TRANSA, TRANSB
 INTEGER M, N, K, LDA, LDB, LDC
 DOUBLE PRECISION ALPHA, BETA
 DOUBLE PRECISION A( LDA, * ), B( LDB, * ), C( LDC, * )
PURPOSE
DGEMM performs one of the matrixmatrix operations
where op( X ) is one of
op( X ) = X or op( X ) = X',
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.
PARAMETERS
TRANSA  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'.
TRANSA = 'C' or 'c', op( A ) = A'.
Unchanged on exit.
TRANSB  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'.
TRANSB = 'C' or 'c', op( B ) = B'.
Unchanged on exit.
 M  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. Unchanged on exit.
 N  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. Unchanged on exit.
 K  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. 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 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. Unchanged on exit.
 LDA  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 ). Unchanged on exit.
 B  DOUBLE PRECISION array of 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. Unchanged on exit.
 LDB  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 ). 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 matrix ( alpha*op( A )*op( B ) + beta*C ).
 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.
Level 3 Blas routine.
 Written on 8February1989. Jack Dongarra, Argonne National Laboratory. Iain Duff, AERE Harwell. Jeremy Du Croz, Numerical Algorithms Group Ltd. Sven Hammarling, Numerical Algorithms Group Ltd.