CGEMM(1)

NAME
LAPACK-3 - performs one of the matrix-matrix operations C := alpha*op( A )*op( B ) + beta*C,

SYNOPSIS

SUBROUTINE CGEMM(TRANSA,TRANSB,M,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC)

COMPLEX
    ALPHA,BETA

INTEGER
    K,LDA,LDB,LDC,M,N

CHARACTER
    TRANSA,TRANSB

COMPLEX
    A(LDA,*),B(LDB,*),C(LDC,*)

PURPOSE
CGEMM performs one of the matrix-matrix operations
 where op( X ) is one of
    op( X ) = X or op( X ) = X**T or op( X ) = X**H,
 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.

ARGUMENTS
 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**T.
 TRANSA = 'C' or 'c', op( A ) = A**H.
 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**T.
 TRANSB = 'C' or 'c', op( B ) = B**H.
 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  - COMPLEX         .
     On entry, ALPHA specifies the scalar alpha.
     Unchanged on exit.

A      - COMPLEX          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      - COMPLEX          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   - COMPLEX         .
     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      - COMPLEX          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.

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.