Purpose
=======

ZGEMM 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' or op( X ) = conjg( 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 ) = conjg( 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 ) = conjg( 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 - COMPLEX*16 .
On entry, ALPHA specifies the scalar alpha.
Unchanged on exit.

A - COMPLEX*16 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*16 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*16 .
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*16 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 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.