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**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.

TRANSA

          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**H.

TRANSB

          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**H.

M

          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.

N

          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.

K

          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.

ALPHA

          ALPHA is COMPLEX*16
           On entry, ALPHA specifies the scalar alpha.

A

          A is COMPLEX*16 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.

LDA

          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 ).

B

          B is COMPLEX*16 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.

LDB

          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 ).

BETA

          BETA is COMPLEX*16
           On entry,  BETA  specifies the scalar  beta.  When  BETA  is
           supplied as zero then C need not be set on input.

C

          C is COMPLEX*16 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 ).

LDC

          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 ).

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

  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.