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## zgemm()

subroutine zgemm | ( | character | transa,
|  | character | transb,
|  | integer | m,
|  | integer | n,
|  | integer | k,
|  | complex*16 | alpha,
|  | complex*16, dimension(lda,*) | a,
|  | integer | lda,
|  | complex*16, dimension(ldb,*) | b,
|  | integer | ldb,
|  | complex*16 | beta,
|  | complex*16, dimension(ldc,*) | c,
|  | integer | ldc )

ZGEMM

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**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.
      !>

Parameters

  [in]

  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.
      !>

  [in]

  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.
      !>

  [in]

  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.
      !>

  [in]

  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.
      !>

  [in]

  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.
      !>

  [in]

  ALPHA

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

  [in]

  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.
      !>

  [in]

  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 ).
      !>

  [in]

  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.
      !>

  [in]

  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 ).
      !>

  [in]

  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.
      !>

  [in,out]

  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 ).
      !>

  [in]

  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 ).
      !>

Author
  Univ. of Tennessee
  Univ. of California Berkeley
  Univ. of Colorado Denver
  NAG Ltd.

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.
      !>