NAME

zgemm - perform one of the matrix-matrix operations   C := alpha∗op( A )∗op( B ) + beta∗C

SYNOPSIS

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

CHARACTER∗1 TRANSA, TRANSB

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

COMPLEX∗16 ALPHA, BETA

COMPLEX∗16 A( LDA, ∗ ), B( LDB, ∗ ), C( LDC, ∗ )

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.

SunSoft, Inc.  —  Last change: 27 Jun 1995