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# zgemm

## man page of zgemm

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

```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

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.

ZGEMM(3)
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