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# zsyr2k

```
NAME
ZSYR2K - perform one of the symmetric rank 2k operations   C
:= alpha*A*B' + alpha*B*A' + beta*C,

SYNOPSIS
SUBROUTINE ZSYR2K( UPLO, TRANS, N, K, ALPHA, A, LDA, B, LDB,
BETA, C, LDC )

CHARACTER*1    UPLO, TRANS

INTEGER        N, K, LDA, LDB, LDC

COMPLEX*16     ALPHA, BETA

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

PURPOSE
ZSYR2K  performs one of the symmetric rank 2k operations

or

C := alpha*A'*B + alpha*B'*A + beta*C,

where  alpha and beta  are scalars,  C is an  n by n sym-
metric matrix and  A and B  are  n by k  matrices  in the
first  case  and  k by n matrices in the second case.

PARAMETERS
UPLO   - CHARACTER*1.
On  entry,   UPLO  specifies  whether  the  upper  or
lower triangular  part  of the  array  C  is to be
referenced  as follows:

UPLO = 'U' or 'u'   Only the  upper triangular part
of  C is to be referenced.

UPLO = 'L' or 'l'   Only the  lower triangular part
of  C is to be referenced.

Unchanged on exit.

TRANS  - CHARACTER*1.
On entry,  TRANS  specifies the operation to be per-
formed as follows:

TRANS = 'N' or 'n'    C := alpha*A*B' + alpha*B*A' +
beta*C.

TRANS = 'T' or 't'    C := alpha*A'*B + alpha*B'*A +
beta*C.

Unchanged on exit.

N      - INTEGER.
On entry,  N specifies the order of the matrix C.  N
must be at least zero.  Unchanged on exit.

K      - INTEGER.
On entry with  TRANS = 'N' or 'n',  K  specifies  the
number of  columns  of the  matrices  A and B,  and
on  entry  with TRANS = 'T' or 't',  K  specifies
the number of rows of the matrices  A and B.  K must
be at least zero.  Unchanged on exit.

ALPHA  - COMPLEX*16      .
On entry, ALPHA specifies the scalar alpha.
Unchanged on exit.

ka is
A      -
COMPLEX*16       array of DIMENSION ( LDA, ka ), where
k  when  TRANS = 'N' or 'n',  and is  n  otherwise.
Before entry with  TRANS = 'N' or 'n',  the  leading
n by k part of the array  A  must contain the matrix
A,  otherwise the leading  k by n  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
TRANS = 'N' or 'n' then  LDA must be at least  max(
1, n ), otherwise  LDA must be at least  max( 1, k ).
Unchanged on exit.

kb is
B      -
COMPLEX*16       array of DIMENSION ( LDB, kb ), where
k  when  TRANS = 'N' or 'n',  and is  n  otherwise.
Before entry with  TRANS = 'N' or 'n',  the  leading
n by k part of the array  B  must contain the matrix
B,  otherwise the leading  k by n  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
TRANS = 'N' or 'n' then  LDB must be at least  max(
1, n ), otherwise  LDB must be at least  max( 1, k ).
Unchanged on exit.

BETA   - COMPLEX*16      .
On entry, BETA specifies the scalar beta.  Unchanged
on exit.

C      - COMPLEX*16       array of DIMENSION ( LDC, n ).
Before entry  with  UPLO = 'U' or 'u',  the leading
n by n upper triangular part of the array C must con-
tain the upper triangular part  of the  symmetric
matrix  and the strictly lower triangular part of C
is not referenced.  On exit, the upper triangular
part of the array  C is overwritten by the upper tri-
angular part of the updated matrix.  Before entry
with  UPLO = 'L' or 'l',  the leading  n by n lower
triangular part of the array C must contain the lower
triangular part  of the  symmetric matrix  and the
strictly upper triangular part of C is not refer-
enced.  On exit, the lower triangular part of the
array  C is overwritten by the lower triangular part
of the updated matrix.

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, n ).  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.
```