# zsyr2k

```ZSYR2K(l)                        BLAS routine                        ZSYR2K(l)

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 symmetric 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 performed 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.

A      - COMPLEX*16       array of DIMENSION ( LDA, ka ), where ka is
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.

B      - COMPLEX*16       array of DIMENSION ( LDB, kb ), where kb is
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 contain 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 triangular 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 referenced.  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.

BLAS routine                    16 October 1992                      ZSYR2K(l)```