Provided by: libblas-doc_1.2.20110419-2ubuntu1_all #### NAME

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

```

#### SYNOPSIS

```       SUBROUTINE ZSYRK ( UPLO, TRANS, N, K, ALPHA, A, LDA, BETA, C, LDC )

CHARACTER*1  UPLO, TRANS

INTEGER      N, K, LDA, LDC

COMPLEX*16   ALPHA, BETA

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

```

#### PURPOSE

```       ZSYRK  performs one of the symmetric rank k operations

or

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

where   alpha and beta  are scalars,  C is an  n by n symmetric matrix and  A  is an  n by
k  matrix in the first case and a  k by n  matrix 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*A' + beta*C.

TRANS = 'T' or 't'   C := alpha*A'*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
matrix    A,   and  on   entry   with TRANS = 'T' or 't',  K  specifies  the number
of rows of the matrix A.  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.

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.
```