# zsyr.f - Man Page

SRC/zsyr.f

## Synopsis

### Functions/Subroutines

subroutine zsyr (uplo, n, alpha, x, incx, a, lda)
ZSYR performs the symmetric rank-1 update of a complex symmetric matrix.

## Function/Subroutine Documentation

### subroutine zsyr (character uplo, integer n, complex*16 alpha, complex*16, dimension( * ) x, integer incx, complex*16, dimension( lda, * ) a, integer lda)

ZSYR performs the symmetric rank-1 update of a complex symmetric matrix.

Purpose:

``` ZSYR   performs the symmetric rank 1 operation

A := alpha*x*x**H + A,

where alpha is a complex scalar, x is an n element vector and A is an
n by n symmetric matrix.```
Parameters

UPLO

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

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

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

Unchanged on exit.```

N

```          N is INTEGER
On entry, N specifies the order of the matrix A.
N must be at least zero.
Unchanged on exit.```

ALPHA

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

X

```          X is COMPLEX*16 array, dimension at least
( 1 + ( N - 1 )*abs( INCX ) ).
Before entry, the incremented array X must contain the N-
element vector x.
Unchanged on exit.```

INCX

```          INCX is INTEGER
On entry, INCX specifies the increment for the elements of
X. INCX must not be zero.
Unchanged on exit.```

A

```          A is COMPLEX*16 array, dimension ( LDA, N )
Before entry, with  UPLO = 'U' or 'u', the leading n by n
upper triangular part of the array A must contain the upper
triangular part of the symmetric matrix and the strictly
lower triangular part of A is not referenced. On exit, the
upper triangular part of the array A 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 A must contain the lower
triangular part of the symmetric matrix and the strictly
upper triangular part of A is not referenced. On exit, the
lower triangular part of the array A is overwritten by the
lower triangular part of the updated matrix.```

LDA

```          LDA is INTEGER
On entry, LDA specifies the first dimension of A as declared
in the calling (sub) program. LDA must be at least
max( 1, N ).
Unchanged on exit.```
Author

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Definition at line 134 of file zsyr.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page zsyr(3) is an alias of zsyr.f(3).

Tue Nov 28 2023 12:08:42 Version 3.12.0 LAPACK