# 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

Univ. of Colorado Denver

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