---
name: "csyr.f"
section: "3"
platform: "linux"
package: "lapack-doc"
version: "3.12.1-2"
release: "Arch Linux 2026-11-01"
platforms: ["linux"]
url: "https://new.carta.tech/csyr.f"
---

# csyr.f(3)

## NAME

SRC/csyr.f

## SYNOPSIS

### Functions/Subroutines

subroutine **csyr** (uplo, n, alpha, x, incx, a, lda)\
 **CSYR** performs the symmetric rank-1 update of a complex symmetric matrix.

## Function/Subroutine Documentation

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

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

**Purpose:**

```
!>
!> CSYR   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
!>           On entry, ALPHA specifies the scalar alpha.
!>           Unchanged on exit.
!>
```

*X*

```
!>          X is COMPLEX 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 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 **csyr.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.