?syr

Performs the symmetric rank-1 update of a complex symmetric matrix.

Syntax

call csyr( uplo, n, alpha, x, incx, a, lda )

call zsyr( uplo, n, alpha, x, incx, a, lda )

Include Files

The FORTRAN 77 interfaces are specified in the mkl_lapack.fi include file (to be used in Fortran programs) and in the mkl_lapack.h include file (to be used in C programs).

Description

The routine performs the symmetric rank 1 operation defined as

a := alpha*x*x' + a,

where:

alpha is a complex scalar

x is an n-element complex vector

a is an n-by-n complex symmetric matrix.

These routines have their real equivalents in BLAS (see ?syr in Chapter "BLAS and Sparse BLAS Routines").

Input Parameters

uplo

CHARACTER*1. Specifies whether the upper or lower triangular part of the array a is used:

If uplo = 'U' or 'u', then the upper triangular part of the array a is used.

If uplo = 'L' or 'l', then the lower triangular part of the array a is used.

n

INTEGER. Specifies the order of the matrix a. The value of n must be at least zero.

alpha

COMPLEX for csyr

COMPLEX*16 for zsyr

Specifies the scalar alpha.

x

COMPLEX for csyr

COMPLEX*16 for zsyr

Array, DIMENSION at least (1 + (n - 1)*abs(incx)). Before entry, the incremented array x must contain the n-element vector x.

incx

INTEGER. Specifies the increment for the elements of x. The value of incx must not be zero.

a

COMPLEX for csyr

COMPLEX*16 for zsyr

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.

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.

lda

INTEGER. Specifies the first dimension of a as declared in the calling (sub)program. The value of lda must be at least max(1,n).

Output Parameters

a

With uplo = 'U' or 'u', the upper triangular part of the array a is overwritten by the upper triangular part of the updated matrix.

With uplo = 'L' or 'l', the lower triangular part of the array a is overwritten by the lower triangular part of the updated matrix.