# ?syr2

Performs a rank-2 update of symmetric matrix.

## Syntax

FORTRAN 77:

call ssyr2(uplo, n, alpha, x, incx, y, incy, a, lda )

call dsyr2(uplo, n, alpha, x, incx, y, incy, a, lda )

Fortran 95:

call syr2(a, x, y [,uplo][,alpha])

## Description

The ?syr2 routines perform a matrix-vector operation defined as
`A := alpha*x*y'+ alpha*y*x' + A,`

where:

alpha is a scalar,

x and y are n-element vectors,

A is an n-by-n symmetric matrix.

## 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 low triangular part of the array a is is used.

n

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

alpha

  REAL for ssyr2

  DOUBLE PRECISION for dsyr2

  Specifies the scalar alpha.

x

  REAL for ssyr2

  DOUBLE PRECISION for dsyr2

  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.

y

  REAL for ssyr2

  DOUBLE PRECISION for dsyr2

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

incy

  INTEGER. Specifies the increment for the elements of y. The value of incy must not be zero.

a

  REAL for ssyr2

  DOUBLE PRECISION for dsyr2

  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.

## Fortran 95 Interface Notes

Routines in Fortran 95 interface have fewer arguments in the calling sequence than their FORTRAN 77 counterparts. For general conventions applied to skip redundant or reconstructible arguments, see Fortran 95 Interface Conventions.

Specific details for the routine syr2 interface are the following:

a

  Holds the matrix A of size (n,n).

x

  Holds the vector x of length (n).

y

  Holds the vector y of length (n).

uplo

  Must be 'U' or 'L'. The default value is 'U'.

alpha

  The default value is 1.

Parent topic: BLAS Level 2 Routines