# LinearAlgebraOperationsExtensions.SymmetricRankUpdate<T>(ILinearAlgebraOperations<T>, MatrixTriangle, Int32, T, ReadOnlySpanSlice<T>, Span2D<T>) Method

Performs the symmetric rank 1 operation A := alpha*x*x**T + A, where alpha is a real scalar, x is an n element vector and A is an n by n symmetric matrix.

## Definition

**Namespace:**Extreme.Collections

**Assembly:**Extreme.Numerics (in Extreme.Numerics.dll) Version: 9.0.0

```
public static void SymmetricRankUpdate<T>(
this ILinearAlgebraOperations<T> operations,
MatrixTriangle uplo,
int n,
T alpha,
ReadOnlySpanSlice<T> x,
Span2D<T> a
)
```

#### Parameters

- operations ILinearAlgebraOperations<T>
- uplo MatrixTriangle
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.

- n Int32
On entry, N specifies the order of the matrix A. N must be at least zero.

- alpha T
ALPHA is DOUBLE PRECISION. On entry, ALPHA specifies the scalar alpha.

- x ReadOnlySpanSlice<T>
X is DOUBLE PRECISION array of dimension at least ( 1 + ( n - 1 )*abs( INCX ) ). Before entry, the incremented array X must contain the n element vector x.

On entry, INCX specifies the increment for the elements of X. INCX must not be zero.

- a Span2D<T>
A is DOUBLE PRECISION array of 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.

On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. LDA must be at least max( 1, n ).

#### Type Parameters

- T

#### Usage Note

In Visual Basic and C#, you can call this method as an instance method on any object of type ILinearAlgebraOperations<T>. When you use instance method syntax to call this method, omit the first parameter. For more information, see Extension Methods (Visual Basic) or Extension Methods (C# Programming Guide).## Remarks

## Further Details:

Level 2 LinearAlgebra routine. -- Written on 22-October-1986. Jack Dongarra, Argonne National Lab. Jeremy Du Croz, Nag Central Office. Sven Hammarling, Nag Central Office. Richard Hanson, Sandia National Labs.Authors: Univ. of Tennessee, Univ. of California Berkeley, Univ. of Colorado Denver, NAG Ltd.

Date: November 2011