# LinearAlgebraOperationsExtensions.SymmetricRankUpdate<T>(ILinearAlgebraOperations<T>, MatrixTriangle, TransposeOperation, Int32, Int32, T, ReadOnlySpan2D<T>, ReadOnlySpan2D<T>, T, Span2D<T>) Method

Performs one of the symmetric rank 2k operations
C := alpha*A*B^{T} + alpha*B*A^{T} + beta*C,
or
C := alpha*A^{T}*B + alpha*B^{T}*A + beta*C,
where alpha and beta are scalars, C is an n by n symmetric matrix
and A and B are n by k matrices in the first case and k by n
matrices in the second case.

## 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,
TransposeOperation trans,
int n,
int k,
T alpha,
ReadOnlySpan2D<T> a,
ReadOnlySpan2D<T> b,
T beta,
Span2D<T> c
)
```

#### Parameters

- operations ILinearAlgebraOperations<T>
- uplo MatrixTriangle
On entry, UPLO specifies whether the upper or lower triangular part of the array C is to be referenced as follows: UPLO = 'U' or 'u' Only the upper triangular part of C is to be referenced. UPLO = 'L' or 'l' Only the lower triangular part of C is to be referenced.

- trans TransposeOperation
On entry, TRANS specifies the operation to be performed as follows: TRANS = 'N' or 'n' C := alpha*A*B

^{T}+ alpha*B*A^{T}+ beta*C. TRANS = 'T' or 't' C := alpha*A^{T}*B + alpha*B^{T}*A + beta*C. TRANS = 'C' or 'c' C := alpha*A^{T}*B + alpha*B^{T}*A + beta*C.- n Int32
On entry, N specifies the order of the matrix C. N must be at least zero.

- k Int32
On entry with TRANS = 'N' or 'n', K specifies the number of columns of the matrices A and B, and on entry with TRANS = 'T' or 't' or 'C' or 'c', K specifies the number of rows of the matrices A and B. K must be at least zero.

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

- a ReadOnlySpan2D<T>
A is DOUBLE PRECISION array of DIMENSION ( LDA, ka ), where ka is k when TRANS = 'N' or 'n', and is n otherwise. Before entry with TRANS = 'N' or 'n', the leading n by k part of the array A must contain the matrix A, otherwise the leading k by n part of the array A must contain the matrix A.

On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. When TRANS = 'N' or 'n' then LDA must be at least max( 1, n ), otherwise LDA must be at least max( 1, k ).

- b ReadOnlySpan2D<T>
B is DOUBLE PRECISION array of DIMENSION ( LDB, kb ), where kb is k when TRANS = 'N' or 'n', and is n otherwise. Before entry with TRANS = 'N' or 'n', the leading n by k part of the array B must contain the matrix B, otherwise the leading k by n part of the array B must contain the matrix B.

On entry, LDB specifies the first dimension of B as declared in the calling (sub) program. When TRANS = 'N' or 'n' then LDB must be at least max( 1, n ), otherwise LDB must be at least max( 1, k ).

- beta T
BETA is DOUBLE PRECISION. On entry, BETA specifies the scalar beta.

- c Span2D<T>
C is DOUBLE PRECISION array of DIMENSION ( LDC, n ). Before entry with UPLO = 'U' or 'u', the leading n by n upper triangular part of the array C must contain the upper triangular part of the symmetric matrix and the strictly lower triangular part of C is not referenced. On exit, the upper triangular part of the array C 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 C must contain the lower triangular part of the symmetric matrix and the strictly upper triangular part of C is not referenced. On exit, the lower triangular part of the array C is overwritten by the lower triangular part of the updated matrix.

On entry, LDC specifies the first dimension of C as declared in the calling (sub) program. LDC 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 3 LinearAlgebra routine. -- Written on 8-February-1989. Jack Dongarra, Argonne National Laboratory. Iain Duff, AERE Harwell. Jeremy Du Croz, Numerical Algorithms Group Ltd. Sven Hammarling, Numerical Algorithms Group Ltd.Authors: Univ. of Tennessee, Univ. of California Berkeley, Univ. of Colorado Denver, NAG Ltd.

Date: November 2011