Performs the matrix-vector operation y := alpha*A*x + beta*y, where alpha and beta are scalars, x and y are n element vectors and A is an n by n symmetric matrix.

## Definition

Namespace: Extreme.Collections
Assembly: Extreme.Numerics (in Extreme.Numerics.dll) Version: 9.0.0
C#
``````public static void SymmetricMultiplyAndAddInPlace<T>(
this ILinearAlgebraOperations<T> operations,
MatrixTriangle uplo,
int n,
T alpha,
T beta,
SpanSlice<T> y
)
``````

#### 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.
```
```            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.
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 entry, LDA specifies the first dimension of A as declared
in the calling (sub) program. LDA must be at least
max( 1, n ).
```
```            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.
```
beta  T
```            BETA is DOUBLE PRECISION.
On entry, BETA specifies the scalar beta. When BETA is
supplied as zero then Y need not be set on input.
```
y  SpanSlice<T>
```            Y is DOUBLE PRECISION array of dimension at least
( 1 + ( n - 1 )*abs( INCY ) ).
Before entry, the incremented array Y must contain the n
element vector y. On exit, Y is overwritten by the updated
vector y.
```
```             On entry, INCY specifies the increment for the elements of
Y. INCY must not be zero.
```

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.
The vector and matrix arguments are not referenced when N = 0, or M = 0
-- 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,