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

Performs one of the matrix-matrix operations
C := alpha*op( A )*op( B ) + beta*C,
where op( X ) is one of
op( X ) = X or op( X ) = X^{T},
alpha and beta are scalars, and A, B and C are matrices, with op( A )
an m by k matrix, op( B ) a k by n matrix and C an m by n matrix.

## Definition

**Namespace:**Extreme.Collections

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

```
public static void MultiplyAndAddInPlace<T>(
this ILinearAlgebraOperations<T> operations,
TransposeOperation transa,
TransposeOperation transb,
int m,
int n,
int k,
T alpha,
ReadOnlySpan2D<T> a,
ReadOnlySpan2D<T> b,
T beta,
Span2D<T> c
)
```

#### Parameters

- operations ILinearAlgebraOperations<T>
- transa TransposeOperation
On entry, TRANSA specifies the form of op( A ) to be used in the matrix multiplication as follows: TRANSA = 'N' or 'n', op( A ) = A. TRANSA = 'T' or 't', op( A ) = A

^{T}. TRANSA = 'C' or 'c', op( A ) = A^{T}.- transb TransposeOperation
On entry, TRANSB specifies the form of op( B ) to be used in the matrix multiplication as follows: TRANSB = 'N' or 'n', op( B ) = B. TRANSB = 'T' or 't', op( B ) = B

^{T}. TRANSB = 'C' or 'c', op( B ) = B^{T}.- m Int32
On entry, M specifies the number of rows of the matrix op( A ) and of the matrix C. M must be at least zero.

- n Int32
On entry, N specifies the number of columns of the matrix op( B ) and the number of columns of the matrix C. N must be at least zero.

- k Int32
On entry, K specifies the number of columns of the matrix op( A ) and the number of rows of the matrix op( 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 TRANSA = 'N' or 'n', and is m otherwise. Before entry with TRANSA = 'N' or 'n', the leading m by k part of the array A must contain the matrix A, otherwise the leading k by m 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 TRANSA = 'N' or 'n' then LDA must be at least max( 1, m ), otherwise LDA must be at least max( 1, k ).

- b ReadOnlySpan2D<T>
B is DOUBLE PRECISION array of DIMENSION ( LDB, kb ), where kb is n when TRANSB = 'N' or 'n', and is k otherwise. Before entry with TRANSB = 'N' or 'n', the leading k by n part of the array B must contain the matrix B, otherwise the leading n by k 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 TRANSB = 'N' or 'n' then LDB must be at least max( 1, k ), otherwise LDB must be at least max( 1, n ).

- beta T
BETA is DOUBLE PRECISION. On entry, BETA specifies the scalar beta. When BETA is supplied as zero then C need not be set on input.

- c Span2D<T>
C is DOUBLE PRECISION array of DIMENSION ( LDC, n ). Before entry, the leading m by n part of the array C must contain the matrix C, except when beta is zero, in which case C need not be set on entry. On exit, the array C is overwritten by the m by n matrix ( alpha*op( A )*op( B ) + beta*C ).

On entry, LDC specifies the first dimension of C as declared in the calling (sub) program. LDC must be at least max( 1, m ).

#### 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