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

Performs one of the matrix-matrix operations
B := alpha*op( A )*B, or B := alpha*B*op( A ),
where alpha is a scalar, B is an m by n matrix, A is a unit, or
non-unit, upper or lower triangular matrix and op( A ) is one of
op( A ) = A or op( A ) = A^{T}.

## Definition

**Namespace:**Extreme.Collections

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

```
public static void TriangularMultiplyInPlace<T>(
this ILinearAlgebraOperations<T> operations,
MatrixOperationSide side,
MatrixTriangle uplo,
TransposeOperation transa,
MatrixDiagonal diag,
int m,
int n,
T alpha,
ReadOnlySpan2D<T> a,
Span2D<T> b
)
```

#### Parameters

- operations ILinearAlgebraOperations<T>
- side MatrixOperationSide
On entry, SIDE specifies whether op( A ) multiplies B from the left or right as follows: SIDE = 'L' or 'l' B := alpha*op( A )*B. SIDE = 'R' or 'r' B := alpha*B*op( A ).

- uplo MatrixTriangle
On entry, UPLO specifies whether the matrix A is an upper or lower triangular matrix as follows: UPLO = 'U' or 'u' A is an upper triangular matrix. UPLO = 'L' or 'l' A is a lower triangular matrix.

- 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}.- diag MatrixDiagonal
On entry, DIAG specifies whether or not A is unit triangular as follows: DIAG = 'U' or 'u' A is assumed to be unit triangular. DIAG = 'N' or 'n' A is not assumed to be unit triangular.

- m Int32
On entry, M specifies the number of rows of B. M must be at least zero.

- n Int32
On entry, N specifies the number of columns of B. N must be at least zero.

- alpha T
ALPHA is DOUBLE PRECISION. On entry, ALPHA specifies the scalar alpha. When alpha is zero then A is not referenced and B need not be set before entry.

- a ReadOnlySpan2D<T>
A is DOUBLE PRECISION array of DIMENSION ( LDA, k ), where k is m when SIDE = 'L' or 'l' and is n when SIDE = 'R' or 'r'. Before entry with UPLO = 'U' or 'u', the leading k by k upper triangular part of the array A must contain the upper triangular matrix and the strictly lower triangular part of A is not referenced. Before entry with UPLO = 'L' or 'l', the leading k by k lower triangular part of the array A must contain the lower triangular matrix and the strictly upper triangular part of A is not referenced. Note that when DIAG = 'U' or 'u', the diagonal elements of A are not referenced either, but are assumed to be unity.

On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. When SIDE = 'L' or 'l' then LDA must be at least max( 1, m ), when SIDE = 'R' or 'r' then LDA must be at least max( 1, n ).

- b Span2D<T>
B is DOUBLE PRECISION array of DIMENSION ( LDB, n ). Before entry, the leading m by n part of the array B must contain the matrix B, and on exit is overwritten by the transformed matrix.

On entry, LDB specifies the first dimension of B as declared in the calling (sub) program. LDB 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