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

Solves one of the matrix equations op( A )*X = alpha*B, or X*op( A ) = alpha*B, where alpha is a scalar, X and B are m by n matrices, A is a unit, or non-unit, upper or lower triangular matrix and op( A ) is one of op( A ) = A or op( A ) = AT.

## Definition

Namespace: Extreme.Collections
Assembly: Extreme.Numerics (in Extreme.Numerics.dll) Version: 9.0.0
C#
``````public static void TriangularSolveInPlace<T>(
this ILinearAlgebraOperations<T> operations,
MatrixOperationSide side,
MatrixTriangle uplo,
TransposeOperation transa,
MatrixDiagonal diag,
int m,
int n,
T alpha,
Span2D<T> b
)
``````

#### Parameters

operations  ILinearAlgebraOperations<T>

side  MatrixOperationSide
```             On entry, SIDE specifies whether op( A ) appears on the left
or right of X as follows:
SIDE = 'L' or 'l'   op( A )*X = alpha*B.
SIDE = 'R' or 'r'   X*op( A ) = alpha*B.
```
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 ) = AT.
TRANSA = 'C' or 'c'   op( A ) = AT.
```
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 is DOUBLE PRECISION array of DIMENSION ( LDA, k ),
where k is m when SIDE = 'L' or 'l'
and k 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  right-hand  side  matrix  B,  and  on exit  is
overwritten by the solution matrix  X.
```
```             On entry, LDB specifies the first dimension of B as declared
in  the  calling  (sub)  program.   LDB  must  be  at  least
max( 1, m ).
```

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

```            The matrix X is overwritten on B.
```

#### 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