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

Solves one of the systems of equations A*x = b, or AT*x = b, where b and x are n element vectors and A is an n by n unit, or non-unit, upper or lower triangular matrix.

## 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,
MatrixTriangle uplo,
TransposeOperation trans,
MatrixDiagonal diag,
int n,
SpanSlice<T> x
)
``````

#### Parameters

operations  ILinearAlgebraOperations<T>

uplo  MatrixTriangle
```             On entry, UPLO specifies whether the matrix 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.
```
trans  TransposeOperation
```             On entry, TRANS specifies the equations to be solved as
follows:
TRANS = 'N' or 'n'   A*x = b.
TRANS = 'T' or 't'   AT*x = b.
TRANS = 'C' or 'c'   AT*x = b.
```
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.
```
n  Int32
```             On entry, N specifies the order of the matrix A.
N must be at least zero.
```
```            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 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 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. LDA must be at least
max( 1, n ).
```
x  SpanSlice<T>
```            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 right-hand side vector b. On exit, X is overwritten
with the solution vector x.
```
```             On entry, INCX specifies the increment for the elements of
X. INCX must not be zero.
2 LinearAlgebra routine.
itten on 22-October-1986.
ack Dongarra, Argonne National Lab.
Jeremy Du Croz, Nag Central Office.
Sven Hammarling, Nag Central Office.
Richard Hanson, Sandia National Labs.
```

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

```            No test for singularity or near-singularity is included in this
routine. Such tests must be performed before calling this routine.
```

Authors: Univ. of Tennessee, Univ. of California Berkeley, Univ. of Colorado Denver, NAG Ltd.

Date: November 2011