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

Performs one of the matrix-vector operations x := A*x, or x := AT*x, where x is an n element vector 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 TriangularMultiplyInPlace<T>(
	this ILinearAlgebraOperations<T> operations,
	MatrixTriangle uplo,
	TransposeOperation trans,
	MatrixDiagonal diag,
	int n,
	ReadOnlySpan2D<T> a,
	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 operation to be performed as
             follows:
                TRANS = 'N' or 'n'   x := A*x.
                TRANS = 'T' or 't'   x := AT*x.
                TRANS = 'C' or 'c'   x := AT*x.
            
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  ReadOnlySpan2D<T>
            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 vector x. On exit, X is overwritten with the
             tranformed vector x.
            
             On entry, INCX specifies the increment for the elements of
             X. INCX must not be zero.
            

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 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, Univ. of Colorado Denver, NAG Ltd.

Date: November 2011

See Also