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 ) = AT.

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,
	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 ) = 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  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

See Also