LinearAlgebraOperationsExtensions.TriangularMultiplyInPlace Method

Definition

Namespace: Numerics.NET.Collections
Assembly: Numerics.NET (in Numerics.NET.dll) Version: 9.0.2

Overload List

TriangularMultiplyInPlace<T>(ILinearAlgebraOperations<T>, MatrixTriangle, TransposeOperation, MatrixDiagonal, Int32, ReadOnlySpan2D<T>, SpanSlice<T>)	Performs one of the matrix-vector operations x := Ax, or x := A^Tx, where x is an n element vector and A is an n by n unit, or non-unit, upper or lower triangular matrix.
TriangularMultiplyInPlace<T>(ILinearAlgebraOperations<T>, MatrixOperationSide, MatrixTriangle, TransposeOperation, MatrixDiagonal, Int32, Int32, T, ReadOnlySpan2D<T>, Span2D<T>)	Performs one of the matrix-matrix operations B := alphaop( A )B, or B := alphaBop( 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.
TriangularMultiplyInPlace<T, TStorage2D>(ILinearAlgebraOperations<T>, MatrixOperationSide, MatrixTriangle, TransposeOperation, MatrixDiagonal, Int32, Int32, T, TStorage2D, TStorage2D)	Product of a triangular and a general matrix.
TriangularMultiplyInPlace<T, TStorage, TStorage2D>(ILinearAlgebraOperations<T>, MatrixTriangle, TransposeOperation, MatrixDiagonal, Int32, TStorage2D, TStorage)	Product of a triangular matrix and a vector.

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

Performs one of the matrix-vector operations x := A*x, or x := A^T*x, where x is an n element vector and A is an n by n unit, or non-unit, upper or lower triangular matrix.

public static void TriangularMultiplyInPlace<T>(
	this ILinearAlgebraOperations<T> operations,
	MatrixTriangle uplo,
	TransposeOperation trans,
	MatrixDiagonal diag,
	int n,
	ReadOnlySpan2D<T> a,
	SpanSlice<T> x
)

Visual Basic

<ExtensionAttribute>
Public Shared Sub TriangularMultiplyInPlace(Of T) ( 
	operations As ILinearAlgebraOperations(Of T),
	uplo As MatrixTriangle,
	trans As TransposeOperation,
	diag As MatrixDiagonal,
	n As Integer,
	a As ReadOnlySpan2D(Of T),
	x As SpanSlice(Of T)
)

C++/CLI

public:
[ExtensionAttribute]
generic<typename T>
static void TriangularMultiplyInPlace(
	ILinearAlgebraOperations<T>^ operations, 
	MatrixTriangle uplo, 
	TransposeOperation trans, 
	MatrixDiagonal diag, 
	int n, 
	ReadOnlySpan2D<T> a, 
	SpanSlice<T> x
)

[<ExtensionAttribute>]
static member TriangularMultiplyInPlace : 
        operations : ILinearAlgebraOperations<'T> * 
        uplo : MatrixTriangle * 
        trans : TransposeOperation * 
        diag : MatrixDiagonal * 
        n : int * 
        a : ReadOnlySpan2D<'T> * 
        x : SpanSlice<'T> -> unit

Parameters

operations ILinearAlgebraOperations<T>

The object that performs the operation.

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 := A^T*x.
                TRANS = 'C' or 'c'   x := A^T*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

TriangularMultiplyInPlace<T, TStorage, TStorage2D>(ILinearAlgebraOperations<T>, MatrixTriangle, TransposeOperation, MatrixDiagonal, Int32, TStorage2D, TStorage)

Product of a triangular matrix and a vector.

public static void TriangularMultiplyInPlace<T, TStorage, TStorage2D>(
	this ILinearAlgebraOperations<T> operations,
	MatrixTriangle storedTriangle,
	TransposeOperation transposeOperation,
	MatrixDiagonal diagonal,
	int n,
	TStorage2D a,
	TStorage x
)
where TStorage : Object, IStorageSlice<T>
where TStorage2D : Object, IStorage2D<T>

Visual Basic

<ExtensionAttribute>
Public Shared Sub TriangularMultiplyInPlace(Of T, TStorage As {Object, IStorageSlice(Of T)}, TStorage2D As {Object, IStorage2D(Of T)}) ( 
	operations As ILinearAlgebraOperations(Of T),
	storedTriangle As MatrixTriangle,
	transposeOperation As TransposeOperation,
	diagonal As MatrixDiagonal,
	n As Integer,
	a As TStorage2D,
	x As TStorage
)

C++/CLI

public:
[ExtensionAttribute]
generic<typename T, typename TStorage, typename TStorage2D>
where TStorage : Object, IStorageSlice<T>
where TStorage2D : Object, IStorage2D<T>
static void TriangularMultiplyInPlace(
	ILinearAlgebraOperations<T>^ operations, 
	MatrixTriangle storedTriangle, 
	TransposeOperation transposeOperation, 
	MatrixDiagonal diagonal, 
	int n, 
	TStorage2D a, 
	TStorage x
)

[<ExtensionAttribute>]
static member TriangularMultiplyInPlace : 
        operations : ILinearAlgebraOperations<'T> * 
        storedTriangle : MatrixTriangle * 
        transposeOperation : TransposeOperation * 
        diagonal : MatrixDiagonal * 
        n : int * 
        a : 'TStorage2D * 
        x : 'TStorage -> unit  when 'TStorage : Object and IStorageSlice<'T> when 'TStorage2D : Object and IStorage2D<'T>

Parameters

operations ILinearAlgebraOperations<T>: The linear algebra operations instance used to perform the calculation.
storedTriangle MatrixTriangle: Specifies whether the matrix is an upper or lower triangular matrix.
transposeOperation TransposeOperation: Specifies the operation to be performed on the matrix a.
diagonal MatrixDiagonal: Specifies whether or not a is unit triangular.
n Int32: The number of rows and columns in the matrix a.
a TStorage2D: A span that contains the elements of the matrix.
x TStorage: A reference to a one-dimensional array containing the elements of the vector x. The elements of x are overwritten with the result.

Type Parameters

T
TStorage
TStorage2D

Usage Note

Remarks

This method is similar to the BLAS routine DTRMV.

TriangularMultiplyInPlace<T>(ILinearAlgebraOperations<T>, MatrixOperationSide, MatrixTriangle, TransposeOperation, MatrixDiagonal, Int32, Int32, T, ReadOnlySpan2D<T>, Span2D<T>)

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.

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
)

Visual Basic

<ExtensionAttribute>
Public Shared Sub TriangularMultiplyInPlace(Of T) ( 
	operations As ILinearAlgebraOperations(Of T),
	side As MatrixOperationSide,
	uplo As MatrixTriangle,
	transa As TransposeOperation,
	diag As MatrixDiagonal,
	m As Integer,
	n As Integer,
	alpha As T,
	a As ReadOnlySpan2D(Of T),
	b As Span2D(Of T)
)

C++/CLI

public:
[ExtensionAttribute]
generic<typename T>
static void TriangularMultiplyInPlace(
	ILinearAlgebraOperations<T>^ operations, 
	MatrixOperationSide side, 
	MatrixTriangle uplo, 
	TransposeOperation transa, 
	MatrixDiagonal diag, 
	int m, 
	int n, 
	T alpha, 
	ReadOnlySpan2D<T> a, 
	Span2D<T> b
)

[<ExtensionAttribute>]
static member TriangularMultiplyInPlace : 
        operations : ILinearAlgebraOperations<'T> * 
        side : MatrixOperationSide * 
        uplo : MatrixTriangle * 
        transa : TransposeOperation * 
        diag : MatrixDiagonal * 
        m : int * 
        n : int * 
        alpha : 'T * 
        a : ReadOnlySpan2D<'T> * 
        b : Span2D<'T> -> unit

Parameters

operations ILinearAlgebraOperations<T>

The object that performs the operation.

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

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

TriangularMultiplyInPlace<T, TStorage2D>(ILinearAlgebraOperations<T>, MatrixOperationSide, MatrixTriangle, TransposeOperation, MatrixDiagonal, Int32, Int32, T, TStorage2D, TStorage2D)

Product of a triangular and a general matrix.

public static void TriangularMultiplyInPlace<T, TStorage2D>(
	this ILinearAlgebraOperations<T> operations,
	MatrixOperationSide side,
	MatrixTriangle storedTriangle,
	TransposeOperation transA,
	MatrixDiagonal diag,
	int m,
	int n,
	T alpha,
	TStorage2D a,
	TStorage2D b
)
where TStorage2D : Object, IStorage2D<T>

Visual Basic

<ExtensionAttribute>
Public Shared Sub TriangularMultiplyInPlace(Of T, TStorage2D As {Object, IStorage2D(Of T)}) ( 
	operations As ILinearAlgebraOperations(Of T),
	side As MatrixOperationSide,
	storedTriangle As MatrixTriangle,
	transA As TransposeOperation,
	diag As MatrixDiagonal,
	m As Integer,
	n As Integer,
	alpha As T,
	a As TStorage2D,
	b As TStorage2D
)

C++/CLI

public:
[ExtensionAttribute]
generic<typename T, typename TStorage2D>
where TStorage2D : Object, IStorage2D<T>
static void TriangularMultiplyInPlace(
	ILinearAlgebraOperations<T>^ operations, 
	MatrixOperationSide side, 
	MatrixTriangle storedTriangle, 
	TransposeOperation transA, 
	MatrixDiagonal diag, 
	int m, 
	int n, 
	T alpha, 
	TStorage2D a, 
	TStorage2D b
)

[<ExtensionAttribute>]
static member TriangularMultiplyInPlace : 
        operations : ILinearAlgebraOperations<'T> * 
        side : MatrixOperationSide * 
        storedTriangle : MatrixTriangle * 
        transA : TransposeOperation * 
        diag : MatrixDiagonal * 
        m : int * 
        n : int * 
        alpha : 'T * 
        a : 'TStorage2D * 
        b : 'TStorage2D -> unit  when 'TStorage2D : Object and IStorage2D<'T>

Parameters

operations ILinearAlgebraOperations<T>: The linear algebra operations instance used to perform the calculation.
side MatrixOperationSide: Specifies on which side the triangular matrix a is to be multiplied.
storedTriangle MatrixTriangle: Specifies whether the elements of the matrix a are stored in the upper or lower triangular part.
transA TransposeOperation: Specifies the operation to be performed on the matrix a.
diag MatrixDiagonal: Specifies whether or not a is unit triangular.
m Int32: The number of rows in the matrix a and the number of columns of the matrix b.
n Int32: The number of columns in the matrix b and the matrix b.
alpha T: The scalar used to multiply the matrix-vector product.
a TStorage2D: A span that contains the elements of the first matrix.
b TStorage2D: A span that contains the elements of the second matrix.

Type Parameters

T
TStorage2D

LinearAlgebraOperationsExtensions.TriangularMultiplyInPlace Method

Definition

Overload List

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

Parameters

Type Parameters

Usage Note

Remarks

Further Details:

TriangularMultiplyInPlace<T, TStorage, TStorage2D>(ILinearAlgebraOperations<T>, MatrixTriangle, TransposeOperation, MatrixDiagonal, Int32, TStorage2D, TStorage)

Parameters

Type Parameters

Usage Note

Remarks

TriangularMultiplyInPlace<T>(ILinearAlgebraOperations<T>, MatrixOperationSide, MatrixTriangle, TransposeOperation, MatrixDiagonal, Int32, Int32, T, ReadOnlySpan2D<T>, Span2D<T>)

Parameters

Type Parameters

Usage Note

Remarks

Further Details:

TriangularMultiplyInPlace<T, TStorage2D>(ILinearAlgebraOperations<T>, MatrixOperationSide, MatrixTriangle, TransposeOperation, MatrixDiagonal, Int32, Int32, T, TStorage2D, TStorage2D)

Parameters

Type Parameters

Usage Note

See Also

Reference