LinearAlgebraOperationsExtensions.TriangularSolveInPlace Method

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

<ExtensionAttribute>
Public Shared Sub TriangularSolveInPlace(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)
)

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

[<ExtensionAttribute>]
static member TriangularSolveInPlace : 
        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 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  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 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.
            

Type Parameters

T

Usage Note

            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

public static void TriangularSolveInPlace<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>

<ExtensionAttribute>
Public Shared Sub TriangularSolveInPlace(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
)

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

[<ExtensionAttribute>]
static member TriangularSolveInPlace : 
        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

This method is similar to the BLAS routine DTRSV.

public static void TriangularSolveInPlace<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
)

<ExtensionAttribute>
Public Shared Sub TriangularSolveInPlace(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)
)

public:
[ExtensionAttribute]
generic<typename T>
static void TriangularSolveInPlace(
	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 TriangularSolveInPlace : 
        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 ) 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  ReadOnlySpan2D<T>

            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 ).
            

Type Parameters

T

Usage Note

            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

public static void TriangularSolveInPlace<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>

<ExtensionAttribute>
Public Shared Sub TriangularSolveInPlace(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
)

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

[<ExtensionAttribute>]
static member TriangularSolveInPlace : 
        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 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

Usage Note

Reference