LinearAlgebraOperationsExtensions.BandTriangularSolveInPlace Method

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

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

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

[<ExtensionAttribute>]
static member BandTriangularSolveInPlace : 
        operations : ILinearAlgebraOperations<'T> * 
        uplo : MatrixTriangle * 
        trans : TransposeOperation * 
        diag : MatrixDiagonal * 
        n : int * 
        k : 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.
            

k  Int32

             On entry with UPLO = 'U' or 'u', K specifies the number of
             super-diagonals of the matrix A.
             On entry with UPLO = 'L' or 'l', K specifies the number of
             sub-diagonals of the matrix A.
             K must satisfy  0 .le. K.
            

a  ReadOnlySpan2D<T>

            A is DOUBLE PRECISION array of DIMENSION ( LDA, n ).
             Before entry with UPLO = 'U' or 'u', the leading ( k + 1 )
             by n part of the array A must contain the upper triangular
             band part of the matrix of coefficients, supplied column by
             column, with the leading diagonal of the matrix in row
             ( k + 1 ) of the array, the first super-diagonal starting at
             position 2 in row k, and so on. The top left k by k triangle
             of the array A is not referenced.
             The following program segment will transfer an upper
             triangular band matrix from conventional full matrix storage
             to band storage:
                   DO 20, J = 1, N
                      M = K + 1 - J
                      DO 10, I = MAX( 1, J - K ), J
                         A( M + I, J ) = matrix( I, J )
                10    CONTINUE
                20 CONTINUE
             Before entry with UPLO = 'L' or 'l', the leading ( k + 1 )
             by n part of the array A must contain the lower triangular
             band part of the matrix of coefficients, supplied column by
             column, with the leading diagonal of the matrix in row 1 of
             the array, the first sub-diagonal starting at position 1 in
             row 2, and so on. The bottom right k by k triangle of the
             array A is not referenced.
             The following program segment will transfer a lower
             triangular band matrix from conventional full matrix storage
             to band storage:
                   DO 20, J = 1, N
                      M = 1 - J
                      DO 10, I = J, MIN( N, J + K )
                         A( M + I, J ) = matrix( I, J )
                10    CONTINUE
                20 CONTINUE
             Note that when DIAG = 'U' or 'u' the elements of the array A
             corresponding to the diagonal elements of the matrix are not
             referenced, 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
             ( k + 1 ).
            

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.
            

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.
            

Further Details:

            Level 2 LinearAlgebra routine.
            -- 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

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

<ExtensionAttribute>
Public Shared Sub BandTriangularSolveInPlace(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,
	k 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 BandTriangularSolveInPlace(
	ILinearAlgebraOperations<T>^ operations, 
	MatrixTriangle storedTriangle, 
	TransposeOperation transposeOperation, 
	MatrixDiagonal diagonal, 
	int n, 
	int k, 
	TStorage2D a, 
	TStorage x
)

[<ExtensionAttribute>]
static member BandTriangularSolveInPlace : 
        operations : ILinearAlgebraOperations<'T> * 
        storedTriangle : MatrixTriangle * 
        transposeOperation : TransposeOperation * 
        diagonal : MatrixDiagonal * 
        n : int * 
        k : 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.

k  Int32

The bandwidth of 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 DTBSV.

Reference