ManagedLinearAlgebraOperations.BandTriangularSolveInPlace Method

public override void BandTriangularSolveInPlace(
	MatrixTriangle storedTriangle,
	TransposeOperation trans,
	MatrixDiagonal diag,
	int n,
	int k,
	Array2D<Complex<double>> a,
	ArraySlice<Complex<double>> x
)

Public Overrides Sub BandTriangularSolveInPlace ( 
	storedTriangle As MatrixTriangle,
	trans As TransposeOperation,
	diag As MatrixDiagonal,
	n As Integer,
	k As Integer,
	a As Array2D(Of Complex(Of Double)),
	x As ArraySlice(Of Complex(Of Double))
)

public:
virtual void BandTriangularSolveInPlace(
	MatrixTriangle storedTriangle, 
	TransposeOperation trans, 
	MatrixDiagonal diag, 
	int n, 
	int k, 
	Array2D<Complex<double>> a, 
	ArraySlice<Complex<double>> x
) override

abstract BandTriangularSolveInPlace : 
        storedTriangle : MatrixTriangle * 
        trans : TransposeOperation * 
        diag : MatrixDiagonal * 
        n : int * 
        k : int * 
        a : Array2D<Complex<float>> * 
        x : ArraySlice<Complex<float>> -> unit 
override BandTriangularSolveInPlace : 
        storedTriangle : MatrixTriangle * 
        trans : TransposeOperation * 
        diag : MatrixDiagonal * 
        n : int * 
        k : int * 
        a : Array2D<Complex<float>> * 
        x : ArraySlice<Complex<float>> -> unit 

Parameters

storedTriangle  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'   AH*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  Array2D<Complex<Double>>

            A is COMPLEX*16 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  ArraySlice<Complex<Double>>

            X is COMPLEX*16 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.
            

Implements

            No test for singularity or near-singularity is included in this
            routine. Such tests must be performed before calling this routine.
            

This method is based on the BLAS routine ZTBSV.

public override void BandTriangularSolveInPlace(
	MatrixTriangle storedTriangle,
	TransposeOperation transA,
	MatrixDiagonal diag,
	int n,
	int k,
	Array2D<double> a,
	ArraySlice<double> x
)

Public Overrides Sub BandTriangularSolveInPlace ( 
	storedTriangle As MatrixTriangle,
	transA As TransposeOperation,
	diag As MatrixDiagonal,
	n As Integer,
	k As Integer,
	a As Array2D(Of Double),
	x As ArraySlice(Of Double)
)

public:
virtual void BandTriangularSolveInPlace(
	MatrixTriangle storedTriangle, 
	TransposeOperation transA, 
	MatrixDiagonal diag, 
	int n, 
	int k, 
	Array2D<double> a, 
	ArraySlice<double> x
) override

abstract BandTriangularSolveInPlace : 
        storedTriangle : MatrixTriangle * 
        transA : TransposeOperation * 
        diag : MatrixDiagonal * 
        n : int * 
        k : int * 
        a : Array2D<float> * 
        x : ArraySlice<float> -> unit 
override BandTriangularSolveInPlace : 
        storedTriangle : MatrixTriangle * 
        transA : TransposeOperation * 
        diag : MatrixDiagonal * 
        n : int * 
        k : int * 
        a : Array2D<float> * 
        x : ArraySlice<float> -> unit 

Parameters

storedTriangle  MatrixTriangle

Specifies whether the matrix is an upper or lower triangular matrix.

transA  TransposeOperation

Specifies the operation to be performed on the matrix a.

diag  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  Array2D<Double>

Reference to the first element in a one-dimensional array that contains the elements of the matrix.

x  ArraySlice<Double>

A reference to a one-dimensional array containing the elements of the vector x. The elements of x are overwritten with the result.

Implements

Reference