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

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

abstract BandTriangularSolveInPlace : 
        storedTriangle : MatrixTriangle * 
        trans : TransposeOperation * 
        diag : MatrixDiagonal * 
        n : int * 
        k : int * 
        a : Array2D<Complex<float32>> * 
        x : ArraySlice<Complex<float32>> -> unit 
override BandTriangularSolveInPlace : 
        storedTriangle : MatrixTriangle * 
        trans : TransposeOperation * 
        diag : MatrixDiagonal * 
        n : int * 
        k : int * 
        a : Array2D<Complex<float32>> * 
        x : ArraySlice<Complex<float32>> -> unit 

Parameters

storedTriangle

Type: Extreme.MathematicsMatrixTriangle

             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

Type: Extreme.MathematicsTransposeOperation

             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

Type: Extreme.MathematicsMatrixDiagonal

             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

Type: SystemInt32

             On entry, N specifies the order of the matrix A.
             N must be at least zero.
            

k

Type: SystemInt32

             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

Type: Extreme.CollectionsArray2DComplexSingle

            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

Type: Extreme.CollectionsArraySliceComplexSingle

            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.

Numerical Libraries

Reference