DecompositionOperations<TReal, TComplex>.BandTriangularSolve Method

public void BandTriangularSolve(
	MatrixTriangle storedTriangle,
	TransposeOperation trans,
	MatrixDiagonal diag,
	int n,
	int kd,
	int nrhs,
	Array2D<TReal> ab,
	Array2D<TReal> b,
	out int info
)

Public Sub BandTriangularSolve ( 
	storedTriangle As MatrixTriangle,
	trans As TransposeOperation,
	diag As MatrixDiagonal,
	n As Integer,
	kd As Integer,
	nrhs As Integer,
	ab As Array2D(Of TReal),
	b As Array2D(Of TReal),
	<OutAttribute> ByRef info As Integer
)

public:
void BandTriangularSolve(
	MatrixTriangle storedTriangle, 
	TransposeOperation trans, 
	MatrixDiagonal diag, 
	int n, 
	int kd, 
	int nrhs, 
	Array2D<TReal> ab, 
	Array2D<TReal> b, 
	[OutAttribute] int% info
)

member BandTriangularSolve : 
        storedTriangle : MatrixTriangle * 
        trans : TransposeOperation * 
        diag : MatrixDiagonal * 
        n : int * 
        kd : int * 
        nrhs : int * 
        ab : Array2D<'TReal> * 
        b : Array2D<'TReal> * 
        info : int byref -> unit 

Parameters

storedTriangle  MatrixTriangle

            = 'U':  A is upper triangular;
            = 'L':  A is lower triangular.
            

trans  TransposeOperation

            Specifies the form the system of equations:
            = 'N':  A * X = B  (No transpose)
            = 'T':  AT * X = B  (Transpose)
            = 'C':  AH * X = B  (Conjugate transpose = Transpose)
            

diag  MatrixDiagonal

            = 'N':  A is non-unit triangular;
            = 'U':  A is unit triangular.
            

n  Int32

            The order of the matrix A.  N >= 0.
            

kd  Int32

            The number of superdiagonals or subdiagonals of the
            triangular band matrix A.  KD >= 0.
            

nrhs  Int32

            The number of right hand sides, i.e., the number of columns
            of the matrix B.  NRHS >= 0.
            

ab  Array2D<TReal>

            AB is TReal array, dimension (LDAB,N)
            The upper or lower triangular band matrix A, stored in the
            first kd+1 rows of AB.  The j-th column of A is stored
            in the j-th column of the array AB as follows:
            if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
            if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).
            If DIAG = 'U', the diagonal elements of A are not referenced
            and are assumed to be 1.
            

            The leading dimension of the array AB.  LDAB >= KD+1.
            

b  Array2D<TReal>

            B is TReal array, dimension (LDB,NRHS)
            On entry, the right hand side matrix B.
            On exit, if INFO = 0, the solution matrix X.
            

            The leading dimension of the array B.  LDB >= max(1,N).
            

info  Int32

            = 0:  successful exit
            < 0:  if INFO = -i, the i-th argument had an illegal value
            > 0:  if INFO = i, the i-th diagonal element of A is zero,
                  indicating that the matrix is singular and the
                  solutions X have not been computed.
            

            A check is made to verify that A is nonsingular.
            

This method corresponds to the LAPACK routine ?TBTRS.

public void BandTriangularSolve(
	MatrixTriangle storedTriangle,
	TransposeOperation trans,
	MatrixDiagonal diag,
	int n,
	int kd,
	int nrhs,
	ReadOnlySpan2D<TReal> ab,
	Span2D<TReal> b,
	out int info
)

Public Sub BandTriangularSolve ( 
	storedTriangle As MatrixTriangle,
	trans As TransposeOperation,
	diag As MatrixDiagonal,
	n As Integer,
	kd As Integer,
	nrhs As Integer,
	ab As ReadOnlySpan2D(Of TReal),
	b As Span2D(Of TReal),
	<OutAttribute> ByRef info As Integer
)

public:
void BandTriangularSolve(
	MatrixTriangle storedTriangle, 
	TransposeOperation trans, 
	MatrixDiagonal diag, 
	int n, 
	int kd, 
	int nrhs, 
	ReadOnlySpan2D<TReal> ab, 
	Span2D<TReal> b, 
	[OutAttribute] int% info
)

member BandTriangularSolve : 
        storedTriangle : MatrixTriangle * 
        trans : TransposeOperation * 
        diag : MatrixDiagonal * 
        n : int * 
        kd : int * 
        nrhs : int * 
        ab : ReadOnlySpan2D<'TReal> * 
        b : Span2D<'TReal> * 
        info : int byref -> unit 

Parameters

storedTriangle  MatrixTriangle

            = 'U':  A is upper triangular;
            = 'L':  A is lower triangular.
            

trans  TransposeOperation

            Specifies the form the system of equations:
            = 'N':  A * X = B  (No transpose)
            = 'T':  AT * X = B  (Transpose)
            = 'C':  AH * X = B  (Conjugate transpose = Transpose)
            

diag  MatrixDiagonal

            = 'N':  A is non-unit triangular;
            = 'U':  A is unit triangular.
            

n  Int32

            The order of the matrix A.  N >= 0.
            

kd  Int32

            The number of superdiagonals or subdiagonals of the
            triangular band matrix A.  KD >= 0.
            

nrhs  Int32

            The number of right hand sides, i.e., the number of columns
            of the matrix B.  NRHS >= 0.
            

ab  ReadOnlySpan2D<TReal>

            AB is TReal array, dimension (LDAB,N)
            The upper or lower triangular band matrix A, stored in the
            first kd+1 rows of AB.  The j-th column of A is stored
            in the j-th column of the array AB as follows:
            if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
            if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).
            If DIAG = 'U', the diagonal elements of A are not referenced
            and are assumed to be 1.
            

            The leading dimension of the array AB.  LDAB >= KD+1.
            

b  Span2D<TReal>

            B is TReal array, dimension (LDB,NRHS)
            On entry, the right hand side matrix B.
            On exit, if INFO = 0, the solution matrix X.
            

            The leading dimension of the array B.  LDB >= max(1,N).
            

info  Int32

            = 0:  successful exit
            < 0:  if INFO = -i, the i-th argument had an illegal value
            > 0:  if INFO = i, the i-th diagonal element of A is zero,
                  indicating that the matrix is singular and the
                  solutions X have not been computed.
            

            A check is made to verify that A is nonsingular.
            

This method corresponds to the LAPACK routine ?TBTRS.

public abstract void BandTriangularSolve(
	MatrixTriangle storedTriangle,
	TransposeOperation trans,
	MatrixDiagonal diag,
	int n,
	int kd,
	int nrhs,
	ReadOnlySpan<TReal> ab,
	int ldab,
	Span<TReal> b,
	int ldb,
	out int info
)

Public MustOverride Sub BandTriangularSolve ( 
	storedTriangle As MatrixTriangle,
	trans As TransposeOperation,
	diag As MatrixDiagonal,
	n As Integer,
	kd As Integer,
	nrhs As Integer,
	ab As ReadOnlySpan(Of TReal),
	ldab As Integer,
	b As Span(Of TReal),
	ldb As Integer,
	<OutAttribute> ByRef info As Integer
)

public:
virtual void BandTriangularSolve(
	MatrixTriangle storedTriangle, 
	TransposeOperation trans, 
	MatrixDiagonal diag, 
	int n, 
	int kd, 
	int nrhs, 
	ReadOnlySpan<TReal> ab, 
	int ldab, 
	Span<TReal> b, 
	int ldb, 
	[OutAttribute] int% info
) abstract

abstract BandTriangularSolve : 
        storedTriangle : MatrixTriangle * 
        trans : TransposeOperation * 
        diag : MatrixDiagonal * 
        n : int * 
        kd : int * 
        nrhs : int * 
        ab : ReadOnlySpan<'TReal> * 
        ldab : int * 
        b : Span<'TReal> * 
        ldb : int * 
        info : int byref -> unit 

Parameters

storedTriangle  MatrixTriangle

            = 'U':  A is upper triangular;
            = 'L':  A is lower triangular.
            

trans  TransposeOperation

            Specifies the form the system of equations:
            = 'N':  A * X = B  (No transpose)
            = 'T':  AT * X = B  (Transpose)
            = 'C':  AH * X = B  (Conjugate transpose = Transpose)
            

diag  MatrixDiagonal

            = 'N':  A is non-unit triangular;
            = 'U':  A is unit triangular.
            

n  Int32

            The order of the matrix A.  N >= 0.
            

kd  Int32

            The number of superdiagonals or subdiagonals of the
            triangular band matrix A.  KD >= 0.
            

nrhs  Int32

            The number of right hand sides, i.e., the number of columns
            of the matrix B.  NRHS >= 0.
            

ab  ReadOnlySpan<TReal>

            AB is TReal array, dimension (LDAB,N)
            The upper or lower triangular band matrix A, stored in the
            first kd+1 rows of AB.  The j-th column of A is stored
            in the j-th column of the array AB as follows:
            if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
            if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).
            If DIAG = 'U', the diagonal elements of A are not referenced
            and are assumed to be 1.
            

ldab  Int32

            The leading dimension of the array AB.  LDAB >= KD+1.
            

b  Span<TReal>

            B is TReal array, dimension (LDB,NRHS)
            On entry, the right hand side matrix B.
            On exit, if INFO = 0, the solution matrix X.
            

ldb  Int32

            The leading dimension of the array B.  LDB >= max(1,N).
            

info  Int32

            = 0:  successful exit
            < 0:  if INFO = -i, the i-th argument had an illegal value
            > 0:  if INFO = i, the i-th diagonal element of A is zero,
                  indicating that the matrix is singular and the
                  solutions X have not been computed.
            

            A check is made to verify that A is nonsingular.
            

This method corresponds to the LAPACK routine ?TBTRS.

Reference