◆ Bintk()

Sub Bintk	(	X() As	Double,
		Y() As	Double,
		T() As	Double,
		N As	Long,
		K As	Long,
		Bcoef() As	Double,
		Q() As	Double,
		Info As	Long
	)

B-representation of the spline interpolation of order k

Purpose: This routine computes the B-representation (T(), Bcoef(), N, K) of the spline of order k which interpolates given data. The spline or any of its derivatives can be evaluated by calls to Bvalu.

Parameters

[in]	X()	Array X(LX - 1) (LX >= Ndata) X vector of abscissae, distinct and in increasing order.
[in]	Y()	Array Y(LY - 1) (LY >= Ndata) Y vector of ordinates.
[in]	T()	Array T(LT - 1) (LT >= N + K) Knot vector. Since T(0), ..., T(K-1) <= X(0) and T(N), ..., T(N+K-1) >= X(N-1), this leaves only N-K knots (not necessarily X(i) values) interior to [X(0), X(N-1)].
[in]	N	Number of data points. (N >= K)
[in]	K	Order of the spline. (K >= 1)
[out]	Bcoef()	Array Bcoef(LBcoef - 1) (LBcoef >= N) B-spline coefficient array.
[out]	Q()	Array Q(LQ - 1) (LQ >= (2K - 1)N) Triangular factorization of the coefficient matrix of the linear system being solved. The coefficients for the interpolant of an additional data set (X(i), YY(i)) (i = 1 to N) with the same abscissa can be obtained by loading YY() into Bcoef() and then executing the following statement. Call Banslv(N, K - 1, K - 1, Q(), Bcoef())
[out]	Info	= 0: Successful exit. = -1: The argument X() had an illegal value. (not distinct or not in increasing ordered) = -2: The argument Y() is invalid. = -3: The argument T() is invalid. = -4: The argument N had an illegal value. (N < K) = -5: The argument K had an illegal value. (K < 1) = -6: The argument Bcoef() is invalid. = -7: The argument Q() is invalid. = 1: Some abscissa was not in the support of the corresponding basis function and the system is singular. = 2: The system of solver detects a singular system although the theoretical conditions for a solution were satisfied.

Reference: SLATEC

Example Program

Compute ln(0.115) by interpolating the following natural logarithm table with B-representation of the cubic spline.

  x       ln(x)
------ ---------
 0.10   -2.3026
 0.11   -2.2073
 0.12   -2.1203
 0.13   -2.0402
------ ---------

Sub Ex_Bintk()
    Const N = 4, K = 4
    Dim X(N - 1) As Double, Y(N - 1) As Double, Xe As Double
    Dim T(N + K - 1) As Double, Bcoef(N - 1) As Double, Q((2 * K - 1) * N - 1) As Double
    Dim Ideriv As Long, Inbv As Long, Info As Long, I As Long
    '-- Data
    X(0) = 0.1: Y(0) = -2.3026
    X(1) = 0.11: Y(1) = -2.2073
    X(2) = 0.12: Y(2) = -2.1203
    X(3) = 0.13: Y(3) = -2.0402
    '-- B-representation of cubic spline interpolation of order k
    For I = 0 To N - K + 1
        T(I + K - 1) = X(0) + I * (X(N - 1) - X(0)) / (N - K + 1)
    Next
    T(0) = T(3): T(1) = T(3): T(2) = T(3)
    T(7) = T(4): T(6) = T(4): T(5) = T(4)
    Call Bintk(X(), Y(), T(), N, K, Bcoef(), Q(), Info)
    If Info <> 0 Then
        Debug.Print "Error in Bintk: Info =", Info
        Exit Sub
    End If
    '-- Compute interpolated value
    Ideriv = 0: Inbv = 1
    Xe = 0.115
    Debug.Print "ln(" + CStr(Xe) + ") =", Bvalue(T(), Bcoef(), N, K, Ideriv, Xe, Inbv, Info)
    Debug.Print "Info =", Info
End Sub

Example Results: ln(0.115) = -2.16285

Info = 0