◆ Bsplpp()

Sub Bsplpp	(	T() As	Double,
		A() As	Double,
		N As	Long,
		K As	Long,
		C() As	Double,
		Xi() As	Double,
		Lxi As	Long,
		Info As	Long
	)

B-representation to PP (piecewise polynomial) form of B-spline conversion

Purpose: This routine converts the B-representation (T(), A(), N, K) of a B-spline to the PP (piecewise polynomial) form (C(), Xi(), Lxi, K) for use with Ppvalu. Here Xi(), the break point array of length Lxi, is the knot array T() with multiplicities removed. The columns of the matrix C(i,j) contain the right Taylor derivatives for the polynomial expansion about Xi(j) for the intervals Xi(j) <= X <= Xi(j+1), i = 0 to k-1, j = 0 to Lxi-1.
Function Ppvalu evaluates the PP form at a specified point X in Xi(0) <= X <= Xi(Lxi).

Parameters

[in]	T()	Array T(LT - 1) (LT >= N + K) Knot vector.
[in]	A()	Array A(LA - 1) (LA >= N) B-spline coefficient array.
[in]	N	Number of B-spline coefficients. (N = sum of knot multiplicities - K)
[in]	K	Order of the B-spline. (K >= 1)
[out]	C()	Array C(LC1 - 1, LC2 - 1) (LC1 >= K, LC2 >= Lxi) Right derivatives at break points.
[out]	Xi()	Array Xi(LXi - 1) (LXi >= Lxi + 1) Break points.
[out]	Lxi	Number of polynomial pieces. (Lxi <= N - K + 1)
[out]	Info	= 0: Successful exit. = -1: The argument T() is invalid. = -2: The argument A() is invalid. = -3: The argument N had an illegal value. (N < K) = -4: The argument K had an illegal value. (K < 1) = -5: The argument C() is invalid. = -6: The argument Xi() is invalid.

Reference: SLATEC

Example Program

Compute the interpolation of the following natural logarithm table with B-representation of the cubic spline using Bint4. After converting its coefficients to PP form, compute the interpolated value of ln(0.115).

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

Sub Ex_Bsplpp()
    Const Ndata = 4
    Dim X(Ndata - 1) As Double, Y(Ndata - 1) As Double, Xe As Double
    Dim Ibcl As Long, Ibcr As Long, Fbcl As Double, Fbcr As Double, Kntopt As Long
    Dim T(Ndata + 5) As Double, Bcoef(Ndata + 1) As Double, N As Long, K As Long
    Dim Lxi As Long, C(3, Ndata - 2) As Double, Xi(Ndata - 1) As Double
    Dim Ideriv As Long, Inppv As Long, Info 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
    Ibcl = 2: Fbcl = 0: Ibcr = 2: Fbcr = 0 '-- Natural spline
    Kntopt = 1
    Call Bint4(X(), Y(), Ndata, Ibcl, Ibcr, Fbcl, Fbcr, Kntopt, T(), Bcoef(), N, K, Info)
    If Info <> 0 Then
        Debug.Print "Error in Bint4: Info =", Info
        Exit Sub
    End If
    '-- Convert to PP form
    Call Bsplpp(T(), Bcoef(), N, K, C(), Xi(), Lxi, Info)
    If Info <> 0 Then
        Debug.Print "Error in Bsplpp: Info =", Info
        Exit Sub
    End If
    '-- Compute interpolated value
    Ideriv = 0: Inppv = 1
    Xe = 0.115
    Debug.Print "ln(" + CStr(Xe) + ") =", Ppvalu(C(), Xi(), Lxi, K, Ideriv, Xe, Inppv, Info)
    Debug.Print "Info =", Info
End Sub

Example Results: ln(0.115) = -2.16266

Info = 0