Banfac Banslv Bint4 Bintk Bspldr Bsplev Bsplpp Bsplvd Bsplvn Bvalue Interv Ppvalu

Bsplvn() Sub Bsplvn ( T() As  Double, Jhigh As  Long, K As  Long, Index As  Long, X As  Double, Ileft As  Long, Vnikx() As  Double, Info As  Long  ) Compute the value of B-spline basis functions Purpose This routine computes the value of all (possibly) nonzero basis functions at X of order max(Jhigh, (j+1)*(Index-1)), where T(K-1) <= X <= T(N) and j = iwork is set to 1 inside the routine on the first call when Index = 1. Ileft is input such that T(Ileft-1) <= X <= T(Ileft). The following statement produces the proper Ileft. Call Interv(T(), N + 1, X, Ilo, Ileft, Info)\n Bsplvn computes using the basic algorithm needed in Bsplvd. If only basis functions are desired, setting jhigh = K and index = 1 can be faster than calling Bsplvd. But extra coding is required for derivatives (Index = 2) and Bsplvd is set up for this purpose. Left limiting values are set up as described in Bsplvd. Parameters [in] T() Array T(LT - 1) (LT >= N + K) Knot vector of length N + K, where N is number of B-spline basis functions (= sum of knot multiplicities - K). [in] Jhigh Order of B-spline to be computed. (1 <= Jhigh <= K) [in] K Highest possible order. (K >= 1) [in] Index = 1: The computation starts from scratch and the entire B-spline values of orders 1, 2, ..., Jhigh is generated order by order. = 2: Only the B-spline values of order j+1, j+2, ..., Jhigh are generated. The previous entry for order j have to be saved. [in] X Argument of basis functions. (T(K - 1) <= X <= T(N)) [in] Ileft Integer such that T(Ileft - 1) <= X <= T(Ileft). [out] Vnikx() Array Vnikx(LVnikx - 1) (LVnikx >= K) Values of basis functions. [out] Info = 0: Successful exit. = -1: The argument T() is invalid. = -2: The argument Jhigh had an illegal value. (Jhigh < 1 or Jhigh > K) = -3: The argument K had an illegal value. (K < 1) = -4: The argument Index had an illegal value. (Index <> 1 and Index <> 2) = -7: The argument Vnikx() is invalid. = 1: Ileft is not properly set. (X < T(Ileft-1) or X > T(Ileft)) Reference SLATEC Example Program Compute the interpolation of the following natural logarithm table with B-representation of the cubic spline using Bint4. Using its coefficients, compute the value of B-spline basis function by Bsplvn and then 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_Bsplvn() 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 Vnikx() As Double, F As Double Dim Ilo As Long, Ileft 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 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 '-- Compute basis function values by Bsplvn Xe = 0.115 Ilo = 1 Call Interv(T(), N + K, Xe, Ilo, Ileft, Info) If Ileft > N Then Ileft = N ReDim Vnikx(K - 1) Call Bsplvn(T(), K, K, 1, Xe, Ileft, Vnikx(), Info) If Info <> 0 Then Debug.Print "Error in Bsplvn: Info =", Info Exit Sub End If '-- Compute interpolated value F = 0 For I = 0 To K - 1 F = F + Bcoef(Ileft - K + I) * Vnikx(I) Next Debug.Print "ln(" + CStr(Xe) + ") =", F Debug.Print "Info =", Info End Sub Example Results ln(0.115) = -2.16266 Info = 0