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

Bsplvd() Sub Bsplvd ( T() As  Double, K As  Long, Nderiv As  Long, X As  Double, Ileft As  Long, Vnikx() As  Double, Info As  Long  ) Compute the value and the derivatives of B-spline basis functions Purpose This routine computes the value and all derivatives of order less than Nderiv of all basis functions which do not (possibly) vanish at X. 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) The output of Bsplvd is an array Vnikx(i,j) of dimension at least K x Nderiv whose columns contain the K nonzero basis functions and their Nderiv-1 right derivatives at X, i = 0 to K-1, j = 0 to Nderiv-1. These basis functions have indices Ileft-K+i, i = 1 to K, K <= Ileft <= N. The nonzero part of the i-th basis function lies in (T(i), T(i+K)), i = 0 to N-1). If X = T(Ileft) then Vnikx contains left limiting values (left derivatives) at T(Ileft). In particular, Ileft = N produces left limiting values at the right end point X = T(N). To obtain left limiting values at T(i), i = K to N, set X = next lower distinct knot, call Interv to get Ileft, set X = T(i), and then call 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] K Order of the B-spline. (K >= 1) [in] Nderiv Number of derivatives + 1. (1 <= Nderiv <= K) [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(LVnikx1 - 1, LVnikx2 - 1) (LVnikx1 >= K, Lvnikx2 >= Nderiv) Matrix containing the nonzero basis functions at X and their derivatives columnwise. [out] Info = 0: Successful exit. = -1: The argument T() is invalid. = -2: The argument K had an illegal value. (K < 1) = -3: The argument Nderiv had an illegal value. (Nderiv < 1 or Nderiv > K) = -6: 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 Bsplvd and then compute the interpolated value of ln(0.115) and its derivative ln'(0.115). x ln(x) ------ --------- 0.10 -2.3026 0.11 -2.2073 0.12 -2.1203 0.13 -2.0402 ------ --------- Sub Ex_Bsplvd() 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, Df As Double Dim Nderiv As Long, 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 Bsplvd Xe = 0.115 Ilo = 1 Call Interv(T(), N + K, Xe, Ilo, Ileft, Info) If Ileft > N Then Ileft = N Nderiv = 2 ReDim Vnikx(K - 1, Nderiv - 1) Call Bsplvd(T(), K, Nderiv, Xe, Ileft, Vnikx(), Info) If Info <> 0 Then Debug.Print "Error in Bsplvd: Info =", Info Exit Sub End If '-- Compute interpolated value F = 0: Df = 0 For I = 0 To K - 1 F = F + Bcoef(Ileft - K + I) * Vnikx(I, 0) Df = Df + Bcoef(Ileft - K + I) * Vnikx(I, 1) Next Debug.Print "ln(" + CStr(Xe) + ") =", F, "ln'(" + CStr(Xe) + ") =", Df Debug.Print "Info =", Info End Sub Example Results ln(0.115) = -2.16266 ln'(0.115) = 8.68833333333335 Info = 0