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

Bsplev() Sub Bsplev ( T() As  Double, Ad() As  Double, N As  Long, K As  Long, Nderiv As  Long, X As  Double, Inev As  Long, Svalue() As  Double, Info As  Long  ) Evaluation of function and derivative values for B-representation of B-spline Purpose This routine computes the value of the B-spline and its derivatives at X from the B-representation (T(), A(), N, K) and returns them in Svalue(i) (i = 0 to Nderiv-1), where T(K-1) <= X <= T(N). Ad(i) can be the B-spline coefficients A(i) (i = 0 to N-1) if Nderiv = 1. Otherwise Ad() must be computed beforehand by the following statement. Call Bspldr(T(), A(), N, K, Nderiv, Ad()) If X = T(i) (K-1 <= i <= N-1), right limiting values are obtained. To compute left derivatives or left limiting values at a knot T(i), replace N by i-1 and set X = T(i) (K <= i <= N). Parameters [in] T() Array T(LT - 1) (LT >= N + K) Knot vector. [in] Ad() Array Ad(LAd - 1) (LAd >= (2*N - Nderiv + 1)*Nderiv/2) Divided difference table. [in] N Number of B-spline coefficients. (N = sum of knot multiplicities - K) [in] K Order of the B-spline. (K >= 1) [in] Nderiv Number of the derivatives. (1 <= Nderiv <= K) Nderiv = 1 returns the zero-th derivative = function value. [in] X Argumrnt. (T(K-1) <= X <= T(N)) [in,out] Inev An initialization parameter. [in] Must be set to 1 when the first time Bsplev is called. [out] Information for efficient processing after the initial call and Inev must not be changed by the user. Distinct splines require distinct Inev parameters. [out] Svalue() Array Svalue(LSvalue - 1) (LSvalue >= Nderiv) The spline value in Svalue(0) and the Nderiv-1 derivatives in the remaining components. [out] Info = 0: Successful exit. = -1: The argument T() is invalid. = -2: The argument Ad() 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 Nderiv had an illegal value. (Nderiv < 1 or Nderiv > K) = -6: The argument X had an illegal value. (X < T(K-1) or X > T(N)) = -8: The argument Svalue() is invalid. = 1: A left limiting value cannot be obtained at T(K-1). Reference SLATEC Example Program Compute ln(0.115) and its derivative ln'(0.115) by interpolating the following natural logarithm table with B-representation of the cubic spline (natuaral spline). x ln(x) ------ --------- 0.10 -2.3026 0.11 -2.2073 0.12 -2.1203 0.13 -2.0402 ------ --------- Sub Ex_Bsplev() 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 Nderiv As Long, Ad() As Double Dim Inev As Long, Svalue() As Double, 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 '-- Prepare divided difference table for Bsplev Nderiv = K ReDim Ad((2 * N - Nderiv + 1) * Nderiv / 2 - 1) Call Bspldr(T(), Bcoef(), N, K, Nderiv, Ad(), Info) If Info <> 0 Then Debug.Print "Error in Bspldr: Info =", Info Exit Sub End If '-- Evaluate by Bsplev Xe = 0.115 Inev = 1 ReDim Svalue(Nderiv - 1) Call Bsplev(T(), Ad(), N, K, Nderiv, Xe, Inev, Svalue(), Info) If Info <> 0 Then Debug.Print "Error in Bsplev: Info =", Info Exit Sub End If Debug.Print "ln(" + CStr(Xe) + ") =", Svalue(0), "ln'(" + CStr(Xe) + ") =", Svalue(1) Debug.Print "Info =", Info End Sub Example Results ln(0.115) = -2.16266 ln'(0.115) = 8.68833333333335 Info = 0