Chfdv Chfev Pchbs Pchcm Pchfd Pchfe Pchic Pchim Pchse Pchsp

Pchbs() Sub Pchbs ( N As  Long, X() As  Double, F() As  Double, D() As  Double, Knotyp As  Long, Nknots As  Long, T() As  Double, Bcoef() As  Double, Ndim As  Long, Kord As  Long, Info As  Long, Optional Idxfd As  Long = 0, Optional Incfd As  Long = 1  ) Piecewise cubic Hermite to B-spline conversion Purpose This routine computes the B-spline representation of the piecewise cubic Hermite function determined by N, X(), F() and D(). The output is the B-representation for the function: Nknots, T(), Bcoef(), Ndim and Kord. Since it is assumed that the input piecewise cubic Hermite function has been computed by one of the other routines in the package, input arguments N, X(), Incfd are not completely checked for validity. Restrictions and assumptions are: N >= 2 (error return if not) X(i) < X(i+1), i = 0 to n-1 (not checked) Incfd > 0 (error return if not) Knotyp <= 2 (error return if not) (*) Nknots = Ndim + 4 = 2*N + 4 (error return if not) (*) T(2*k + 1) = T(2*k) = X(k), k = 0 to n-1 (not checked) (*): indicates this applies only if Knotyp < 0. Parameters [in] N Number of data points (N >= 2) [in] X() Array X(LX - 1) (LX >= N) Independent variable values. The elements of X() must be strictly increasing. [in] F() Array F(LF - 1) (LF >= Incfd*(N - 1) + 1) Function values. F(Idxfd + I*Incfd) is the value corresponding to X(I) (I = 0 to N - 1). [in] D() Array D(LD - 1) (LD >= Incfd*(N - 1) + 1) Derivative values. D(Idxfd + I*Incfd) is the value corresponding to X(I) (I = 0 to N - 1). [in] Knotyp Flag to control the knot sequence. The knot sequence T() is normally computed from X by putting a double knot at each X and setting the end knot pairs according to the value of Knotyp. = 0: Quadruple knots at X(0) and X(N-1) = 1: Replicate lengths of extreme subintervals:   T(0) = T(1) = X(0) - (X(1) - X(0))   T(M + 3) = T(M + 2) = X(N - 1) + (X(N - 1) - X(N - 2)) = 2: Periodic placement of boundary knots:   T(0) = T(1) = X(0) - (X(N - 1) - X(N - 2))   T(M + 3) = T(M + 2) = X(N - 1) + (X(1) - X(0)) Here M = Ndim = 2 * N. If the input value of Knotyp is negative, however, it is assumed that Nknots and T() were set in a previous call. This option is provided for improved efficiency when used in a parametric setting. [in,out] Nknots Number of knots. [in] When Knotyp < 0: Nknots is an input variable, and an error return will be taken if it is not equal to Ndim + 4. [out] When Knotyp >= 0: Nknots will be set to Ndim + 4. [in,out] T() Array T(LT - 1) (LT >= 2 * N + 4) Knots for the B-representation. [in] When Knotyp < 0: It is assumed that T() was set by a previous call to Pchbs (This routine does not verify that T() forms a legitimate knot sequence). [out] When Knotyp >= 0: T() will be returned by Pchbs with the interior double knots equal to the X-values and the boundary knots set as indicated above. [out] Bcoef() Array Bcoef(LBcoef - 1) (LBcoef >= 2 * N) B-spline coefficients. [out] Ndim Dimension of the B-spline space (to be set to 2 * N). [out] Kord Order of the B-spline (to be set to 4). [out] Info = 0: Successful exit. = -1: The argument N had an illegal value. (N < 2) = -2: The argument X() is invalid. = -3: The argument F() is invalid. = -4: The argument D() is invalid. = -5: The argument Knotyp had an illegal value. (Knotyp > 2) = -6: The argument Nknots had an illegal value. (Nknots <> 2*N+4 when Knotyp < 0) = -7: The argument T() is invalid. = -8: The argument Bcoef() is invalid. = -13: The argument Incfd had an illegal value. (Incfd < 1) [in] Idxfd (Optional) Index of the first data in F() and D(). (default = 0) [in] Incfd (Optional) Increment between successive values in F() and D(). (Incfd >= 1) (default = 1) Reference SLATEC (PCHIP) Example Program Compute the B-spline representation of the piecewise cubic Hermite interpolation of the following natural logarithm table. x ln(x) ------ --------- 0.10 -2.3026 0.11 -2.2073 0.12 -2.1203 0.13 -2.0402 ------ --------- Sub Ex_Pchbs() Const N = 4, Ne = 2 Dim X(N - 1) As Double, Y(N - 1) As Double, D(N - 1) As Double Dim Ic(1) As Long, Vc(1) As Double Dim Knotyp As Long, Nknots As Long, T(2 * N + 3) As Double, Bcoef(2 * N - 1) As Double Dim Ndim As Long, Kord As Long Dim 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 '-- Cubic Hermite interpolation Ic(0) = 1: Ic(1) = 1 Vc(0) = 1 / X(0): Vc(1) = 1 / X(3) Call Pchic(Ic(), Vc(), 0, N, X(), Y(), D(), Info) If Info <> 0 Then Debug.Print "Error in Pchic: Info =", Info Exit Sub End If '-- Convert to B-spline Knotyp = 0 Call Pchbs(N, X(), Y(), D(), Knotyp, Nknots, T(), Bcoef(), Ndim, Kord, Info) Debug.Print "Info =", Info End Sub