◆ Chfev()

Sub Chfev	(	X1 As	Double,
		X2 As	Double,
		F1 As	Double,
		F2 As	Double,
		D1 As	Double,
		D2 As	Double,
		Ne As	Long,
		Xe() As	Double,
		Fe() As	Double,
		Nex() As	Long,
		Info As	Long
	)

Cubic Hermite function values

Purpose: This routine evaluates a cubic polynomial given in Hermite form at an array of points, i.e. evaluates the cubic polynomial determined by function values f1, f2 and derivatives d1, d2 on interval [x1, x2] at the points Xe(j), j = 1 to Ne.

While designed for use by Pchfe, it may be useful directly as an evaluator for a piecewise cubic Hermite function in applications, such as graphing, where the interval is known in advance.

Parameters

[in]	X1	Endpoint of interval of definition of cubic. (X1 <> X2)
[in]	X2	Endpoint of interval of definition of cubic. (X1 <> X2)
[in]	F1	Value of function at X1.
[in]	F2	Value of function at X2.
[in]	D1	Value of derivative at X1.
[in]	D2	Value of derivative at X2.
[in]	Ne	Number of evaluation points. (Ne >= 1)
[in]	Xe()	Array Xe(LXe - 1) (LXe >= Ne) Points at which the function is to be evaluated. If any of the Xe() are outside the interval [X1, X2], a warning error is returned in Nex().
[out]	Fe()	Array Fe(LFe - 1) (LFe >= Ne) Values of the cubic function defined by X1, X2, F1, F2, D1, D2 at the points Xe().
[out]	Nex()	Array Nex(LNex - 1) (LNex >= 2) Number of extrapolation points. Nex(0) = number of evaluation points to left of interval. Nex(1) = number of evaluation points to right of interval.
[out]	Info	= 0: Successful exit. = -2: The argument X2 had an illegal value. (X2 = X1) = -7: The argument Ne had an illegal value. (Ne < 1) = -8: The argument Xe() is invalid. = -9: The argument Fe() is invalid. = -10: The argument Nex() is invalid.

Reference: SLATEC (PCHIP)

Example Program

Compute cubic spline interpolation of the following natural logarithm table. And compute ln(0.115) and ln(0.125) by evaluating the cubic polynomial on the interval [0.11, 0.12]. Nex(1) = 1 indicates that these is a evaluation point to right of interval (0.125 is outside the interval).

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

Sub Ex_Chfev()
    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 Xe(Ne - 1) As Double, Ye(Ne - 1) As Double, Nex(1) 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
    Call Pchim(N, X(), Y(), D(), Info)
    If Info <> 0 Then
        Debug.Print "Error in Pchim: Info =", Info
        Exit Sub
    End If
    '-- Compute interpolated values
    Xe(0) = 0.115: Xe(1) = 0.125
    Call Chfev(X(1), X(2), Y(1), Y(2), D(1), D(2), Ne, Xe(), Ye(), Nex(), Info)
    Debug.Print "ln(" + CStr(Xe(0)) + ") =", Ye(0)
    Debug.Print "ln(" + CStr(Xe(1)) + ") =", Ye(1)
    Debug.Print "Info =", Info, "Nex(0) =", Nex(0), "Nex(1) =", Nex(1)
End Sub

Example Results: ln(0.115) = -2.16285581089825

ln(0.125) = -2.07935612210228

Info = 0 Nex(0) = 0 Nex(1) = 1