◆ Pchim()

Sub Pchim	(	N As	Long,
		X() As	Double,
		F() As	Double,
		D() As	Double,
		Info As	Long,
		Optional Idxfd As	Long = `0`,
		Optional Incfd As	Long = `1`
	)

Piecewise cubic Hermite interpolation (default boundary conditions)

Purpose: This routine sets derivatives needed to determine a monotone piecewise cubic Hermite interpolant. Default boundary conditions are provided which are compatible with monotonicity. Use Pchic if user control of boundary conditions is desired.

The resulting piecewise cubic Hermite function may be evaluated by Pchfe or Pchfd.

Parameters

[in]	N	Number of data points. (N >= 2) If N = 2, simply does linear interpolation.
[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) Dependent variable values to be interpolated.
[out]	D()	Array D(LD - 1) (LD >= Incfd*(N - 1) + 1) Derivative values at the data points.
[out]	Info	= 0: Successful exit. = -1: The argument N had an illegal value. (N < 2) = -2: The argument X() had an illegal value. (X() is not strictly increasing) = -3: The argument F() is invalid. = -4: The argument D() is invalid. = -7: The argument Incfd had an illegal value. (Incfd < 1) = i > 0: i switches in the direction of monotonicity were detected.
[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 ln(0.115) and ln(0.125) by interpolating the following natural logarithm table with cubic spline.

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

Sub Ex_Pchim()
    Const N = 4, Ne = 2
    Dim X(N - 1) As Double, Y(N - 1) As Double, D(N - 1) As Double
    Dim Xe(Ne - 1) As Double, Ye(Ne - 1) As Double
    Dim 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
    '-- 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 Pchfe(N, X(), Y(), D(), Ne, Xe(), Ye(), Info)
    Debug.Print "ln(" + CStr(Xe(0)) + ") =", Ye(0)
    Debug.Print "ln(" + CStr(Xe(1)) + ") =", Ye(1)
    Debug.Print "Info =", Info
End Sub

Example Results: ln(0.115) = -2.16285581089825

ln(0.125) = -2.07940530745063

Info = 0