◆ Pchse()

Sub Pchse	(	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 spline interpolation ("not a knot" condition)

Purpose: This routine computes the derivatives needed to determine the Hermite representation of the cubic spline interpolant to given data, with with the default boundary conditions ("not a knot" condition).

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

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) Dependent variable values to be interpolated. F(Idxfd + IIncfd) is the value corresponding to X(I) (I = 0 to N - 1).
[out]	D()	Array D(LD - 1) (LD >= Incfd(N - 1) + 1) Derivative values at the data points. These values will determine the cubic spline interpolant with the requested boundary conditions. The value corresponding to X(I) is stored in D(Idxfd + IIncfd) (I = 0 to N - 1). No other entries in D() are changed.
[out]	Info	= 0: Successful exit. = -1: The argument N had an illegal value. (N < 2) = -2: The argument X() is invalid or 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)
[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(). This argument is provided primarily for 2-D applications. (Incfd >= 1) (default = 1)

Reference: SLATEC (PCHIP) (Driver for PCHSP)

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_Pchse()
    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
    '-- 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
    '-- Spline interpolation
    Call Pchse(N, X(), Y(), D(), Info)
    If Info <> 0 Then
        Debug.Print "Error in Pchse: 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) = -2.16285

ln(0.125) = -2.079475

Info = 0