◆ Polint()

Sub Polint	(	N As	Long,
		X() As	Double,
		Y() As	Double,
		C() As	Double,
		Info As	Long
	)

Polynomial interpolation

Purpose: This routine produces a polynomial which interpolates a set of discrete data points. Polint sets up information in the array c[] which can be used by subroutine Polyvl to evaluate the polynomial and its derivatives and by subroutine Polcof to produce the coefficients.

Parameters

[in]	N	The number of data points. (N >= 1)
[in]	X()	Array X(LX - 1) (LX >= N) The array of abscissas. (All of which must be distinct)
[in]	Y()	Array Y(LY - 1) (LY >= N) The array of ordinates.
[out]	C()	Array C(LC - 1) (LC >= N) An array of information used by subroutines Polyvl and Polcof.
[out]	Info	= 0: Successful exit. = -1: The argument N had an illegal value. (N <= 0) = -2: The argument X() is invalid. = -3: The argument Y() is invalid. = -4: The argument C() is invalid. = 1: The abscissas are not distinct.

Reference: SLATEC

Example Program

Compute ln(0.115) and its derivative ln'(0.115) by interpolating 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_Polint()
    Const N As Long = 4
    Dim X(N - 1) As Double, Y(N - 1) As Double, C(N - 1) As Double
    Dim Xe As Double, Ye As Double, Yep(0) 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
    '-- Polynomial interpolation
    Call Polint(N, X(), Y(), C(), Info)
    If Info <> 0 Then
        Debug.Print "Error in Polint: Info =", Info
        Exit Sub
    End If
    '-- Compute interpolated values
    Xe = 0.115
    Call Polyvl(1, Xe, Ye, Yep(), N, X(), C(), Info)
    Debug.Print "ln(" + CStr(Xe) + ") =", Ye
    Debug.Print "ln'(" + CStr(Xe) + ") =", Yep(0)
    Debug.Print "Info =", Info
End Sub

Example Results: ln(0.115) = -2.16285

ln'(0.115) = 8.69416666666669

Info = 0