◆ Polcof()

Sub Polcof	(	XX As	Double,
		N As	Long,
		X() As	Double,
		C() As	Double,
		D() As	Double,
		Info As	Long
	)

補間多項式の係数

目的: 本ルーチンはPolintにより生成された補間多項式の係数を求める.

引数

[in]	XX	XXのまわりでテイラー展開する.
[in]	N	データ点数. (Polintに入力したもの)
[in]	X()	配列 X(LX - 1) (LX >= N) データのx座標. (Polintに入力したもの)
[in]	C()	配列 C(LC - 1) (LC >= N) 補間多項式情報. (Polintが生成したもの)
[out]	D()	配列 D(LD - 1) (LD >= N) テイラー展開式の係数. P(Z) = D(0) + D(1)(Z-XX) +D(2)((Z-XX)^2) + ... + D(N-1)*((Z-XX)^(N-1))
[out]	Info	= 0: 正常終了. = -2: パラメータ N の誤り. (N < 1) = -3: パラメータ X() の誤り. = -4: パラメータ C() の誤り. = -5: パラメータ D() の誤り.

出典: SLATEC

使用例

次の自然対数表を補間して補間多項式を求め, それを使ってln(0.115)およびln(0.125)を求める.

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

Sub Ex_Polcof()
    Const N As Long = 4
    Dim X(N - 1) As Double, Y(N - 1) As Double, C(N - 1) As Double, D(N - 1) As Double
    Dim Xe As Double, XX As Double, 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 coefficients of polynomial
    XX = 0.12
    Call Polcof(XX, N, X(), C(), D(), Info)
    Debug.Print D(0), D(1), D(2), D(3)
    '-- Compute ln(0.115) and ln(0.125)
    Xe = 0.115
    Debug.Print "ln(" + CStr(Xe) + ") =", D(0) + D(1) * (Xe - XX) + D(2) * ((Xe - XX) ^ 2) + D(3) * ((Xe - XX) ^ 3)
    Xe = 0.125
    Debug.Print "ln(" + CStr(Xe) + ") =", D(0) + D(1) * (Xe - XX) + D(2) * ((Xe - XX) ^ 2) + D(3) * ((Xe - XX) ^ 3)
    Debug.Print "Info =", Info
End Sub

実行結果: -2.1203 8.33166666666668 -34.5000000000022 233.333333333222

ln(0.115) = -2.16285

ln(0.125) = -2.079475

Info = 0