应用实例

function s=Newton(x,y,x0,nn)
%Newton插值，x与y为已知的插值点及其函数值
%x0为要求的插值点的x坐标值。nn为Newton插值多项式的阶数
nx=length(x);
ny=length(y);
if nx~=ny
	warning('矢量x与y的长度应该相同。')
	return
end
m=length(x0);
%按照公式，对要求的插值点x0的每个元素进行计算
for i=1:m
	t=0.0;
	j=1;
	yy=y;
	kk=j;
	%求各级均差
	while(kk<=nn)
		kk=kk+1;
		for k=kk:nx
			yy(k)=(yy(k)-yy(kk-1))/(x(k)-x(kk-1));
		end
	end
	%求差值结果
	t=yy(1);
	for k=2:nn
		u=1.0;
		jj=1;
		while(jj<k)
			u=u*(x0(i)-x(jj));
			jj=jj+1;
		end
		t=t+yy(k)*u;
	end
	s(i)=t;
end

function Draw(x,y,varargin)
switch nargin
case 2
   	plot(x,y);
   	saveas(gcf,'D:\temp1.bmp');
case 4
   	plot(x,y);
   	hold on
   	x0=varargin{1};
   	y0=varargin{2};
   	plot(x0,y0,'+');
   	saveas(gcf,'D:\temp2.bmp');
   	hold off
otherwise
   	error('参数个数错误。')
end

Imports System
Imports MathWorks.MATLAB.NET.Utility
Imports MathWorks.MATLAB.NET.Arrays
Imports Newton

Dim ntNewton As Newton.Newtonclass

Public Sub New()
	'此调用时Windows窗体设计器所必需的
	InitializeComponent()
	'在InitializeComponent()调用之后添加任何初始化
	ntNewton=New Newton.Newtonclass
End Sub

Private Sub btnAddX_Click(ByVal sender As System.Object, ByVal e As System.EventArgs)  _					Handles btnAddX.Click
    '将数据X输入到X列表框中
    lstDataX.Items.Add(txtDataX.Text)
    txtDataX.Clear()
End Sub
Private Sub btnAddY_Click(ByVal sender Ad System.Object, ByVal e As System.EventArgs)  _
Handles btnAddY.Click
    '将数据X输入到X列表框中
    lstDataY.Items.Add(txtDataY.Text)
    txtDataY.Clear()
End Sub

Dim intPoints As Integer
Dim intI as integer
Dim numDataX As MWNumericArray
Dim numDataY As MWNumericArray
Dim numPoints As MWNumericArray
Private Sub GetData()
    If lstDataX.Items.Count<>lstDataY.Items.Count Then
        MsgBox("给定的数据不配对，请检查数据。")
        Exit Sub
    End If
    intPoints=lstDataX.Items.Count
    Dim dblDataX() As Double=New Double(intPoints-1){}
    Dim dblDataY() As Double=New Double(intPoints-1){}
    '获得向量数据X和Y的值
    For intI=0 To lstDataX.Items.Count-1
        dblDataX(intI)=CDbl(lstDataX.Items(intI))
        dblDataY(intI)=CDbl(lstDataY.Items(intI))
    Next
    '将本地类型转换为MATLAB数据类型
    numDataX=New MWNumericArray(dblDataX)
    numDataY=New MWNumericArray(dblDataY)
End Sub

Private Sub btnPlot_Click(ByVal sender As System.Object, ByVal e As System.EventArgs)  _
      Handles btnPlot.Click
    '获取数据
    GetData()
    '绘给定数据的图形
    ntNewton.Draw(numDataX, numDataY)
    '在图片框中显示图形
    picGraph.ImageLocation="D:\temp1.bmp"
End Sub

Private Sub btnCompute_Click(ByVal sender As System.Object, ByVal e As System.EventArgs) _
      Handles btnCompute.Click
    Dim dblPosX As Double
    Dim intPolyNum As Integer
    Dim numPosX As MWNumericArray
    Dim numPosY As MWNumericArray
    '获取数据
    GetData()
    '获取插值点位置数据并转换为MATLAB数据类型
    dblPosX=CDbl(txtPosX.Text)
    numPosX=New MWNumericArray(dblPosX)
    '获取用于插值计算的多项式的阶次数据并
    '转换为MATLAB数据类型
    intPolyNum=CInt(txtPolyNum.Text)
    numPoints=New MWNumericArray(intPolyNum)
    '进行插值计算并指定数据类型
    numPosY=CType(ntNewton.Newton(numDataX,numDataY,numPosX,numPoints), _
      MWNumericArray)
    '转换数据类型并显示
    txtPosY.Text=CStr(CDbl(numPosY))
End Sub

Private Sub btnPlotPos_Click(ByVal sender As System.Object, ByVal e As System.EventArgs)  _					Handles btnPlotPos.Click
    Dim dblPosX As Double
    Dim dblPosY As Double
    Dim numPosX As MWNumericArray
    Dim numPosY As MWNumericArray
    '获取数据
    GetData()
    '获取插值点位置数据并转换为MATLAB数据类型
    dblPosX=CDbl(txtPosX.Text)
    numPosX=New MWNumericArray(dblPosX)
    dblPosY=CDbl(txtPosY.Text)
    numPosY=New MWNumericArray(dblPosY)
    '绘给定数据的图形并叠加插值点的图形
    ntNewton.Draw(numDataX,numDataY,numPosX,numPosY)
    '在图片框中显示图形
    picGraph.ImageLocation="D:\temp2.bmp"
End Sub