ScientificComputing.rar

package lab8; import java.util.*; import java.awt.*; import javax.swing.*; public class Interpolation { JFrame frame; Lines lines;//画单项式基底得到的曲线 Lines1 lines1;//画牛顿插值得到的曲线 Lines2 lines2;//画拉格朗日插值得到的曲线 /** * 单项式基底，拉格朗日插值，牛顿插值 */ double t[] = { 0d, 1d, 2d, 3d, 4d }; double y[] = { 0d, 11, 29d, 65d, 125d }; double y1[] = { 0d, 11, 29d, 65d, 125d }; double y2[] = { 0d, 11, 29d, 65d, 125d }; double[][] A = new double[5][5]; double[][] A1 = new double[5][5]; double[] x = new double[5]; double[] x1 = new double[5]; void Monomial(double[] t, double[] y) { // 初始化范德蒙矩阵a； for (int i = 1; i <= 4; i++) { for (int j = 1; j <= 4; j++) { A[i][j] = Math.pow(t[i], j - 1); } } double[][] M = new double[5][5]; double num = 0, num1 = 0; int p = 0; for (int k = 1; k < 4; k++) { // 找出p double max = -1; for (int j = k; j <= 4; j++) { if (Math.abs(A[j][k]) > max) { max = Math.abs(A[j][k]); p = j; } } // 交换 if (k != p) { for (int l = 1; l <= 4; l++) { num = A[k][l]; A[k][l] = A[p][l]; A[p][l] = num; } // B交换 num1 = y[k]; y[k] = y[p]; y[p] = num1; } // 得到M[][] if (A[k][k] != 0) { for (int i = k + 1; i <= 4; i++) { M[i][k] = A[i][k] / A[k][k]; } // 得到A[][] for (int j = k; j <= 4; j++) { for (int i = k + 1; i <= 4; i++) { A[i][j] = A[i][j] - M[i][k] * A[k][j]; } } // 得到B[][] for (int h = k + 1; h <= 4; h++) { y[h] = y[h] - y[k] * M[h][k]; } } } //回代求x for (int j = 4; j >= 1; j--) { if (A[j][j] == 0) return; x[j] = y[j] / A[j][j]; for (int i = 1; i <= j - 1; i++) { y[i] = y[i] - A[i][j] * x[j]; } } } // 牛顿插值 void Newton(double[] t, double[] y) { // 将下三角矩阵每个值初始化为1 for (int i = 1; i <= 4; i++) for (int j = 1; j <= i; j++) A1[i][j] = 1; // 求得下三角矩阵 for (int i = 1; i <= 4; i++) { for (int j = 2; j <= i; j++) { for (int k = 1; k < j; k++) { A1[i][j] = A1[i][j] * (t[i] - t[k]); } } } // 前代法求得系数矩阵x1 for (int j = 1; j <= 4; j++) { if (A1[j][j] == 0) return; x1[j] = y1[j] / A1[j][j]; for (int i = j + 1; i <= 4; i++) { y1[i] = y1[i] - A1[i][j] * x1[j]; } } } void run() { frame = new JFrame("曲线图"); frame.setLayout(new GridLayout(1, 3)); Monomial(t, y);//求x[], lines = new Lines(t, y2, x);//画单项式基底得到的曲线 lines.setSize(400, 400); frame.add(lines); Newton(t, y1);//求x1[] lines1 = new Lines1(t, y2, x1);//画牛顿插值得到的曲线 lines1.setSize(400, 400); frame.add(lines1); lines2 = new Lines2(t, y2);//画拉格朗日插值得到的曲线 lines2.setSize(400, 400); frame.add(lines2); frame.setSize(1200, 400); frame.setVisible(true); frame.setLocation(75, 100); frame.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE); } public static void main(String[] args) { new Interpolation().run(); } } //单项式基底 class Lines extends JPanel { double t[], y[], x[]; public Lines(double[] t, double[] y, double[] x) { this.t = t; this.y = y; this.x = x; } public void paint(Graphics g) { double x1, y1; g.drawLine(50, 30, 50, 320);//画x轴 g.drawLine(30, 300, 370, 300);//画y轴 //标注x轴 g.drawString("0", 43, 310); g.drawLine(110, 298, 110, 302); g.drawString("1", 108, 315); g.drawLine(170, 298, 170, 302); g.drawString("2", 168, 315); g.drawLine(230, 298, 230, 302); g.drawString("3", 228, 315); g.drawLine(290, 298, 290, 302); g.drawString("4", 288, 315); g.drawLine(350, 298, 350, 302); g.drawString("5", 348, 315); //标注y轴 g.drawLine(48, 250, 52, 250); g.drawString("30", 25, 255); g.drawLine(48, 200, 52, 200); g.drawString("60", 25, 205); g.drawLine(48, 150, 52, 150); g.drawString("90", 25, 155); g.drawLine(48, 100, 52, 100); g.drawString("120", 25, 105); g.drawLine(48, 50, 52, 50); g.drawString("150", 25, 55); g.drawString("单项式基底", 150, 350); g.setColor(Color.red); for (int i = 1; i < t.length; i++) {// 画出各个点 x1 = t[i] * 60 + 50; y1 = y[i] * 50 / 30; g.drawOval((int) x1, (int) (300 - y1), 4, 4); } g.setColor(Color.black); for (double i = 50; i < 370; i++) {// 根据多项式系数，画曲线 y1 = 0; for (int j = 1; j < x.length; j++) { y1 += x[j] * Math.pow(((double) ((i - 50) / 60)), (double) (j - 1));// 求y } y1 = y1 * ((double) 50 / (double) 30); g.drawLine((int) i, 300 - ((int) y1), (int) i, 300 - ((int) y1)); } } } //牛顿插值 class Lines1 extends JPanel { double t[], y[], x[]; public Lines1(double[] t, double[] y, double[] x) { this.t = t; this.y = y; this.x = x; } public void paint(Graphics g) { double x1, y1; g.drawLine(50, 30, 50, 320); g.drawLine(30, 300, 370, 300); g.drawString("0", 43, 310); g.drawLine(110, 298, 110, 302); g.drawString("1", 108, 315); g.drawLine(170, 298, 170, 302); g.drawString("2", 168, 315); g.drawLine(230, 298, 230, 302); g.drawString("3", 228, 315); g.drawLine(290, 298, 290, 302); g.drawString("4", 288, 315); g.drawLine(350, 298, 350, 302); g.drawString("5", 348, 315); g.drawLine(48, 250, 52, 250); g.drawString("30", 25, 255); g.drawLine(48, 200, 52, 200); g.drawString("60", 25, 205); g.drawLine(48, 150, 52, 150); g.drawString("90", 25, 155); g.drawLine(48, 100, 52, 100); g.drawString("120", 25, 105); g.drawLine(48, 50, 52, 50); g.drawString("150", 25, 55); g.drawString("牛顿插值", 150, 350); g.setColor(Color.red); for (int i = 1; i < t.length; i++) {// 画出各个点 x1 = t[i] * 60 + 50; y1 = y[i] * 50 / 30; g.drawOval((int) x1, (int) (300 - y1), 4, 4); } g.setColor(Color.black); for (double i = 50; i < 370; i++) {// 根据多项式系数，画曲线 y1 = 0; for (int j = 1; j < x.length; j++) { double temp = 1, te = 0; for (int k = 1; k < j; k++) { temp = temp * ((double) ((i - 50) / 60) - t[k]); } te = temp * x[j]; y1 = y1 + te; } y1 = y1 * ((double) 50 / (double) 30); g.drawLine((int) i, (int) (300 - y1), (int) i, (int) (300 - y1)); } } } //拉格朗日插值 class Lines2 extends JPanel { double t[], y[]; public Lines2(double[] t, double[] y) { this.t = t; this.y = y; } public void paint(Graphics g) { double x1, y1; g.drawLine(50, 30, 50, 320); g.drawLine(30, 300, 370, 300); g.drawString("0", 43, 310); g.drawLine(110, 298, 110, 302); g.drawString("1", 108, 315); g.drawLine(170, 298, 170, 302); g.drawString("2", 168, 315); g.drawLine(230, 298, 230, 302); g.drawString("3", 228, 315); g.drawLine(290, 298, 290, 302); g.drawString("4", 288, 315); g.drawLine(350, 298, 350, 302); g.drawString("5", 348, 315); g.drawLine(48, 250, 52, 250); g.drawString("30", 25, 255); g.drawLine(48, 200, 52, 200); g.drawString("60", 25, 205); g.drawLine(48, 150, 52, 150); g.drawString("90", 25, 155); g.drawLine(48, 100, 52, 100); g.drawString("120", 25, 105); g.drawLine(48, 50, 52, 50); g.drawString("150", 25, 55); g.drawString("拉格朗日插值", 150, 350); g.setColor(Color.red); for (int i = 1; i < t.length; i++) {// 画出各个点 x1 = t[i] * 60 + 50; y1 = y[i] * 50 / 30; g.drawOval((int) x1, (int) (300 - y1), 4, 4); } g.setColor(Color.black); for (double i = 50; i < 370; i++) {// 根据多项式系数，画曲线 double z = (double) ((i - 50) / 60); y1 = 0; double[] l = new double[t.length]; for (int n = 1; n < t.length; n++) { l[n] = 1; } for (int j = 1; j < t.length; j++) { for (int k = 1; k < t.length; k++) { if (k != j) { l[j] = l[j] * (z - t[k]) / (t[j] -