最小二乘法求多次拟合

[Java]代码    

import java.util.*;

public class Nihe {

	/**
	 * @param args
	 */
	public static void main(String[] args) {
		// TODO Auto-generated method stub
		int n, m, i, j, k;
		System.out.println("输入x的个数");
		Scanner sc = new Scanner(System.in);
		n = sc.nextInt();
		double a[] = new double[n];
		double b[] = new double[n];
		System.out.println("输入x");
		Scanner str1 = new Scanner(System.in);
		for (i = 0; i < n; i++)
			a[i] = str1.nextDouble();// 数组a存储x的值
		System.out.println("输入y");
		Scanner str2 = new Scanner(System.in);
		for (i = 0; i < n; i++)
			b[i] = str2.nextDouble();// 数组b存储y的值
		double sumx = 0;
		double sumy = 0;
		for (i = 0; i < n; i++) {
			sumx += a[i];// x的类和；
			sumy += b[i];// y的类和；
		}
		// System.out.println("x的类和"+sumx);
		// System.out.println("y的类和"+sumy);
		System.out.println("输入拟合次数");
		Scanner str3 = new Scanner(System.in);
		m = str3.nextInt();
		int s = 2 * m;
		double Sumx[] = new double[s];
		for (i = 0; i < s; i++) {
			double sum = 0;
			for (j = 0; j < n; j++) {
				double r = 1;
				for (k = 0; k <= i; k++)
					r = r * a[j];
				sum += r;
			}

			Sumx[i] = sum;
		}
		/*
		 * for(i=0;i<s;i++){ System.out.print(Sumx[i]+"  "); }
		 */
		// System.out.println();
		double Sumxy[] = new double[m];
		for (i = 0; i < m; i++) {
			double sumxy = 0;
			for (j = 0; j < n; j++) {
				double p = 1;
				double w = 0;
				for (k = 0; k <= i; k++)
					p = p * a[j];
				w = p * b[j];
				sumxy += w;
			}
			Sumxy[i] = sumxy;
		}
		/*
		 * for(i=0;i<m;i++){ System.out.print(Sumxy[i]+"  "); }
		 */
		// System.out.println();
		int t = m + 1;
		int q = m + 2;
		double A[][] = new double[t][q];
		A[0][0] = n;
		A[0][q - 1] = sumy;
		for (j = 1; j < q - 1; j++)
			A[0][j] = Sumx[j - 1];
		for (i = 1; i < t; i++)
			for (j = 0; j < q - 1; j++)
				A[i][j] = Sumx[i + j - 1];
		for (i = 1; i < t; i++)
			A[i][q - 1] = Sumxy[i - 1];
		/*
		 * for (i = 0; i < t; i++) { int count1 = 0; for (j= 0; j < q;j++) {
		 * System.out.print(A[i][j] + "  "); count1++; if (count1 == q)
		 * System.out.println(); } }
		 */
		for (k = 0; k < t; k++) {
			for (i = k + 1; i < t; i++) {
				double L = A[i][k] / A[k][k];
				for (j = 0; j < q; j++)
					A[i][j] = A[i][j] - L * A[k][j];
			}
		}
		for (k = t - 1; k >= 0; k--) {
			for (i = k - 1; i >= 0; i--) {
				double L = A[i][k] / A[k][k];
				for (j = q - 1; j >= k; j--)
					A[i][j] = A[i][j] - L * A[k][j];
			}
		} // 求多项式的系数
		/*
		 * for (i = 0; i < t; i++) { int count1 = 0; for (j= 0; j < q;j++) {
		 * System.out.print(A[i][j] + "  "); count1++; if (count1 == q)
		 * System.out.println(); } }
		 */
		double r[] = new double[t];
		for (i = 0; i < t; i++) {
			r[i] = A[i][q - 1] / A[i][i];
			// System.out.println("x"+i+"="+r[i]);
		}
		double x;
		System.out.println("输入计算的值");
		Scanner sc1 = new Scanner(System.in);
		x = sc1.nextDouble();

		double SUM = 0;
		double Z[] = new double[t];
		for (i = 0; i < t; i++) {
			double z = 1;
			for (j = 1; j <= i; j++)
				z = z * x;
			Z[i] = z * r[i];

		}
		for (i = 0; i < t; i++)
			SUM += Z[i];
		System.out.println("f(" + x + ")" + "=" + SUM);
	}
}

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