最小二乘法拟合

/**
* 最小二乘法拟合
*
*
* @authorKen转发
*
*/
public class Linest {
/**
* <p>
* 函数功能：最小二乘法曲线拟合
* </p>
*
* @param x
* 实型一维数组，长度为 n 。存放给定 n 个数据点的 X 坐标
* @param y
* 实型一维数组，长度为 n 。存放给定 n 个数据点的 Y 坐标
* @param n
* 变量。给定数据点的个数
* @param a
* 实型一维数组，长度为 m 。返回 m-1 次拟合多项式的 m 个系数
* @param m
* 拟合多项式的项数，即拟合多项式的最高次数为 m-1. 要求 m<=n 且m<=20。若 m>n 或 m>20
* ，则本函数自动按 m=min{n,20} 处理.
* <p>
* Date:2007-12-25 16:21 PM
* </p>
* @author qingbao-gao
* @return
*/
public static double[] PolyFit(double x[], double y[], int n, double a[],
int m) {
int i, j, k;
double z, p, c, g, q = 0, d1, d2;
double[] s = new double[20];
double[] t = new double[20];
double[] b = new double[20];
double[] dt = new double[3];
for (i = 0; i <= m - 1; i++) {
a[i] = 0.0;
}
if (m > n) {
m = n;
}
if (m > 20) {
m = 20;
}
z = 0.0;
for (i = 0; i <= n - 1; i++) {
z = z + x[i] / (1.0 * n);
}
b[0] = 1.0;
d1 = 1.0 * n;
p = 0.0;
c = 0.0;
for (i = 0; i <= n - 1; i++) {
p = p + (x[i] - z);
c = c + y[i];
}
c = c / d1;
p = p / d1;
a[0] = c * b[0];
if (m > 1) {
t[1] = 1.0;
t[0] = -p;
d2 = 0.0;
c = 0.0;
g = 0.0;
for (i = 0; i <= n - 1; i++) {
q = x[i] - z - p;
d2 = d2 + q * q;
c = c + y[i] * q;
g = g + (x[i] - z) * q * q;
}
c = c / d2;
p = g / d2;
q = d2 / d1;
d1 = d2;
a[1] = c * t[1];
a[0] = c * t[0] + a[0];
}
for (j = 2; j <= m - 1; j++) {
s[j] = t[j - 1];
s[j - 1] = -p * t[j - 1] + t[j - 2];
if (j >= 3)
for (k = j - 2; k >= 1; k--) {
s[k] = -p * t[k] + t[k - 1] - q * b[k];
}
s[0] = -p * t[0] - q * b[0];
d2 = 0.0;
c = 0.0;
g = 0.0;
for (i = 0; i <= n - 1; i++) {
q = s[j];
for (k = j - 1; k >= 0; k--) {
q = q * (x[i] - z) + s[k];
}
d2 = d2 + q * q;
c = c + y[i] * q;
g = g + (x[i] - z) * q * q;
}
c = c / d2;
p = g / d2;
q = d2 / d1;
d1 = d2;
a[j] = c * s[j];
t[j] = s[j];
for (k = j - 1; k >= 0; k--) {
a[k] = c * s[k] + a[k];
b[k] = t[k];
t[k] = s[k];
}
}
dt[0] = 0.0;
dt[1] = 0.0;
dt[2] = 0.0;
for (i = 0; i <= n - 1; i++) {
q = a[m - 1];
for (k = m - 2; k >= 0; k--) {
q = a[k] + q * (x[i] - z);
}
p = q - y[i];
if (Math.abs(p) > dt[2]) {
dt[2] = Math.abs(p);
}
dt[0] = dt[0] + p * p;
dt[1] = dt[1] + Math.abs(p);
}
return a;
}

/**
* <p>
* 对X轴数据节点球平均值
* </p>
*
* @param x
* 存储X轴节点的数组
* <p>
* Date:2007-12-25 20:21 PM
* </p>
* @author qingbao-gao
* @return 平均值
*/
public static double ave(double[] x) {
double ave = 0;
double sum = 0;
if (x != null) {
for (int i = 0; i < x.length; i++) {
sum += x[i];
}
System.out.println("sum-->" + sum);
ave = sum / x.length;
System.out.println("ave" + ave + "x.length" + x.length);
}
return ave;
}

/**
* <p>
* 由X值获得Y值
* </p>
*
* @param x
* 当前X轴输入值,即为预测的月份
* @param xx
* 当前X轴输入值的前X数据点
* @param a
* 存储多项式系数的数组
* @param m
* 存储多项式的最高次数的数组
* <p>
* Date:2007-12-25 PM 20:07
* </p>
* <P>
* Author:qingbao-gao
* </P>
* @return 对应X轴节点值的Y轴值
*/
public static double getY(double x, double[] xx, double[] a, int m) {
double y = 0;
double ave = ave(xx);

double l = 0;
for (int i = 0; i < m; i++) {
l = a[0];
if (i > 0) {
y += a[i] * Math.pow((x - ave), i);
System.out.println(i + "--|-->" + y + "--a[i]--" + a[i]);
}
System.out.println("a[0]|" + a[0]);
}
System.out.println("l--|" + (l));
return (y + l);
}

// --------------------------------------------测试代码

public static void main(String[] args) {

double[] x = { 200401, 200402, 200403, 200404, 200405, 200406, 200407,
200408, 200409, 2004010, 2004011, 2004012, 200501, 200502,
200503, 200504 };
double[] y = { 51, 51, 53, 53, 54, 55, 57, 60, 63, 64, 66, 66, 69, 71,
72, 75 };
double[] a = new double[20];
double[] aa = PolyFit(x, y, 16, a, 3);
double yy = 0;
System.out.println("拟合-->" + getY(200505, x, aa, 3));
}

}