public class LeastSquares {public static void matching(double[] x, double[] y, double[] input, double fully) {double k = getK(x, y);double b = getB(x, y);System.out.println("線性回歸系數(shù)k值：\t"+k+"\n" + "線性回歸系數(shù)b值：\t" + b);double maxy = 0; //用來記錄最大偏差//尋找最大偏差for (int i = 0; i < input.length; i++) {if (Math.abs(k * input[i] + b - y[i]) > maxy){maxy = Math.abs(k * input[i] + b - y[i]);}}System.out.println("最大偏差為：" + maxy);//求靈敏度double s = 0;double sum = 0;for (int i = 1; i < y.length; i++) {sum += y[i] - y[i-1];}s = sum / (y.length - 1) / 20;System.out.println("靈敏度為：" + s);//求線性誤差System.out.println("非線性誤差為：" + maxy/fully);}//返回x的系數(shù)k公式：k=( n sum( xy ) - sum( x ) sum( y ) )/( n sum( x^2 )-sum(x) ^ 2 )public static double getK(double[] x, double[] y) {int n = x.length;return (double) ((n * pSum(x, y) - sum(x) * sum(y)) / (n * sqSum(x) - Math.pow(sum(x), 2)));}//返回常量系數(shù)系數(shù)b 公式：b = sum( y ) / n - k * sum( x ) / npublic static double getB(double[] x, double[] y) {int n = x.length;double k = getK(x, y);return sum(y) / n - k * sum(x) / n;}//求和private static double sum(double[] ds) {double s = 0;for (double d : ds) {s = s + d;}return s;} //求平方和private static double sqSum(double[] ds) {double s = 0;for (double d : ds) {s = (double) (s + Math.pow(d, 2));}return s;} //返回對應(yīng)項(xiàng)相乘后的和private static double pSum(double[] x, double[] y) {double s = 0;for (int i = 0; i < x.length; i++) {s = s + x[i] * y[i];}return s;}public static void main(String[] args) {double[] x1 = {0,0.2,0.4,0.6,0.8,1.0};double[] y1 = {17.6,73.6,133,200,256,312};double[] inputs1 = x1;double[] x2 = {0,-0.2,-0.4,-0.6,-0.8,-1.0};double[] y2 = {40.0,96,152,208,264,328};double[] inputs2 = x2;double[] x3 = {0,0.2,0.4,0.6,0.8,1.0,1.2,1.4,1.6,1.8,2.0,2.2,2.4,2.6,2.8,3.0};double[] y3 = {17.6,73.6,133,200,256,312,372,428,484,548,600,672,712,776,832,888};double[] inputs3 = x3;double[] x4 = {0,-0.2,-0.4,-0.6,-0.8,-1.0,-1.2,-1.4,-1.6,-1.8,-2.0,-2.2,-2.4,-2.6,-2.8,-3.0};double[] y4 = {40.0,96,152,208,264,328,384,440,496,552,616,666,720,784,840,898};double[] inputs4 = x4;System.out.println("+1區(qū)間");matching(x1, y1,inputs1,y1[y1.length-1]);System.out.println("-1區(qū)間");matching(x2, y2,inputs2,y2[y2.length-1]);System.out.println("+3區(qū)間");matching(x3, y3,inputs3,y3[y3.length-1]);System.out.println("-3區(qū)間");matching(x4, y4,inputs4,y4[y4.length-1]);} }

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