package com.util;

/**
 * 作者：杜航 功能：最小二乘法 線性迴歸（Least squares）
 * 
 * y = a x + b b = sum( y ) / n - a * sum( x ) / n a = ( n * sum( xy ) - sum( x
 * ) * sum( y ) ) / ( n * sum( x^2 ) - sum(x) ^ 2 )
 * 
 */
public class LeastSquares
{

	/*
	 * 杜航 功能：返回估計的y值
	 */
	public static float estimate(float[] x, float[] y, float input)
	{
		float a = getA(x, y);
		float b = getB(x, y);
		System.out.println("線性迴歸係數a值：\t" + a + "\n" + "線性迴歸係數b值：\t" + b);
		return (a * input + b);
	}

	/*
	 * 杜航 功能：返回x的係數a 公式：a = ( n sum( xy ) - sum( x ) sum( y ) ) / ( n sum( x^2 )
	 * - sum(x) ^ 2 )
	 */
	public static float getA(float[] x, float[] y)
	{
		int n = x.length;
		return (float) ((n * pSum(x, y) - sum(x) * sum(y)) / (n * sqSum(x) - Math
				.pow(sum(x), 2)));
	}

	/*
	 * 杜航 功能：返回常量係數係數b 公式：b = sum( y ) / n - a sum( x ) / n
	 */
	public static float getB(float[] x, float[] y)
	{
		int n = x.length;
		float a = getA(x, y);
		return sum(y) / n - a * sum(x) / n;
	}

	/*
	 * 杜航 功能：求和
	 */
	private static float sum(float[] ds)
	{
		float s = 0;
		for (float d : ds)
		{
			s = s + d;
		}
		return s;
	}

	/*
	 * 杜航 功能：求平方和
	 */
	private static float sqSum(float[] ds)
	{
		float s = 0;
		for (float d : ds)
		{
			s = (float) (s + Math.pow(d, 2));
		}
		return s;
	}

	/*
	 * 杜航 功能：返回對應項相乘後的和
	 */
	private static float pSum(float[] x, float[] y)
	{
		float s = 0;
		for (int i = 0; i < x.length; i++)
		{
			s = s + x[i] * y[i];
		}
		return s;
	}

	/*
	 * 杜航 功能：main()測試線性迴歸的最小二乘法java實現函式
	 */
	public static void main(String[] args)
	{
		float[] x =
//		{ 540, 360, 240, 480, 420 };
		{ 205, 325, 445, 505, 625 };
		float[] y =
//		{  520, 475, 430, 386, 500 };
		{ 100, 123, 148, 407, 319, 301 };
		System.out.println("經線性迴歸後的y值：\t" + estimate(x, y,240));
	}
}