package commonAlgorithm;
import commonAlgorithm.PolynomialSoluter;
import java.lang.Math;
public class LeastSquare {
  private double[][] matrixA;
  private double[] arrayB;
  private double[] factors;
  private int order;
  public LeastSquare() {
  }
  /*
   * 實(shí)例化后，計(jì)算前，先要輸入?yún)?shù)并生成公式 arrayX為采樣點(diǎn)的x軸坐標(biāo)，按照采樣順序排列
   * arrayY為采樣點(diǎn)的y軸坐標(biāo)，按照采樣順序與x一一對應(yīng)排列 order
   * 為進(jìn)行擬合的階數(shù)。用低階來擬合高階曲線時(shí)可能會不準(zhǔn)確，但階數(shù)過高會導(dǎo)致計(jì)算緩慢
   */
  public boolean generateFormula(double[] arrayX, double[] arrayY, int order) {
    if (arrayX.length != arrayY.length)
      return false;
    this.order = order;
    int len = arrayX.length;
    // 擬合運(yùn)算中的x矩陣和y矩陣
    matrixA = new double[order + 1][order + 1];
    arrayB = new double[order + 1];
    // 生成y矩陣以及x矩陣中冪<=order的部分
    for (int i = 0; i < order + 1; i++) {
      double sumX = 0;
      for (int j = 0; j < len; j++) {
        double tmp = Math.pow(arrayX[j], i);
        sumX += tmp;
        arrayB[i] += tmp * arrayY[j];
      }
      for (int j = 0; j <= i; j++)
        matrixA[j][i - j] = sumX;
    }
    // 生成x矩陣中冪>order的部分
    for (int i = order + 1; i <= order * 2; i++) {
      double sumX = 0;
      for (int j = 0; j < len; j++)
        sumX += Math.pow(arrayX[j], i);
      for (int j = i - order; j < order + 1; j++) {
        matrixA[i - j][j] = sumX;
      }
    }
    // 實(shí)例化PolynomiaSoluter并解方程組，得到各階的系數(shù)序列factors
    PolynomialSoluter soluter = new PolynomialSoluter();
    factors = soluter.getResult(matrixA, arrayB);
    if (factors == null)
      return false;
    else
      return true;
  }
  // 根據(jù)輸入坐標(biāo)，以及系數(shù)序列factors計(jì)算指定坐標(biāo)的結(jié)果
  public double calculate(double x) {
    double result = factors[0];
    for (int i = 1; i <= order; i++)
      result += factors[i] * Math.pow(x, i);
    return result;
  }
}