LstSquQuadRegr.h

/********************************************************************************************
                                  Class LstSquQuadRegr
             A C#  Class for Least Squares Regression for Quadratic Curve Fitting
                                  Alex Etchells  2010    
 ********************************************************************************************/
/*
using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Collections;
*/

class LstSquQuadRegr
{
     /* instance variables */
    ArrayList pointArray = new ArrayList(); 
    private int numOfEntries; 
    private double[] pointpair;          

    /*constructor */
    public LstSquQuadRegr()
    {
        numOfEntries = 0;
        pointpair = new double[2];
    }

    /*instance methods */
    
    
    /// <summary>
    /// add point pairs
    /// </summary>
    /// <param name="x">x value</param>
    /// <param name="y">y value</param>
    public void AddPoints(double x, double y) 
    {
        pointpair = new double[2]; 
        numOfEntries +=1; 
        pointpair[0] = x; 
        pointpair[1] = y;
        pointArray.Add(pointpair);
    }

    /// <summary>
    /// returns the a term of the equation ax^2 + bx + c
    /// </summary>
    /// <returns>a term</returns>
    public double aTerm()
    {
        if (numOfEntries < 3)
        {
            throw new InvalidOperationException("Insufficient pairs of co-ordinates");
        }
        //notation sjk to mean the sum of x_i^j*y_i^k. 
        double s40 = getSx4(); //sum of x^4
        double s30 = getSx3(); //sum of x^3
        double s20 = getSx2(); //sum of x^2
        double s10 = getSx();  //sum of x
        double s00 = numOfEntries;  //sum of x^0 * y^0  ie 1 * number of entries

        double s21 = getSx2y(); //sum of x^2*y
        double s11 = getSxy();  //sum of x*y
        double s01 = getSy();   //sum of y

        //a = Da/D
        return (s21*(s20 * s00 - s10 * s10) - s11*(s30 * s00 - s10 * s20) + s01*(s30 * s10 - s20 * s20))
                /
                (s40*(s20 * s00 - s10 * s10) - s30*(s30 * s00 - s10 * s20) + s20*(s30 * s10 - s20 * s20));
    }

    /// <summary>
    /// returns the b term of the equation ax^2 + bx + c
    /// </summary>
    /// <returns>b term</returns>
    public double bTerm()
    {
        if (numOfEntries < 3)
        {
            throw new InvalidOperationException("Insufficient pairs of co-ordinates");
        }
        //notation sjk to mean the sum of x_i^j*y_i^k.  
        double s40 = getSx4(); //sum of x^4
        double s30 = getSx3(); //sum of x^3
        double s20 = getSx2(); //sum of x^2
        double s10 = getSx();  //sum of x
        double s00 = numOfEntries;  //sum of x^0 * y^0  ie 1 * number of entries

        double s21 = getSx2y(); //sum of x^2*y
        double s11 = getSxy();  //sum of x*y
        double s01 = getSy();   //sum of y

        //b = Db/D
        return (s40*(s11 * s00 - s01 * s10) - s30*(s21 * s00 - s01 * s20) + s20*(s21 * s10 - s11 * s20))
                /
                (s40 * (s20 * s00 - s10 * s10) - s30 * (s30 * s00 - s10 * s20) + s20 * (s30 * s10 - s20 * s20));
    }

    /// <summary>
    /// returns the c term of the equation ax^2 + bx + c
    /// </summary>
    /// <returns>c term</returns>
    public double cTerm()
    {
        if (numOfEntries < 3)
        {
            throw new InvalidOperationException("Insufficient pairs of co-ordinates");
        }
        //notation sjk to mean the sum of x_i^j*y_i^k.  
        double s40 = getSx4(); //sum of x^4
        double s30 = getSx3(); //sum of x^3
        double s20 = getSx2(); //sum of x^2
        double s10 = getSx();  //sum of x
        double s00 = numOfEntries;  //sum of x^0 * y^0  ie 1 * number of entries

        double s21 = getSx2y(); //sum of x^2*y
        double s11 = getSxy();  //sum of x*y
        double s01 = getSy();   //sum of y

        //c = Dc/D
        return (s40*(s20 * s01 - s10 * s11) - s30*(s30 * s01 - s10 * s21) + s20*(s30 * s11 - s20 * s21))
                /
                (s40 * (s20 * s00 - s10 * s10) - s30 * (s30 * s00 - s10 * s20) + s20 * (s30 * s10 - s20 * s20));
    }
    
    public double rSquare() // get r-squared
    {
        if (numOfEntries < 3)
        {
            throw new InvalidOperationException("Insufficient pairs of co-ordinates");
        }
        // 1 - (total sum of squares / residual sum of squares)
        return 1 - getSSerr() / getSStot();
    }
   

    /*helper methods*/
    private double getSx() // get sum of x
    {
        double Sx = 0;
        foreach (double[] ppair in pointArray)
        {
            Sx += ppair[0];
        }
        return Sx;
    }

    private double getSy() // get sum of y
    {
        double Sy = 0;
        foreach (double[] ppair in pointArray)
        {
            Sy += ppair[1];
        }
        return Sy;
    }

    private double getSx2() // get sum of x^2
    {
        double Sx2 = 0;
        foreach (double[] ppair in pointArray)
        {
            Sx2 += Math.Pow(ppair[0], 2); // sum of x^2
        }
        return Sx2;
    }

    private double getSx3() // get sum of x^3
    {
        double Sx3 = 0;
        foreach (double[] ppair in pointArray)
        {
            Sx3 += Math.Pow(ppair[0], 3); // sum of x^3
        }
        return Sx3;
    }

    private double getSx4() // get sum of x^4
    {
        double Sx4 = 0;
        foreach (double[] ppair in pointArray)
        {
            Sx4 += Math.Pow(ppair[0], 4); // sum of x^4
        }
        return Sx4;
    }

    private double getSxy() // get sum of x*y
    {
        double Sxy = 0;
        foreach (double[] ppair in pointArray)
        {
            Sxy += ppair[0] * ppair[1]; // sum of x*y
        }
        return Sxy;
    }

    private double getSx2y() // get sum of x^2*y
    {
        double Sx2y = 0;
        foreach (double[] ppair in pointArray)
        {
            Sx2y += Math.Pow(ppair[0], 2) * ppair[1]; // sum of x^2*y
        }
        return Sx2y;
    }

    private double getYMean() // mean value of y
    {
        double y_tot = 0;
        foreach (double[] ppair in pointArray)
        {
            y_tot += ppair[1]; 
        }
        return y_tot/numOfEntries;
    }

    private double getSStot() // total sum of squares
    {
        //the sum of the squares of the differences between 
        //the measured y values and the mean y value
        double ss_tot = 0;
        foreach (double[] ppair in pointArray)
        {
            ss_tot += Math.Pow(ppair[1] - getYMean(), 2);
        }
        return ss_tot;
    }

    private double getSSerr() // residual sum of squares
    {
        //the sum of the squares of te difference between 
        //the measured y values and the values of y predicted by the equation
        double ss_err = 0;
        foreach (double[] ppair in pointArray)
        {
            ss_err += Math.Pow(ppair[1] - getPredictedY(ppair[0]), 2);
        }
        return ss_err;
    }

    private double getPredictedY(double x)
    {
        //returns value of y predicted by the equation for a given value of x
        return aTerm() * Math.Pow(x, 2) + bTerm() * x + cTerm();
    }
}