Implementing the Problem-Specific Part

Now it's time to implement the problem-specific part of the least squares fit analysis. The problem-specific elements of the analysis are the type of polynomial equation to be used and the data that will be modeled. The data to be modeled can be stored in 1-D arrays. Information about the curve fit polynomial equation will be stored in an instance of the Polynomial class, which encapsulates a general polynomial equation.

Equation 23.2

The order of the polynomial equation in Eq. (23.2) is equal to the largest exponent in the equation. For example, the quadratic equation, y = c ₂ x ² + c ₁ x + c , would be a second-order polynomial expression.

The Polynomial class defines four data members . The first is an integer variable that stores the order of the equation. The A[][] array stores the values of A ^T A . The b[] array stores the values of A ^T b . The coeffs[] array stores the coefficients of the polynomial curve fit equation.

The Polynomial class then defines a series of methods to get or set the values of its data members. The getA() and getB() methods return a reference to the A[][] and b[] arrays. In the leastSquaresFit() method, the getA() and getB() methods are used to send the A[][] and b[] arrays to the gaussian() method. The setA() and setB() methods are used by Polynomial subclasses.

The loadArrays() method loads the values for A ^T A and A ^T b into the A[][] and b[] arrays. The implementation is to load the arrays for a general polynomial equation. The mathematical formulation of the A ^T A and A ^T b arrays for a general polynomial is provided in Chapter 24. Finally, the getValue() method returns a value along the curve fit equation. This method would be called after the least squares fit had been performed.

The Polynomial class source code is shown here.

 package TechJava.MathLib; public class Polynomial {   private int order;   private double A[][];   private double b[];   private double coeff[];   public Polynomial(int order){     this.order = order;     A = new double[order+1][order+1];     b = new double[order+1];     coeff = new double[order+1];   }   //  These methods return the current value   //  of the data members.   public int getOrder() {     return order;   }   public double[][] getA(){     return A;   }   public double[] getB() {     return b;   }   public double getCoefficient(int index) {     return coeff[index];   }   public double[] getCoefficients() {     return coeff;   }   //  These methods are to change one or more elements   //  of the A[][], b[], or coeff[] arrays   public void setA(int i, int j, double value){     A[i][j] = value;   }   public void setB(int j, double value) {     b[j] = value;   }   public void setCoefficients(double coeff[]) {     this.coeff = coeff;   }   //  Load the A[][] and b[] arrays. The A[][] array   //  stores the values of AT*A. The b[] array stores   //  the values of AT*b. This implementation   //  is for a general polynomial expression   public void loadArrays(double x[], double y[]) {     int numPoints = x.length;     for(int j=0; j<order+1; ++j) {       b[j] = 0.0;       for(int k=0; k<numPoints; ++k) {         b[j] += Math.pow(x[k],order - j)*y[k];       }     }     for(int i=0; i<order+1; ++i) {       for(int j=0; j<order+1; ++j) {         A[i][j] = 0.0;         for(int k=0; k<numPoints; ++k) {           A[i][j] += Math.pow(x[k],2.0*order  i - j);         }       }     }   }   //  Return a value along the least squares fit line.   //  This implementation is for a general polynomial   //  expression.   public double getValue(double x) {     double y = 0.0;     for(int i=0; i<getOrder()+1; ++i) {       y += coeff[i]*Math.pow(x,order - i);     }     return y;   } }