[math] help writing a solver for equation

[mickeydog]

I have an equation like so:
z = Sum of a = 1 to n [ e**(y - x(a))/ e**(x(a)]
I want to solve for y.
I have z and x(a).

I have created a class EquationSolver which has these methods and inner
class:

private EstimatedParameter xa;

public VintageQualityFitter() {

  xa = new EstimatedParameter("xa", 0.0);

  // provide the parameters to the base class which
  // implements the getAllParameters and getUnboundParameters methods
  addParameter(xa);
}

public double theoreticalValue(double z) {
  double summand = ( Math.exp(y * xa.getEstimate()) /
Math.exp(xa.getEstimate());
  return summand;
}

public void addPoint(double xa) {
  addMeasurement(new LocalMeasurement(xa, 1.0)); // all weights same
}

public double getXa() {
  return xa.getEstimate();
}

private class LocalMeasurement extends WeightedMeasurement {

  private final double z;

  // constructor
  public LocalMeasurement(double xa, double weight) {
     super(xa, weight);
     this.z = xa;
  }

  public double getTheoreticalValue() {
    // the value is provided by the model for the local xa
    return theoreticalValue(z);
  }

// don't need this i think
  public double getPartial(EstimatedParameter parameter) {
    return 0.0;
  }
}

I use this like so:

EquationFitter equationFitter = new EquationFitter();

for (int a = 0; a <= numberOfAs; a++) {
  double xa = <get x(a)>
  equationFitter.addPoint(xa.doubleValue());
 }

try {
    // solve the problem, using a Levenberg-Marquardt algorithm with
default settings
        LevenbergMarquardtEstimator estimator = new 
LevenbergMarquardtEstimator();
    estimator.estimate(equationFitter);
} catch (EstimationException e) {
        e.printStackTrace();
}

// fitter.theoreticalValue() is alpha
<get some z>
y = equationFitter.theoreticalValue(z);

but something in all this isn't right, especially with theoreticalValue(),
i think.
Can anyone help?


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