roger.ball@creoss.com a écrit :
> Luc
> Thanks for your comments. I have taken the 2DCurveExponentialX as a first attempt here. The basic equation is y = a + b*e^(c*x) (is the math e, natural exponential function). I have written the following implementation of the of the ParametricRealFunction for this, see below. Not having any experience with this type a implementation I did the best I could. However, I am getting this exception:
>
> org.apache.commons.math.optimization.OptimizationException: unable to compute covariances: singular problem
> I unfortunately do not have any idea what this means or how to remedy it. Your help is appreciated
>
> Thanks
> Roger
>
> /**
> * implementation of ParametricRealFunction clase for
> * y = a + be^(cx)
> */
> public static class TwoDCurveNaturalLogX implements ParametricRealFunction
> {
> /*
> *"double[] coeffs = must include at least 1 but not more than 3 coefficients."
> */
> @Override
> public double value(double x, double[] coeffs) throws FunctionEvaluationException
> {
> if(coeffs == null || coeffs.length == 0 || coeffs.length > 3)
> {
> if (coeffs != null)
> {
> for (int ii=0; ii < coeffs.length; ii++)
> {
> //System.out.println("\t coeffs ["+ii+"]"+coeffs[ii]);
> }
> }
> else
> {
> //System.out.println("No coeffs were passed in");
> }
> throw new FunctionEvaluationException(coeffs);
> }
> double a = coeffs[0];
> double b = 0;
> double c = 0;
> if(coeffs.length >= 2)
> b = coeffs[1];
> if(coeffs.length >= 3)
> c = coeffs[2];
> double value = a + b*Math.pow(Math.E, (c*x));
> //System.out.println("\t value ["+value+"]");
> return value;
> }
> /*
> * derivative: y = b*c*e^(c*x)
> * double[] coeffs = must include at least 1 but not more than 3 coefficients."
> */
> @Override
> public double[] gradient(double x, double[] coeffs) throws FunctionEvaluationException {
> if(coeffs == null || coeffs.length ==0 || coeffs.length > 3)
> {
> throw new FunctionEvaluationException(coeffs);
> }
> System.out.println("\t coeffs length = ["+coeffs.length+"]");
> double a = coeffs[0];
> double b = 0;
> double c = 0;
> if(coeffs.length >= 2)
> b = coeffs[1];
> if(coeffs.length >= 3)
> c = coeffs[2];
> double gradient = b*c*Math.pow(Math.E, (c*x));
> double[] gradientVector = new double[3];
> gradientVector[0] = gradient;
> gradientVector[1] = 0;
> gradientVector[2] = 0;
The gradient is computed with respect to the coefficients (i.e. a, b and
c here), not with respect to the independant variable x. It also *must*
have the same length as the parameters array. So you should probably use:
public double[] gradient(double x, double[] coeffs)
throws FunctionEvaluationException {
final n = coeffs.length;
final double b = (n > 1) ? coeffs[1] : 0;
final double c = (n > 2) ? coeffs[2] : 0;
double[] gradient = new double[n];
gradient[0] = 1.0; // this is dy/da
if (n > 1) {
final double exp = Math.exp(c * x);
gradient[1] = exp; // this is dy/db
if (n > 2) {
gradient[2] = b * x * exp; // this is dy/dc
}
}
return gradient;
}
The reason you get a singular problem is proably because of your wrong
gradient, the optimizer thinks the problem does not depend on b and c
(you tell it dy/db = 0 and dy/dc = 0), so it has no way to know how to
choose b and c. The jacobian matrix has too many zeroes.
I also suggest to use Math.exp(c * x) rather than Math.pow(Math.E, c *
x), it is more stable numerically and probably faster.
hope this helps
Luc
> System.out.println("\t gradient ["+gradient+"]");
> return gradientVector;
> }
> }
>
>
> Luc
> ________________________________
> From: roger.ball@creoss.com
> Sent: Thursday, January 21, 2010 11:46 AM
> To: user@commons.apache.org
> Subject: [MATH] Need help on math libraries for curve generation
>
>
> We are evaluating the apache math library (http://commons.apache.org/math/index.html) for use on one of projects. In this project we need to generate curves based on the following functions:
>
> 2DCurve3rdOrderXPolynomial
> 2DCurveExponentialX
> 2DCurveNaturalLogX
> 2DCurveSquareRootX
> 2DCurveTimeConstantX
> 2DCurveExponentialDecayX
> 2DCurveLogarithmicDecayX
> 3DCurve4thOrderXPolynomial
> 3DCurveExponentialX
> 3DCurveNaturalLogX
> 3DCurveSquareRootX
> 3DCurveTimeConstantX
> 3DCurve3rdOrderZTimes4thOrderX
> 3DCurveExponentialDecayX
> 3DCurveLogarithmicDecayX
> 3DCurveExponentialDecayZ
> 3DCurveLogarithmicDecayZ
> 3DCurveHyprebolicDecayX
>
> For each function generated from data we also need:
>
> Coefficient of Determination
> Sum of Squares
> Standard Error of Regression
>
> Does anyone have experience with this library to direct us to which classes can be used to handle these requirements?
>
> Thanks
> Roger Ball
>
>
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