roger.ball@creoss.com a écrit :
> Luc
> Thanks for tips on the parametric real function (see botton). Based on these changes
and a data set I am getting the following results, see below. I am not quite sure how to use
this information to compute:
>
> Coefficient of Determination
> Sum of Squares
> Standard Error of Regression
>
>
> Thanks
>
> Roger
>
>
> CurveFitter using LevenbergMarquardtOptimizer
> function is y = a + be^(cx)
> 16 data points for "Trail Shaft Configuration"
> best coeff [0]291.14035683044796
> best coeff [1]182.57603828133813
> best coeff [2]0.09714949397797856
The coefficients above are the coefficients of your function. a =
291.140..., b = 182.576..., c = 0.0971...
> Root Mean Square [26.34790434234611]
The RMS above is linked to the sum of squares (which is the objective
function the optimizer minimizes) by : rms = sqrt(sum / n) where n is
the number of data points. So you can retrieve sume by computing n * RMS^2.
> Covariances [0][0]8.856485460793724
> Covariances [0][1]5.701795559353768
> Covariances [0][2]0.0012611571197298362
> Covariances [1][0]5.701795559353772
> Covariances [1][1]3.7453325583603876
> Covariances [1][2]8.360156212815445E4
> Covariances [2][0]0.0012611571197298384
> Covariances [2][1]8.36015621281545E4
> Covariances [2][2]1.8778882839946132E7
The covariance above is linked to the standard error, but when you have
multiple parameters (here 3) it is a complete matrix.
Perhaps what you want is rather the chisquare value provided by
getChiSquare() ? I'm not sure about what it means, I don't know anything
about the statistical aspects of optimization algorithms.
Luc
> guessParametersError [0]86.98915260216266
> guessParametersError [1]56.56914127885704
> guessParametersError [2]0.012666868717084282
> chi Square [11107.393011734734]
> 
> Function value as 5 = 587.8975295919015, Actual = 576.0
> Function value as 20 = 1565.445870365208, Actual = 1590.0
>
> 
>
> 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
>
>
>
>
> Roger Ball
> ________________________________
> From: roger.ball@creoss.com
> Sent: Friday, January 22, 2010 10:59 AM
> To: user@commons.apache.org
> Subject: RE: [MATH] Need help on math libraries for curve generation
>
> 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;
> 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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