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Posted to user@commons.apache.org by "roger.ball@creoss.com" <ro...@creoss.com> on 2010/01/21 19:46:21 UTC
[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
Re: [MATH] Need help on math libraries for curve generation
Posted by Luc Maisonobe <Lu...@free.fr>.
roger.ball@creoss.com a écrit :
> 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?
>
The classes you need are located in the
org.apache.commons.math.optimization.fitting package. The CurveFitter
class is the most general fitter. The PolynomialFitter class is
specialized for polynomials. Both classes need an underlying optimizer
as the engine that will do the real work (the classes are mainly
wrappers that convert a curve fitting problem into a general least
squares problem). Once built, you add the observed points in a loop.
When all observed points have been added, the fit methods should be
called to perform the fitting and they will provide you the coefficients
(for Polynomial, you will directly get a PolynomialFunction instance
that holds the coefficients.
Neither class will directly provide the residuals, sum of squares or
standard deviation. However, you can get them if you use one of the
least squares optimizers as the engine when you build the curve fitter.
This would be something along the following lines:
// set up the optimizer and the fitter
LevenbergMarquardtOptimizer optimizer =
new LevenbergMarquardtOptimizer();
CurveFitter fitter = new CurveFitter(optimizer);
for (int i = 0; i < n; ++i) {
fitter.addObservedPoint(x[i], y[i]);
}
// you should provide an implementation for your function
ParametricRealFunction myFunction =
new 2DCurveNaturalLogX();
// perform the fitting
double[] fittingParameters = fitter.fit(myFunction, initialGuess);
double rms = optimizer.getRMS();
double[][] cov = optimizer.getCovariances();
double[] e = optimizer.guessParameterErrors();
...
For 3D curve fitting, you should create you own fitters, probably using
the 2D CurveFitter class as a guide.
Luc
> Thanks
> Roger Ball
>
>
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Re: [MATH] Need help on math libraries for curve generation
Posted by Luc Maisonobe <Lu...@free.fr>.
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]-8.360156212815445E-4
> Covariances [2][0]0.0012611571197298384
> Covariances [2][1]-8.36015621281545E-4
> Covariances [2][2]1.8778882839946132E-7
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 chi-square 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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RE: [MATH] Need help on math libraries for curve generation
Posted by "roger.ball@creoss.com" <ro...@creoss.com>.
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
Root Mean Square [26.34790434234611]
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]-8.360156212815445E-4
Covariances [2][0]0.0012611571197298384
Covariances [2][1]-8.36015621281545E-4
Covariances [2][2]1.8778882839946132E-7
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
Re: [MATH] Need help on math libraries for curve generation
Posted by Luc Maisonobe <Lu...@free.fr>.
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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To unsubscribe, e-mail: user-unsubscribe@commons.apache.org
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RE: [MATH] Need help on math libraries for curve generation
Posted by "roger.ball@creoss.com" <ro...@creoss.com>.
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