Le 13/08/2010 03:15, Juan Barandiaran a écrit : > Hi, I'm working in a theoretical physics problem in which I have to find the > roots of a function for every point in x,y,z.
I did not find time to look at this. I'll give it a try in a day or two. Sorry for the delay Luc > I can bracket quite precisely where every root will be found and I know the > exact solution for many points: > For every point (x= 1, y= n*2*PI, z= 0) the root is in -n*2*PI. > > I have been using the newBrentSolver function, but to my surprise, even when > I set the Accuracy settings to very > small values and the MaxIterationCount to Integer.MAX_VALUE I get an error > of 1.427E-5 (too much). > > The function to be solved is alfa in > : > alfa+Math.sqrt(Math.pow(x-Math.cos(alfa),2.0)+Math.pow(y-Math.sin(alfa),2.0)+z*z); > > Any hint of how could I get more precision on a root finder solver? > I attach the code of a short Test Case program that shows the error I'm > getting. > > Thanks and best regards, > > JBB > > /***************************************************************************************************************************************** > > ELECTRON DENSITY OF ENERGY: ALFA Retarded Position Calculation > SpinningParticles Model > > @author Martin Rivas (SpinningParticles theory) & Juan Barandiaran > (Numerical Analysis & Calculation Program) > @web http://spinningparticles.com/ > > Test case to try different solvers from the Apache Commons-Math library, > showing 1.427E-5 (too much) error in the resulting roots. > > Compiled in JAVA with Eclipse SDK 3.6: > http://www.eclipse.org/downloads/packages/eclipse-classic-360/heliosr > and with the Apache Commons-Math library 2.1 < > http://commons.apache.org/math/> > > > ******************************************************************************************************************************************/ > > > package testCaseRootFindingSolversPackage; > > import org.apache.commons.math.analysis.UnivariateRealFunction; > import org.apache.commons.math.analysis.solvers.*; > import org.apache.commons.math.ConvergenceException; > import org.apache.commons.math.FunctionEvaluationException; > > public class TestCaseRootFindingSolvers { > > public static class AlfaFunctionClass implements UnivariateRealFunction { > //Alfa is the angle of the point dependent retarded position where the > electron charge was when it produced the field that influences the evaluated > x,y,z point > //To calculate it we must find the root of its equation between > -sqr((x^2+y^2+z^2))-1 and -sqr((x^2+y^2+z^2))+1 as the correct root must be > negative (retarded) > //and bracketed around the module of the position vector > > private double x; > private double y; > private double z; > > public AlfaFunctionClass(double x, double y, double z) { > this.x = x; > this.y = y; > this.z = z; > } > // this is the method specified by interface UnivariateRealFunction > public double value(double alfa) { > // here, we have to evaluate the function that calculates the retarded > position angle alfa. > return > alfa+Math.sqrt(Math.pow(x-Math.cos(alfa),2.0)+Math.pow(y-Math.sin(alfa),2.0)+z*z); > } > } > > public static class EnergyDensityFunctionAlfaClass { > public double evaluate(double x, double y, double z) { > double alfa; > UnivariateRealFunction alfaFunction = new AlfaFunctionClass(x,y,z); > UnivariateRealSolverFactory factory = > UnivariateRealSolverFactory.newInstance(); > UnivariateRealSolver solver = factory.newBrentSolver(); //Fails when the > result in the two bracketing points has the same sign > // UnivariateRealSolver solver = factory.newBisectionSolver(); > > //Trying to get the maximal precision with the available settings > solver.setAbsoluteAccuracy(1E-90); > solver.setMaximalIterationCount(Integer.MAX_VALUE); > solver.setRelativeAccuracy(1E-90); > solver.setFunctionValueAccuracy(1E-90); > try { > alfa = solver.solve(alfaFunction, -1.0*Math.sqrt(x*x+y*y+z*z)-1.0, > -1.0*Math.sqrt(x*x+y*y+z*z)+1.0); > } catch (ConvergenceException e) { > // TODO Auto-generated catch block > e.printStackTrace(); > alfa= 0.0; > } catch (FunctionEvaluationException e) { > // TODO Auto-generated catch block > e.printStackTrace(); > alfa= 0.0; > } > System.out.println("getFunctionValue="+String.valueOf(solver.getFunctionValue())+"??? > Can't be cero with 1,42E-5 error?????"); > System.out.println("getResult="+String.valueOf(solver.getResult())); > System.out.println("getAbsoluteAccuracy="+String.valueOf(solver.getAbsoluteAccuracy())); > > System.out.println("getRelativeAccuracy="+String.valueOf(solver.getRelativeAccuracy())); > System.out.println("getFunctionValueAccuracy="+String.valueOf(solver.getFunctionValueAccuracy())); > return alfa; > } > } > public static void main(String args[]) { > // Variables > double alfa=0.0; > double error; > EnergyDensityFunctionAlfaClass energyDensityFunction= new > EnergyDensityFunctionAlfaClass(); > //Example point, although we have to evaluate the function for every point > in space. > double x=1.0; > double n=1.0; > double y=n*2.0*Math.PI; > double z=0.0; > alfa= energyDensityFunction.evaluate(x, y, z); > System.out.println(); > System.out.println("Alfa= Root calculated with Apache Solver= > "+String.valueOf(alfa)); > error= alfa+n*2*Math.PI; > System.out.println(); > System.out.println("Error= Difference between the Alfa Root calculated with > Apache Solver and n*2*PI (exact root for any integer n)= > "+String.valueOf(error)); > } // End of main > } //End > --------------------------------------------------------------------- To unsubscribe, e-mail: [email protected] For additional commands, e-mail: [email protected]
