org.fraid.math
Class MathHelper

java.lang.Object
  org.fraid.math.MathHelper

public class MathHelper
extends java.lang.Object

Different mathematical routines. All methods are static.

Field Summary

static java.util.Random	random Systemwide random generator.
protected static int	smoothing The parameter which determines how smooth the lagrangeHermite approximation will be arround the sampling points.

Constructor Summary

MathHelper()

Method Summary

static Complex[]	calc(java.util.Vector aFunctions, Complex[] aArgs, double aTime) Calculates the system given by aFunctions at the point aArgs.
static int	getSmoothing() Returns the smoothing value.
static double	lagrangeHermite(double aPoint, double aPX, double aPY, double aSX, double aSY, double aEX, double aEY, double aNX, double aNY) Given four points p1,p2,p3,p4 approximates the y-value of a point which is between p2.x and p3.x.
static int	log2int(int aValue)
static void	main(java.lang.String[] args) Test driver for MathHelper
static int	nextpow2(double aValue)
static int	pow2length(int aValue)
static void	printComplexArray(Complex[] aArray) Test function.
static Complex	quad(ComplexFunction aFun, double aLLimit, double aULimit, int aPoints) Test function.
static void	rotate3D(DoublePoint3D aInitialPoint, DoublePoint3D aTransformedPoint, DoublePoint3D aVectorToRotateAround, double aRotationAngle, double aScale)
static void	setSmoothing(int newSmoothing) Sets the smoothing value.
static Complex[]	sumScalVect(double aScalar1, Complex[] aVect1, double aScalar2, Complex[] aVect2) Performs aScalar1*aVect1 + aScalar2*aVect2
static void	transform(java.util.Vector aFunctions, Complex[] aArgs, Complex[] aTransformed) Transform the n-dimensional point aArgs with the transformation in aFunctions.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Field Detail

random

public static java.util.Random random

Systemwide random generator.

smoothing

protected static int smoothing

The parameter which determines how smooth the lagrangeHermite approximation will be arround the sampling points. The bigger the value the smoother the approximation. Too big value may generate rounding errors. Shouldn't be smaller than 1; The default is 100.

Constructor Detail

MathHelper

public MathHelper()

Method Detail

getSmoothing

public static int getSmoothing()

Returns the smoothing value.

Returns:

an int value

setSmoothing

public static void setSmoothing(int newSmoothing)
                         throws MathException

Sets the smoothing value.

Parameters:

newSmoothing - an int value

Throws:

MathException - if newSmoothing < 1

lagrangeHermite

public static double lagrangeHermite(double aPoint,
                                     double aPX,
                                     double aPY,
                                     double aSX,
                                     double aSY,
                                     double aEX,
                                     double aEY,
                                     double aNX,
                                     double aNY)

Given four points p1,p2,p3,p4 approximates the y-value of a point which is between p2.x and p3.x. Uses Hermite's idea with two points and two derivatives but approximated with third degree Lagrange schema.

Parameters:

aPoint - the abscisa of the point we are trying to approximate;

aPX - the point before the first point of the interval (aSX), needed to calculate the derivative at aSX;

aSX - the first(start) point of the interval;

aEX - the second(end) point of the interval;

aNX - the point after the end of the interval (aEX), used to calculate the derivative at the end of the interval (aEX);

Returns:

the approximated value of the function at x=a_point

See Also:

DoublePoint

sumScalVect

public static Complex[] sumScalVect(double aScalar1,
                                    Complex[] aVect1,
                                    double aScalar2,
                                    Complex[] aVect2)

Performs aScalar1*aVect1 + aScalar2*aVect2

Parameters:

aScalar1 - a double value

aVect1 - a Complex[] value

aScalar2 - a double value

aVect2 - a Complex[] value

Returns:

a Complex[] value

calc

public static Complex[] calc(java.util.Vector aFunctions,
                             Complex[] aArgs,
                             double aTime)
                      throws java.lang.Exception

Calculates the system given by aFunctions at the point aArgs. Use when solving differential equations;

Parameters:

aFunctions - the system

aArgs - the point at which we need the value calculated

aTime - optional time variable

Returns:

the result

Throws:

java.lang.Exception - if an error occurs

transform

public static void transform(java.util.Vector aFunctions,
                             Complex[] aArgs,
                             Complex[] aTransformed)
                      throws java.lang.Exception

Transform the n-dimensional point aArgs with the transformation in aFunctions.

Parameters:

the - transformation given by a system of n, n-dimensional equations;

the - point we are transforming;

Throws:

java.lang.Exception - if an error occurs

rotate3D

public static void rotate3D(DoublePoint3D aInitialPoint,
                            DoublePoint3D aTransformedPoint,
                            DoublePoint3D aVectorToRotateAround,
                            double aRotationAngle,
                            double aScale)

quad

public static Complex quad(ComplexFunction aFun,
                           double aLLimit,
                           double aULimit,
                           int aPoints)
                    throws java.lang.Exception

Test function.

Parameters:

aArray - a Complex[] value

Throws:

java.lang.Exception

log2int

public static int log2int(int aValue)
                   throws ComplexFunctionException

Throws:

ComplexFunctionException

nextpow2

public static int nextpow2(double aValue)

pow2length

public static int pow2length(int aValue)

printComplexArray

public static void printComplexArray(Complex[] aArray)

Test function.

Parameters:

aArray - a Complex[] value

main

public static void main(java.lang.String[] args)
                 throws java.lang.Exception

Test driver for MathHelper

Parameters:

args - a String[] value

Throws:

java.lang.Exception - if an error occurs