vmm3d.core

Class ComplexODE

java.lang.Object

vmm3d.core.ComplexODE

public class ComplexODE
extends java.lang.Object

Constructor Summary

Constructors

Constructor and Description
ComplexODE(Complex a0, Complex a1, Complex a2, Complex a3, Complex a4)

Method Summary

Modifier and Type	Method and Description
Complex[]	ComplexMultiStepIntegrator(Complex zInitial, Complex zFinal, Complex valInitial, Complex approxInitDeriv, double subs) The following integrates 1/sqrt(Poly) and continues the value of the root.
Complex	firstDerivOfPoly(Complex z)
Complex[]	ODEstep2_2(Complex zInitial, Complex zFinal, Complex initialVal, Complex approxInitDeriv, int numSubdivision) A first quadratic Taylorstep to the middle, then average the second derivative at these two points, complete with a second quadratic step using the average second derivative.
Complex[]	ODEstep4(Complex zInitial, Complex zFinal, Complex initialVal, Complex approxInitDeriv, int numSubdivision)
Complex	RootOfPolynomial(Complex f, Complex approxInitDeriv)
Complex	RootOfPolynomialInverse(Complex f, Complex approxInitDerivInv)
Complex	secondDerivOfPoly(Complex z)
Complex[]	setPoly(Complex[] a)
Complex[]	setPoly(Complex a0, Complex a1, Complex a2, Complex a3, Complex a4)
Complex	thirdDerivOfPoly(Complex z)
Complex	valueOfPoly(Complex z)

Methods inherited from class java.lang.Object

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

Constructor Detail

ComplexODE

public ComplexODE(Complex a0,
                  Complex a1,
                  Complex a2,
                  Complex a3,
                  Complex a4)

Method Detail

setPoly

public Complex[] setPoly(Complex[] a)

setPoly

public Complex[] setPoly(Complex a0,
                         Complex a1,
                         Complex a2,
                         Complex a3,
                         Complex a4)

valueOfPoly

public Complex valueOfPoly(Complex z)

firstDerivOfPoly

public Complex firstDerivOfPoly(Complex z)

secondDerivOfPoly

public Complex secondDerivOfPoly(Complex z)

thirdDerivOfPoly

public Complex thirdDerivOfPoly(Complex z)

ODEstep2_2

public Complex[] ODEstep2_2(Complex zInitial,
                            Complex zFinal,
                            Complex initialVal,
                            Complex approxInitDeriv,
                            int numSubdivision)

A first quadratic Taylorstep to the middle, then average the second derivative at these two points, complete with a second quadratic step using the average second derivative. A 4th order method. (f')^2 = sqrt(Polynomial(f)).

ODEstep4

public Complex[] ODEstep4(Complex zInitial,
                          Complex zFinal,
                          Complex initialVal,
                          Complex approxInitDeriv,
                          int numSubdivision)

RootOfPolynomial

public Complex RootOfPolynomial(Complex f,
                                Complex approxInitDeriv)

RootOfPolynomialInverse

public Complex RootOfPolynomialInverse(Complex f,
                                       Complex approxInitDerivInv)

ComplexMultiStepIntegrator

public Complex[] ComplexMultiStepIntegrator(Complex zInitial,
                                            Complex zFinal,
                                            Complex valInitial,
                                            Complex approxInitDeriv,
                                            double subs)

The following integrates 1/sqrt(Poly) and continues the value of the root. The integrater is exact on polynomials of degree 7. The indefinite integral is the inverse function of the elliptic function defined by (f')^2 = Poly(f). This is used to compute periods of f.