vmm.core
Class Complex

java.lang.Object
  vmm.core.Complex

public class Complex
extends java.lang.Object

A complex number, with a real and an imaginary part. (Possibley to be replaced with a class that has better support for complex arithmetic and functions of a complex variable.)

Field Summary

static Complex	I_C
double	im
static Complex	ONE_C
double	re
static Complex	ZERO_C

Constructor Summary

Complex()
Create a complex number initially equal to zero

Complex(Complex c)
Create a new complex number that is initially equal to a given complex number.

Complex(double x)
Create a complex number initially equal to the real number x.

Complex(double x, double y)
Create a complex number initially equal to x + iy

Method Summary

double	abs2() Returns the absolute value squared of this.
void	assign_PlusTimes(Complex a, Complex b)
void	assign_PlusTimes(Complex a, double d)
void	assign(Complex c)
void	assign(double x, double y)
void	assignDivide(Complex c)
void	assignInvert()
void	assignMinus(Complex c)
void	assignPlus(Complex c)
void	assignPlus(Complex a, Complex b)
void	assignPlusTimes(Complex a, Complex b)
void	assignPow(Complex z, double x)
void	assignTimes_PlusTimes(Complex a, Complex b, double d)
void	assignTimes(Complex c)
void	assignTimes(Complex a, Complex b)
void	assignTimes(Complex c, double d)
void	assignTimes(double d)
void	assignTimesPlus(Complex a, Complex b)
void	assignTimesTimes(Complex a, double d)
Complex	complexLinComb(Complex a, Complex b, Complex c) z.complexLinComb(a,b,c) returns a*z+b*c, Complex a,b;
Complex	conj() Computes the conjugate of a complex number.
double	cosh(double x)
double	det(Complex c)
Complex	dividedBy(Complex c) Returns this / c; c must be non-null.
Complex	dividedBy(double x)
double	dot(Complex c) z.dot(c) returns the scalar product z.re*c.re + z.im*c.im
boolean	equals(java.lang.Object obj) Returns true if obj is equal to this complex number.
Complex	exponential() Computes the complex exponential function, e^z, where z is this complex number.
Complex	integerPower(int k) Returns new Complex(this^k), for |k|< 9 using multiplication, for larger |k| using exp(k*log(this))
Complex	integerRoot(int k) Returns a complex k-th root of this complex number.
Complex	inverse() Computes the complex reciprocal function, 1/z, where z is this complex number.
Complex	invert()
Complex	log()
Complex	logNearer(Complex previous) Computes that complex logarithm of this complex number that is nearest to previous.
Complex	minus(Complex c) Returns this - c; c must be non-null.
Complex	minus(double x)
Complex	mobius1_1(double r) The Moebius transformation ((1+r)z + r)/(rz + 1+r) has +1,-1 as fixed points.
Complex	plus(Complex c) Returns this + c; c must be non-null.
Complex	plus(double x)
static Complex	polar(double r, double theta) Returns the complex number (r*cos(theta)) + i*(r*sin(theta)).
Complex	power(double x)
double	r() Returns the absolute value, "r" in polar coordinates, of this.
Complex	realLinComb(double a, double b, Complex c) z.realLinComb(a,b,c) returns a*z+b*c, double a,b;
Complex	sine()
double	sinh(double x)
Complex	squareRootNearer(Complex previous) Computes that square root of this complex number that is nearer to previous than to minus previous.
double[]	stereographicProjection()
double	theta() Returns arg(this), the angular polar coordinate of this complex number, in the range -pi to pi.
Complex	times(Complex c) Returns this * c; c must be non-null.
Complex	times(double x)
java.lang.String	toString() Returns a string representation of the form a, i, -i, i*b, -i*b, a + i, a - i, a + i*b, or a - i*b.

Methods inherited from class java.lang.Object

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

Field Detail

ZERO_C

public static final Complex ZERO_C

ONE_C

public static final Complex ONE_C

I_C

public static final Complex I_C

re

public double re

im

public double im

Constructor Detail

Complex

public Complex()

Create a complex number initially equal to zero

Complex

public Complex(double x)

Create a complex number initially equal to the real number x.

Complex

public Complex(double x,
               double y)

Create a complex number initially equal to x + iy

Complex

public Complex(Complex c)

Create a new complex number that is initially equal to a given complex number.

Parameters:

c - The complex number to be copied. If null, it is treated as zero.

Method Detail

equals

public boolean equals(java.lang.Object obj)

Returns true if obj is equal to this complex number. If obj is null or is not of type Complex, the return value is false.

Overrides:

equals in class java.lang.Object

conj

public Complex conj()

Computes the conjugate of a complex number.

polar

public static Complex polar(double r,
                            double theta)

Returns the complex number (r*cos(theta)) + i*(r*sin(theta)).

plus

public Complex plus(Complex c)

Returns this + c; c must be non-null.

minus

public Complex minus(Complex c)

Returns this - c; c must be non-null.

times

public Complex times(Complex c)

Returns this * c; c must be non-null.

dividedBy

public Complex dividedBy(Complex c)

Returns this / c; c must be non-null.

times

public Complex times(double x)

plus

public Complex plus(double x)

minus

public Complex minus(double x)

dividedBy

public Complex dividedBy(double x)

realLinComb

public Complex realLinComb(double a,
                           double b,
                           Complex c)

z.realLinComb(a,b,c) returns a*z+b*c, double a,b;

complexLinComb

public Complex complexLinComb(Complex a,
                              Complex b,
                              Complex c)

z.complexLinComb(a,b,c) returns a*z+b*c, Complex a,b;

dot

public double dot(Complex c)

z.dot(c) returns the scalar product z.re*c.re + z.im*c.im

abs2

public double abs2()

Returns the absolute value squared of this.

Returns:

real part squared plus imaginary part squared

r

public double r()

Returns the absolute value, "r" in polar coordinates, of this.

Returns:

the square root of (real part squared plus imaginary part squared)

theta

public double theta()

Returns arg(this), the angular polar coordinate of this complex number, in the range -pi to pi. The return value is simply Math.atan2(imaginary part, real part).

exponential

public Complex exponential()

Computes the complex exponential function, e^z, where z is this complex number.

inverse

public Complex inverse()

Computes the complex reciprocal function, 1/z, where z is this complex number.

log

public Complex log()

logNearer

public Complex logNearer(Complex previous)

Computes that complex logarithm of this complex number that is nearest to previous. A test code is in fractals.TestAnalyticContinuation.

sinh

public double sinh(double x)

cosh

public double cosh(double x)

sine

public Complex sine()

power

public Complex power(double x)

integerPower

public Complex integerPower(int k)

Returns new Complex(this^k), for |k|< 9 using multiplication, for larger |k| using exp(k*log(this))

integerRoot

public Complex integerRoot(int k)

Returns a complex k-th root of this complex number. The root that is returned is the one with the smallest positive arg. (If k is 0, the return value is 1. If k is negative, the value is 1/integerRoot(-k).)

squareRootNearer

public Complex squareRootNearer(Complex previous)

Computes that square root of this complex number that is nearer to previous than to minus previous. A test code is in fractals.TestAnalyticContinuation.

mobius1_1

public Complex mobius1_1(double r)

The Moebius transformation ((1+r)z + r)/(rz + 1+r) has +1,-1 as fixed points. It maps the real line and the unit circle to itsself

stereographicProjection

public double[] stereographicProjection()

assign

public void assign(double x,
                   double y)

toString

public java.lang.String toString()

Returns a string representation of the form a, i, -i, i*b, -i*b, a + i, a - i, a + i*b, or a - i*b. (Except when the real or imaginary part is undefined or infinite, the form is "(re) + i*(im)" where NaN, +INF, and -INF are used to indicate undefined and infinite values.)

Overrides:

toString in class java.lang.Object

assign

public void assign(Complex c)

det

public double det(Complex c)

assignTimes

public void assignTimes(double d)

assignInvert

public void assignInvert()

assignPow

public void assignPow(Complex z,
                      double x)

assignPlus

public void assignPlus(Complex a,
                       Complex b)

assignPlus

public void assignPlus(Complex c)

assignMinus

public void assignMinus(Complex c)

assignTimes

public void assignTimes(Complex c,
                        double d)

assignTimes

public void assignTimes(Complex c)

assignTimes

public void assignTimes(Complex a,
                        Complex b)

assignDivide

public void assignDivide(Complex c)

assignTimesTimes

public void assignTimesTimes(Complex a,
                             double d)

assignPlusTimes

public void assignPlusTimes(Complex a,
                            Complex b)

assignTimesPlus

public void assignTimesPlus(Complex a,
                            Complex b)

assign_PlusTimes

public void assign_PlusTimes(Complex a,
                             Complex b)

assign_PlusTimes

public void assign_PlusTimes(Complex a,
                             double d)

assignTimes_PlusTimes

public void assignTimes_PlusTimes(Complex a,
                                  Complex b,
                                  double d)

invert

public Complex invert()