Complex

Documentation of 'vmm3d.core.Complex' Java class Complex

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java.lang.Object
- vmm3d.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

Fields
Modifier and Type Field and Description

static Complex I_C

double im

static Complex ONE_C

double re

static Complex ZERO_C

Fields
Modifier and Type	Field and Description
`static Complex`	`I_C`
`double`	`im`
`static Complex`	`ONE_C`
`double`	`re`
`static Complex`	`ZERO_C`

Constructor Summary

Constructors
Constructor and Description
`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

All Methods Static Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`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 az+bc, 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.rec.re + z.imc.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 (rcos(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 az+bc, 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, ib, -ib, a + i, a - i, a + ib, or a - ib.

Methods inherited from class java.lang.Object
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()
```

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All Classes

Summary:
Nested |
Field |
Constr |
Method

Detail:
Field |
Constr |
Method

Class Complex

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

ZERO_C

ONE_C

I_C

re

im

Constructor Detail

Complex

Complex

Complex

Complex

Method Detail

equals

conj

polar

plus

minus

times

dividedBy

times

plus

minus

dividedBy

realLinComb

complexLinComb

dot

abs2

r

theta

exponential

inverse

log

logNearer

sinh

cosh

sine

power

integerPower

integerRoot

squareRootNearer

mobius1_1

stereographicProjection

assign

toString

assign

det

assignTimes

assignInvert

assignPow

assignPlus

assignPlus

assignMinus

assignTimes

assignTimes

assignTimes

assignDivide

assignTimesTimes

assignPlusTimes

assignTimesPlus

assign_PlusTimes

assign_PlusTimes

assignTimes_PlusTimes

invert