Complex

net.sourceforge.javacomplex
Class Complex

java.lang.Object
  net.sourceforge.javacomplex.Complex

public abstract class Complex
extends java.lang.Object

JavaComplex is a complex number library for Java.

Project
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Version:: 1.0b1
Author:: Nuno Cruces

Field Summary
`static Complex`	`E` The `Complex` value closest to e, the base of the natural logarithms.
`static Complex`	`I` The `Complex` value for i, the imaginary unit.
`static Complex`	`INFINITY` The `Complex` value for ∞, the point at infinity.
`static Complex`	`NaN` The `Complex` not-a-number.
`static Complex`	`ONE` The `Complex` value for 1, the multiplicative identity.
`static Complex`	`PI` The `Complex` value closest to π, the ratio of a circle's circumference to its diameter.
`static Complex`	`ZERO` The `Complex` value for 0, the additive identity.

Constructor Summary
`Complex()`

Method Summary
`abstract double`	`abs()` Returns the absolute value of this `Complex` value.
`Complex`	`add(Complex z)` Returns the addition of a given `Complex` with this `Complex` value.
`abstract double`	`arg()` Returns the argument of this `Complex` value.
`static Complex`	`arg(double arg)` Creates a `Complex` value from its argument.
`static Complex`	`cart(double real, double imag)` Creates a `Complex` value from its real and imaginary parts.
`abstract Complex`	`conj()` Returns the conjugate of this `Complex` value.
`abstract double`	`decl()` Returns the declination of this `Complex` value.
`Complex`	`div(Complex z)` Returns the division by a given `Complex` of this `Complex` value.
`boolean`	`equals(java.lang.Object o)` Indicates wheather a given `Object` is equal to this `Complex` value.
`int`	`hashCode()` Returns a hash code value for this `Complex` value.
`abstract double`	`imag()` Returns the imaginary part of this `Complex` value.
`static Complex`	`imag(double imag)` Creates a `Complex` value from its imaginary part.
`abstract Complex`	`inv()` Returns the inverse of this `Complex` value.
`boolean`	`isInfinite()` Checks whether this `Complex` value is infinite.
`boolean`	`isNaN()` Checks whether this `Complex` value is not-a-number.
`Complex`	`mul(Complex z)` Returns the multiplication of a given `Complex` with this `Complex` value.
`abstract Complex`	`neg()` Returns the negation of this `Complex` value.
`abstract Complex`	`opp()` Returns the oposite of this `Complex` value.
`static Complex`	`polar(double abs, double arg)` Creates a `Complex` value from its absolute value and argument.
`abstract double`	`real()` Returns the real part of this `Complex` value.
`static Complex`	`real(double real)` Creates a `Complex` value from its real part.
`static Complex`	`riemann(double arg, double decl)` Creates a `Complex` value from its argument and declination.
`Complex`	`scale(double x)` Returns this `Complex` value scaled by a given `double` number.
`Complex`	`sqr()` Returns the square of this `Complex` value.
`Complex`	`sqrt()` Returns the principal squareroot of this `Complex` value.
`Complex`	`sub(Complex z)` Returns the subtraction of a given `Complex` from this `Complex` value.

Methods inherited from class java.lang.Object

getClass, notify, notifyAll, toString, wait, wait, wait

Field Detail

ZERO

public static final Complex ZERO

The Complex value for 0, the additive identity.

ONE

public static final Complex ONE

The Complex value for 1, the multiplicative identity.

I

public static final Complex I

The Complex value for i, the imaginary unit.

E

public static final Complex E

The Complex value closest to e, the base of the natural logarithms.

PI

public static final Complex PI

The Complex value closest to π, the ratio of a circle's circumference to its diameter.

NaN

public static final Complex NaN

The Complex not-a-number.

INFINITY

public static final Complex INFINITY

The Complex value for ∞, the point at infinity.

Constructor Detail

Complex

public Complex()

Method Detail

real

public static final Complex real(double real)

Creates a Complex value from its real part.

Factory method that creates a Complex object from its real part.

Special cases:

if the argument is nan, nan is returned;
if the argument is infinite, infinity is returned;

Parameters:: real - the real part
Returns:: the Complex of real part real and imaginary part 0

imag

public static final Complex imag(double imag)

Creates a Complex value from its imaginary part.

Factory method that creates a Complex object from its imaginary part.

Special cases:

if the argument is nan, nan is returned;
if the argument is infinite, infinity is returned;

Parameters:: imag - the imaginary part
Returns:: the Complex of imaginary part imag and real part 0

arg

public static final Complex arg(double arg)

Creates a Complex value from its argument.

Factory method that creates a Complex object from its argument.
This corresponds to the cis(x) = cos(x) + i sin(x) function.

Special case:

if the argument is nan or infinite, nan is returned;

Parameters:: arg - the argument
Returns:: the Complex of and argument arg absolute value 1

cart

public static final Complex cart(double real,
                                 double imag)

Creates a Complex value from its real and imaginary parts.

Factory method that creates a Complex object from its real and imaginary parts.

Special cases:

if either argument is nan, nan is returned;
if either argument is infinite and neither is nan, infinity is returned;

Parameters:: real - the real part; imag - the imaginary part
Returns:: the Complex of real part real and imaginary part imag

polar

public static final Complex polar(double abs,
                                  double arg)

Creates a Complex value from its absolute value and argument.

Factory method that creates a Complex object from its absolute value and argument.

Special cases:

if either argument is nan, nan is returned;
if the first argument is negative, nan is returned;
if the second argument is infinite, nan is returned;
if the first argument is positive infinity and the second is finite, infinity is returned;

Parameters:: abs - theabsolute value; arg - the argument
Returns:: the Complex of absolute value abs and argument arg

riemann

public static final Complex riemann(double arg,
                                    double decl)

Creates a Complex value from its argument and declination.

Factory method that creates a Complex object from argument and declination.

Special cases:

if either argument is infinite or nan, nan is returned;
if the second argument belongs to the third or fourth quadrants, nan is returned;

Parameters:: arg - the argument; decl - the declination
Returns:: the Complex with argument arg and declination decl
See Also:: decl()

isNaN

public final boolean isNaN()

Checks whether this Complex value is not-a-number.

Returns:: true if the value represented by this object is nan, false otherwise

isInfinite

public final boolean isInfinite()

Checks whether this Complex value is infinite.

Returns:: true if the value represented by this object is infinity, false otherwise

real

public abstract double real()

Returns the real part of this Complex value.

Special cases:

if the Complex is nan, nan is returned;
if the Complex is infinite, positive infinity is returned;

Returns:: the real part of the value represented by this object

imag

public abstract double imag()

Returns the imaginary part of this Complex value.

Special cases:

if the Complex is nan, nan is returned;
if the Complex is infinite, 0 is returned;

Returns:: the imaginary part of the value represented by this object

abs

public abstract double abs()

Returns the absolute value of this Complex value.

Special cases:

if the Complex is nan, nan is returned;
if the Complex is infinite, positive infinity is returned;

Returns:: the absolute value of the value represented by this object

arg

public abstract double arg()

Returns the argument of this Complex value.

Special cases:

if the Complex is nan, nan is returned;
if the Complex is infinite, 0 is returned;

Returns:: the argument of the value represented by this object

decl

public abstract double decl()

Returns the declination of this Complex value.

The declination is the angular distance mesured north from the south pole of Riemann's sphere. Also, note that this value belongs to [0+2kπ, π+2kπ] for some integer k.

Special cases:

if the Complex is nan, nan is returned;
if the Complex is infinite, the double value closest to pi is returned;

Returns:: the declination of the value represented by this object

conj

public abstract Complex conj()

Returns the conjugate of this Complex value.

Special cases:

if the Complex is nan, nan is returned;
if the Complex is infinite, infinity is returned;

Returns:: the conjugate of the value represented by this object

neg

public abstract Complex neg()

Returns the negation of this Complex value.

Special cases:

if the Complex is nan, nan is returned;
if the Complex is infinite, infinity is returned;

Returns:: the negation of the value represented by this object

inv

public abstract Complex inv()

Returns the inverse of this Complex value.

Special cases:

if the Complex is nan, nan is returned;
if the Complex is zero, infinity is returned;
if the Complex is infinite, zero is returned;

Returns:: the inverse of the value represented by this object

opp

public abstract Complex opp()

Returns the oposite of this Complex value.

The opposite of a Complex value is the value that oposes it in the Riemann sphere representation of complex numbers.

Special cases:

if the Complex is nan, nan is returned;
if the Complex is zero, infinity is returned;
if the Complex is infinite, zero is returned;

Returns:: the oposite of the value represented by this object

equals

public final boolean equals(java.lang.Object o)

Indicates wheather a given Object is equal to this Complex value.

Complex objects are equal if and only if their real and imaginary parts are equal.
The equals method implements an equivalence relation, being reflexive, symmetric and transitive.

Exceptional cases:

nan is considered unequal to itself (which actually breaks reflexivity)

Parameters:: o - the reference object with which to compare
Returns:: true if this Complex value is the same as o, false otherwise

hashCode

public final int hashCode()

Returns a hash code value for this Complex value.

If two Complex values are equal according to the equals(Object) method, then calling the hashCode() method on each of those Complex values produces the same integer result.

Returns:: a hash code value for this Complex value
See Also:: equals(Object)

add

public Complex add(Complex z)

Returns the addition of a given Complex with this Complex value.

Special cases:

if either Complex is nan, nan is returned;
if both Complex values are infinite, nan is returned;
if one Complex is infinite and the other is finite, infinity is returned;

Returns:: the value represented by this object added to the argument

sub

public Complex sub(Complex z)

Returns the subtraction of a given Complex from this Complex value.

Special cases:

if either Complex is nan, nan is returned;
if both Complex values are infinite, nan is returned;
if one Complex is infinite and the other is finite, infinity is returned;

Returns:: the value represented by this object minus the argument

mul

public Complex mul(Complex z)

Returns the multiplication of a given Complex with this Complex value.

Special cases:

if either Complex is nan, nan is returned;
if either Complex is infinite and neither is nan nor zero, infinity is returned;
if one Complex is infinite and the other is zero, nan is returned;

Returns:: the value represented by this object multiplied by the argument

div

public Complex div(Complex z)

Returns the division by a given Complex of this Complex value.

Special cases:

if either Complex is nan, nan is returned;
if this Complex is infinite and the other is finite, infinity is returned;
if this Complex is finite and the other is infinite, zero is returned;
if this Complex is neither nan nor zero and the other is zero, infinity is returned;
if both Complex values are infinite, nan is returned;
if both Complex values are zero nan is returned;

Returns:: the value represented by this object divided by the argument

scale

public Complex scale(double x)

Returns this Complex value scaled by a given double number.

Special cases:

if either the Complex or the double is nan, nan is returned;
if either the Complex or the double is infinite and neither is nan nor zero, infinity is returned;
if the Complex is infinite and the double is zero, nan is returned;
if the Complex is zero and the double is infinite, nan is returned;

Returns:: the value represented by this object multiplied by the argument

sqr

public Complex sqr()

Returns the square of this Complex value.

Special cases:

if the Complex is nan, nan is returned;
if the Complex is infinite, infinity is returned;

Returns:: the value represented by this object multiplied by itself

sqrt

public Complex sqrt()

Returns the principal squareroot of this Complex value.

Special cases:

if the Complex is nan, nan is returned;
if the Complex is infinite, infinity is returned;

Returns:: the principal squareroot of the value represented by this object

net.sourceforge.javacomplex Class Complex

ZERO

ONE

I

E

PI

NaN

INFINITY

Complex

real

imag

arg

cart

polar

riemann

isNaN

isInfinite

real

imag

abs

arg

decl

conj

neg

inv

opp

equals

hashCode

add

sub

mul

div

scale

sqr

sqrt

net.sourceforge.javacomplex
Class Complex