JSci.maths
Class Complex

java.lang.Object
  JSci.maths.Complex

All Implemented Interfaces:

java.io.Serializable, Algebra.Member, BanachSpace.Member, CStarAlgebra.Member, Module.Member, VectorSpace.Member, Field.Member, Ring.Member, AbelianGroup.Member, Member

public final class Complex
extends java.lang.Object
implements Field.Member, CStarAlgebra.Member

The Complex class encapsulates complex numbers.

See Also:

Serialized Form

PlanetMath references:

Complex

Wikipedia references:

Complex_number

Field Summary

static Complex	I The complex number 0+1i.
static Complex	ONE The complex number 1+0i.
static Complex	ZERO The complex number 0+0i.

Constructor Summary

Complex(double x, double y)
Constructs the complex number x+iy.

Complex(java.lang.String s)
Constructs the complex number represented by a string.

Method Summary

static Complex	acos(Complex z) Returns the arc cosine of a complex number, in the range of (0.0 through , 0.0 through ).
static Complex	acosh(Complex z) Returns the arc hyperbolic cosine of a complex number, in the range of (0.0 through , 0.0 through ).
AbelianGroup.Member	add(AbelianGroup.Member x) Returns the addition of this number and another.
Complex	add(Complex z) Returns the addition of this complex number and another.
Complex	addImag(double imag) Returns the addition of this complex number with an imaginary part.
Complex	addReal(double real) Returns the addition of this complex number with a real part.
double	arg() Returns the argument of this complex number.
static Complex	asin(Complex z) Returns the arc sine of a complex number, in the range of (-/2 through /2, - through ).
static Complex	asinh(Complex z) Returns the arc hyperbolic sine of a complex number, in the range of (- through , -/2 through /2).
static Complex	atan(Complex z) Returns the arc tangent of a complex number, in the range of (-/2 through /2, - through ).
static Complex	atanh(Complex z) Returns the arc hyperbolic tangent of a complex number, in the range of (- through , -/2 through /2).
Complex	conjugate() Returns the complex conjugate of this complex number.
static Complex	cos(Complex z) Returns the trigonometric cosine of a complex angle.
static Complex	cosh(Complex z) Returns the hyperbolic cosine of a complex number.
Complex	divide(Complex z) Returns the division of this complex number by another.
Complex	divide(double x) Returns the division of this complex number by a scalar.
Field.Member	divide(Field.Member x) Returns the division of this number and another.
boolean	equals(double real, double imag) Compares two complex numbers for equality.
boolean	equals(double real, double imag, double tol)
boolean	equals(java.lang.Object obj) Compares two complex numbers for equality.
boolean	equals(java.lang.Object obj, double tol)
static Complex	exp(Complex z) Returns the exponential number e (2.718...) raised to the power of a complex number.
java.lang.Object	getSet()
int	hashCode() Returns a hashcode for this complex number.
double	imag() Returns the imaginary part of this complex number.
Field.Member	inverse() Returns the inverse of this complex number.
CStarAlgebra.Member	involution() Returns the involution of this complex number.
boolean	isInfinite() Returns true if either the real or imaginary part is infinite.
boolean	isNaN() Returns true if either the real or imaginary part is NaN.
boolean	isZero() Returns true if the modulus of this complex number is within the zero tolerance.
static Complex	log(Complex z) Returns the natural logarithm (base e) of a complex number.
double	mod() Returns the modulus of this complex number.
double	modSqr() Returns the square of the modulus of this complex number.
Complex	multiply(Complex z) Returns the multiplication of this complex number and another.
Complex	multiply(double x) Returns the multiplication of this complex number by a scalar.
Ring.Member	multiply(Ring.Member x) Returns the multiplication of this number and another.
AbelianGroup.Member	negate() Returns the negative of this complex number.
double	norm() Returns the C* norm.
static Complex	polar(double mod, double arg) Creates a complex number with the given modulus and argument.
Complex	pow(Complex z) Returns this complex number raised to the power of another.
Complex	pow(double x) Returns this complex number raised to the power of a scalar.
double	real() Returns the real part of this complex number.
VectorSpace.Member	scalarDivide(Field.Member x) Returns the division of this number by a complex scalar.
Module.Member	scalarMultiply(Ring.Member x) Returns the multiplication of this number by a complex scalar.
static Complex	sin(Complex z) Returns the trigonometric sine of a complex angle.
static Complex	sinh(Complex z) Returns the hyperbolic sine of a complex number.
Complex	sqr() Returns the square of this complex number.
Complex	sqrt() Returns the square root of this complex number.
AbelianGroup.Member	subtract(AbelianGroup.Member x) Returns the subtraction of this number and another.
Complex	subtract(Complex z) Returns the subtraction of this complex number by another.
Complex	subtractImag(double imag) Returns the subtraction of this complex number by an imaginary part.
Complex	subtractReal(double real) Returns the subtraction of this complex number by a real part.
static Complex	tan(Complex z) Returns the trigonometric tangent of a complex angle.
static Complex	tanh(Complex z) Returns the hyperbolic tangent of a complex number.
java.lang.String	toString() Returns a string representing the value of this complex number.
static java.lang.String	toString(double real, double imag) Returns a string representing the value of this complex number.

Methods inherited from class java.lang.Object

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

Field Detail

I

public static final Complex I

The complex number 0+1i.

ONE

public static final Complex ONE

The complex number 1+0i.

ZERO

public static final Complex ZERO

The complex number 0+0i.

Constructor Detail

Complex

public Complex(double x,
               double y)

Constructs the complex number x+iy.

Parameters:

x - the real value of a complex number.

y - the imaginary value of a complex number.

Complex

public Complex(java.lang.String s)
        throws java.lang.NumberFormatException

Constructs the complex number represented by a string.

Parameters:

s - a string representing a complex number.

Throws:

java.lang.NumberFormatException - if the string does not contain a parsable number.

Method Detail

polar

public static Complex polar(double mod,
                            double arg)

Creates a complex number with the given modulus and argument.

Parameters:

mod - the modulus of a complex number.

arg - the argument of a complex number.

equals

public boolean equals(java.lang.Object obj)

Compares two complex numbers for equality.

Overrides:

equals in class java.lang.Object

Parameters:

obj - a complex number.

equals

public boolean equals(java.lang.Object obj,
                      double tol)

equals

public boolean equals(double real,
                      double imag)

Compares two complex numbers for equality.

equals

public boolean equals(double real,
                      double imag,
                      double tol)

toString

public java.lang.String toString()

Returns a string representing the value of this complex number.

Overrides:

toString in class java.lang.Object

toString

public static java.lang.String toString(double real,
                                        double imag)

Returns a string representing the value of this complex number.

hashCode

public int hashCode()

Returns a hashcode for this complex number.

Overrides:

hashCode in class java.lang.Object

isZero

public boolean isZero()

Returns true if the modulus of this complex number is within the zero tolerance.

isNaN

public boolean isNaN()

Returns true if either the real or imaginary part is NaN.

isInfinite

public boolean isInfinite()

Returns true if either the real or imaginary part is infinite.

real

public double real()

Returns the real part of this complex number.

imag

public double imag()

Returns the imaginary part of this complex number.

mod

public double mod()

Returns the modulus of this complex number.

modSqr

public double modSqr()

Returns the square of the modulus of this complex number.

arg

public double arg()

Returns the argument of this complex number.

norm

public double norm()

Returns the C^* norm.

Specified by:

norm in interface BanachSpace.Member

getSet

public java.lang.Object getSet()

Specified by:

getSet in interface Member

negate

public AbelianGroup.Member negate()

Returns the negative of this complex number.

Specified by:

negate in interface AbelianGroup.Member

inverse

public Field.Member inverse()

Returns the inverse of this complex number.

Specified by:

inverse in interface Field.Member

involution

public CStarAlgebra.Member involution()

Returns the involution of this complex number.

Specified by:

involution in interface CStarAlgebra.Member

conjugate

public Complex conjugate()

Returns the complex conjugate of this complex number.

add

public AbelianGroup.Member add(AbelianGroup.Member x)

Returns the addition of this number and another.

Specified by:

add in interface AbelianGroup.Member

Parameters:

x - a group member

add

public Complex add(Complex z)

Returns the addition of this complex number and another.

Parameters:

z - a complex number.

addReal

public Complex addReal(double real)

Returns the addition of this complex number with a real part.

Parameters:

real - a real part.

addImag

public Complex addImag(double imag)

Returns the addition of this complex number with an imaginary part.

Parameters:

imag - an imaginary part.

subtract

public AbelianGroup.Member subtract(AbelianGroup.Member x)

Returns the subtraction of this number and another.

Specified by:

subtract in interface AbelianGroup.Member

Parameters:

x - a group member

subtract

public Complex subtract(Complex z)

Returns the subtraction of this complex number by another.

Parameters:

z - a complex number.

subtractReal

public Complex subtractReal(double real)

Returns the subtraction of this complex number by a real part.

Parameters:

real - a real part.

subtractImag

public Complex subtractImag(double imag)

Returns the subtraction of this complex number by an imaginary part.

Parameters:

imag - an imaginary part.

scalarMultiply

public Module.Member scalarMultiply(Ring.Member x)

Returns the multiplication of this number by a complex scalar.

Specified by:

scalarMultiply in interface Module.Member

Parameters:

x - a ring member

multiply

public Ring.Member multiply(Ring.Member x)

Returns the multiplication of this number and another.

Specified by:

multiply in interface Ring.Member

Parameters:

x - a ring member

multiply

public Complex multiply(Complex z)

Returns the multiplication of this complex number and another.

Parameters:

z - a complex number.

multiply

public Complex multiply(double x)

Returns the multiplication of this complex number by a scalar.

Parameters:

x - a real number.

scalarDivide

public VectorSpace.Member scalarDivide(Field.Member x)

Returns the division of this number by a complex scalar.

Specified by:

scalarDivide in interface VectorSpace.Member

Parameters:

x - a field member

divide

public Field.Member divide(Field.Member x)

Returns the division of this number and another.

Specified by:

divide in interface Field.Member

Parameters:

x - a field member

divide

public Complex divide(Complex z)

Returns the division of this complex number by another.

Parameters:

z - a complex number.

Throws:

java.lang.ArithmeticException - If divide by zero.

divide

public Complex divide(double x)

Returns the division of this complex number by a scalar.

Parameters:

x - a real number.

Throws:

java.lang.ArithmeticException - If divide by zero.

pow

public Complex pow(Complex z)

Returns this complex number raised to the power of another.

Parameters:

z - a complex number.

pow

public Complex pow(double x)

Returns this complex number raised to the power of a scalar.

Parameters:

x - a real number.

sqr

public Complex sqr()

Returns the square of this complex number.

sqrt

public Complex sqrt()

Returns the square root of this complex number.

exp

public static Complex exp(Complex z)

Returns the exponential number e (2.718...) raised to the power of a complex number.

Parameters:

z - a complex number.

PlanetMath references:

ExponentialFunction

log

public static Complex log(Complex z)

Returns the natural logarithm (base e) of a complex number.

Parameters:

z - a complex number.

PlanetMath references:

NaturalLogarithm2

sin

public static Complex sin(Complex z)

Returns the trigonometric sine of a complex angle.

Parameters:

z - an angle that is measured in radians.

cos

public static Complex cos(Complex z)

Returns the trigonometric cosine of a complex angle.

Parameters:

z - an angle that is measured in radians.

tan

public static Complex tan(Complex z)

Returns the trigonometric tangent of a complex angle.

Parameters:

z - an angle that is measured in radians.

sinh

public static Complex sinh(Complex z)

Returns the hyperbolic sine of a complex number.

Parameters:

z - a complex number.

cosh

public static Complex cosh(Complex z)

Returns the hyperbolic cosine of a complex number.

Parameters:

z - a complex number.

tanh

public static Complex tanh(Complex z)

Returns the hyperbolic tangent of a complex number.

Parameters:

z - a complex number.

asin

public static Complex asin(Complex z)

Returns the arc sine of a complex number, in the range of (-/2 through /2, - through ).

Parameters:

z - a complex number.

acos

public static Complex acos(Complex z)

Returns the arc cosine of a complex number, in the range of (0.0 through , 0.0 through ).

Parameters:

z - a complex number.

atan

public static Complex atan(Complex z)

Returns the arc tangent of a complex number, in the range of (-/2 through /2, - through ).

Parameters:

z - a complex number.

asinh

public static Complex asinh(Complex z)

Returns the arc hyperbolic sine of a complex number, in the range of (- through , -/2 through /2).

Parameters:

z - a complex number.

acosh

public static Complex acosh(Complex z)

Returns the arc hyperbolic cosine of a complex number, in the range of (0.0 through , 0.0 through ).

Parameters:

z - a complex number.

atanh

public static Complex atanh(Complex z)

Returns the arc hyperbolic tangent of a complex number, in the range of (- through , -/2 through /2).

Parameters:

z - a complex number.