Complex

Documentation of 'jsci.maths.Complex' Java class Complex

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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

Field Summary

Fields
Modifier and Type Field and Description

static Complex I
The complex number 0+1i.

static Complex ONE
The complex number 1+0i.

static Complex ZERO
The complex number 0+0i.

Fields
Modifier and Type	Field and Description
`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

Constructors
Constructor and Description
`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

All Methods Static Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`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
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.
  - log
```
public static Complex log(Complex z)
```
    Returns the natural logarithm (base e) of a complex number.
    
    Parameters:
    
    z - a complex number.
  - 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.

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Summary:
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Field |
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Detail:
Field |
Constr |
Method

Class Complex

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

I

ONE

ZERO

Constructor Detail

Complex

Complex

Method Detail

polar

equals

equals

equals

equals

toString

toString

hashCode

isZero

isNaN

isInfinite

real

imag

mod

modSqr

arg

norm

getSet

negate

inverse

involution

conjugate

add

add

addReal

addImag

subtract

subtract

subtractReal

subtractImag

scalarMultiply

multiply

multiply

multiply

scalarDivide

divide

divide

divide

pow

pow

sqr

sqrt

exp

log

sin

cos

tan

sinh

cosh

tanh

asin

acos

atan

asinh

acosh

atanh