Package org.sm.smtools.math.complex

Class ComplexNumber

java.lang.Object
org.sm.smtools.math.complex.ComplexNumber
public final class ComplexNumber
extends java.lang.Object
The ComplexNumber class provides mathematical operations on complex numbers.

The class has a partial ordering imposed, which is measured via the modulus.

Note that this class is final cannot be subclassed!

Version:
21/09/2016
Author:
Sven Maerivoet

  • Field Summary

    Fields
    Modifier and Type Field Description
    static ComplexNumber kE
    The constant e.
    static ComplexNumber kI
    The constant i.
    static ComplexNumber kOne
    The constant 1 + 0i.
    static ComplexNumber kThree
    The constant 3 + 0i.
    static ComplexNumber kTwo
    The constant 2 + 0i.
    static ComplexNumber kZero
    The constant 0 + 0i.

  • Constructor Summary

    Constructors
    Constructor Description
    ComplexNumber()
    Constructs a complex number equal to 0 + 0i.
    ComplexNumber​(double realComponent)
    Constructs a complex number as a real number with a zero imaginary component.
    ComplexNumber​(double realComponent, double imaginaryComponent)
    Constructs a complex number with a specified value.
    ComplexNumber​(ComplexNumber c)
    The copy-constructor.

  • Method Summary

    Modifier and Type Method Description
    ComplexNumber add​(ComplexNumber c)
    Add the specified complex number to this one and returns a reference to the result.
    double argument()
    Returns the argument (phase) of this complex number (the result lies between 0 and 2 * Math.PI).
    ComplexNumber cabs()
    Returns the complex absolute of this complex number.
    ComplexNumber cbrt()
    Calculates the cubic root of this complex number and returns a reference to the result.
    java.lang.Object clone()  
    int compareTo​(ComplexNumber c)
    Compares this complex number to another one, via a partial ordering based on their moduli.
    ComplexNumber conjugate()
    Returns a reference to the conjugate of this complex number.
    ComplexNumber convertPolarToComplex​(java.lang.Double modulus, java.lang.Double argument)
    Converts from polar to complex form.
    ComplexNumber cos()
    Takes the cosine of this complex number and returns a reference to the result.
    ComplexNumber cosec()
    Takes the cosecans (= 1/sin) of this complex number and returns a reference to the result.
    ComplexNumber cosh()
    Takes the hyperbolic cosine of this complex number and returns a reference to the result.
    ComplexNumber cot()
    Takes the cotangent (= cos/sin) of this complex number and returns a reference to the result.
    ComplexNumber cotanh()
    Takes the hyperbolic cotangent of this complex number and returns a reference to the result.
    ComplexNumber cube()
    Returns a reference to the cube of this complex number.
    ComplexNumber divide​(ComplexNumber c)
    Divides this complex number by the specified one and returns a reference to the result.
    boolean equals​(ComplexNumber c)
    Compares this complex number to another one for total equality.
    ComplexNumber exp()
    Takes the exponential of this complex number and returns a reference to the result.
    static void forcePartialOrder​(ComplexNumber c1, ComplexNumber c2)
    Forces a partial order on two complex numbers c1 and c2 such that (Re1',Im1') ≤ (Re2',Im2').
    double imaginaryComponent()
    Returns the imaginary component of this complex number.
    ComplexNumber inverse()
    Returns the multiplicative inverse and returns a reference to the result.
    boolean isImaginary()
    Returns whether or not this complex number is only imaginary.
    boolean isReal()
    Returns whether or not this complex number is only real.
    ComplexNumber ln()
    Takes the natural logarithm of this complex number and returns a reference to the result.
    ComplexNumber log()
    Takes the base 10 logarithm of this complex number and returns a reference to the result.
    ComplexNumber logBase​(ComplexNumber base)
    Takes a custom logarithm of this complex number and returns a reference to the result.
    double modulus()
    Returns the modulus of this complex number.
    double modulusSquared()
    Returns the squared modulus of this complex number.
    ComplexNumber multiply​(ComplexNumber c)
    Multiplies the specified complex number with this one and returns a reference to the result.
    ComplexNumber negate()
    Returns the negative of this complex number.
    ComplexNumber pow​(double n)
    Exponentiates this complex number to a specified real power and returns a reference to the result.
    ComplexNumber pow​(ComplexNumber n)
    Exponentiates this complex number to a specified complex power and returns a reference to the result.
    double realComponent()
    Returns the real component of this complex number.
    ComplexNumber reciprocal()
    Returns a reference to the reciprocal of this complex number.
    ComplexNumber sec()
    Takes the secans (= 1/cos) of this complex number and returns a reference to the result.
    void set​(double realComponent, double imaginaryComponent)
    Explicitly sets the real and imaginary components of the complex number.
    ComplexNumber sin()
    Takes the sine of this complex number and returns a reference to the result.
    ComplexNumber sinh()
    Takes the hyperbolic sine of this complex number and returns a reference to the result.
    ComplexNumber sqr()
    Returns a reference to the square of this complex number.
    ComplexNumber sqrt()
    Calculates the absolute value of the square root (i.e., the principal square root) of this complex number and returns a reference to the result.
    ComplexNumber subtract​(ComplexNumber c)
    Subtracts the specified complex number from this one and returns a reference to the result.
    ComplexNumber tan()
    Takes the tangent (= sin/cos) of this complex number and returns a reference to the result.
    ComplexNumber tanh()
    Takes the hyperbolic tangent of this complex number and returns a reference to the result.
    java.lang.String toString()
    Returns a String representation of this complex number.

    Methods inherited from class java.lang.Object

    equals, getClass, hashCode, notify, notifyAll, wait, wait, wait

  • Field Details

    • kZero

      public static final ComplexNumber kZero
      The constant 0 + 0i.

    • kOne

      public static final ComplexNumber kOne
      The constant 1 + 0i.

    • kTwo

      public static final ComplexNumber kTwo
      The constant 2 + 0i.

    • kThree

      public static final ComplexNumber kThree
      The constant 3 + 0i.

    • kE

      public static final ComplexNumber kE
      The constant e.

    • kI

      public static final ComplexNumber kI
      The constant i.

  • Constructor Details

    • ComplexNumber

      public ComplexNumber()
      Constructs a complex number equal to 0 + 0i.

    • ComplexNumber

      public ComplexNumber​(double realComponent)
      Constructs a complex number as a real number with a zero imaginary component.
      Parameters:
      realComponent - the real component

    • ComplexNumber

      public ComplexNumber​(double realComponent, double imaginaryComponent)
      Constructs a complex number with a specified value.
      Parameters:
      realComponent - the real component
      imaginaryComponent - the imaginary component

    • ComplexNumber

      public ComplexNumber​(ComplexNumber c)
      The copy-constructor.
      Parameters:
      c - the complex number to copy

  • Method Details

    • set

      public void set​(double realComponent, double imaginaryComponent)
      Explicitly sets the real and imaginary components of the complex number.
      Parameters:
      realComponent - the real component
      imaginaryComponent - the imaginary component

    • realComponent

      public double realComponent()
      Returns the real component of this complex number.
      Returns:
      the real component of this complex number

    • imaginaryComponent

      public double imaginaryComponent()
      Returns the imaginary component of this complex number.
      Returns:
      the imaginary component of this complex number

    • isReal

      public boolean isReal()
      Returns whether or not this complex number is only real.
      Returns:
      whether or not this complex number is only real

    • isImaginary

      public boolean isImaginary()
      Returns whether or not this complex number is only imaginary.
      Returns:
      whether or not this complex number is only imaginary

    • negate

      public ComplexNumber negate()
      Returns the negative of this complex number.
      Returns:
      the negative of this complex number

    • cabs

      public ComplexNumber cabs()
      Returns the complex absolute of this complex number.

      It is defined as abs(real) + i abs(imaginary).

      Returns:
      the complex absolute of this complex number

    • add

      public ComplexNumber add​(ComplexNumber c)
      Add the specified complex number to this one and returns a reference to the result.
      Parameters:
      c - the complex number to add
      Returns:
      a reference to the result

    • subtract

      public ComplexNumber subtract​(ComplexNumber c)
      Subtracts the specified complex number from this one and returns a reference to the result.
      Parameters:
      c - the complex number to subtract
      Returns:
      a reference to the subtraction

    • multiply

      public ComplexNumber multiply​(ComplexNumber c)
      Multiplies the specified complex number with this one and returns a reference to the result.
      Parameters:
      c - the complex number to multiply with
      Returns:
      a reference to the multiplication

    • inverse

      public ComplexNumber inverse()
      Returns the multiplicative inverse and returns a reference to the result.
      Returns:
      a reference to the multiplicative inverse

    • modulus

      public double modulus()
      Returns the modulus of this complex number.
      Returns:
      the modulus of this complex number

    • modulusSquared

      public double modulusSquared()
      Returns the squared modulus of this complex number.
      Returns:
      the squared modulus of this complex number

    • argument

      public double argument()
      Returns the argument (phase) of this complex number (the result lies between 0 and 2 * Math.PI).
      Returns:
      the argument (phase) of this complex number

    • conjugate

      public ComplexNumber conjugate()
      Returns a reference to the conjugate of this complex number.
      Returns:
      a reference to the conjugate

    • reciprocal

      public ComplexNumber reciprocal()
      Returns a reference to the reciprocal of this complex number.
      Returns:
      a reference to the reciprocal

    • divide

      public ComplexNumber divide​(ComplexNumber c)
      Divides this complex number by the specified one and returns a reference to the result.
      Parameters:
      c - the complex number to divide by
      Returns:
      a reference to the division

    • sqrt

      public ComplexNumber sqrt()
      Calculates the absolute value of the square root (i.e., the principal square root) of this complex number and returns a reference to the result.
      Returns:
      a reference to the absolute value of the square root of this complex number

    • cbrt

      public ComplexNumber cbrt()
      Calculates the cubic root of this complex number and returns a reference to the result.
      Returns:
      a reference to the cubic root of this complex number

    • sqr

      public ComplexNumber sqr()
      Returns a reference to the square of this complex number.
      Returns:
      a reference to the square of this complex number

    • cube

      public ComplexNumber cube()
      Returns a reference to the cube of this complex number.
      Returns:
      a reference to the cube of this complex number

    • pow

      public ComplexNumber pow​(double n)
      Exponentiates this complex number to a specified real power and returns a reference to the result.

      If the modulus is 0, then the result is 0 + 0i.

      Parameters:
      n - the real power for the exponentiation
      Returns:
      a reference to this exponentiated complex number

    • pow

      public ComplexNumber pow​(ComplexNumber n)
      Exponentiates this complex number to a specified complex power and returns a reference to the result.

      If the modulus is 0, then the result is 0 + 0i.

      Parameters:
      n - the complex power for the exponentiation
      Returns:
      a reference to this exponentiated complex number

    • ln

      public ComplexNumber ln()
      Takes the natural logarithm of this complex number and returns a reference to the result.
      Returns:
      a reference to the natural logarithm of this complex number

    • log

      public ComplexNumber log()
      Takes the base 10 logarithm of this complex number and returns a reference to the result.
      Returns:
      a reference to the base 10 logarithm of this complex number

    • logBase

      public ComplexNumber logBase​(ComplexNumber base)
      Takes a custom logarithm of this complex number and returns a reference to the result.
      Parameters:
      base - the base of the custom logarithm
      Returns:
      a reference to the custom logarithm of this complex number

    • exp

      public ComplexNumber exp()
      Takes the exponential of this complex number and returns a reference to the result.
      Returns:
      a reference to the exponential of this complex number

    • cos

      public ComplexNumber cos()
      Takes the cosine of this complex number and returns a reference to the result.
      Returns:
      a reference to the cosine of this complex number

    • sin

      public ComplexNumber sin()
      Takes the sine of this complex number and returns a reference to the result.
      Returns:
      a reference to the sine of this complex number

    • tan

      public ComplexNumber tan()
      Takes the tangent (= sin/cos) of this complex number and returns a reference to the result.
      Returns:
      a reference to the tangent of this complex number

    • cot

      public ComplexNumber cot()
      Takes the cotangent (= cos/sin) of this complex number and returns a reference to the result.
      Returns:
      a reference to the cotangent of this complex number

    • sec

      public ComplexNumber sec()
      Takes the secans (= 1/cos) of this complex number and returns a reference to the result.
      Returns:
      a reference to the secans of this complex number

    • cosec

      public ComplexNumber cosec()
      Takes the cosecans (= 1/sin) of this complex number and returns a reference to the result.
      Returns:
      a reference to the cosecans of this complex number

    • sinh

      public ComplexNumber sinh()
      Takes the hyperbolic sine of this complex number and returns a reference to the result.
      Returns:
      a reference to the hyperbolic sine of this complex number

    • cosh

      public ComplexNumber cosh()
      Takes the hyperbolic cosine of this complex number and returns a reference to the result.
      Returns:
      a reference to the hyperbolic cosine of this complex number

    • tanh

      public ComplexNumber tanh()
      Takes the hyperbolic tangent of this complex number and returns a reference to the result.
      Returns:
      a reference to the hyperbolic tangent of this complex number

    • cotanh

      public ComplexNumber cotanh()
      Takes the hyperbolic cotangent of this complex number and returns a reference to the result.
      Returns:
      a reference to the hyperbolic cotangent of this complex number

    • toString

      public java.lang.String toString()
      Returns a String representation of this complex number.
      Overrides:
      toString in class java.lang.Object
      Returns:
      a String representation of this complex number

    • convertPolarToComplex

      public ComplexNumber convertPolarToComplex​(java.lang.Double modulus, java.lang.Double argument)
      Converts from polar to complex form.
      Parameters:
      modulus - the modulus of the specified polar form
      argument - the argument of the specified polar form
      Returns:
      a complex number corresponding to the specified polar form

    • compareTo

      public int compareTo​(ComplexNumber c)
      Compares this complex number to another one, via a partial ordering based on their moduli.
      Parameters:
      c - the complex number to compare to
      Returns:
      -1, 0, or 1 as this complex number's modulus is numerically less than, equal to, or greater than that of c

    • equals

      public boolean equals​(ComplexNumber c)
      Compares this complex number to another one for total equality.
      Parameters:
      c - the complex number to compare to
      Returns:
      true if both complex numbers are equal, false otherwise

    • clone

      public java.lang.Object clone()
      Overrides:
      clone in class java.lang.Object

    • forcePartialOrder

      public static void forcePartialOrder​(ComplexNumber c1, ComplexNumber c2)
      Forces a partial order on two complex numbers c1 and c2 such that (Re1',Im1') ≤ (Re2',Im2').
      Parameters:
      c1 - the first complex number
      c2 - the second complex number