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## org.nfunk.jep.type
Class Complex

    java.lang.Object
      org.nfunk.jep.type.Complex

    public class Complex

extends java.lang.Object

Represents a complex number with double precision real and imaginary components. Includes complex arithmetic functions.

The two main sources of reference used for creating this class were:
- "Numerical Recipes in C - The Art of Scientific Computing" (ISBN 0-521-43108-5) http://www.nr.com and
- The org.netlib.math.complex package (http://www.netlib.org) which was developed by Sandy Anderson and Priyantha Jayanetti (published under GPL).

Some of the arithmetic functions in this class are based on the mathematical equations given in the source of the netlib package. The functions were validated by comparing results with the netlib complex class.

It is important to note that the netlib complex package is more extensive and efficient (e.g. Garbage collector friendly) than this implementation. If high precision and efficiency if of necessity it is recommended to use the netlib package.

Version:
  2.3.0 alpha now extends Number, has add and sub methods., 2.3.0 beta 1 now overrides equals and hashCode. /* @version 2.3.0 beta 2 does not implement Number anymore, as caused too many problems.
Author:
  Nathan Funk

Constructor Summary
`Complex()` Default constructor.
`Complex(Complex z)` Copy constructor
`Complex(double re_in)` Constructor from a single double value.
`Complex(double re_in, double im_in)` Initialize the real and imaginary components to the values given by the parameters.
`Complex(java.lang.Number re_in)` Construct from a Number.

Method Summary
`double` | `abs()` Returns the absolute value of the complex number.
`double` | `abs2()` Returns the square of the absolute value (re*re+im*im).
`Complex` | `acos()`
`Complex` | `acosh()`
`Complex` | `add(Complex b)` Adds the complex number with another complex value.
`double` | `arg()` Returns the argument of this complex number (Math.atan2(re,im))
`Complex` | `asin()`
`Complex` | `asinh()`
`Complex` | `atan()`
`Complex` | `atanh()`
`Complex` | `conj()` Returns the complex conjugate.
`Complex` | `cos()` Returns the cosine of this complex number.
`Complex` | `cosh()`
`Complex` | `div(Complex b)` Returns the result of dividing this complex number by the parameter.
`double` | `doubleValue()` Returns real part.
`boolean` | `equals(Complex b, double tolerance)` Compares this object with the Complex number given as parameter b.
`boolean` | `equals(java.lang.Object o)` Compares this object against the specified object.
`float` | `floatValue()` Returns real part.
`int` | `hashCode()` Always override hashCode when you override equals.
`double` | `im()` Returns the imaginary component of this object
`int` | `intValue()` Returns real part.
`boolean` | `isInfinite()` Returns `true` if either the real or imaginary component of this `Complex` is an infinite value.
`boolean` | `isNaN()` Returns `true` if either the real or imaginary component of this `Complex` is a Not-a-Number (`NaN`) value.
`Complex` | `log()` Returns the logarithm of this complex number.
`long` | `longValue()` Returns real part.
`Complex` | `mul(Complex b)` Multiply the complex number with another complex value.
`Complex` | `mul(double b)` Multiply the complex number with a double value.
`Complex` | `neg()` Returns the negative value of this complex number.
`static Complex` | `polarValueOf(java.lang.Number r, java.lang.Number theta)` Converts an [r,theta] pair to a complex number r * e^(i theta).
`Complex` | `power(Complex exponent)` Returns the value of this complex number raised to the power of a complex exponent
`Complex` | `power(double exponent)` Returns the value of this complex number raised to the power of a real component (in double precision).
`double` | `re()` Returns the real component of this object
`void` | `set(Complex z)` Copies the values from the parameter object to this object
`void` | `set(double re_in, double im_in)` Sets the real and imaginary values of the object.
`void` | `setIm(double im_in)` Sets the imaginary component of the object
`void` | `setRe(double re_in)` Sets the real component of the object
`Complex` | `sin()` Returns the sine of this complex number.
`Complex` | `sinh()`
`Complex` | `sqrt()` Calculates the square root of this object.
`Complex` | `sub(Complex b)` Adds the complex number with another complex value.
`Complex` | `tan()` Returns the tangent of this complex number.
`Complex` | `tanh()`
`java.lang.String` | `toString()` Returns the value of this complex number as a string in the format: (real, imaginary).
`java.lang.String` | `toString(java.text.NumberFormat format)`
`java.lang.String` | `toString(java.text.NumberFormat format, boolean flag)` Prints using specified number format in format or "2" or "3 i" or "(2+3 i)" if flag is true or "2+3 i" if flag is false

Methods inherited from class java.lang.Object
`clone, finalize, getClass, notify, notifyAll, wait, wait, wait`

Constructor Detail

### Complex

    public Complex()

  Default constructor.

### Complex

    public Complex(double re_in)

  Constructor from a single double value. The complex number is initialized with the real component equal to the parameter, and the imaginary component equal to zero.

### Complex

    public Complex(java.lang.Number re_in)

  Construct from a Number. This constructor uses the doubleValue() method of the parameter to initialize the real component of the complex number. The imaginary component is initialized to zero.

### Complex

    public Complex(Complex z)

  Copy constructor

### Complex

    public Complex(double re_in,
                   double im_in)

  Initialize the real and imaginary components to the values given by the parameters.

Method Detail

### re

    public double re()

  Returns the real component of this object

### im

    public double im()

  Returns the imaginary component of this object

### set

    public void set(Complex z)

  Copies the values from the parameter object to this object

### set

    public void set(double re_in,
                    double im_in)

  Sets the real and imaginary values of the object.

### setRe

    public void setRe(double re_in)

  Sets the real component of the object

### setIm

    public void setIm(double im_in)

  Sets the imaginary component of the object

### equals

    public boolean equals(Complex b,
                          double tolerance)

  Compares this object with the Complex number given as parameter

      b

  . The

      tolerance

  parameter is the radius within which the

      b

  number must lie for the two complex numbers to be considered equal.

  Returns:

        true

    if the complex number are considered equal,

        false

    otherwise.

### equals

    public boolean equals(java.lang.Object o)

  Compares this object against the specified object. The result is true if and only if the argument is not null and is a Complex object that represents the same complex number. Equality follows the same pattern as Double aplies to each field:
  - If d1 and d2 both represent Double.NaN, then the equals method returns true, even though Double.NaN==Double.NaN has the value false.
  - If d1 represents +0.0 while d2 represents -0.0, or vice versa, the equal test has the value false, even though +0.0==-0.0 has the value true.
  This definition allows hash tables to operate properly.

  Overrides:
    `equals` in class `java.lang.Object`
  Since:
    2.3.0.2

### hashCode

    public int hashCode()

  Always override hashCode when you override equals. Efective Java, Joshua Bloch, Sun Press

  Overrides:
    `hashCode` in class `java.lang.Object`

### toString

    public java.lang.String toString()

  Returns the value of this complex number as a string in the format:

      (real, imaginary)

  .

  Overrides:
    `toString` in class `java.lang.Object`

### toString

    public java.lang.String toString(java.text.NumberFormat format)

### toString

    public java.lang.String toString(java.text.NumberFormat format,
                                     boolean flag)

  Prints using specified number format in format or "2" or "3 i" or "(2+3 i)" if flag is true or "2+3 i" if flag is false

### isInfinite

    public boolean isInfinite()

  Returns `true` if either the real or imaginary component of this `Complex` is an infinite value.

  Returns:
    `true` if either component of the `Complex` object is infinite; `false`, otherwise.

### isNaN

    public boolean isNaN()

  Returns `true` if either the real or imaginary component of this `Complex` is a Not-a-Number (`NaN`) value.

  Returns:
    `true` if either component of the `Complex` object is `NaN`; `false`, otherwise.

### abs

    public double abs()

  Returns the absolute value of the complex number.

  Adapted from Numerical Recipes in C - The Art of Scientific Computing
  ISBN 0-521-43108-5

### abs2

    public double abs2()

  Returns the square of the absolute value (re*re+im*im).

### arg

    public double arg()

  Returns the argument of this complex number (Math.atan2(re,im))

### neg

    public Complex neg()

  Returns the negative value of this complex number.

### mul

    public Complex mul(double b)

  Multiply the complex number with a double value.

  Returns:
    The result of the multiplication

### add

    public Complex add(Complex b)

  Adds the complex number with another complex value.

  Returns:
    The result of the addition
  Since:
    2.3.0.1

### sub

    public Complex sub(Complex b)

  Adds the complex number with another complex value.

  Returns:
    The result of the addition
  Since:
    2.3.0.1

### mul

    public Complex mul(Complex b)

  Multiply the complex number with another complex value.

  Returns:
    The result of the multiplication

### div

    public Complex div(Complex b)

  Returns the result of dividing this complex number by the parameter.

### power

    public Complex power(double exponent)

  Returns the value of this complex number raised to the power of a real component (in double precision).

  This method considers special cases where a simpler algorithm would return "ugly" results.
  For example when the expression (-1e40)^0.5 is evaluated without considering the special case, the argument of the base is the double number closest to pi. When sin and cos are used for the final evaluation of the result, the slight difference of the argument from pi causes a non-zero value for the real component of the result. Because the value of the base is so high, the error is magnified.Although the error is normal for floating point calculations, the consideration of commonly occuring special cases improves the accuracy and aesthetics of the results.

  If you know a more elegant way to solve this problem, please let me know at nathanfunk@hotmail.com .

### power

    public Complex power(Complex exponent)

  Returns the value of this complex number raised to the power of a complex exponent

### conj

    public Complex conj()

  Returns the complex conjugate.

### log

    public Complex log()

  Returns the logarithm of this complex number.

### sqrt

    public Complex sqrt()

  Calculates the square root of this object. Adapted from Numerical Recipes in C - The Art of Scientific Computing (ISBN 0-521-43108-5)

### sin

    public Complex sin()

  Returns the sine of this complex number.

### cos

    public Complex cos()

  Returns the cosine of this complex number.

### tan

    public Complex tan()

  Returns the tangent of this complex number.

### asin

    public Complex asin()

### acos

    public Complex acos()

### atan

    public Complex atan()

### sinh

    public Complex sinh()

### cosh

    public Complex cosh()

### tanh

    public Complex tanh()

### asinh

    public Complex asinh()

### acosh

    public Complex acosh()

### atanh

    public Complex atanh()

### polarValueOf

    public static Complex polarValueOf(java.lang.Number r,
                                       java.lang.Number theta)

  Converts an [r,theta] pair to a complex number r * e^(i theta).

  Parameters:
    `r` - The radius
    `theta` - The angle
  Returns:
    The complex result.
  Since:
    2.3.0.1

### doubleValue

    public double doubleValue()

  Returns real part.

  Since:
    2.3.0.1

### floatValue

    public float floatValue()

  Returns real part.

  Since:
    2.3.0.1

### intValue

    public int intValue()

  Returns real part.

  Since:
    2.3.0.1

### longValue

    public long longValue()

  Returns real part.

  Since:
    2.3.0.1

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