org.opensourcephysics.numerics
Class Complex

java.lang.Object
  org.opensourcephysics.numerics.Complex

public class Complex
extends java.lang.Object

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 z) Returns the sum of two complex numbers
Complex	add(double d) Returns the sum of a complex number and a double
double	arg() Returns the argument of this complex number (Math.atan2(re,im))
Complex	asin()
Complex	asinh()
Complex	atan()
Complex	atanh()
Complex	cartesian() Convert polar to Cartesian
Complex	conjugate() Conjugats the complex number
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.
Complex	div(double d) Devide the complex number by a double value.
boolean	equals(Complex b, double tolerance) Compares this object with the Complex number given as parameter
Complex	exp() Returns e to the power of the complex number
double	im() Returns the imaginary component of this object
Complex	invert()
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.
double	mag() Returns the magnitude of the complex number
Complex	mul(Complex b) Multiplies the complex number with another complex value.
Complex	mul(double b) Multiplies the complex number with a double value.
Complex	neg() Returns the negative value of this complex number.
static Complex	parseComplex(java.lang.String s) Convert text representation to a Complex.
Complex	polar() Convert Cartesian to polar
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	subtract(Complex z) Returns the subtraction of complex z from a complex number
Complex	subtract(double d) Subtracts the double d from the complex number Returns the subtraction of complex z from a complex number
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:

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, 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.

Parameters:

re_in -

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.

Parameters:

re_in -

Complex

public Complex(Complex z)

Copy constructor

Parameters:

z -

Complex

public Complex(double re_in,
               double im_in)

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

Parameters:

re_in -

im_in -

Method Detail

polar

public Complex polar()

Convert Cartesian to polar

cartesian

public Complex cartesian()

Convert polar to Cartesian

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.

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

abs

public double abs()

Returns the absolute value of the complex number.

abs2

public double abs2()

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

mag

public double mag()

Returns the magnitude of the complex number

arg

public double arg()

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

parseComplex

public static Complex parseComplex(java.lang.String s)

Convert text representation to a Complex. input format (real_double,imaginary_double)

add

public Complex add(Complex z)

Returns the sum of two complex numbers

add

public Complex add(double d)

Returns the sum of a complex number and a double

subtract

public Complex subtract(Complex z)

Returns the subtraction of complex z from a complex number

subtract

public Complex subtract(double d)

Subtracts the double d from the complex number Returns the subtraction of complex z from a complex number

neg

public Complex neg()

Returns the negative value of this complex number.

mul

public Complex mul(double b)

Multiplies the complex number with a double value.

Returns:

The result of the multiplication

mul

public Complex mul(Complex b)

Multiplies 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.

div

public Complex div(double d)

Devide the complex number by a double value.

Returns:

The result of the division

invert

public Complex invert()

conjugate

public Complex conjugate()

Conjugats the complex number

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 occurring special cases improves the accuracy and esthetics 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

exp

public Complex exp()

Returns e to the power of the complex number

log

public Complex log()

Returns the logarithm of this complex number.

sqrt

public Complex sqrt()

Calculates the square root of this object.

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()

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.