Class VisualNumerics.math.Complex

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Class VisualNumerics.math.Complex

java.lang.Object
   |
   +----VisualNumerics.math.Complex

public class Complex
extends Object

This class implements complex numbers. It provides the basic operations (addition, subtraction, multiplication, division) as well as a set of complex functions.

im: Imaginary part of the Complex.
INFINITY: Complex infinity.
re: Real part of the Complex.
suffix: String used in converting Complex to String.

Complex(): Construct a Complex equal to zero.
Complex(Complex): Construct a Complex equal to the argument.
Complex(double): Construct a Complex with a zero imaginary part.
Complex(double, double): Construct a Complex with real and imaginary parts given by the input arguments.

abs(Complex): Returns the absolute value (modulus) of a Complex, |z|.
acos(Complex): Returns the inverse cosine (arc cosine) of a Complex.
add(Complex): Adds a Complex and returns the sum, this += y.
add(Complex, Complex): Returns the sum of two Complex's, x+y.
add(Complex, double): Returns the sum of a Complex and a double, x+y.
add(double): Adds a double and returns the sum, this += y.
add(double, Complex): Returns the sum of a double and a Complex, x+y.
argument(Complex): Returns the argument (phase) of a Complex, in radians.
asin(Complex)
conjugate(Complex): Returns the complex conjugate of a Complex.
cos(Complex): Returns the cosine of a Complex.
divide(Complex): Divides by a Complex and returns the result, this /= y.
divide(Complex, Complex): Returns Complex x divided by Complex y, x/y.
divide(Complex, double): Returns a Complex divided by a double, x/y.
divide(double): Divides by a double and returns the result, this /= y.
equals(Complex): Compares this Complex with another.
equals(Object): Compares this object against the specified object.
exp(Complex): Returns the exponential of a Complex z, exp(z).
isInfinite(Complex): Returns true if either component is an infinite value.
isNaN(Complex): Returns true if either component is a Not-a-Number (NaN) value.
log(Complex): Returns the logarithm of a Complex z, log(z).
multiply(Complex): Multiplies by a Complex and returns the product, this *= y.
multiply(Complex, Complex): Returns the product of two Complexs, x*y.
multiply(Complex, double): Returns the product of a Complex and a double, x*y.
multiply(double): Multiplies by a double and returns the product, this *= y.
multiply(double, Complex): Returns the product of a double and a Complex, x*y.
negate(Complex): Returns the negative of a Complex, -z.
pow(Complex, Complex): Returns the Complex x raised to the Complex y power.
pow(Complex, double): Returns the Complex z raised to the x power.
sin(Complex): Returns the sine of a Complex.
sqrt(Complex): Returns the square root of a Complex.
subtract(Complex): Subtracts a Complex and returns the difference, this -= y.
subtract(Complex, Complex): Returns the difference of two Complexes, x-y.
subtract(Complex, double): Returns the difference of a Complex and a double, x-y.
subtract(double): Subtracts a double and returns the difference, this -= y.
subtract(double, Complex): Returns the difference of a double and a Complex, x-y.
tan(Complex)
toString(): Returns a String representation for the specified Complex.

INFINITY

  public final static Complex INFINITY

Complex infinity.

  public double re

Real part of the Complex.

  public double im

Imaginary part of the Complex.

suffix

  public static String suffix

String used in converting Complex to String. Default is "i", but sometimes "j" is desired. Note that this is set for the class, not for a particular instance of a Complex.

Complex

  public Complex(Complex z)

Construct a Complex equal to the argument.

Parameters:: z - A Complex object.

Complex

  public Complex(double re,
                 double im)

Construct a Complex with real and imaginary parts given by the input arguments.

Parameters:: re - A double value equal to the real part of the Complex object.; im - A double value equal to the imaginary part of the Complex object.

Complex

  public Complex(double re)

Construct a Complex with a zero imaginary part.

Parameters:: re - A double value equal to the real part of the Complex object.

Complex

  public Complex()

Construct a Complex equal to zero.

toString

  public String toString()

Returns a String representation for the specified Complex.

Returns:: A String representation for this object.
Overrides:: toString in class Object

isNaN

  public static boolean isNaN(Complex z)

Returns true if either component is a Not-a-Number (NaN) value.

Parameters:: z - A Complex object.
Returns:: True if either component of the Complex object is NaN; false, otherwise.

isInfinite

  public static boolean isInfinite(Complex z)

Returns true if either component is an infinite value.

Parameters:: z - A Complex object.
Returns:: True if either component of the Complex object is NaN; false, otherwise.

equals

  public boolean equals(Complex z)

Compares this Complex with another.

Parameters:: z - A Complex object.
Returns:: True if the real and imaginary parts of this object are equal to their counterparts in the argument; false, otherwise.

equals

  public boolean equals(Object obj)

Compares this object against the specified object.

Note: To be useful in hashtables this method considers two NaN double values to be equal. This is not according to IEEE specification

Parameters:: obj - the object to compare with
Returns:: True if the objects are the same; false otherwise.
Overrides:: equals in class Object

negate

  public static Complex negate(Complex z)

Returns the negative of a Complex, -z.

Parameters:: z - A Complex object.
Returns:: A Complex object equal to the negative of the argument.

conjugate

  public static Complex conjugate(Complex z)

Returns the complex conjugate of a Complex.

Parameters:: z - A Complex object.
Returns:: The complex conjugate of the argument.

add

  public static Complex add(Complex x,
                            Complex y)

Returns the sum of two Complex's, x+y.

Parameters:: x - A Complex object.; y - A Complex object.
Returns:: The sum of the arguments.

add

  public static Complex add(double x,
                            Complex y)

Returns the sum of a double and a Complex, x+y.

Parameters:: x - A double value.; y - A Complex object.
Returns:: A Complex object equal to the sum of the arguments.

add

  public static Complex add(Complex x,
                            double y)

Returns the sum of a Complex and a double, x+y.

Parameters:: x - A Complex object.; y - A double value.
Returns:: A Complex object equal to the sum of the arguments.

add

  public Complex add(Complex y)

Adds a Complex and returns the sum, this += y.

Parameters:: y - A Complex object.
Returns:: This object augmented by the argument.

add

  public Complex add(double y)

Adds a double and returns the sum, this += y.

Parameters:: y - A double value.
Returns:: This object augmented by the argument.

subtract

  public static Complex subtract(Complex x,
                                 Complex y)

Returns the difference of two Complexes, x-y.

Parameters:: x - A Complex object.; y - A Complex object.
Returns:: The difference between the input arguments.

subtract

  public static Complex subtract(double x,
                                 Complex y)

Returns the difference of a double and a Complex, x-y.

Parameters:: x - A double value.; y - A Complex object.
Returns:: The difference between the input arguments.

subtract

  public static Complex subtract(Complex x,
                                 double y)

Returns the difference of a Complex and a double, x-y.

Parameters:: x - A Complex object.; y - A double value.
Returns:: A Complex object equal to the difference between the arguments.

subtract

  public Complex subtract(Complex y)

Subtracts a Complex and returns the difference, this -= y.

Parameters:: y - A Complex object.
Returns:: This object less the input argument.

subtract

  public Complex subtract(double y)

Subtracts a double and returns the difference, this -= y.

Parameters:: y - A double value.
Returns:: This object less the input argument.

multiply

  public static Complex multiply(double x,
                                 Complex y)

Returns the product of a double and a Complex, x*y.

Parameters:: x - A double value.; y - A Complex object.
Returns:: The product of the arguments.

multiply

  public static Complex multiply(Complex x,
                                 double y)

Returns the product of a Complex and a double, x*y.

Parameters:: x - A Complex object.; y - A double value.
Returns:: The product of the arguments.

multiply

  public Complex multiply(double y)

Multiplies by a double and returns the product, this *= y.

Parameters:: y - A double value.
Returns:: This object multiplied by the input argument.

multiply

  public static Complex multiply(Complex x,
                                 Complex y)

Returns the product of two Complexs, x*y.

Parameters:: x - A Complex object.; y - A Complex object.
Returns:: The product of the input arguments.

multiply

  public Complex multiply(Complex y)

Multiplies by a Complex and returns the product, this *= y.

Parameters:: y - A Complex object.
Returns:: This object multiplied by the input argument.

divide

  public static Complex divide(Complex x,
                               double y)

Returns a Complex divided by a double, x/y.

Parameters:: x - A Complex object.; y - A double value.
Returns:: The quotient of the input arguments.

divide

  public Complex divide(double y)

Divides by a double and returns the result, this /= y.

Parameters:: y - A double value.
Returns:: This object divided by the input argument.

divide

  public static Complex divide(Complex x,
                               Complex y)

Returns Complex x divided by Complex y, x/y.

Parameters:: x - A Complex object.; y - A Complex object.
Returns:: The quotient of the input arguments.

divide

  public Complex divide(Complex y)

Divides by a Complex and returns the result, this /= y.

Parameters:: y - A Complex object.
Returns:: This object divided by the input argument.

abs

  public static double abs(Complex z)

Returns the absolute value (modulus) of a Complex, |z|.

Parameters:: z - A Complex object.
Returns:: A double value equal to the absolute value of the argument.

argument

  public static double argument(Complex z)

Returns the argument (phase) of a Complex, in radians.

Parameters:: z - A Complex object.
Returns:: A double value equal to the argument or phase of a Complex.

sqrt

  public static Complex sqrt(Complex z)

Returns the square root of a Complex.

Parameters:: z - A Complex object.
Returns:: The square root of the input argument.

exp

  public static Complex exp(Complex z)

Returns the exponential of a Complex z, exp(z).

Parameters:: z - A Complex object.
Returns:: The exponential of the argument.

log

  public static Complex log(Complex z)

Returns the logarithm of a Complex z, log(z).

Parameters:: z - A Complex object.
Returns:: The logarithm of the argument.

sin

  public static Complex sin(Complex z)

Returns the sine of a Complex.

Parameters:: z - A Complex object.
Returns:: The sine of the argument.

cos

  public static Complex cos(Complex z)

Returns the cosine of a Complex.

Parameters:: z - A Complex object.
Returns:: The cosine of the argument.

tan

  public static Complex tan(Complex z)

asin

  public static Complex asin(Complex zinp)

acos

  public static Complex acos(Complex z)

Returns the inverse cosine (arc cosine) of a Complex.

Parameters:: z - A Complex object.
Returns:: The inverse cosine of the argument.

pow

  public static Complex pow(Complex z,
                            double x)

Returns the Complex z raised to the x power.

Parameters:: z - A Complex object.; x - A double value.
Returns:: A Complex object equal to z^x.

pow

  public static Complex pow(Complex x,
                            Complex y)

Returns the Complex x raised to the Complex y power.

Parameters:: x - A Complex object.; y - A Complex object.
Returns:: A Complex object equal to x^y.

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