edu.sc.seis.TauP
Class Complex

java.lang.Object
  extended by edu.sc.seis.TauP.Complex
All Implemented Interfaces:
java.io.Serializable, java.lang.Cloneable

public class Complex
extends java.lang.Object
implements java.io.Serializable, java.lang.Cloneable

This class implements complex numbers. It provides the basic operations (addition, subtraction, multiplication, division) as well as a set of complex functions. The binary operations have the form, where op is plus, minus, times or over.

 public static Complex op(Complex x, Complex y)   // x op y
 public static Complex op(Complex x, double y)    // x op y
 public static Complex op(double x, Complex y)    // x op y
 public Complex op(Complex y)                     // this op y
 public Complex op(double y)                      // this op y
 public Complex opReverse(double x)               // x op this
 public Complex opEquals(Complex y)               // this op= y
 public Complex opEquals(double y)                // this op= y
 
The functions in this class follow the rules for complex arithmetic as defined C9x Annex G:"IEC 559-compatible complex arithmetic." The API is not the same, but handling of infinities, NaNs, and positive and negative zeros is intended to follow the same rules. This class depends on the standard java.lang.Math class following certain rules, as defined in the C9x Annex F, for the handling of infinities, NaNs, and positive and negative zeros. Sun's specification is that java.lang.Math should reproduce the results in the Sun's fdlibm C library. This library appears to follow the Annex F specification. At least on Windows, Sun's JDK 1.0 and 1.1 do NOT follow this specification. Sun's JDK 1.2(RC2) does follow the Annex F specification. Thesefore, this class will not give the expected results for edge cases with JDK 1.0 and 1.1.

See Also:
Serialized Form

Field Summary
 double im
           
 double re
           
static java.lang.String suffix
          String used in converting Complex to String.
 
Constructor Summary
Complex()
          Constructs a Complex equal to zero.
Complex(Complex z)
          Constructs a Complex equal to the argument.
Complex(double re)
          Constructs a Complex with a zero imaginary part.
Complex(double re, double im)
          Constructs a Complex with real and imaginary parts given by the input arguments.
 
Method Summary
static double abs(Complex z)
          Returns the absolute value (modulus) of a Complex, |z|.
static Complex acos(Complex z)
          Returns the inverse cosine (arc cosine) of a Complex, with branch cuts outside the interval [-1,1] along the real axis.
static Complex acosh(Complex z)
          Returns the inverse hyperbolic cosine (arc cosh) of a Complex, with a branch cut at values less than one along the real axis.
static double argument(Complex z)
          Returns the argument (phase) of a Complex, in radians, with a branch cut along the negative real axis.
static Complex asin(Complex z)
          Returns the inverse sine (arc sine) of a Complex, with branch cuts outside the interval [-1,1] along the real axis.
static Complex asinh(Complex z)
          Returns the inverse hyperbolic sine (arc sinh) of a Complex, with a branch cuts outside the interval [-i,i].
 Complex assign(Complex z)
          Copies the contents of a Complex into this Complex.
 Complex assign(double x)
          Copies the contents of a double into this Complex.
static Complex atan(Complex z)
          Returns the inverse tangent (arc tangent) of a Complex, with branch cuts outside the interval [-i,i] along the imaginary axis.
static Complex atanh(Complex z)
          Returns the inverse hyperbolic tangent (arc tanh) of a Complex, with a branch cuts outside the interval [-1,1] on the real axis.
static Complex conjugate(Complex z)
          Returns the complex conjugate of a Complex object.
static Complex cos(Complex z)
          Returns the cosine of a Complex.
static Complex cosh(Complex z)
          Returns the hyperbolic cosh of a Complex.
 boolean equals(Complex z)
          Compares with another Complex.
 boolean equals(java.lang.Object obj)
          Compares this object against the specified object.
static Complex exp(Complex z)
          Returns the exponential of a Complex z, exp(z).
 int hashCode()
          Returns a hashcode for this Complex.
static double imag(Complex z)
          Returns the imaginary part of a Complex object.
 boolean isInfinite()
          Tests if this is an infinite complex number.
 boolean isNaN()
          Tests if this is a complex Not-a-Number (NaN) value.
static Complex log(Complex z)
          Returns the logarithm of a Complex z, with a branch cut along the negative real axis.
 Complex minus(Complex y)
          Returns the difference of this Complex object and another Complex object, this-y.
static Complex minus(Complex x, Complex y)
          Returns the difference of two Complex objects, x-y.
static Complex minus(Complex x, double y)
          Returns the difference of a Complex object and a double, x-y.
 Complex minus(double y)
          Subtracts a double from this Complex and returns the difference, this-y.
static Complex minus(double x, Complex y)
          Returns the difference of a double and a Complex object, x-y.
 Complex minusEquals(Complex y)
          Subtracts a Complex from this Complex and returns the difference, this -= y.
 Complex minusEquals(double y)
          Subtracts a double from this Complex and returns the difference, this -= y.
 Complex minusReverse(double x)
          Returns the difference of this Complex object and a double, this-y.
static Complex negative(Complex z)
          Returns the negative of a Complex object, -z.
 Complex over(Complex y)
          Returns this Complex object divided by another Complex object, this/y.
static Complex over(Complex x, Complex y)
          Returns Complex object divided by a Complex object, x/y.
static Complex over(Complex x, double y)
          Returns Complex object divided by a double, x/y.
 Complex over(double y)
          Returns this Complex object divided by double, this/y.
static Complex over(double x, Complex y)
          Returns a double divided by a Complex object, x/y.
 Complex overEquals(Complex y)
          Divides this Complex by a Complex and returns the result, this /= y.
 Complex overEquals(double y)
          Divides this Complex by a double and returns the result, this /= y.
 Complex overReverse(double x)
          Returns a double dividied by this Complex object, x/this.
 Complex plus(Complex y)
          Returns the sum of this Complex and another Complex, this+y.
static Complex plus(Complex x, Complex y)
          Returns the sum of two Complex objects, x+y.
static Complex plus(Complex x, double y)
          Returns the sum of a Complex and a double, x+y.
 Complex plus(double y)
          Returns the sum of this Complex a double, this+y.
static Complex plus(double x, Complex y)
          Returns the sum of a double and a Complex, x+y.
 Complex plusEquals(Complex y)
          Adds a Complex to this Complex and returns the sum, this += y.
 Complex plusEquals(double y)
          Adds a double into this Complex and returns the sum, this += y.
 Complex plusReverse(double x)
          Returns the sum of this Complex and a double, x+this.
static Complex pow(Complex x, Complex y)
          Returns the Complex x raised to the Complex y power.
static Complex pow(Complex z, double x)
          Returns the Complex z raised to the x power, with a branch cut for the first parameter (z) along the negative real axis.
static double real(Complex z)
          Returns the real part of a Complex object.
static Complex sin(Complex z)
          Returns the sine of a Complex.
static Complex sinh(Complex z)
          Returns the hyperbolic sine of a Complex.
static Complex sqrt(Complex z)
          Returns the square root of a Complex, with a branch cut along the negative real axis.
static Complex tan(Complex z)
          Returns the tangent of a Complex.
static Complex tanh(Complex z)
          Returns the hyperbolic tanh of a Complex.
 Complex times(Complex y)
          Returns the product of this Complex object and another Complex object, this*y.
static Complex times(Complex x, Complex y)
          Returns the product of two Complex objects, x*y.
static Complex times(Complex x, double y)
          Returns the product of a Complex object and a double, x*y.
 Complex times(double y)
          Returns the product of this Complex object and a double, this*y.
static Complex times(double x, Complex y)
          Returns the product of a double and a Complex object, x*y.
 Complex timesEquals(Complex y)
          Multiplies this Complex object by another Complex and returns the product, this *= y.
 Complex timesEquals(double y)
          Multiplies this Complex by a double and returns the product, this *= y.
 Complex timesReverse(double x)
          Returns the product of a double and this Complex, x*this.
 java.lang.String toString()
          Returns a String representation for the specified Complex.
static Complex valueOf(java.lang.String s)
          Parses a string into a Complex.
 
Methods inherited from class java.lang.Object
clone, finalize, getClass, notify, notifyAll, wait, wait, wait
 

Field Detail

re

public double re

im

public double im

suffix

public static java.lang.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.

Constructor Detail

Complex

public Complex(Complex z)
Constructs a Complex equal to the argument.

Parameters:
z - A Complex object If z is null then a NullPointerException is thrown.

Complex

public Complex(double re,
               double im)
Constructs 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)
Constructs a Complex with a zero imaginary part.

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

Complex

public Complex()
Constructs a Complex equal to zero.

Method Detail

isNaN

public boolean isNaN()
Tests if this is a complex Not-a-Number (NaN) value.

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

isInfinite

public boolean isInfinite()
Tests if this is an infinite complex number.

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

equals

public boolean equals(Complex z)
Compares with another Complex.

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

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(java.lang.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

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

hashCode

public int hashCode()
Returns a hashcode for this Complex.

Overrides:
hashCode in class java.lang.Object
Returns:
A hash code value for this object.

real

public static double real(Complex z)
Returns the real part of a Complex object.

Parameters:
z - A Complex object.
Returns:
The real part of z.

imag

public static double imag(Complex z)
Returns the imaginary part of a Complex object.

Parameters:
z - A Complex object.
Returns:
The imaginary part of z.

assign

public Complex assign(double x)
Copies the contents of a double into this Complex.

Parameters:
x - The real part.
Returns:
The modified Complex number. The real part is set to x and the imaginary part is set to zero.

assign

public Complex assign(Complex z)
Copies the contents of a Complex into this Complex.

Parameters:
z - A Complex object.
Returns:
The modified Complex number. If the argument is null then a NullPointerException is thrown.

negative

public static Complex negative(Complex z)
Returns the negative of a Complex object, -z.

Parameters:
z - A Complex object.
Returns:
A newly constructed Complex initialized to the negative of the argument.

conjugate

public static Complex conjugate(Complex z)
Returns the complex conjugate of a Complex object.

Parameters:
z - A Complex object.
Returns:
A newly constructed Complex initialized to complex conjugate of z.

plus

public static Complex plus(Complex x,
                           Complex y)
Returns the sum of two Complex objects, x+y.

Parameters:
x - A Complex object.
y - A Complex object.
Returns:
A newly constructed Complex initialized to x+y.

plus

public static Complex plus(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 newly constructed Complex initialized to x+y.

plus

public static Complex plus(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 newly constructed Complex initialized to x+y.

plus

public Complex plus(Complex y)
Returns the sum of this Complex and another Complex, this+y.

Parameters:
y - A Complex object.
Returns:
A newly constructed Complex initialized to this+y.

plus

public Complex plus(double y)
Returns the sum of this Complex a double, this+y.

Parameters:
y - A double value.
Returns:
A newly constructed Complex initialized to this+y.

plusReverse

public Complex plusReverse(double x)
Returns the sum of this Complex and a double, x+this.

Parameters:
x - A double value.
Returns:
A newly constructed Complex initialized to x+this.

plusEquals

public Complex plusEquals(Complex y)
Adds a Complex to this Complex and returns the sum, this += y.

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

plusEquals

public Complex plusEquals(double y)
Adds a double into this Complex and returns the sum, this += y.

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

minus

public static Complex minus(Complex x,
                            Complex y)
Returns the difference of two Complex objects, x-y.

Parameters:
x - A Complex object.
y - A Complex object.
Returns:
A newly constructed Complex initialized to x-y.

minus

public static Complex minus(Complex x,
                            double y)
Returns the difference of a Complex object and a double, x-y.

Parameters:
x - A Complex object.
y - A double value.
Returns:
A newly constructed Complex initialized to x-y.

minus

public static Complex minus(double x,
                            Complex y)
Returns the difference of a double and a Complex object, x-y.

Parameters:
x - A double value.
y - A Complex object.
Returns:
A newly constructed Complex initialized to x-y..

minus

public Complex minus(Complex y)
Returns the difference of this Complex object and another Complex object, this-y.

Parameters:
y - A Complex object.
Returns:
A newly constructed Complex initialized to this-y.

minus

public Complex minus(double y)
Subtracts a double from this Complex and returns the difference, this-y.

Parameters:
y - A double value.
Returns:
A newly constructed Complex initialized to this-y.

minusReverse

public Complex minusReverse(double x)
Returns the difference of this Complex object and a double, this-y.

Parameters:
x - A double value.
Returns:
A newly constructed Complex initialized to x-this.

minusEquals

public Complex minusEquals(Complex y)
Subtracts a Complex from this Complex and returns the difference, this -= y.

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

minusEquals

public Complex minusEquals(double y)
Subtracts a double from this Complex and returns the difference, this -= y.

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

times

public static Complex times(Complex x,
                            Complex y)
Returns the product of two Complex objects, x*y.

Parameters:
x - A Complex object.
y - A Complex object.
Returns:
A newly constructed Complex initialized to x*y.

times

public static Complex times(Complex x,
                            double y)
Returns the product of a Complex object and a double, x*y.

Parameters:
x - A Complex object.
y - A double value.
Returns:
A newly constructed Complex initialized to x*y.

times

public static Complex times(double x,
                            Complex y)
Returns the product of a double and a Complex object, x*y.

Parameters:
x - A double value.
y - A Complex object.
Returns:
A newly constructed Complex initialized to x*y.

times

public Complex times(Complex y)
Returns the product of this Complex object and another Complex object, this*y.

Parameters:
y - A Complex object.
Returns:
A newly constructed Complex initialized to this*y.

times

public Complex times(double y)
Returns the product of this Complex object and a double, this*y.

Parameters:
y - A double value.
Returns:
A newly constructed Complex initialized to this*y.

timesReverse

public Complex timesReverse(double x)
Returns the product of a double and this Complex, x*this.

Parameters:
x - A double value.
Returns:
A newly constructed Complex initialized to x*this.

timesEquals

public Complex timesEquals(Complex y)
Multiplies this Complex object by another Complex and returns the product, this *= y.

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

timesEquals

public Complex timesEquals(double y)
Multiplies this Complex by a double and returns the product, this *= y.

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

over

public static Complex over(Complex x,
                           Complex y)
Returns Complex object divided by a Complex object, x/y.

Parameters:
x - The numerator, a Complex object.
y - The denominator, a Complex object.
Returns:
A newly constructed Complex initialized to x/y.

over

public static Complex over(Complex x,
                           double y)
Returns Complex object divided by a double, x/y.

Parameters:
x - The numerator, a Complex object.
y - The denominator, a double.
Returns:
A newly constructed Complex initialized to x/y.

over

public static Complex over(double x,
                           Complex y)
Returns a double divided by a Complex object, x/y.

Parameters:
x - A double value.
y - The denominator, a Complex object.
Returns:
A newly constructed Complex initialized to x/y.

over

public Complex over(Complex y)
Returns this Complex object divided by another Complex object, this/y.

Parameters:
y - The denominator, a Complex object.
Returns:
A newly constructed Complex initialized to x/y.

over

public Complex over(double y)
Returns this Complex object divided by double, this/y.

Parameters:
y - The denominator, a double.
Returns:
A newly constructed Complex initialized to x/y.

overReverse

public Complex overReverse(double x)
Returns a double dividied by this Complex object, x/this.

Parameters:
x - The numerator, a double.
Returns:
A newly constructed Complex initialized to x/this.

overEquals

public Complex overEquals(Complex y)
Divides this Complex by a Complex and returns the result, this /= y.

Parameters:
y - The denominator, a Complex object.
Returns:
This object divided by the input argument.

overEquals

public Complex overEquals(double y)
Divides this Complex by a double and returns the result, this /= y.

Parameters:
y - The denominator, a double.
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, with a branch cut along the negative real axis.

Parameters:
z - A Complex object.
Returns:
A double value equal to the argument (or phase) of a Complex. It is in the interval [-pi,pi].

sqrt

public static Complex sqrt(Complex z)
Returns the square root of a Complex, with a branch cut along the negative real axis.

Parameters:
z - A Complex object.
Returns:
A newly constructed Complex initialized to square root of z. Its real part is non-negative.

exp

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

Parameters:
z - A Complex object.
Returns:
A newly constructed Complex initialized to exponential of the argument.

log

public static Complex log(Complex z)
Returns the logarithm of a Complex z, with a branch cut along the negative real axis.

Parameters:
z - A Complex object.
Returns:
A newly constructed Complex initialized to logarithm of the argument. Its imaginary part is in the interval [-i*pi,i*pi].

sin

public static Complex sin(Complex z)
Returns the sine of a Complex.

Parameters:
z - A Complex object.
Returns:
A newly constructed Complex initialized to sine of the argument.

cos

public static Complex cos(Complex z)
Returns the cosine of a Complex.

Parameters:
z - A Complex object.
Returns:
A newly constructed Complex initialized to cosine of the argument.

tan

public static Complex tan(Complex z)
Returns the tangent of a Complex.

Parameters:
z - A Complex object.
Returns:
A newly constructed Complex initialized to tangent of the argument.

asin

public static Complex asin(Complex z)
Returns the inverse sine (arc sine) of a Complex, with branch cuts outside the interval [-1,1] along the real axis.

Parameters:
z - A Complex object.
Returns:
A newly constructed Complex initialized to inverse (arc) sine of the argument. The real part of the result is in the interval [-pi/2,+pi/2].

acos

public static Complex acos(Complex z)
Returns the inverse cosine (arc cosine) of a Complex, with branch cuts outside the interval [-1,1] along the real axis.

Parameters:
z - A Complex object.
Returns:
A newly constructed Complex initialized to inverse (arc) cosine of the argument. The real part of the result is in the interval [0,pi].

atan

public static Complex atan(Complex z)
Returns the inverse tangent (arc tangent) of a Complex, with branch cuts outside the interval [-i,i] along the imaginary axis.

Parameters:
z - A Complex object.
Returns:
A newly constructed Complex initialized to inverse (arc) tangent of the argument. Its real part is in the interval [-pi/2,pi/2].

sinh

public static Complex sinh(Complex z)
Returns the hyperbolic sine of a Complex.

Parameters:
z - A Complex object.
Returns:
A newly constructed Complex initialized to hyperbolic sine of the argument.

cosh

public static Complex cosh(Complex z)
Returns the hyperbolic cosh of a Complex.

Parameters:
z - A Complex object.
Returns:
A newly constructed Complex initialized to the hyperbolic cosine of the argument.

tanh

public static Complex tanh(Complex z)
Returns the hyperbolic tanh of a Complex.

Parameters:
z - A Complex object.
Returns:
A newly constructed Complex initialized to the hyperbolic tangent of the argument.

pow

public static Complex pow(Complex z,
                          double x)
Returns the Complex z raised to the x power, with a branch cut for the first parameter (z) along the negative real axis.

Parameters:
z - A Complex object.
x - A double value.
Returns:
A newly constructed Complex initialized to z to the power x.

asinh

public static Complex asinh(Complex z)
Returns the inverse hyperbolic sine (arc sinh) of a Complex, with a branch cuts outside the interval [-i,i].

Parameters:
z - A Complex object.
Returns:
A newly constructed Complex initialized to inverse (arc) hyperbolic sine of the argument. Its imaginary part is in the interval [-i*pi/2,i*pi/2].

acosh

public static Complex acosh(Complex z)
Returns the inverse hyperbolic cosine (arc cosh) of a Complex, with a branch cut at values less than one along the real axis.

Parameters:
z - A Complex object.
Returns:
A newly constructed Complex initialized to inverse (arc) hyperbolic cosine of the argument. The real part of the result is non-negative and its imaginary part is in the interval [-i*pi,i*pi].

atanh

public static Complex atanh(Complex z)
Returns the inverse hyperbolic tangent (arc tanh) of a Complex, with a branch cuts outside the interval [-1,1] on the real axis.

Parameters:
z - A Complex object.
Returns:
A newly constructed Complex initialized to inverse (arc) hyperbolic tangent of the argument. The imaginary part of the result is in the interval [-i*pi/2,i*pi/2].

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 newly constructed Complex initialized to xy.

toString

public java.lang.String toString()
Returns a String representation for the specified Complex.

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

valueOf

public static Complex valueOf(java.lang.String s)
                       throws java.lang.NumberFormatException
Parses a string into a Complex.

Parameters:
s - The string to be parsed.
Returns:
A newly constructed Complex initialized to the value represented by the string argument.
Throws:
java.lang.NumberFormatException - If the string does not contain a parsable Complex number.
java.lang.NullPointerException - If the input argument is null.