Package edu.sc.seis.TauP
Class Complex
java.lang.Object
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= yThe 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
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Field Summary
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Constructor Summary
Constructors Constructor Description Complex()
Constructs a Complex equal to zero.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.Complex(Complex z)
Constructs a Complex equal to the argument. -
Method Summary
Modifier and Type Method Description 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(double x)
Copies the contents of a double into this Complex.Complex
assign(Complex z)
Copies the contents of a Complex 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(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
minus(Complex y)
Returns the difference of this Complex object and another Complex object, this-y.static Complex
minus(Complex x, double y)
Returns the difference of a Complex object and a double, x-y.static Complex
minus(Complex x, Complex y)
Returns the difference of two Complex objects, x-y.Complex
minusEquals(double y)
Subtracts a double from this Complex and returns the difference, this -= y.Complex
minusEquals(Complex y)
Subtracts a Complex 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(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
over(Complex y)
Returns this Complex object divided by another Complex object, this/y.static Complex
over(Complex x, double y)
Returns Complex object divided by a double, x/y.static Complex
over(Complex x, Complex y)
Returns Complex object divided by a Complex object, x/y.Complex
overEquals(double y)
Divides this Complex by a double and returns the result, this /= y.Complex
overEquals(Complex y)
Divides this Complex by a Complex and returns the result, this /= y.Complex
overReverse(double x)
Returns a double dividied by this Complex object, x/this.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
plus(Complex y)
Returns the sum of this Complex and another Complex, this+y.static Complex
plus(Complex x, double y)
Returns the sum of a Complex and a double, x+y.static Complex
plus(Complex x, Complex y)
Returns the sum of two Complex objects, x+y.Complex
plusEquals(double y)
Adds a double into this Complex and returns the sum, this += y.Complex
plusEquals(Complex y)
Adds a Complex to 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 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 Complex
pow(Complex x, Complex y)
Returns the Complex x raised to the Complex y power.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(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
times(Complex y)
Returns the product of this Complex object and another Complex object, this*y.static Complex
times(Complex x, double y)
Returns the product of a Complex object and a double, x*y.static Complex
times(Complex x, Complex y)
Returns the product of two Complex objects, x*y.Complex
timesEquals(double y)
Multiplies this Complex by a double and returns the product, this *= y.Complex
timesEquals(Complex y)
Multiplies this Complex object by another Complex 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
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Field Details
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re
public double re -
im
public double im -
suffix
public static java.lang.String suffixString 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.
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Constructor Details
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Complex
Constructs a Complex equal to the argument.- Parameters:
z
- A Complex object If z is null then a NullPointerException is thrown.
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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.
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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.
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Complex
public Complex()Constructs a Complex equal to zero.
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Method Details
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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.
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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.
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equals
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.
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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 classjava.lang.Object
- Parameters:
obj
- The object to compare with.- Returns:
- True if the objects are the same; false otherwise.
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hashCode
public int hashCode()Returns a hashcode for this Complex.- Overrides:
hashCode
in classjava.lang.Object
- Returns:
- A hash code value for this object.
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real
Returns the real part of a Complex object.- Parameters:
z
- A Complex object.- Returns:
- The real part of z.
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imag
Returns the imaginary part of a Complex object.- Parameters:
z
- A Complex object.- Returns:
- The imaginary part of z.
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assign
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.
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assign
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.
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negative
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.
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conjugate
Returns the complex conjugate of a Complex object.- Parameters:
z
- A Complex object.- Returns:
- A newly constructed Complex initialized to complex conjugate of z.
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plus
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.
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plus
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.
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plus
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.
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plus
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.
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plus
Returns the sum of this Complex a double, this+y.- Parameters:
y
- A double value.- Returns:
- A newly constructed Complex initialized to this+y.
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plusReverse
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.
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plusEquals
Adds a Complex to this Complex and returns the sum, this += y.- Parameters:
y
- A Complex object.- Returns:
- This object augmented by the argument.
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plusEquals
Adds a double into this Complex and returns the sum, this += y.- Parameters:
y
- A double value.- Returns:
- This object augmented by the argument.
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minus
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.
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minus
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.
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minus
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..
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minus
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.
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minus
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.
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minusReverse
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.
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minusEquals
Subtracts a Complex from this Complex and returns the difference, this -= y.- Parameters:
y
- A Complex object.- Returns:
- This object less the input argument.
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minusEquals
Subtracts a double from this Complex and returns the difference, this -= y.- Parameters:
y
- A double value.- Returns:
- This object less the input argument.
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times
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.
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times
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.
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times
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.
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times
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.
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times
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.
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timesReverse
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.
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timesEquals
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.
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timesEquals
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.
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over
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.
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over
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.
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over
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.
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over
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.
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over
Returns this Complex object divided by double, this/y.- Parameters:
y
- The denominator, a double.- Returns:
- A newly constructed Complex initialized to x/y.
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overReverse
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.
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overEquals
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.
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overEquals
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.
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abs
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.
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argument
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].
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sqrt
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.
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exp
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.
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log
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].
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sin
Returns the sine of a Complex.- Parameters:
z
- A Complex object.- Returns:
- A newly constructed Complex initialized to sine of the argument.
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cos
Returns the cosine of a Complex.- Parameters:
z
- A Complex object.- Returns:
- A newly constructed Complex initialized to cosine of the argument.
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tan
Returns the tangent of a Complex.- Parameters:
z
- A Complex object.- Returns:
- A newly constructed Complex initialized to tangent of the argument.
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asin
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].
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acos
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].
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atan
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].
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sinh
Returns the hyperbolic sine of a Complex.- Parameters:
z
- A Complex object.- Returns:
- A newly constructed Complex initialized to hyperbolic sine of the argument.
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cosh
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.
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tanh
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.
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pow
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.
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asinh
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].
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acosh
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].
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atanh
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].
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pow
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.
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toString
public java.lang.String toString()Returns a String representation for the specified Complex.- Overrides:
toString
in classjava.lang.Object
- Returns:
- A String representation for this object.
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valueOf
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.
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