Complex (jPicEdt 1.6-pre1 API documentation)

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jpicedt.util.math
Class Complex

java.lang.Object
  jpicedt.util.math.Complex

All Implemented Interfaces:: Serializable, Cloneable

public class Complex
extends Object
implements Cloneable, Serializable
extends Object
implements Cloneable, Serializable

Version:

1.0.1
Last change: ALM 23 Mar 2001 8:56 pm

A Java class for performing complex number arithmetic to double precision.

Author:

Sandy Anderson, Priyantha Jayanetti

  Copyright (c) 1997 - 2001, Alexander Anderson.

  This  program is free software; you can redistribute it and/or modify
  it under the terms of the GNU General Public License as published  by
  the Free Software Foundation; either version 2 of the License, or (at
  your option) any later version.

  This program is distributed in the hope that it will be  useful,  but
  WITHOUT   ANY   WARRANTY;   without  even  the  implied  warranty  of
  MERCHANTABILITY or FITNESS FOR A PARTICULAR  PURPOSE.   See  the  GNU
  General Public License for more details.

  You  should  have  received  a copy of the GNU General Public License
  along  with  this  program;  if  not,  write  to  the  Free  Software
  Foundation,  Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307
  USA.

The latest version of this Complex class is available from the Netlib Repository.

Here's an example of the style the class permits:

         import  ORG.netlib.math.complex.Complex;

         public class Test {

             public boolean isInMandelbrot (Complex c, int maxIter) {
                 Complex z= new Complex(0, 0);

                 for (int i= 0; i < maxIter; i++) {
                     z= z.cMul(z).cAdd(c);
                     if (z.abs() > 2) return false;
                 }

                 return true;
             }

         }

This class was developed by Sandy Anderson at the School of Electronic Engineering, Middlesex University, UK, and Priyantha Jayanetti at The Power Systems Program, the University of Maine, USA.

And many, many thanks to Mr. Daniel Hirsch, for his constant advice on the mathematics, his exasperating ability to uncover bugs blindfold, and for his persistent badgering over the exact wording of this documentation.

For instance, he starts to growl like a badger if you say "infinite set".

"Grrr...What's that mean? Countably infinite?"

You think for a while.

"Grrr..."

"Yes."

"Ah! Then you mean infinitely many."

See Also:

Serialized Form

Field Summary
`static String`	`AUTHOR`
`static String`	`DATE`
`static Complex`	`I` A constant representing i, the famous square root of -1.
`static Complex`	`ONE`
`static String`	`REMARK`
`static double`	`TWO_PI` Twice `PI` radians is the same thing as 360 degrees.
`static String`	`VERSION`
`static Complex`	`ZERO`

Constructor Summary
`Complex()` Constructs a `Complex` representing the number zero.
`Complex(Complex z)` Constructs a separate new `Complex` from an existing `Complex`.
`Complex(double re)` Constructs a `Complex` representing a real number.
`Complex(double re, double im)` Constructs a `Complex` from real and imaginary parts.

Method Summary
`double`	`abs()` Returns the magnitude of a `Complex` number.
`double`	`abs2()` Returns the square of the "length" of a `Complex` number.
`boolean`	`absoluteIsCloseTo(Complex z, double tolerance)` Renvoie `cSub(z).normInf() <= tolerance`.
`Complex`	`acos()` Returns the principal arc cosine of a `Complex` number.
`Complex`	`acosh()` Returns the principal inverse hyperbolic cosine of a `Complex` number.
`Complex`	`add(Complex z)`
`double`	`arg()` Returns the principal angle of a `Complex` number, in radians, measured counter-clockwise from the real axis.
`Complex`	`asin()` Returns the principal arc sine of a `Complex` number.
`Complex`	`asinh()` Returns the principal inverse hyperbolic sine of a `Complex` number.
`Complex`	`atan()` Returns the principal arc tangent of a `Complex` number.
`Complex`	`atanh()` Returns the principal inverse hyperbolic tangent of a `Complex` number.
`Complex`	`cAdd(Complex z)` To perform z1 + z2, you write `z1.cAdd(z2)`.
`Complex`	`cAdd(double z)` CAdd z to this without modifying this, and returns the result.
`static Complex`	`cart(double re, double im)` Returns a `Complex` from real and imaginary parts.
`Complex`	`cConj()` Returns the `Complex` "conjugate" of this.
`Complex`	`cCos()` Returns the cosine of a `Complex` number.
`Complex`	`cCot()` Returns the cotangent of a `Complex` number.
`Complex`	`cDiv(Complex z)` To perform z1 / z2, you write `z1.cDiv(z2)` .
`Complex`	`cIMul()` multiply this by i, without modifying this.
`Complex`	`cLog()` Returns the principal natural logarithm of a `Complex` number.
`Object`	`clone()` Overrides the `Cloneable` interface.
`Complex`	`cMIMul()` multiply this by -i, without modifying this.
`Complex`	`cMul(Complex z)` To perform z1 * z2, you write `z1.cMul(z2)` .
`Complex`	`cMul(double z)`
`Complex`	`cNeg()` Returns the "negative" of a `Complex` number.
`Complex`	`conj()` conjugate this, and return it for convenience
`Complex`	`cosec()` Returns the cosecant of a `Complex` number.
`Complex`	`cosh()` Returns the hyperbolic cosine of a `Complex` number.
`Complex`	`cPow(Complex exponent)` Renvoie la valeur `Complex` du `this` �lev�e raised to the power of a � la puissance d'un exposant `Complex` sans que `this` ne soit modifi�
`Complex`	`cScale(double scalar)` Returns the `Complex` scaled by a real number.
`Complex`	`cSin()` Returns the sine of a `Complex` number.
`Complex`	`cSqrt()` Returns a `Complex` representing one of the two square roots.
`Complex`	`cSub(Complex z)`
`Complex`	`cSub(double z)` Subtracts z from this without modifying this, and returns the result.
`Complex`	`cTan()` Returns the tangent of a `Complex` number.
`Complex`	`div(Complex z)`
`boolean`	`equals(Complex z, double tolerance)` Renvoie `absoluteIsCloseTo(z,Math.abs(tolerance))`.
`Complex`	`exp()` Returns the number e "raised to" a `Complex` power.
`double`	`im()` Extracts the imaginary part of a `Complex` as a `double`.
`Complex`	`iMul()` multiply this by i, which modifies this.
`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.
`static void`	`main(String[] args)` Useful for checking up on the exact version.
`Complex`	`miMul()` multiply this by -i, which modifies this.
`Complex`	`mul(Complex z)`
`Complex`	`mul(double z)`
`Complex`	`neg()` negate this, which modifies this.
`double`	`norm1()`
`double`	`normInf()`
`static Complex`	`polar(double r, double theta)` Returns a `Complex` from a size and direction.
`static Complex`	`pow(Complex base, Complex exponent)` Returns the `Complex` base raised to the power of the `Complex` exponent.
`static Complex`	`pow(Complex base, double exponent)` Returns the `Complex` base raised to the power of the exponent.
`static Complex`	`pow(double base, Complex exponent)` Returns the base raised to the power of the `Complex` exponent.
`double`	`re()` Extracts the real part of a `Complex` as a `double`.
`boolean`	`relativeIsCloseTo(Complex z, double tolerance)` Renvoie `cSub(z).normInf() <= tolerance * Math.max(normInf(), z.normInf())`.
`Complex`	`sec()` Returns the secant of a `Complex` number.
`Complex`	`sinh()` Returns the hyperbolic sine of a `Complex` number.
`Complex`	`sub(Complex z)`
`Complex`	`sub(double z)`
`Complex`	`tanh()` Returns the hyperbolic tangent of a `Complex` number.
`String`	`toString()` Converts a `Complex` into a `String` of the form `(`a `+` b`i)`.

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

Field Detail

VERSION

public static final String VERSION

See Also:: Constant Field Values

DATE

public static final String DATE

See Also:: Constant Field Values

AUTHOR

public static final String AUTHOR

See Also:: Constant Field Values

REMARK

public static final String REMARK

See Also:: Constant Field Values

TWO_PI

public static final double TWO_PI

Twice PI radians is the same thing as 360 degrees.

Since:: jPicEdt 1.6
See Also:: Constant Field Values

I

public static final Complex I

A constant representing i, the famous square root of -1.

The other square root of -1 is - i.

Since:: jPicEdt 1.6

ZERO

public static final Complex ZERO

ONE

public static final Complex ONE

Constructor Detail

Complex

public Complex()

Constructs a Complex representing the number zero.

Since:: jPicEdt 1.6

Complex

public Complex(double re)

Constructs a Complex representing a real number.

Parameters:: re - The real number
Since:: jPicEdt 1.6

Complex

public Complex(Complex z)

Constructs a separate new Complex from an existing Complex.

Parameters:: z - A Complex number
Since:: jPicEdt 1.6

Complex

public Complex(double re,
               double im)

Constructs a Complex from real and imaginary parts.

Note:

All methods in class Complex which deliver a Complex are written such that no intermediate Complex objects get generated. This means that you can easily anticipate the likely effects on garbage collection caused by your own coding.

Parameters:: re - Real part; im - Imaginary part
Since:: jPicEdt 1.6
See Also:: cart(double re, double im), polar(double, double)

Method Detail

main

public static void main(String[] args)

Useful for checking up on the exact version.

Since:: jPicEdt 1.6

cart

public static Complex cart(double re,
                           double im)

Returns a Complex from real and imaginary parts.

Parameters:: re - Real part; im - Imaginary part
Returns:: Complex from Cartesian coordinates
Since:: jPicEdt 1.6
See Also:: re(), im(), polar(double, double), toString()

polar

public static Complex polar(double r,
                            double theta)

Returns a Complex from a size and direction.

Parameters:: r - Size; theta - Direction (in radians)
Returns:: Complex from Polar coordinates
Since:: jPicEdt 1.6
See Also:: abs(), arg(), cart(double re, double im)

pow

public static Complex pow(Complex base,
                          double exponent)

Returns the Complex base raised to the power of the exponent.

Parameters:: base - The base "to raise"; exponent - The exponent "by which to raise"
Returns:: base "raised to the power of" exponent
Since:: jPicEdt 1.6
See Also:: pow(double, Complex)

pow

public static Complex pow(double base,
                          Complex exponent)

Returns the base raised to the power of the Complex exponent.

Parameters:: base - The base "to raise"; exponent - The exponent "by which to raise"
Returns:: base "raised to the power of" exponent
Since:: jPicEdt 1.6
See Also:: pow(Complex, Complex), exp()

pow

public static Complex pow(Complex base,
                          Complex exponent)

Returns the Complex base raised to the power of the Complex exponent.

Parameters:: base - The base "to raise"; exponent - The exponent "by which to raise"
Returns:: base "raised to the power of" exponent
Since:: jPicEdt 1.6
See Also:: pow(Complex, double), cPow(Complex)

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.
Since:: jPicEdt 1.6

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.
Since:: jPicEdt 1.6

equals

public boolean equals(Complex z,
                      double tolerance)

Renvoie absoluteIsCloseTo(z,Math.abs(tolerance)). Veuillez pr�f�rer la m�thode absoluteIsCloseTo(jpicedt.util.math.Complex, double) si vous savez que tolerance > 0.

Parameters:: z - Le Complex auquel on compare this; tolerance - LA tol�rance pour la comparaison
Returns:: true ou false
Since:: jPicEdt 1.6
See Also:: absoluteIsCloseTo(jpicedt.util.math.Complex, double)

absoluteIsCloseTo

public boolean absoluteIsCloseTo(Complex z,
                                 double tolerance)

Renvoie cSub(z).normInf() <= tolerance.

Parameters:: z - une valeur Complex � laquelle this est compar�.; tolerance - une valeur double, donnant la limite jusqu'� laquelle this et z sont consid�r�s proches.
Returns:: une valeur boolean, vraie la distance de this � z selon la norme infinie normInf() n'exc�de pas la tol�rance tolerance.
Since:: jPicEdt 1.6
See Also:: relativeIsCloseTo(jpicedt.util.math.Complex, double)

relativeIsCloseTo

public boolean relativeIsCloseTo(Complex z,
                                 double tolerance)

Renvoie

cSub(z).normInf() <= tolerance *
 Math.max(normInf(), z.normInf())

Parameters:: z - une valeur Complex � laquelle this est compar�.; tolerance - une valeur double, donnant la limite jusqu'� laquelle this et z sont consid�r�s proches.
Returns:: une valeur boolean, vraie la distance de this � z selon la norme infinie normInf() n'exc�de pas tolerance partie-pour-un de la plus grande des normes normInf() de this et z.
Since:: jPicEdt 1.6
See Also:: absoluteIsCloseTo(jpicedt.util.math.Complex, double)

clone

public Object clone()

Overrides the Cloneable interface.

Standard override; no change in semantics.

The following Java code example illustrates how to clone, or copy, a Complex number:

     Complex z1 =  new Complex(0, 1);
     Complex z2 =  (Complex) z1.clone();

Overrides:: clone in class Object

Returns:: An Object that is a copy of this Complex object.
Since:: jPicEdt 1.6
See Also:: Cloneable, Object.clone()

re

public double re()

Extracts the real part of a Complex as a double.

     re(x + i*y)  =  x

Returns:: The real part
Since:: jPicEdt 1.6
See Also:: im(), cart(double re, double im)

im

public double im()

Extracts the imaginary part of a Complex as a double.

     im(x + i*y)  =  y

Returns:: The imaginary part
Since:: jPicEdt 1.6
See Also:: re(), cart(double re, double im)

abs2

public double abs2()

Returns the square of the "length" of a Complex number.

     (x + i*y).abs2()  =  x*x + y*y

Always non-negative.

Returns:: The square norm
Since:: jPicEdt 1.6
See Also:: abs()

norm1

public double norm1()

Returns:: |re(this)|+|im(this)|

normInf

public double normInf()

Returns:: max(|re(this)|,|im(this)|)

abs

public double abs()

Returns the magnitude of a Complex number.

     abs(z)  =  sqrt(abs2(z))

In other words, it's Pythagorean distance from the origin (0 + 0i, or zero).

The magnitude is also referred to as the "modulus" or "length".

Always non-negative.

Returns:: The magnitude (or "length")
Since:: jPicEdt 1.6
See Also:: arg(), polar(double, double), abs2()

arg

public double arg()

Returns the principal angle of a Complex number, in radians, measured counter-clockwise from the real axis. (Think of the reals as the x-axis, and the imaginaries as the y-axis.)

There are infinitely many solutions, besides the principal solution. If A is the principal solution of arg(z), the others are of the form:

     A + 2*k*PI

where k is any integer.

arg() always returns a double between -PI and +PI.

Note:

2*PI radians is the same as 360 degrees.

Domain Restrictions:

There are no restrictions: the class defines arg(0) to be 0

Returns:: Principal angle (in radians)
Since:: jPicEdt 1.6
See Also:: abs(), polar(double, double)

cNeg

public Complex cNeg()

Returns the "negative" of a Complex number.

     cNeg(a + i*b)  =  -a - i*b

The magnitude of the negative is the same, but the angle is flipped through PI (or 180 degrees).

Returns:: Negative of the Complex
Since:: jPicEdt 1.6
See Also:: cScale(double)

neg

public Complex neg()

negate this, which modifies this.

Since:: jPicEdt 1.6

cConj

public Complex cConj()

Returns the Complex "conjugate" of this.

     cConj(x + i*y)  =  x - i*y

The conjugate appears "flipped" across the real axis.

Returns:: The Complex conjugate
Since:: jPicEdt 1.6

conj

public Complex conj()

conjugate this, and return it for convenience

Since:: jPicEdt 1.6

cScale

public Complex cScale(double scalar)

Returns the Complex scaled by a real number.

     cScale((x + i*y), s)  =  (x*s + i*y*s)

Scaling by the real number 2.0, doubles the magnitude, but leaves the arg() unchanged. Scaling by -1.0 keeps the magnitude the same, but flips the arg() by PI (180 degrees).

Parameters:: scalar - A real number scale factor
Returns:: Complex scaled by a real number
Since:: jPicEdt 1.6
See Also:: cMul(Complex), cDiv(Complex), cNeg(), cNeg()

cAdd

public Complex cAdd(Complex z)

To perform z1 + z2, you write z1.cAdd(z2).

     (a + i*b) + (c + i*d)  =  ((a+c) + i*(b+d))

Since:: jPicEdt 1.6

add

public Complex add(Complex z)

Returns:: this+z
Since:: jPicEdt 1.6

cSub

public Complex cSub(Complex z)

Returns:: this-z
Since:: jPicEdt 1.6

sub

public Complex sub(Complex z)

Returns:: this -= z
Since:: jPicEdt 1.6

sub

public Complex sub(double z)

Returns:: this -= z
Since:: jPicEdt 1.6

cSub

public Complex cSub(double z)

Subtracts z from this without modifying this, and returns the result.

Returns:: this-z
Since:: jPicEdt 1.6

cAdd

public Complex cAdd(double z)

CAdd z to this without modifying this, and returns the result.

Returns:: this+z
Since:: jPicEdt 1.6

cMul

public Complex cMul(Complex z)

To perform z1 * z2, you write z1.cMul(z2) .

     (a + i*b) * (c + i*d)  =  ( (a*c) - (b*d) + i*((a*d) + (b*c)) )

Since:: jPicEdt 1.6
See Also:: cScale(double)

cMul

public Complex cMul(double z)

Since:: jPicEdt 1.6

mul

public Complex mul(Complex z)

Since:: jPicEdt 1.6

mul

public Complex mul(double z)

Since:: jPicEdt 1.6

cDiv

public Complex cDiv(Complex z)

To perform z1 / z2, you write z1.cDiv(z2) .

     (a + i*b) / (c + i*d)  =  ( (a*c) + (b*d) + i*((b*c) - (a*d)) ) / norm(c + i*d)

Take care not to divide by zero!

Note:

Complex arithmetic in Java never causes exceptions. You have to deliberately check for overflow, division by zero, and so on, for yourself.

Domain Restrictions:

z1/z2 is undefined if z2 = 0

Since:: jPicEdt 1.6
See Also:: cScale(double)

div

public Complex div(Complex z)

cSqrt

public Complex cSqrt()

Returns a Complex representing one of the two square roots.

     sqrt(z)  =  sqrt(abs(z)) * ( cos(arg(z)/2) + i * sin(arg(z)/2) )

For any complex number z, sqrt(z) will return the complex root whose arg is arg(z)/2.

Note:

There are always two square roots for each Complex number, except for 0 + 0i, or zero. The other root is the cNeg() of the first one. Just as the two roots of 4 are 2 and -2, the two roots of -1 are i and - i.

Returns:: The square root whose arg is arg(z)/2.
Since:: jPicEdt 1.6
See Also:: pow(Complex, double)

cPow

public Complex cPow(Complex exponent)

Renvoie la valeur Complex du this �lev�e raised to the power of a � la puissance d'un exposant Complex sans que this ne soit modifi�

Parameters:: exponent - L'exposant "auquel on �l�ve"
Returns:: ce Complex "raised to the power of" the exponent
Since:: jPicEdt 1.6
See Also:: pow(Complex, Complex)

exp

public Complex exp()

Returns the number e "raised to" a Complex power.

     exp(x + i*y)  =  exp(x) * ( cos(y) + i * sin(y) )

Note:

The value of e, a transcendental number, is roughly 2.71828182846...
Also, the following is quietly amazing:
e^PI*i = - 1

Returns:: e "raised to the power of" this Complex
Since:: jPicEdt 1.6
See Also:: cLog(), cPow(Complex exponent)

cLog

public Complex cLog()

Returns the principal natural logarithm of a Complex number.

     log(z)  =  log(abs(z)) + i * arg(z)

There are infinitely many solutions, besides the principal solution. If L is the principal solution of log(z), the others are of the form:

     L + (2*k*PI)*i

where k is any integer.

Returns:: Principal Complex natural logarithm
Since:: jPicEdt 1.6
See Also:: exp()

cSin

public Complex cSin()

Returns the sine of a Complex number.

     sin(z)  =  ( exp(i*z) - exp(-i*z) ) / (2*i)

Returns:: The Complex sine
Since:: jPicEdt 1.6
See Also:: asin(), sinh(), cosec(), cCos(), cTan()

cCos

public Complex cCos()

Returns the cosine of a Complex number.

     cos(z)  =  ( exp(i*z) + exp(-i*z) ) / 2

Returns:: The Complex cosine
Since:: jPicEdt 1.6
See Also:: acos(), cosh(), sec(), cSin(), cTan()

iMul

public Complex iMul()

multiply this by i, which modifies this.

Since:: jPicEdt 1.6

cIMul

public Complex cIMul()

multiply this by i, without modifying this.

Since:: jPicEdt 1.6

miMul

public Complex miMul()

multiply this by -i, which modifies this.

Since:: jPicEdt 1.6

cMIMul

public Complex cMIMul()

multiply this by -i, without modifying this.

Since:: jPicEdt 1.6

cTan

public Complex cTan()

Returns the tangent of a Complex number.

     tan(z)  =  sin(z) / cos(z)

Domain Restrictions:

tan(z) is undefined whenever z = (k + 1/2) * PI
where k is any integer

Returns:: The Complex tangent
Since:: jPicEdt 1.6
See Also:: atan(), tanh(), cCot(), cSin(), cCos()

cosec

public Complex cosec()

Returns the cosecant of a Complex number.

     cosec(z)  =  1 / sin(z)

Domain Restrictions:

cosec(z) is undefined whenever z = k * PI
where k is any integer

Returns:: The Complex cosecant
Since:: jPicEdt 1.6
See Also:: cSin(), sec(), cCot()

sec

public Complex sec()

Returns the secant of a Complex number.

     sec(z)  =  1 / cos(z)

Domain Restrictions:

sec(z) is undefined whenever z = (k + 1/2) * PI
where k is any integer

Returns:: The Complex secant
Since:: jPicEdt 1.6
See Also:: cCos(), cosec(), cCot()

cCot

public Complex cCot()

Returns the cotangent of a Complex number.

     cot(z)  =  1 / tan(z)

Domain Restrictions:

cot(z) is undefined whenever z = k * PI
where k is any integer

Returns:: The Complex cotangent
Since:: jPicEdt 1.6
See Also:: cTan(), cosec(), sec()

sinh

public Complex sinh()

Returns the hyperbolic sine of a Complex number.

     sinh(z)  =  ( exp(z) - exp(-z) ) / 2

Returns:: The Complex hyperbolic sine
Since:: jPicEdt 1.6
See Also:: cSin(), asinh()

cosh

public Complex cosh()

Returns the hyperbolic cosine of a Complex number.

     cosh(z)  =  ( exp(z) + exp(-z) ) / 2

Returns:: The Complex hyperbolic cosine
Since:: jPicEdt 1.6
See Also:: cCos(), acosh()

tanh

public Complex tanh()

Returns the hyperbolic tangent of a Complex number.

     tanh(z)  =  sinh(z) / cosh(z)

Returns:: The Complex hyperbolic tangent
Since:: jPicEdt 1.6
See Also:: cTan(), atanh()

asin

public Complex asin()

Returns the principal arc sine of a Complex number.

     asin(z)  =  -i * log(i*z + sqrt(1 - z*z))

There are infinitely many solutions, besides the principal solution. If A is the principal solution of asin(z), the others are of the form:

     k*PI + (-1)^k  * A

where k is any integer.

Returns:: Principal Complex arc sine
Since:: jPicEdt 1.6
See Also:: cSin(), sinh()

acos

public Complex acos()

Returns the principal arc cosine of a Complex number.

     acos(z)  =  -i * log( z + i * sqrt(1 - z*z) )

There are infinitely many solutions, besides the principal solution. If A is the principal solution of acos(z), the others are of the form:

     2*k*PI +/- A

where k is any integer.

Returns:: Principal Complex arc cosine
Since:: jPicEdt 1.6
See Also:: cCos(), cosh()

atan

public Complex atan()

Returns the principal arc tangent of a Complex number.

     atan(z)  =  -i/2 * log( (i-z)/(i+z) )

There are infinitely many solutions, besides the principal solution. If A is the principal solution of atan(z), the others are of the form:

     A + k*PI

where k is any integer.

Domain Restrictions:

atan(z) is undefined for z = + i or z = - i

Returns:: Principal Complex arc tangent
Since:: jPicEdt 1.6
See Also:: cTan(), tanh()

asinh

public Complex asinh()

Returns the principal inverse hyperbolic sine of a Complex number.

     asinh(z)  =  log(z + sqrt(z*z + 1))

There are infinitely many solutions, besides the principal solution. If A is the principal solution of asinh(z), the others are of the form:

     k*PI*i + (-1)^k  * A

where k is any integer.

Returns:: Principal Complex inverse hyperbolic sine
Since:: jPicEdt 1.6
See Also:: sinh()

acosh

public Complex acosh()

Returns the principal inverse hyperbolic cosine of a Complex number.

     acosh(z)  =  log(z + sqrt(z*z - 1))

There are infinitely many solutions, besides the principal solution. If A is the principal solution of acosh(z), the others are of the form:

     2*k*PI*i +/- A

where k is any integer.

Returns:: Principal Complex inverse hyperbolic cosine
Since:: jPicEdt 1.6
See Also:: cosh()

atanh

public Complex atanh()

Returns the principal inverse hyperbolic tangent of a Complex number.

     atanh(z)  =  1/2 * log( (1+z)/(1-z) )

There are infinitely many solutions, besides the principal solution. If A is the principal solution of atanh(z), the others are of the form:

     A + k*PI*i

where k is any integer.

Domain Restrictions:

atanh(z) is undefined for z = + 1 or z = - 1

Returns:: Principal Complex inverse hyperbolic tangent
Since:: jPicEdt 1.6
See Also:: tanh()

toString

public String toString()

Converts a Complex into a String of the form (a + bi).

This enables a Complex to be easily printed. For example, if z was 2 - 5i, then

     System.out.println("z = " + z);

would print something like

     z = (2.0 - 5.0i)

Overrides:: toString in class Object

Returns:: String containing the cartesian coordinate representation
Since:: jPicEdt 1.6
See Also:: cart(double re, double im)

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jpicedt.util.math Class Complex

VERSION

DATE

AUTHOR

REMARK

TWO_PI

I

ZERO

ONE

Complex

Complex

Complex

Complex

main

cart

polar

pow

pow

pow

isInfinite

isNaN

equals

absoluteIsCloseTo

relativeIsCloseTo

clone

re

im

abs2

norm1

normInf

abs

arg

cNeg

neg

cConj

conj

cScale

cAdd

add

cSub

sub

sub

cSub

cAdd

cMul

cMul

mul

mul

cDiv

div

cSqrt

cPow

exp

cLog

cSin

cCos

iMul

cIMul

miMul

cMIMul

cTan

cosec

sec

cCot

sinh

cosh

tanh

asin

acos

atan

asinh

acosh

atanh

toString

jpicedt.util.math
Class Complex