Documentation of 'jv.number.PuComplex' Java class
PuComplex ("JavaView Reference Manual")
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jv.number

Class PuComplex

  • All Implemented Interfaces:
    java.io.Serializable, java.lang.Cloneable

    public class PuComplex
extends java.lang.Object
implements java.lang.Cloneable, java.io.Serializable
    Complex number and basic complex functions.

    Static methods typically allocate a new complex number as return value while non-static methods try to avoid allocations as far as possible.

    Here is a listing with all implemented functions. 

     
  set(re, im)        u=(re,im)       with u PuComplex, re, im double
  copy(v)            u=(v.re,v.im)   with u PuComplex, v PuComplex
  add(u,v)           w=u+v           with u PuComplex, v PuComplex or double
  u.add(v)           u+=v            with u PuComplex, v PuComplex or double
  sub(u,v)           w=u-v           with u PuComplex, v PuComplex or double
  u.sub(v)           u-=v            with u PuComplex, v PuComplex or double
  mult(u,v)          w=u*v           with u PuComplex, v PuComplex or double
  u.mult(v)          u*=v            with u PuComplex, v PuComplex or double
  div(u,v)           w=u/v           with u PuComplex, v PuComplex or double
  u.div(v)           u/=v            with u PuComplex, v PuComplex or double
  sqr(u)             w=u*u           with u PuComplex
  u.sqr()            u=u*u           with u PuComplex
  cube(u)            w=u*u*u         with u PuComplex
  u.cube()           u=u*u*u         with u PuComplex
  abs(u)             r=|u|           with u PuComplex
  u.abs()            r=|u|           with u PuComplex
  u.sqrAbs()         r=|u|^2         with u PuComplex
  inv(u)             w=1/u           with u PuComplex
  u.inv()            u=1/u           with u PuComplex
  re(u)              r=re(u)         with u PuComplex
  u.re()             r=re(u)         with u PuComplex
  im(u)              r=im(u)         with u PuComplex
  u.im()             r=im(u)         with u PuComplex
  conj(u)            w=re(u)-i*im(u) with u PuComplex
  u.conj()           u=re(u)-i*im(u) with u PuComplex
  neg(u)             w=-u            with u PuComplex
  u.neg()            u=-u            with u PuComplex
  rot(u, f)          w=u*exp(i*f)    with u PuComplex, f double
  rot(u, f)          u=u*exp(i*f)    with u PuComplex, f double
  rotJ(u)            w=J*u           with u PuComplex
  rotJ()             u=J*u           with u PuComplex
  arg(u)             r=arg(u)        with u PuComplex
  u.arg()            r=arg(u)        with u PuComplex
  argPB(u)           r=argPB(u)      with u PuComplex
  u.argPB()          r=argPB(u)      with u PuComplex
  polarToRect(r,f)   w=r*exp(i*f)    with r double, f double
  exp(u)             w=exp(u)        with u PuComplex
  u.exp()            u=exp(u)        with u PuComplex
  log(u)             w=log(u)        with u PuComplex
  u.log()            u=log(u)        with u PuComplex
  logPB(u)           w=logPB(u)      with u PuComplex
  u.logPB()          u=logPB(u)      with u PuComplex
  sqrt(u)            w=sqrt(u)       with u PuComplex, result with im >= 0.
  u.sqrt()           u=sqrt(u)       with u PuComplex, result with im >= 0.
  pow(u,v)           w=u**v          with u PuComplex, v PuComplex
  pow(u,d)           w=u**d          with u PuComplex, d double
  pow(u,i)           w=u**i          with u PuComplex, i integer
  sin(u)             w=sin(u)        with u PuComplex
  cos(u)             w=cos(u)        with u PuComplex
  sinh(u)            w=sinh(u)       with u PuComplex
  cosh(u)            w=cosh(u)       with u PuComplex
  blend(a, u, b, v)  w=a*u+b*v       with u,v PuComplex, a,b double
  moebius(a, b, c, d, v)  w=(a*u+b)/(c*u+d)  with u PuComplex, a,b,c,d double
  moebius(a, b, c, d, v)  w=(a*u+b)/(c*u+d)  with u PuComplex, a,b,c,d PuComplex
    See Also:
    Serialized Form
    Author:
    Konrad Polthier and Ulrich Reitebuch
    Version:
    09.04.07, 2.40 revised (kp) New methods rot(), rotJ, pow(.,int), blend(), moebius().
    04.08.03, 2.30 revised (pl) Added toString method.
    26.09.99, 2.20 revised (kp) Methods set and copy added. Now most methods return 'this'.
    14.06.99, 2.10 revised (kp) isNaN and others added. In case of error function now return NaN etc.
    00.05.99, 2.00 revised (ur) Converted to Java and revisions.
    29.06.98, 1.00 created (kp)

    • Field Detail

      • NEG_ONE

        public static final PuComplex NEG_ONE

      • PI_OVER_4

        public static final PuComplex PI_OVER_4

      • PI3_OVER_4

        public static final PuComplex PI3_OVER_4

      • PI5_OVER_4

        public static final PuComplex PI5_OVER_4

      • PI7_OVER_4

        public static final PuComplex PI7_OVER_4

      • re

        public double re

      • im

        public double im

    • Constructor Detail

      • PuComplex

        public PuComplex()

      • PuComplex

        public PuComplex(double r)

      • PuComplex

        public PuComplex(double aReal,
                 double aImag)

    • Method Detail

      • set

        public PuComplex set(double aReal,
                     double aImag)
        this = (re, im)

      • toString

        public java.lang.String toString()
        Create a string in the form "a+b*i".
        Overrides:
        toString in class java.lang.Object
        Since:
        JavaView 2.90.001
        Author:
        Peter Liepa
        Version:
        29.08.08, 2.00 revised (kp) String has a multiplication star in front of i.
        10.08.03, 1.00 created (pl)

      • isInfinite

        public boolean isInfinite()

      • isNaN

        public boolean isNaN()

      • equals

        public static boolean equals(PuComplex w,
                             PuComplex z,
                             double tolerance)
        Compare two complex numbers of (nearly) equality.
        Version:
        21.04.13, 1.50 revised (kp) Changed to 'static' since now access to an instance.

      • equals

        public boolean equals(PuComplex z,
                      double tolerance)
        Compare two complex numbers of (nearly) equality. Calls static method.

      • add

        public PuComplex add(double r)
        this += r.

      • sub

        public PuComplex sub(double r)
        this -= r.

      • mult

        public PuComplex mult(double r)
        this *= r.

      • div

        public static PuComplex div(PuComplex u,
                            PuComplex v)
        w = u / v

        In case of zero division the following result occurs: 

         
 If |v|==0 and u.re==0 then w.re==Double.NaN.
 If |v|==0 and u.re>0 then w.re==Double.POSITIVE_INFINITY.
 If |v|==0 and u.re<0 then w.re==Double.NEGATIVE_INFINITY.
        Same handling is taken for imaginary part of u.

      • div

        public static PuComplex div(double r,
                            PuComplex v)
        w = r / v

        In case of zero division the following result occurs: 

        
 If |v|==0 and r==0 then w.re==Double.NaN.
 If |v|==0 and r>0 then w.re==Double.POSITIVE_INFINITY.
 If |v|==0 and r<0 then w.re==Double.NEGATIVE_INFINITY.

      • div

        public PuComplex div(PuComplex v)
        this /=v

        In case of zero division the following result occurs: 

        
 If |v|==0 and re==0 then re==Double.NaN.
 If |v|==0 and re>0 then re==Double.POSITIVE_INFINITY.
 If |v|==0 and re<0 then re==Double.NEGATIVE_INFINITY.
        Same handling is taken for imaginary part of 'this'.

      • div

        public static PuComplex div(PuComplex u,
                            double r)
        w = u / r

        In case of zero division the following result occurs: 

        
 If |r|==0 and re==0 then re==Double.NaN.
 If |r|==0 and re>0 then re==Double.POSITIVE_INFINITY.
 If |r|==0 and re<0 then re==Double.NEGATIVE_INFINITY.
 Same handling is taken for imaginary part of 'this'.

      • div

        public PuComplex div(double r)
        this /= r

        In case of zero division the following result occurs: 

        
 If |r|==0 and re==0 then re==Double.NaN.
 If |r|==0 and re>0 then re==Double.POSITIVE_INFINITY.
 If |r|==0 and re<0 then re==Double.NEGATIVE_INFINITY.
 Same handling is taken for imaginary part of 'this'.

      • cube

        public PuComplex cube()
        u = this**3.

      • abs

        public static double abs(PuComplex u)
        r = |u|

      • abs

        public double abs()
        r = |this|

      • sqrAbs

        public double sqrAbs()
        r = |this|^2

      • inv

        public static PuComplex inv(PuComplex u)
        w = 1./u

        In case of |u|==0 the following result occurs: w = PuComplex(Double.POSITIVE_INFINITY, Double.POSITIVE_INFINITY)

      • inv

        public PuComplex inv()
        u = 1./this

        In case of |u|==0 the following result occurs: u.re = Double.POSITIVE_INFINITY, u.im = Double.POSITIVE_INFINITY.

      • re

        public static double re(PuComplex u)
        Deprecated. since JavaView 3.97.061, use this.re() instead.
        r = re(u)

      • re

        public double re()
        r = re(this)

      • im

        public static double im(PuComplex u)
        Deprecated. since JavaView 3.97.061, use this.im() instead.
        r = im(u)

      • im

        public double im()
        r = im(this)

      • conj

        public PuComplex conj()
        u = re(this) - i*im(this)

      • rot

        public PuComplex rot(double f)
        u = J(f)*this

      • arg

        public static double arg(PuComplex u)
        r = arg(u) in [0,2Pi), with slit at positive real axis.

      • arg

        public double arg()
        r = arg(this) in [0,2Pi), with slit at positive real axis.

      • argPB

        public static double argPB(PuComplex u)
        r = argPB(u) in [-Pi,Pi), principal branch with slit at negative real axis.

      • argPB

        public double argPB()
        r = argPB(this) in [0,2Pi), principal branch with slit at negative real axis.

      • polarToRect

        public static PuComplex polarToRect(double r,
                                    double f)
        w = r*exp(i*f)

      • logPB

        public static PuComplex logPB(PuComplex u)
        w = logPB(u), principal branch of complex logarithm with slit at negative real axis.

        By definition, logPB is defined on the complex plane slit at the negative real axis, denoted by C-. Thus, the argument is expected to be greater than -π and less or equal than π. Therefore, the given parameter z is considered as an element in C-. This interpretation does not affect the norm, but the argument of z.

        Note that every z with arg(z)>pi will be considered as an element w such that |w| =|z| and arg(w)=arg(z)-2pi;.

        Returns:
        the principal branch of z, i.e. w=logPB(z) = ln|z|+i*arg(z).

      • logPB

        public PuComplex logPB()
        u = logPB(this), principal branch with slit at negative real axis.

      • sqrt

        public PuComplex sqrt()
        u= sqrt(this)

      • pow

        public PuComplex pow(double r)
        u = this**r.

      • pow

        public static PuComplex pow(PuComplex u,
                            int n)
        w = u**n

        For small integer exponents, including negative exponents. Method avoids transcendental functions and uses float multiplication only.

        Since:
        JavaView 3.97.061
        Version:
        09.04.07, 1.00 created (kp)

      • sinh

        public PuComplex sinh()
        u = sinh(this)

      • cosh

        public PuComplex cosh()
        u = cosh(this)

      • tanh

        public PuComplex tanh()
        u = tanh(this)

      • coth

        public PuComplex coth()
        u = coth(this)

      • blend

        public static PuComplex blend(double a,
                              PuComplex v,
                              double b,
                              PuComplex w)
        Create a new complex number this = a*v + b*w.
        Parameters:
        a - weight of first complex number
        v - first complex number
        b - weight of second complex number
        w - second complex number
        Returns:
        new complex number
        Since:
        JavaView 3.97.061
        Version:
        08.04.07, 1.00 created (kp)

      • moebius

        public static PuComplex moebius(PuComplex a,
                                PuComplex b,
                                PuComplex c,
                                PuComplex d,
                                PuComplex u)
        Applies Moebius transformation given by complex parameters a,b,c,d to complex argument u. 

                             au + b
    w = moebius(u) = ------  with complex a,b,c,d,u.
                     cu + d
        Parameters:
        a - complex number
        b - complex number
        c - complex number
        d - complex number
        u - complex number argument
        Returns:
        new complex number
        Since:
        JavaView 3.97.061
        Version:
        09.04.07, 1.00 created (kp)

      • moebius

        public static PuComplex moebius(double a,
                                double b,
                                double c,
                                double d,
                                PuComplex u)
        Applies Moebius transformation given by real parameters a,b,c,d to complex argument u. 

                              au + b
    w = moebius(u) =  ------  with double a,b,c,d and complex u.
                      cu + d
        Parameters:
        a - double number
        b - double number
        c - double number
        d - double number
        u - complex number argument
        Returns:
        new complex number
        Since:
        JavaView 3.97.061
        Version:
        09.04.07, 1.00 created (kp)
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