Code-Beispiel

Komplexe Zahlen

Lizenz:	Erster Autor:	Letzte Bearbeitung:
GPL	nemored	15.09.2007

In der Physik und angewandten Mathematik lassen sich viele Berechnungen mit Hilfe der komplexen Zahlen einfacher ausführen. Der unten stehende Code stellt einige Funktionen zum Rechnen mit komplexen Zahlen zur Verfügung. Die Zahlen können dabei in der algebraischen Form oder in der Polarform angesprochen werden.

type complex

  as double real, imag  ' Real- und Imaginaerteil

  as double abs, arg    ' Betrag und Argument

end type



declare function newCartesian(byval real as double, byval imag as double) as complex

declare function newPolar(byval abs as double, byval arg as double) as complex

declare function complexAdd(byval c1 as complex, byval c2 as complex) as complex

declare function complexSub(byval c1 as complex, byval c2 as complex) as complex

declare function complexMult(byval c1 as complex, byval c2 as complex) as complex

declare function complexDiv(byval c1 as complex, byval c2 as complex) as complex

declare function complexConj(byval c as complex) as complex

declare function complexReci(byval c as complex) as complex

declare sub polar2cartesian(byref c as complex)

declare sub cartesian2polar(byref c as complex)

declare function strCartesian overload (byval c as complex) as string

declare function strCartesian(byval c as complex, byval p as ubyte) as string

declare function strPolar overload (byval c as complex) as string

declare function strPolar(byval c as complex, byval p as ubyte) as string



function newCartesian(byval real as double, byval imag as double) as complex

  ' neue komplexe Zahl anhand von Real- und Imaginaerteil definieren

  dim as complex ret

  ret.real = real

  ret.imag = imag

  cartesian2polar(ret)

  return ret

end function



function newPolar(byval r as double, byval phi as double) as complex

  ' neue komplexe Zahl anhand der Polarkoordinaten definieren

  dim as complex ret

  ret.abs = r

  ret.arg = phi

  polar2cartesian(ret)

  return ret

end function



function complexAdd(byval c1 as complex, byval c2 as complex) as complex

  ' addiert zwei komplexe Zahlen

  dim as complex ret

  ret.real = c1.real + c2.real

  ret.imag = c1.imag + c2.imag

  cartesian2polar(ret)

  return ret

end function



function complexSub(byval c1 as complex, byval c2 as complex) as complex

  ' subtrahiert zwei komplexe Zahlen

  dim as complex ret

  ret.real = c1.real - c2.real

  ret.imag = c1.imag - c2.imag

  cartesian2polar(ret)

  return ret

end function



function complexMult(byval c1 as complex, byval c2 as complex) as complex

  ' multipliziert zwei komplexe Zahlen

  dim as complex ret

  ret.abs = c1.abs * c2.abs

  ret.arg = c1.arg + c2.arg

  polar2cartesian(ret)

  return ret

end function



function complexDiv(byval c1 as complex, byval c2 as complex) as complex

  ' dividiert zwei komplexe Zahlen

  dim as complex ret

  ret.abs = c1.abs / c2.abs

  ret.arg = c1.arg - c2.arg

  polar2cartesian(ret)

  return ret

end function



function complexConj(byval c as complex) as complex

  ' bildet die konjugiert komplexe Zahl

  dim as complex ret

  ret = newCartesian(c.real, -c.imag)

  cartesian2polar(ret)

  return ret

end function



function complexReci(byval c as complex) as complex

  dim ret as complex

  if c.real=0 and c.imag=0 then

    ret = newCartesian(0, 0)

  else

    ret = newCartesian(c.real/c.abs^2, -c.imag/c.abs^2)

  end if

  cartesian2polar(ret)

  return ret

end function



sub polar2cartesian(byref c as complex)

  ' ermittelt Real- und Imaginaerteil, wenn die Polarkoordinaten bekannt sind

  dim as complex ret

  c.real = c.abs * cos(c.arg)

  c.imag = c.abs * sin(c.arg)

end sub



sub cartesian2polar(byref c as complex)

  ' ermittelt die Polarkoordinaten, wenn Real- und Imaginaerteil bekannt sind

  dim as complex ret

  c.abs = sqr(c.real^2 + c.imag^2)

  if c.abs = 0 then

    c.arg = -1

  elseif c.imag >= 0 then

    c.arg = acos(c.real/c.abs)

  else

    c.arg = -acos(c.real/c.abs)

  end if

end sub



function strCartesian(byval c as complex) as string

  return strCartesian(c, 8)

end function

function strCartesian(byval c as complex, byval p as ubyte) as string

  ' gibt die komplexe Zahl in der Form a+bi zurueck (gerundet auf p Stellen)

  dim as string ret

  ret = str(int(c.real*10^p+.5)/10^p)

  if c.imag > 0 then ret += "+"

  if c.imag <> 0 then ret += str(int(c.imag*10^p+.5)/10^p) + "i"

  return ret

end function



function strPolar(byval c as complex) as string

  return strPolar(c, 8)

end function

function strPolar(byval c as complex, byval p as ubyte) as string

  ' gibt die komplexe Zahl in der Form rE(phi) zurueck

  dim as string ret

  ret = str(int(c.abs*10^p+.5)/10^p)

  if c.arg<>0 and c.abs<>0 then ret += "E(" + str(int(c.arg*10^p+.5)/10^p) + ")"

  return ret

end function

Einfache Rechenbeispiele:

dim as complex c, d

c = newCartesian(5, 7)   ' c = 5 + 7i

d = newCartesian(3, -4)  ' d = 2 - 4i

' Addition; Ausgabe in algebraischer Form

print strCartesian(c); " + "; strCartesian(d);

print " = "; strCartesian(complexAdd(c, d))

' Multiplikation; Ausgabe in Polarform (4 Nachkommastellen)

print strPolar(c, 4); " * "; strPolar(d, 4);

print " = "; strPolar(complexMult(c, d), 4)

'reziproker Wert

print "1 / ("; strCartesian(d);

print ") = "; strCartesian(complexReci(d))

sleep

Zusätzliche Informationen und Funktionen

Das Code-Beispiel wurde am 15.09.2007 von nemored angelegt.
Die aktuellste Version wurde am 15.09.2007 von nemored gespeichert.

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