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Python offers a powerful data type for complex numbers in Cartesian form. Unfortunately, python does not offer support for complex numbers in polar form. This recipe contains a class that supports complex numbers in both Cartesian and polar form, and allows for arithmetic that mixes both forms.

Python, 83 lines
 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 import math as m import cmath as c class Complex: """ Author: César Otero Description: A complex number class which can do complex arithmetic in both Cartesian and polar coordinates, or a mix of the two """ def __init__(self, num=0, phase=0): if type(num) == complex: # cnum is in Cartesian form self.cnum = num self.magnitude = abs(num) phaseRad = m.atan2(num.imag, num.real) self.phase = m.degrees(phaseRad) else: # cnum is in polar form self.cnum = m.cos(phase) + complex(0,m.sin(phase)) self.magnitude = num self.phase = phase def __str__(self): return str(self.magnitude) + " /_ (" + str(self.phase) + ") deg" def __add__(self,n): if type(n) == int: re = self.cnum.real + n im = self.cnum.imag elif type(n) == float: re = self.cnum.real + n im = self.cnum.imag else: re = self.cnum.real + n.cnum.real im = self.cnum.imag + n.cnum.imag z = re+complex(0,im) return Complex(z) def __radd__(self,n): if type(n) == int: re = self.cnum.real + n im = self.cnum.imag elif type(n) == float: re = self.cnum.real + n im = self.cnum.imag else: re = self.cnum.real + n.cnum.real im = self.cnum.imag + n.cnum.imag z = re+complex(0,im) return Complex(z) def __div__(self,n): magnitude = self.magnitude / n.magnitude phase = self.phase - n.phase return Complex(magnitude, phase) def __rdiv__(self,n): magnitude = n.magnitude / self.magnitude phase = n.phase - self.phase return Complex(magnitude, phase) if __name__=="__main__": ----------r=90 Ohms--------L = 160j Ohms ----------| | pSource = 750 /_ 30 deg C = -40j Ohms | | |--------------------------------------------------| pSource = Complex(750,30) # power source, in polar form # with a magnitude of 750 volts, and angle of 30 # degrees. r = 90 # Ohms ( real part only ) L = Complex(0+160j) # Ohms ( Cartesian form ) C = Complex(0-40j) # Ohms ( Cartesian form ) Z = r+L+C # total impedance print "Impedance is ", Z I = pSource / Z print "Phase current is ", I

In some engineering and scientific applications it is useful to represent complex numbers in polar form, or mix polar form complex numbers with Cartesian form without having to worry about the details of converting from one type to the other before doing any arithmetic. This ability is inherit in other languages such as Matlab or IDL. This recipe is useful for extending python to be able to handle these types of calculations.

A better implementation could be achieved by inheriting directly from the python complex type.

1 comment Akira Fora 14 years ago

Lots of code for nothing. A common (the most common, as far as I know) way to write complex numbers in polar form is:

mag*pow(e,j*phase)                    (MathML support would be nice here)

were mag is the magnitude, e is the Neperian constant, phase is the phase in radian. This writing is allowed in Python. See the following code:

def mainWithNativeComplex():
pSource = 750*e**(1j*pi/6)# power source, in polar form
# with a magnitude of 750 volts, and angle of 30
r = 90                    # Ohms ( real part only )
L = 0+160j                # Ohms ( Cartesian form )
C = 0-40j                 # Ohms ( Cartesian form )
Z = r+L+C                 # total impedance
print "Impedance is ", Z, "(mag=", abs(Z), "; phase=", m.degrees(m.atan2(Z.imag, Z.real)), ")"

I = pSource / Z
print "Phase current is ", I, "(mag=", abs(I), "; phase=", m.degrees(m.atan2(I.imag, I.real)), ")"

The only lack in the native type is that you have to compute the phase by yourself. You may want to write a 1 line function for this, but certainly not a 50 lines class. Created by cesar otero on Sat, 5 Jan 2008 (PSF)

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