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-# Complex numbers
-# ---------------
-
-# [Now that Python has a complex data type built-in, this is not very
-# useful, but it's still a nice example class]
-
-# This module represents complex numbers as instances of the class Complex.
-# A Complex instance z has two data attribues, z.re (the real part) and z.im
-# (the imaginary part). In fact, z.re and z.im can have any value -- all
-# arithmetic operators work regardless of the type of z.re and z.im (as long
-# as they support numerical operations).
-#
-# The following functions exist (Complex is actually a class):
-# Complex([re [,im]) -> creates a complex number from a real and an imaginary part
-# IsComplex(z) -> true iff z is a complex number (== has .re and .im attributes)
-# ToComplex(z) -> a complex number equal to z; z itself if IsComplex(z) is true
-# if z is a tuple(re, im) it will also be converted
-# PolarToComplex([r [,phi [,fullcircle]]]) ->
-# the complex number z for which r == z.radius() and phi == z.angle(fullcircle)
-# (r and phi default to 0)
-# exp(z) -> returns the complex exponential of z. Equivalent to pow(math.e,z).
-#
-# Complex numbers have the following methods:
-# z.abs() -> absolute value of z
-# z.radius() == z.abs()
-# z.angle([fullcircle]) -> angle from positive X axis; fullcircle gives units
-# z.phi([fullcircle]) == z.angle(fullcircle)
-#
-# These standard functions and unary operators accept complex arguments:
-# abs(z)
-# -z
-# +z
-# not z
-# repr(z) == `z`
-# str(z)
-# hash(z) -> a combination of hash(z.re) and hash(z.im) such that if z.im is zero
-# the result equals hash(z.re)
-# Note that hex(z) and oct(z) are not defined.
-#
-# These conversions accept complex arguments only if their imaginary part is zero:
-# int(z)
-# float(z)
-#
-# The following operators accept two complex numbers, or one complex number
-# and one real number (int, long or float):
-# z1 + z2
-# z1 - z2
-# z1 * z2
-# z1 / z2
-# pow(z1, z2)
-# cmp(z1, z2)
-# Note that z1 % z2 and divmod(z1, z2) are not defined,
-# nor are shift and mask operations.
-#
-# The standard module math does not support complex numbers.
-# The cmath modules should be used instead.
-#
-# Idea:
-# add a class Polar(r, phi) and mixed-mode arithmetic which
-# chooses the most appropriate type for the result:
-# Complex for +,-,cmp
-# Polar for *,/,pow
-
-import math
-import sys
-
-twopi = math.pi*2.0
-halfpi = math.pi/2.0
-
-def IsComplex(obj):
- return hasattr(obj, 're') and hasattr(obj, 'im')
-
-def ToComplex(obj):
- if IsComplex(obj):
- return obj
- elif isinstance(obj, tuple):
- return Complex(*obj)
- else:
- return Complex(obj)
-
-def PolarToComplex(r = 0, phi = 0, fullcircle = twopi):
- phi = phi * (twopi / fullcircle)
- return Complex(math.cos(phi)*r, math.sin(phi)*r)
-
-def Re(obj):
- if IsComplex(obj):
- return obj.re
- return obj
-
-def Im(obj):
- if IsComplex(obj):
- return obj.im
- return 0
-
-class Complex:
-
- def __init__(self, re=0, im=0):
- _re = 0
- _im = 0
- if IsComplex(re):
- _re = re.re
- _im = re.im
- else:
- _re = re
- if IsComplex(im):
- _re = _re - im.im
- _im = _im + im.re
- else:
- _im = _im + im
- # this class is immutable, so setting self.re directly is
- # not possible.
- self.__dict__['re'] = _re
- self.__dict__['im'] = _im
-
- def __setattr__(self, name, value):
- raise TypeError('Complex numbers are immutable')
-
- def __hash__(self):
- if not self.im:
- return hash(self.re)
- return hash((self.re, self.im))
-
- def __repr__(self):
- if not self.im:
- return 'Complex(%r)' % (self.re,)
- else:
- return 'Complex(%r, %r)' % (self.re, self.im)
-
- def __str__(self):
- if not self.im:
- return repr(self.re)
- else:
- return 'Complex(%r, %r)' % (self.re, self.im)
-
- def __neg__(self):
- return Complex(-self.re, -self.im)
-
- def __pos__(self):
- return self
-
- def __abs__(self):
- return math.hypot(self.re, self.im)
-
- def __int__(self):
- if self.im:
- raise ValueError("can't convert Complex with nonzero im to int")
- return int(self.re)
-
- def __float__(self):
- if self.im:
- raise ValueError("can't convert Complex with nonzero im to float")
- return float(self.re)
-
- def __cmp__(self, other):
- other = ToComplex(other)
- return cmp((self.re, self.im), (other.re, other.im))
-
- def __rcmp__(self, other):
- other = ToComplex(other)
- return cmp(other, self)
-
- def __bool__(self):
- return not (self.re == self.im == 0)
-
- abs = radius = __abs__
-
- def angle(self, fullcircle = twopi):
- return (fullcircle/twopi) * ((halfpi - math.atan2(self.re, self.im)) % twopi)
-
- phi = angle
-
- def __add__(self, other):
- other = ToComplex(other)
- return Complex(self.re + other.re, self.im + other.im)
-
- __radd__ = __add__
-
- def __sub__(self, other):
- other = ToComplex(other)
- return Complex(self.re - other.re, self.im - other.im)
-
- def __rsub__(self, other):
- other = ToComplex(other)
- return other - self
-
- def __mul__(self, other):
- other = ToComplex(other)
- return Complex(self.re*other.re - self.im*other.im,
- self.re*other.im + self.im*other.re)
-
- __rmul__ = __mul__
-
- def __div__(self, other):
- other = ToComplex(other)
- d = float(other.re*other.re + other.im*other.im)
- if not d: raise ZeroDivisionError('Complex division')
- return Complex((self.re*other.re + self.im*other.im) / d,
- (self.im*other.re - self.re*other.im) / d)
-
- def __rdiv__(self, other):
- other = ToComplex(other)
- return other / self
-
- def __pow__(self, n, z=None):
- if z is not None:
- raise TypeError('Complex does not support ternary pow()')
- if IsComplex(n):
- if n.im:
- if self.im: raise TypeError('Complex to the Complex power')
- else: return exp(math.log(self.re)*n)
- n = n.re
- r = pow(self.abs(), n)
- phi = n*self.angle()
- return Complex(math.cos(phi)*r, math.sin(phi)*r)
-
- def __rpow__(self, base):
- base = ToComplex(base)
- return pow(base, self)
-
-def exp(z):
- r = math.exp(z.re)
- return Complex(math.cos(z.im)*r,math.sin(z.im)*r)
-
-
-def checkop(expr, a, b, value, fuzz = 1e-6):
- print(' ', a, 'and', b, end=' ')
- try:
- result = eval(expr)
- except:
- result = sys.exc_info()[0]
- print('->', result)
- if isinstance(result, str) or isinstance(value, str):
- ok = (result == value)
- else:
- ok = abs(result - value) <= fuzz
- if not ok:
- print('!!\t!!\t!! should be', value, 'diff', abs(result - value))
-
-def test():
- print('test constructors')
- constructor_test = (
- # "expect" is an array [re,im] "got" the Complex.
- ( (0,0), Complex() ),
- ( (0,0), Complex() ),
- ( (1,0), Complex(1) ),
- ( (0,1), Complex(0,1) ),
- ( (1,2), Complex(Complex(1,2)) ),
- ( (1,3), Complex(Complex(1,2),1) ),
- ( (0,0), Complex(0,Complex(0,0)) ),
- ( (3,4), Complex(3,Complex(4)) ),
- ( (-1,3), Complex(1,Complex(3,2)) ),
- ( (-7,6), Complex(Complex(1,2),Complex(4,8)) ) )
- cnt = [0,0]
- for t in constructor_test:
- cnt[0] += 1
- if ((t[0][0]!=t[1].re)or(t[0][1]!=t[1].im)):
- print(" expected", t[0], "got", t[1])
- cnt[1] += 1
- print(" ", cnt[1], "of", cnt[0], "tests failed")
- # test operators
- testsuite = {
- 'a+b': [
- (1, 10, 11),
- (1, Complex(0,10), Complex(1,10)),
- (Complex(0,10), 1, Complex(1,10)),
- (Complex(0,10), Complex(1), Complex(1,10)),
- (Complex(1), Complex(0,10), Complex(1,10)),
- ],
- 'a-b': [
- (1, 10, -9),
- (1, Complex(0,10), Complex(1,-10)),
- (Complex(0,10), 1, Complex(-1,10)),
- (Complex(0,10), Complex(1), Complex(-1,10)),
- (Complex(1), Complex(0,10), Complex(1,-10)),
- ],
- 'a*b': [
- (1, 10, 10),
- (1, Complex(0,10), Complex(0, 10)),
- (Complex(0,10), 1, Complex(0,10)),
- (Complex(0,10), Complex(1), Complex(0,10)),
- (Complex(1), Complex(0,10), Complex(0,10)),
- ],
- 'a/b': [
- (1., 10, 0.1),
- (1, Complex(0,10), Complex(0, -0.1)),
- (Complex(0, 10), 1, Complex(0, 10)),
- (Complex(0, 10), Complex(1), Complex(0, 10)),
- (Complex(1), Complex(0,10), Complex(0, -0.1)),
- ],
- 'pow(a,b)': [
- (1, 10, 1),
- (1, Complex(0,10), 1),
- (Complex(0,10), 1, Complex(0,10)),
- (Complex(0,10), Complex(1), Complex(0,10)),
- (Complex(1), Complex(0,10), 1),
- (2, Complex(4,0), 16),
- ],
- 'cmp(a,b)': [
- (1, 10, -1),
- (1, Complex(0,10), 1),
- (Complex(0,10), 1, -1),
- (Complex(0,10), Complex(1), -1),
- (Complex(1), Complex(0,10), 1),
- ],
- }
- for expr in sorted(testsuite):
- print(expr + ':')
- t = (expr,)
- for item in testsuite[expr]:
- checkop(*(t+item))
-
-
-if __name__ == '__main__':
- test()
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