diff options
| -rwxr-xr-x | Demo/classes/Complex.py | 323 |
1 files changed, 263 insertions, 60 deletions
diff --git a/Demo/classes/Complex.py b/Demo/classes/Complex.py index b7ba2e0..5ac6b18 100755 --- a/Demo/classes/Complex.py +++ b/Demo/classes/Complex.py @@ -1,85 +1,288 @@ # Complex numbers +# --------------- +# 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) +# +# 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) +# long(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. +# (I suppose it would be easy to implement a cmath module.) +# +# 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 -from math import sqrt +import types, math -class complex: +twopi = math.pi*2.0 +halfpi = math.pi/2.0 - def __init__(self, re, im): - self.re = float(re) - self.im = float(im) +def IsComplex(obj): + return hasattr(obj, 're') and hasattr(obj, 'im') - def __coerce__(self, other): - if type(other) == type(self): - if other.__class__ == self.__class__: - return self, other - else: - raise TypeError, 'cannot coerce to complex' - else: - # The cast to float() may raise an exception! - return self, complex(float(other), 0.0) +def ToComplex(obj): + if IsComplex(obj): + return obj + elif type(obj) == types.TupleType: + return apply(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 + else: + return obj + +def Im(obj): + if IsComplex(obj): + return obj.im + else: + return obj + +class Complex: + + def __init__(self, re=0, im=0): + if IsComplex(re): + im = i + Complex(0, re.im) + re = re.re + if IsComplex(im): + re = re - im.im + im = im.re + 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) + mod = sys.maxint + 1L + return int((hash(self.re) + 2L*hash(self.im) + mod) % (2L*mod) - mod) def __repr__(self): - return 'complex' + `self.re, self.im` + if not self.im: + return 'Complex(%s)' % `self.re` + else: + return 'Complex(%s, %s)' % (`self.re`, `self.im`) - def __cmp__(a, b): - a = a.__abs__() - b = b.__abs__() - return (a > b) - (a < b) + def __str__(self): + if not self.im: + return `self.re` + else: + return 'Complex(%s, %s)' % (`self.re`, `self.im`) + + def __neg__(self): + return Complex(-self.re, -self.im) + + def __pos__(self): + return self + + def __abs__(self): + # XXX could be done differently to avoid overflow! + return math.sqrt(self.re*self.re + self.im*self.im) + + def __int__(self): + if self.im: + raise ValueError, "can't convert Complex with nonzero im to int" + return int(self.re) + + def __long__(self): + if self.im: + raise ValueError, "can't convert Complex with nonzero im to long" + return long(self.re) def __float__(self): if self.im: - raise ValueError, 'cannot convert complex to float' + raise ValueError, "can't convert Complex with nonzero im to float" return float(self.re) - def __long__(self): - return long(float(self)) + def __cmp__(self, other): + other = ToComplex(other) + return cmp((self.re, self.im), (other.re, other.im)) - def __int__(self): - return int(float(self)) + def __rcmp__(self, other): + other = ToComplex(other) + return cmp(other, self) + + def __nonzero__(self): + return not (self.re == self.im == 0) - def __abs__(self): - # XXX overflow? - return sqrt(self.re*self.re + self.im*self.im) + abs = radius = __abs__ - def __add__(a, b): - return complex(a.re + b.re, a.im + b.im) + def angle(self, fullcircle = twopi): + return (fullcircle/twopi) * ((halfpi - math.atan2(self.re, self.im)) % twopi) - def __sub__(a, b): - return complex(a.re - b.re, a.im - b.im) + phi = angle - def __mul__(a, b): - return complex(a.re*b.re - a.im*b.im, a.re*b.im + a.im*b.re) + def __add__(self, other): + other = ToComplex(other) + return Complex(self.re + other.re, self.im + other.im) - def __div__(a, b): - q = (b.re*b.re + b.im*b.im) - re = (a.re*b.re + a.im*b.im) / q - im = (a.im*b.re - b.im*a.re) / q - return complex(re, im) + __radd__ = __add__ - def __neg__(self): - return complex(-self.re, -self.im) + 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: raise TypeError, 'Complex to the Complex power' + 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 checkop(expr, a, b, value, fuzz = 1e-6): + import sys + print ' ', a, 'and', b, + try: + result = eval(expr) + except: + result = sys.exc_type + print '->', result + if (type(result) == type('') or type(value) == type('')): + ok = result == value + else: + ok = abs(result - value) <= fuzz + if not ok: + print '!!\t!!\t!! should be', value, 'diff', abs(result - value) def test(): - a = complex(2, 0) - b = complex(3, 4) - print a - print b - print a+b - print a-b - print a*b - print a/b - print b+a - print b-a - print b*a - print b/a - i = complex(0, 1) - print i, i*i, i*i*i, i*i*i*i - j = complex(1, 1) - print j, j*j, j*j*j, j*j*j*j - print abs(j), abs(j*j), abs(j*j*j), abs(j*j*j*j) - print i/-i - -test() + 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), 'TypeError'), + (Complex(0,10), 1, Complex(0,10)), + (Complex(0,10), Complex(1), Complex(0,10)), + (Complex(1), Complex(0,10), 'TypeError'), + (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), + ], + } + exprs = testsuite.keys() + exprs.sort() + for expr in exprs: + print expr + ':' + t = (expr,) + for item in testsuite[expr]: + apply(checkop, t+item) + + +if __name__ == '__main__': + test() |