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