# 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()
projects / thirdparty / Python / cpython.git / commitdiff
