# cpython-withatomic / Lib / Complex.py

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 ``` 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 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275``` ```# 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) # Polar([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 import types, math if not hasattr(math, 'hypot'): def hypot(x, y): # XXX I know there's a way to compute this without possibly causing # overflow, but I can't remember what it is right now... return math.sqrt(x*x + y*y) math.hypot = hypot twopi = math.pi*2.0 halfpi = math.pi/2.0 def IsComplex(obj): return hasattr(obj, 're') and hasattr(obj, 'im') def Polar(r = 0, phi = 0, fullcircle = twopi): phi = phi * (twopi / fullcircle) return Complex(math.cos(phi)*r, math.sin(phi)*r) class Complex: def __init__(self, re=0, im=0): if IsComplex(re): im = im + re.im re = re.re if IsComplex(im): re = re - im.im im = im.re self.re = re self.im = im def __setattr__(self, name, value): if hasattr(self, name): raise TypeError, "Complex numbers have set-once attributes" self.__dict__[name] = value def __repr__(self): if not self.im: return 'Complex(%s)' % `self.re` else: return 'Complex(%s, %s)' % (`self.re`, `self.im`) def __str__(self): if not self.im: return `self.re` else: return 'Complex(%s, %s)' % (`self.re`, `self.im`) def __coerce__(self, other): if IsComplex(other): return self, other return self, Complex(other) # May fail def __cmp__(self, other): return cmp(self.re, other.re) or cmp(self.im, other.im) 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 __neg__(self): return Complex(-self.re, -self.im) def __pos__(self): return self def __abs__(self): return math.hypot(self.re, self.im) ##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, "can't convert Complex with nonzero im to float" return float(self.re) def __nonzero__(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): return Complex(self.re + other.re, self.im + other.im) __radd__ = __add__ def __sub__(self, other): return Complex(self.re - other.re, self.im - other.im) def __rsub__(self, other): return Complex(other.re - self.re, other.im - self.im) def __mul__(self, 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): # Deviating from the general principle of not forcing re or im # to be floats, we cast to float here, otherwise division # of Complex numbers with integer re and im parts would use # the (truncating) integer division 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): 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): return pow(base, self) # Everything below this point is part of the test suite 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(): 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() ```
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