Mercurial > cpython-lru_cache-weakref

annotate Demo/classes/Complex.py @ 3720:b341def4eef8 legacy-trunk

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author Guido van Rossum <guido@python.org>
date Wed, 26 Jun 1996 19:30:01 +0000
parents 545e235831b7
children 2ac2a601205b
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1 # Complex numbers
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2 # ---------------
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3
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4 # This module represents complex numbers as instances of the class Complex.
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5 # A Complex instance z has two data attribues, z.re (the real part) and z.im
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6 # (the imaginary part). In fact, z.re and z.im can have any value -- all
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7 # arithmetic operators work regardless of the type of z.re and z.im (as long
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8 # as they support numerical operations).
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9 #
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10 # The following functions exist (Complex is actually a class):
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11 # Complex([re [,im]) -> creates a complex number from a real and an imaginary part
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12 # IsComplex(z) -> true iff z is a complex number (== has .re and .im attributes)
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13 # ToComplex(z) -> a complex number equal to z; z itself if IsComplex(z) is true
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14 # if z is a tuple(re, im) it will also be converted
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15 # PolarToComplex([r [,phi [,fullcircle]]]) ->
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16 # the complex number z for which r == z.radius() and phi == z.angle(fullcircle)
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17 # (r and phi default to 0)
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18 #
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19 # Complex numbers have the following methods:
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20 # z.abs() -> absolute value of z
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21 # z.radius() == z.abs()
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22 # z.angle([fullcircle]) -> angle from positive X axis; fullcircle gives units
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23 # z.phi([fullcircle]) == z.angle(fullcircle)
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24 #
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25 # These standard functions and unary operators accept complex arguments:
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26 # abs(z)
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27 # -z
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28 # +z
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29 # not z
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30 # repr(z) == `z`
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31 # str(z)
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32 # hash(z) -> a combination of hash(z.re) and hash(z.im) such that if z.im is zero
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33 # the result equals hash(z.re)
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34 # Note that hex(z) and oct(z) are not defined.
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35 #
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36 # These conversions accept complex arguments only if their imaginary part is zero:
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37 # int(z)
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38 # long(z)
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39 # float(z)
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40 #
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41 # The following operators accept two complex numbers, or one complex number
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42 # and one real number (int, long or float):
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43 # z1 + z2
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44 # z1 - z2
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45 # z1 * z2
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46 # z1 / z2
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47 # pow(z1, z2)
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48 # cmp(z1, z2)
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49 # Note that z1 % z2 and divmod(z1, z2) are not defined,
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50 # nor are shift and mask operations.
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51 #
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52 # The standard module math does not support complex numbers.
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53 # (I suppose it would be easy to implement a cmath module.)
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54 #
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55 # Idea:
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56 # add a class Polar(r, phi) and mixed-mode arithmetic which
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57 # chooses the most appropriate type for the result:
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58 # Complex for +,-,cmp
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59 # Polar for *,/,pow
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60
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61
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62 import types, math
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63
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64 twopi = math.pi*2.0
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65 halfpi = math.pi/2.0
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66
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67 def IsComplex(obj):
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68 return hasattr(obj, 're') and hasattr(obj, 'im')
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69
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70 def ToComplex(obj):
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71 if IsComplex(obj):
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72 return obj
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73 elif type(obj) == types.TupleType:
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74 return apply(Complex, obj)
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75 else:
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76 return Complex(obj)
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77
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78 def PolarToComplex(r = 0, phi = 0, fullcircle = twopi):
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79 phi = phi * (twopi / fullcircle)
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80 return Complex(math.cos(phi)*r, math.sin(phi)*r)
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81
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82 def Re(obj):
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83 if IsComplex(obj):
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84 return obj.re
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85 else:
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86 return obj
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87
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88 def Im(obj):
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89 if IsComplex(obj):
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90 return obj.im
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91 else:
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92 return obj
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93
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94 class Complex:
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95
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96 def __init__(self, re=0, im=0):
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97 if IsComplex(re):
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98 im = i + Complex(0, re.im)
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99 re = re.re
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100 if IsComplex(im):
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101 re = re - im.im
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102 im = im.re
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103 self.__dict__['re'] = re
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104 self.__dict__['im'] = im
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105
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106 def __setattr__(self, name, value):
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107 raise TypeError, 'Complex numbers are immutable'
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108
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109 def __hash__(self):
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110 if not self.im: return hash(self.re)
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111 mod = sys.maxint + 1L
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112 return int((hash(self.re) + 2L*hash(self.im) + mod) % (2L*mod) - mod)
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113
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114 def __repr__(self):
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115 if not self.im:
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116 return 'Complex(%s)' % `self.re`
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117 else:
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118 return 'Complex(%s, %s)' % (`self.re`, `self.im`)
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119
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120 def __str__(self):
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121 if not self.im:
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122 return `self.re`
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123 else:
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124 return 'Complex(%s, %s)' % (`self.re`, `self.im`)
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125
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126 def __neg__(self):
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127 return Complex(-self.re, -self.im)
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128
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129 def __pos__(self):
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130 return self
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131
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132 def __abs__(self):
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133 # XXX could be done differently to avoid overflow!
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134 return math.sqrt(self.re*self.re + self.im*self.im)
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135
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136 def __int__(self):
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137 if self.im:
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138 raise ValueError, "can't convert Complex with nonzero im to int"
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139 return int(self.re)
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140
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141 def __long__(self):
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142 if self.im:
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143 raise ValueError, "can't convert Complex with nonzero im to long"
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144 return long(self.re)
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145
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146 def __float__(self):
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147 if self.im:
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148 raise ValueError, "can't convert Complex with nonzero im to float"
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149 return float(self.re)
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150
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151 def __cmp__(self, other):
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152 other = ToComplex(other)
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153 return cmp((self.re, self.im), (other.re, other.im))
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154
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155 def __rcmp__(self, other):
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156 other = ToComplex(other)
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157 return cmp(other, self)
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158
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159 def __nonzero__(self):
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160 return not (self.re == self.im == 0)
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161
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162 abs = radius = __abs__
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163
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164 def angle(self, fullcircle = twopi):
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165 return (fullcircle/twopi) * ((halfpi - math.atan2(self.re, self.im)) % twopi)
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166
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167 phi = angle
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168
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169 def __add__(self, other):
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170 other = ToComplex(other)
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171 return Complex(self.re + other.re, self.im + other.im)
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172
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173 __radd__ = __add__
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174
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175 def __sub__(self, other):
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176 other = ToComplex(other)
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177 return Complex(self.re - other.re, self.im - other.im)
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178
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179 def __rsub__(self, other):
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180 other = ToComplex(other)
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181 return other - self
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182
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183 def __mul__(self, other):
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184 other = ToComplex(other)
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185 return Complex(self.re*other.re - self.im*other.im,
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186 self.re*other.im + self.im*other.re)
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187
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188 __rmul__ = __mul__
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189
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190 def __div__(self, other):
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191 other = ToComplex(other)
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192 d = float(other.re*other.re + other.im*other.im)
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193 if not d: raise ZeroDivisionError, 'Complex division'
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194 return Complex((self.re*other.re + self.im*other.im) / d,
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195 (self.im*other.re - self.re*other.im) / d)
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196
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197 def __rdiv__(self, other):
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198 other = ToComplex(other)
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199 return other / self
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200
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201 def __pow__(self, n, z=None):
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202 if z is not None:
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203 raise TypeError, 'Complex does not support ternary pow()'
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204 if IsComplex(n):
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205 if n.im: raise TypeError, 'Complex to the Complex power'
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206 n = n.re
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207 r = pow(self.abs(), n)
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208 phi = n*self.angle()
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209 return Complex(math.cos(phi)*r, math.sin(phi)*r)
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210
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211 def __rpow__(self, base):
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212 base = ToComplex(base)
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213 return pow(base, self)
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214
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215
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216 def checkop(expr, a, b, value, fuzz = 1e-6):
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217 import sys
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218 print ' ', a, 'and', b,
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219 try:
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220 result = eval(expr)
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221 except:
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222 result = sys.exc_type
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223 print '->', result
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224 if (type(result) == type('') or type(value) == type('')):
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225 ok = result == value
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226 else:
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227 ok = abs(result - value) <= fuzz
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228 if not ok:
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229 print '!!\t!!\t!! should be', value, 'diff', abs(result - value)
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230
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231
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232 def test():
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233 testsuite = {
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234 'a+b': [
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235 (1, 10, 11),
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236 (1, Complex(0,10), Complex(1,10)),
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237 (Complex(0,10), 1, Complex(1,10)),
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238 (Complex(0,10), Complex(1), Complex(1,10)),
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239 (Complex(1), Complex(0,10), Complex(1,10)),
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240 ],
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241 'a-b': [
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242 (1, 10, -9),
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243 (1, Complex(0,10), Complex(1,-10)),
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244 (Complex(0,10), 1, Complex(-1,10)),
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245 (Complex(0,10), Complex(1), Complex(-1,10)),
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246 (Complex(1), Complex(0,10), Complex(1,-10)),
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247 ],
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248 'a*b': [
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249 (1, 10, 10),
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250 (1, Complex(0,10), Complex(0, 10)),
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251 (Complex(0,10), 1, Complex(0,10)),
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252 (Complex(0,10), Complex(1), Complex(0,10)),
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253 (Complex(1), Complex(0,10), Complex(0,10)),
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254 ],
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255 'a/b': [
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256 (1., 10, 0.1),
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257 (1, Complex(0,10), Complex(0, -0.1)),
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258 (Complex(0, 10), 1, Complex(0, 10)),
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259 (Complex(0, 10), Complex(1), Complex(0, 10)),
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260 (Complex(1), Complex(0,10), Complex(0, -0.1)),
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261 ],
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262 'pow(a,b)': [
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263 (1, 10, 1),
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264 (1, Complex(0,10), 'TypeError'),
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265 (Complex(0,10), 1, Complex(0,10)),
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266 (Complex(0,10), Complex(1), Complex(0,10)),
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267 (Complex(1), Complex(0,10), 'TypeError'),
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268 (2, Complex(4,0), 16),
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269 ],
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270 'cmp(a,b)': [
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271 (1, 10, -1),
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272 (1, Complex(0,10), 1),
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273 (Complex(0,10), 1, -1),
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274 (Complex(0,10), Complex(1), -1),
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275 (Complex(1), Complex(0,10), 1),
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276 ],
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277 }
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278 exprs = testsuite.keys()
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279 exprs.sort()
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280 for expr in exprs:
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281 print expr + ':'
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282 t = (expr,)
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283 for item in testsuite[expr]:
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284 apply(checkop, t+item)
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285
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286
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287 if __name__ == '__main__':
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288 test()