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Diffstat (limited to 'AppPkg/Applications/Python/Python-2.7.2/Demo/classes/Complex.py')
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1 files changed, 320 insertions, 0 deletions
diff --git a/AppPkg/Applications/Python/Python-2.7.2/Demo/classes/Complex.py b/AppPkg/Applications/Python/Python-2.7.2/Demo/classes/Complex.py new file mode 100644 index 0000000000..9d631b8739 --- /dev/null +++ b/AppPkg/Applications/Python/Python-2.7.2/Demo/classes/Complex.py @@ -0,0 +1,320 @@ +# Complex numbers
+# ---------------
+
+# [Now that Python has a complex data type built-in, this is not very
+# useful, but it's still a nice example class]
+
+# 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)
+# exp(z) -> returns the complex exponential of z. Equivalent to pow(math.e,z).
+#
+# 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.
+# The cmath modules should be used instead.
+#
+# 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 math
+import sys
+
+twopi = math.pi*2.0
+halfpi = math.pi/2.0
+
+def IsComplex(obj):
+ return hasattr(obj, 're') and hasattr(obj, 'im')
+
+def ToComplex(obj):
+ if IsComplex(obj):
+ return obj
+ elif isinstance(obj, tuple):
+ return 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
+ return obj
+
+def Im(obj):
+ if IsComplex(obj):
+ return obj.im
+ return 0
+
+class Complex:
+
+ def __init__(self, re=0, im=0):
+ _re = 0
+ _im = 0
+ if IsComplex(re):
+ _re = re.re
+ _im = re.im
+ else:
+ _re = re
+ if IsComplex(im):
+ _re = _re - im.im
+ _im = _im + im.re
+ else:
+ _im = _im + im
+ # this class is immutable, so setting self.re directly is
+ # not possible.
+ 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)
+ return hash((self.re, self.im))
+
+ def __repr__(self):
+ if not self.im:
+ return 'Complex(%r)' % (self.re,)
+ else:
+ return 'Complex(%r, %r)' % (self.re, self.im)
+
+ def __str__(self):
+ if not self.im:
+ return repr(self.re)
+ else:
+ return 'Complex(%r, %r)' % (self.re, self.im)
+
+ def __neg__(self):
+ return Complex(-self.re, -self.im)
+
+ def __pos__(self):
+ return self
+
+ def __abs__(self):
+ return math.hypot(self.re, 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 __cmp__(self, other):
+ other = ToComplex(other)
+ return cmp((self.re, self.im), (other.re, other.im))
+
+ def __rcmp__(self, other):
+ other = ToComplex(other)
+ return cmp(other, self)
+
+ 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):
+ other = ToComplex(other)
+ return Complex(self.re + other.re, self.im + other.im)
+
+ __radd__ = __add__
+
+ 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:
+ if self.im: raise TypeError, 'Complex to the Complex power'
+ else: return exp(math.log(self.re)*n)
+ 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 exp(z):
+ r = math.exp(z.re)
+ return Complex(math.cos(z.im)*r,math.sin(z.im)*r)
+
+
+def checkop(expr, a, b, value, fuzz = 1e-6):
+ print ' ', a, 'and', b,
+ try:
+ result = eval(expr)
+ except:
+ result = sys.exc_type
+ print '->', result
+ if isinstance(result, str) or isinstance(value, str):
+ ok = (result == value)
+ else:
+ ok = abs(result - value) <= fuzz
+ if not ok:
+ print '!!\t!!\t!! should be', value, 'diff', abs(result - value)
+
+def test():
+ print 'test constructors'
+ constructor_test = (
+ # "expect" is an array [re,im] "got" the Complex.
+ ( (0,0), Complex() ),
+ ( (0,0), Complex() ),
+ ( (1,0), Complex(1) ),
+ ( (0,1), Complex(0,1) ),
+ ( (1,2), Complex(Complex(1,2)) ),
+ ( (1,3), Complex(Complex(1,2),1) ),
+ ( (0,0), Complex(0,Complex(0,0)) ),
+ ( (3,4), Complex(3,Complex(4)) ),
+ ( (-1,3), Complex(1,Complex(3,2)) ),
+ ( (-7,6), Complex(Complex(1,2),Complex(4,8)) ) )
+ cnt = [0,0]
+ for t in constructor_test:
+ cnt[0] += 1
+ if ((t[0][0]!=t[1].re)or(t[0][1]!=t[1].im)):
+ print " expected", t[0], "got", t[1]
+ cnt[1] += 1
+ print " ", cnt[1], "of", cnt[0], "tests failed"
+ # test operators
+ 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), 1),
+ (Complex(0,10), 1, Complex(0,10)),
+ (Complex(0,10), Complex(1), Complex(0,10)),
+ (Complex(1), Complex(0,10), 1),
+ (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),
+ ],
+ }
+ for expr in sorted(testsuite):
+ print expr + ':'
+ t = (expr,)
+ for item in testsuite[expr]:
+ checkop(*(t+item))
+
+
+if __name__ == '__main__':
+ test()
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