/usr/lib/python2.7/dist-packages/Scientific/Functions/Rational.py is in python-scientific 2.9.4-1.
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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 | # This module defines a univariate rational function class
#
# Written by Konrad Hinsen <hinsen@cnrs-orleans.fr>
# last revision: 2006-6-12
#
"""
Rational functions in one variable
"""
from Polynomial import Polynomial
from Scientific import N; Numeric = N
class RationalFunction:
"""Rational Function
Instances of this class represent rational functions
in a single variable. They can be evaluated like functions.
Rational functions support addition, subtraction, multiplication,
and division.
"""
def __init__(self, numerator, denominator=[1.]):
"""
@param numerator: polynomial in one variable, or a list
of polynomial coefficients
@type numerator: L{Scientific.Functions.Polynomial.Polynomial}
or C{list} of numbers
@param denominator: polynomial in one variable, or a list
of polynomial coefficients
@type denominator: L{Scientific.Functions.Polynomial.Polynomial}
or C{list} of numbers
"""
if hasattr(numerator, 'is_polynomial'):
self.numerator = numerator
else:
self.numerator = Polynomial(numerator)
if hasattr(denominator, 'is_polynomial'):
self.denominator = denominator
else:
self.denominator = Polynomial(denominator)
self._normalize()
is_rational_function = 1
def __call__(self, value):
return self.numerator(value)/self.denominator(value)
def __repr__(self):
return "RationalFunction(%s,%s)" % (repr(list(self.numerator.coeff)),
repr(list(self.denominator.coeff)))
def _normalize(self):
self.numerator = self._truncate(self.numerator)
self.denominator = self._truncate(self.denominator)
n = 0
while 1:
if self.numerator.coeff[n] != 0:
break
if self.denominator.coeff[n] != 0:
break
n = n + 1
if n == len(self.numerator.coeff):
break
if n > 0:
self.numerator = Polynomial(self.numerator.coeff[n:])
self.denominator = Polynomial(self.denominator.coeff[n:])
factor = self.denominator.coeff[-1]
if factor != 1.:
self.numerator = self.numerator/factor
self.denominator = self.denominator/factor
def _truncate(self, poly):
if poly.coeff[-1] != 0.:
return poly
coeff = poly.coeff
while len(coeff) > 1 and coeff[-1] == 0.:
coeff = coeff[:-1]
return Polynomial(coeff)
def __coerce__(self, other):
if hasattr(other, 'is_rational_function'):
return (self, other)
elif hasattr(other, 'is_polynomial'):
return (self, RationalFunction(other, [1.]))
else:
return (self, RationalFunction([other], [1.]))
def __mul__(self, other):
return RationalFunction(self.numerator*other.numerator,
self.denominator*other.denominator)
__rmul__ = __mul__
def __div__(self, other):
return RationalFunction(self.numerator*other.denominator,
self.denominator*other.numerator)
__truediv__ = __div__
def __rdiv__(self, other):
return RationalFunction(other.numerator*self.denominator,
other.denominator*self.numerator)
def __add__(self, other):
return RationalFunction(self.numerator*other.denominator+
self.denominator*other.numerator,
self.denominator*other.denominator)
__radd__ = __add__
def __sub__(self, other):
return RationalFunction(self.numerator*other.denominator-
self.denominator*other.numerator,
self.denominator*other.denominator)
def __rsub__(self, other):
return RationalFunction(other.numerator*self.denominator-
other.denominator*self.numerator,
self.denominator*other.denominator)
def divide(self, shift=0):
"""
@param shift: the power of the independent variable by which
the numerator is multiplied prior to division
@type shift: C{int} (non-negative)
@return: a polynomial and a rational function such that the
sum of the two is equal to the original rational function. The
returned rational function's numerator is of lower order than
its denominator.
@rtype: (L{Scientific.Functions.Polynomial.Polynomial},
L{RationalFunction})
"""
num = Numeric.array(self.numerator.coeff, copy=1)
if shift > 0:
num = Numeric.concatenate((shift*[0.], num))
den = self.denominator.coeff
den_order = len(den)
coeff = []
while len(num) >= den_order:
q = num[-1]/den[-1]
coeff.append(q)
num[-den_order:] = num[-den_order:]-q*den
num = num[:-1]
if not coeff:
coeff = [0]
coeff.reverse()
if len(num) == 0:
num = [0]
return Polynomial(coeff), RationalFunction(num, den)
def zeros(self):
"""
Find the X{zeros} (X{roots}) of the numerator by diagonalization
of the associated Frobenius matrix.
@returns: an array containing the zeros
@rtype: C{Numeric.array}
"""
return self.numerator.zeros()
def poles(self):
"""
Find the X{poles} (zeros of the denominator) by diagonalization
of the associated Frobenius matrix.
@returns: an array containing the poles
@rtype: C{Numeric.array}
"""
return self.denominator.zeros()
# Test code
if __name__ == '__main__':
p = Polynomial([1., 1.])
invp = 1./p
pr = RationalFunction(p)
print pr+invp
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