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100 lines
2.8 KiB
100 lines
2.8 KiB
"""
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Contains the base class for series
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Made using sequences in mind
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"""
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from sympy.core.expr import Expr
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from sympy.core.singleton import S
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from sympy.core.cache import cacheit
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class SeriesBase(Expr):
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"""Base Class for series"""
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@property
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def interval(self):
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"""The interval on which the series is defined"""
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raise NotImplementedError("(%s).interval" % self)
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@property
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def start(self):
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"""The starting point of the series. This point is included"""
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raise NotImplementedError("(%s).start" % self)
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@property
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def stop(self):
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"""The ending point of the series. This point is included"""
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raise NotImplementedError("(%s).stop" % self)
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@property
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def length(self):
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"""Length of the series expansion"""
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raise NotImplementedError("(%s).length" % self)
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@property
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def variables(self):
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"""Returns a tuple of variables that are bounded"""
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return ()
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@property
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def free_symbols(self):
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"""
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This method returns the symbols in the object, excluding those
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that take on a specific value (i.e. the dummy symbols).
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"""
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return ({j for i in self.args for j in i.free_symbols}
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.difference(self.variables))
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@cacheit
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def term(self, pt):
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"""Term at point pt of a series"""
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if pt < self.start or pt > self.stop:
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raise IndexError("Index %s out of bounds %s" % (pt, self.interval))
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return self._eval_term(pt)
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def _eval_term(self, pt):
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raise NotImplementedError("The _eval_term method should be added to"
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"%s to return series term so it is available"
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"when 'term' calls it."
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% self.func)
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def _ith_point(self, i):
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"""
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Returns the i'th point of a series
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If start point is negative infinity, point is returned from the end.
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Assumes the first point to be indexed zero.
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Examples
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========
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TODO
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"""
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if self.start is S.NegativeInfinity:
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initial = self.stop
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step = -1
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else:
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initial = self.start
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step = 1
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return initial + i*step
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def __iter__(self):
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i = 0
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while i < self.length:
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pt = self._ith_point(i)
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yield self.term(pt)
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i += 1
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def __getitem__(self, index):
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if isinstance(index, int):
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index = self._ith_point(index)
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return self.term(index)
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elif isinstance(index, slice):
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start, stop = index.start, index.stop
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if start is None:
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start = 0
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if stop is None:
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stop = self.length
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return [self.term(self._ith_point(i)) for i in
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range(start, stop, index.step or 1)]
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