80 lines
1.8 KiB
Python
80 lines
1.8 KiB
Python
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from sympy.core import Basic, Expr
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from sympy.core.numbers import oo
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from sympy.core.symbol import symbols
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from sympy.multipledispatch import Dispatcher
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from sympy.sets.setexpr import set_mul
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from sympy.sets.sets import Interval, Set
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_x, _y = symbols("x y")
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_set_mul = Dispatcher('_set_mul')
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_set_div = Dispatcher('_set_div')
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@_set_mul.register(Basic, Basic)
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def _(x, y):
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return None
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@_set_mul.register(Set, Set)
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def _(x, y):
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return None
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@_set_mul.register(Expr, Expr)
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def _(x, y):
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return x*y
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@_set_mul.register(Interval, Interval)
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def _(x, y):
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"""
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Multiplications in interval arithmetic
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https://en.wikipedia.org/wiki/Interval_arithmetic
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"""
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# TODO: some intervals containing 0 and oo will fail as 0*oo returns nan.
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comvals = (
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(x.start * y.start, bool(x.left_open or y.left_open)),
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(x.start * y.end, bool(x.left_open or y.right_open)),
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(x.end * y.start, bool(x.right_open or y.left_open)),
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(x.end * y.end, bool(x.right_open or y.right_open)),
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)
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# TODO: handle symbolic intervals
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minval, minopen = min(comvals)
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maxval, maxopen = max(comvals)
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return Interval(
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minval,
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maxval,
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minopen,
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maxopen
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)
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@_set_div.register(Basic, Basic)
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def _(x, y):
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return None
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@_set_div.register(Expr, Expr)
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def _(x, y):
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return x/y
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@_set_div.register(Set, Set)
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def _(x, y):
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return None
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@_set_div.register(Interval, Interval)
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def _(x, y):
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"""
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Divisions in interval arithmetic
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https://en.wikipedia.org/wiki/Interval_arithmetic
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"""
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if (y.start*y.end).is_negative:
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return Interval(-oo, oo)
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if y.start == 0:
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s2 = oo
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else:
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s2 = 1/y.start
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if y.end == 0:
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s1 = -oo
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else:
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s1 = 1/y.end
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return set_mul(x, Interval(s1, s2, y.right_open, y.left_open))
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