83 lines
3.9 KiB
Python
83 lines
3.9 KiB
Python
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from sympy.concrete.summations import Sum
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from sympy.core.add import Add
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from sympy.core.mul import Mul
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from sympy.core.numbers import (Integer, oo, pi)
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from sympy.core.power import Pow
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from sympy.core.relational import (Eq, Ne)
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from sympy.core.symbol import (Dummy, Symbol, symbols)
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from sympy.functions.combinatorial.factorials import factorial
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from sympy.functions.elementary.exponential import exp
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from sympy.functions.elementary.miscellaneous import sqrt
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from sympy.functions.elementary.piecewise import Piecewise
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from sympy.functions.special.delta_functions import DiracDelta
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from sympy.functions.special.gamma_functions import gamma
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from sympy.integrals.integrals import Integral
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from sympy.simplify.simplify import simplify
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from sympy.tensor.indexed import (Indexed, IndexedBase)
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from sympy.functions.elementary.piecewise import ExprCondPair
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from sympy.stats import (Poisson, Beta, Exponential, P,
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Multinomial, MultivariateBeta)
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from sympy.stats.crv_types import Normal
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from sympy.stats.drv_types import PoissonDistribution
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from sympy.stats.compound_rv import CompoundPSpace, CompoundDistribution
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from sympy.stats.joint_rv import MarginalDistribution
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from sympy.stats.rv import pspace, density
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from sympy.testing.pytest import ignore_warnings
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def test_density():
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x = Symbol('x')
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l = Symbol('l', positive=True)
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rate = Beta(l, 2, 3)
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X = Poisson(x, rate)
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assert isinstance(pspace(X), CompoundPSpace)
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assert density(X, Eq(rate, rate.symbol)) == PoissonDistribution(l)
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N1 = Normal('N1', 0, 1)
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N2 = Normal('N2', N1, 2)
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assert density(N2)(0).doit() == sqrt(10)/(10*sqrt(pi))
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assert simplify(density(N2, Eq(N1, 1))(x)) == \
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sqrt(2)*exp(-(x - 1)**2/8)/(4*sqrt(pi))
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assert simplify(density(N2)(x)) == sqrt(10)*exp(-x**2/10)/(10*sqrt(pi))
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def test_MarginalDistribution():
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a1, p1, p2 = symbols('a1 p1 p2', positive=True)
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C = Multinomial('C', 2, p1, p2)
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B = MultivariateBeta('B', a1, C[0])
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MGR = MarginalDistribution(B, (C[0],))
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mgrc = Mul(Symbol('B'), Piecewise(ExprCondPair(Mul(Integer(2),
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Pow(Symbol('p1', positive=True), Indexed(IndexedBase(Symbol('C')),
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Integer(0))), Pow(Symbol('p2', positive=True),
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Indexed(IndexedBase(Symbol('C')), Integer(1))),
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Pow(factorial(Indexed(IndexedBase(Symbol('C')), Integer(0))), Integer(-1)),
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Pow(factorial(Indexed(IndexedBase(Symbol('C')), Integer(1))), Integer(-1))),
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Eq(Add(Indexed(IndexedBase(Symbol('C')), Integer(0)),
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Indexed(IndexedBase(Symbol('C')), Integer(1))), Integer(2))),
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ExprCondPair(Integer(0), True)), Pow(gamma(Symbol('a1', positive=True)),
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Integer(-1)), gamma(Add(Symbol('a1', positive=True),
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Indexed(IndexedBase(Symbol('C')), Integer(0)))),
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Pow(gamma(Indexed(IndexedBase(Symbol('C')), Integer(0))), Integer(-1)),
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Pow(Indexed(IndexedBase(Symbol('B')), Integer(0)),
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Add(Symbol('a1', positive=True), Integer(-1))),
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Pow(Indexed(IndexedBase(Symbol('B')), Integer(1)),
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Add(Indexed(IndexedBase(Symbol('C')), Integer(0)), Integer(-1))))
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assert MGR(C) == mgrc
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def test_compound_distribution():
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Y = Poisson('Y', 1)
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Z = Poisson('Z', Y)
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assert isinstance(pspace(Z), CompoundPSpace)
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assert isinstance(pspace(Z).distribution, CompoundDistribution)
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assert Z.pspace.distribution.pdf(1).doit() == exp(-2)*exp(exp(-1))
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def test_mix_expression():
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Y, E = Poisson('Y', 1), Exponential('E', 1)
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k = Dummy('k')
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expr1 = Integral(Sum(exp(-1)*Integral(exp(-k)*DiracDelta(k - 2), (k, 0, oo)
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)/factorial(k), (k, 0, oo)), (k, -oo, 0))
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expr2 = Integral(Sum(exp(-1)*Integral(exp(-k)*DiracDelta(k - 2), (k, 0, oo)
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)/factorial(k), (k, 0, oo)), (k, 0, oo))
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assert P(Eq(Y + E, 1)) == 0
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assert P(Ne(Y + E, 2)) == 1
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with ignore_warnings(UserWarning): ### TODO: Restore tests once warnings are removed
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assert P(E + Y < 2, evaluate=False).rewrite(Integral).dummy_eq(expr1)
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assert P(E + Y > 2, evaluate=False).rewrite(Integral).dummy_eq(expr2)
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