442 lines
13 KiB
Python
442 lines
13 KiB
Python
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from sympy.concrete.summations import Sum
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from sympy.core.basic import Basic
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from sympy.core.containers import Tuple
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from sympy.core.function import Lambda
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from sympy.core.numbers import (Rational, nan, oo, pi)
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from sympy.core.relational import Eq
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from sympy.core.singleton import S
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from sympy.core.symbol import (Symbol, symbols)
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from sympy.functions.combinatorial.factorials import (FallingFactorial, binomial)
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from sympy.functions.elementary.exponential import (exp, log)
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from sympy.functions.elementary.trigonometric import (cos, sin)
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from sympy.functions.special.delta_functions import DiracDelta
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from sympy.integrals.integrals import integrate
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from sympy.logic.boolalg import (And, Or)
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from sympy.matrices.dense import Matrix
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from sympy.sets.sets import Interval
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from sympy.tensor.indexed import Indexed
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from sympy.stats import (Die, Normal, Exponential, FiniteRV, P, E, H, variance,
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density, given, independent, dependent, where, pspace, GaussianUnitaryEnsemble,
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random_symbols, sample, Geometric, factorial_moment, Binomial, Hypergeometric,
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DiscreteUniform, Poisson, characteristic_function, moment_generating_function,
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BernoulliProcess, Variance, Expectation, Probability, Covariance, covariance, cmoment,
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moment, median)
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from sympy.stats.rv import (IndependentProductPSpace, rs_swap, Density, NamedArgsMixin,
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RandomSymbol, sample_iter, PSpace, is_random, RandomIndexedSymbol, RandomMatrixSymbol)
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from sympy.testing.pytest import raises, skip, XFAIL, warns_deprecated_sympy
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from sympy.external import import_module
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from sympy.core.numbers import comp
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from sympy.stats.frv_types import BernoulliDistribution
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from sympy.core.symbol import Dummy
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from sympy.functions.elementary.piecewise import Piecewise
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def test_where():
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X, Y = Die('X'), Die('Y')
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Z = Normal('Z', 0, 1)
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assert where(Z**2 <= 1).set == Interval(-1, 1)
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assert where(Z**2 <= 1).as_boolean() == Interval(-1, 1).as_relational(Z.symbol)
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assert where(And(X > Y, Y > 4)).as_boolean() == And(
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Eq(X.symbol, 6), Eq(Y.symbol, 5))
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assert len(where(X < 3).set) == 2
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assert 1 in where(X < 3).set
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X, Y = Normal('X', 0, 1), Normal('Y', 0, 1)
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assert where(And(X**2 <= 1, X >= 0)).set == Interval(0, 1)
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XX = given(X, And(X**2 <= 1, X >= 0))
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assert XX.pspace.domain.set == Interval(0, 1)
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assert XX.pspace.domain.as_boolean() == \
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And(0 <= X.symbol, X.symbol**2 <= 1, -oo < X.symbol, X.symbol < oo)
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with raises(TypeError):
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XX = given(X, X + 3)
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def test_random_symbols():
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X, Y = Normal('X', 0, 1), Normal('Y', 0, 1)
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assert set(random_symbols(2*X + 1)) == {X}
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assert set(random_symbols(2*X + Y)) == {X, Y}
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assert set(random_symbols(2*X + Y.symbol)) == {X}
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assert set(random_symbols(2)) == set()
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def test_characteristic_function():
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# Imports I from sympy
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from sympy.core.numbers import I
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X = Normal('X',0,1)
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Y = DiscreteUniform('Y', [1,2,7])
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Z = Poisson('Z', 2)
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t = symbols('_t')
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P = Lambda(t, exp(-t**2/2))
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Q = Lambda(t, exp(7*t*I)/3 + exp(2*t*I)/3 + exp(t*I)/3)
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R = Lambda(t, exp(2 * exp(t*I) - 2))
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assert characteristic_function(X).dummy_eq(P)
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assert characteristic_function(Y).dummy_eq(Q)
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assert characteristic_function(Z).dummy_eq(R)
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def test_moment_generating_function():
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X = Normal('X',0,1)
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Y = DiscreteUniform('Y', [1,2,7])
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Z = Poisson('Z', 2)
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t = symbols('_t')
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P = Lambda(t, exp(t**2/2))
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Q = Lambda(t, (exp(7*t)/3 + exp(2*t)/3 + exp(t)/3))
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R = Lambda(t, exp(2 * exp(t) - 2))
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assert moment_generating_function(X).dummy_eq(P)
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assert moment_generating_function(Y).dummy_eq(Q)
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assert moment_generating_function(Z).dummy_eq(R)
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def test_sample_iter():
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X = Normal('X',0,1)
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Y = DiscreteUniform('Y', [1, 2, 7])
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Z = Poisson('Z', 2)
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scipy = import_module('scipy')
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if not scipy:
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skip('Scipy is not installed. Abort tests')
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expr = X**2 + 3
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iterator = sample_iter(expr)
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expr2 = Y**2 + 5*Y + 4
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iterator2 = sample_iter(expr2)
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expr3 = Z**3 + 4
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iterator3 = sample_iter(expr3)
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def is_iterator(obj):
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if (
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hasattr(obj, '__iter__') and
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(hasattr(obj, 'next') or
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hasattr(obj, '__next__')) and
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callable(obj.__iter__) and
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obj.__iter__() is obj
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):
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return True
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else:
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return False
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assert is_iterator(iterator)
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assert is_iterator(iterator2)
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assert is_iterator(iterator3)
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def test_pspace():
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X, Y = Normal('X', 0, 1), Normal('Y', 0, 1)
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x = Symbol('x')
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raises(ValueError, lambda: pspace(5 + 3))
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raises(ValueError, lambda: pspace(x < 1))
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assert pspace(X) == X.pspace
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assert pspace(2*X + 1) == X.pspace
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assert pspace(2*X + Y) == IndependentProductPSpace(Y.pspace, X.pspace)
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def test_rs_swap():
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X = Normal('x', 0, 1)
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Y = Exponential('y', 1)
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XX = Normal('x', 0, 2)
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YY = Normal('y', 0, 3)
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expr = 2*X + Y
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assert expr.subs(rs_swap((X, Y), (YY, XX))) == 2*XX + YY
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def test_RandomSymbol():
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X = Normal('x', 0, 1)
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Y = Normal('x', 0, 2)
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assert X.symbol == Y.symbol
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assert X != Y
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assert X.name == X.symbol.name
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X = Normal('lambda', 0, 1) # make sure we can use protected terms
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X = Normal('Lambda', 0, 1) # make sure we can use SymPy terms
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def test_RandomSymbol_diff():
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X = Normal('x', 0, 1)
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assert (2*X).diff(X)
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def test_random_symbol_no_pspace():
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x = RandomSymbol(Symbol('x'))
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assert x.pspace == PSpace()
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def test_overlap():
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X = Normal('x', 0, 1)
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Y = Normal('x', 0, 2)
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raises(ValueError, lambda: P(X > Y))
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def test_IndependentProductPSpace():
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X = Normal('X', 0, 1)
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Y = Normal('Y', 0, 1)
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px = X.pspace
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py = Y.pspace
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assert pspace(X + Y) == IndependentProductPSpace(px, py)
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assert pspace(X + Y) == IndependentProductPSpace(py, px)
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def test_E():
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assert E(5) == 5
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def test_H():
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X = Normal('X', 0, 1)
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D = Die('D', sides = 4)
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G = Geometric('G', 0.5)
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assert H(X, X > 0) == -log(2)/2 + S.Half + log(pi)/2
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assert H(D, D > 2) == log(2)
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assert comp(H(G).evalf().round(2), 1.39)
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def test_Sample():
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X = Die('X', 6)
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Y = Normal('Y', 0, 1)
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z = Symbol('z', integer=True)
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scipy = import_module('scipy')
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if not scipy:
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skip('Scipy is not installed. Abort tests')
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assert sample(X) in [1, 2, 3, 4, 5, 6]
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assert isinstance(sample(X + Y), float)
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assert P(X + Y > 0, Y < 0, numsamples=10).is_number
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assert E(X + Y, numsamples=10).is_number
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assert E(X**2 + Y, numsamples=10).is_number
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assert E((X + Y)**2, numsamples=10).is_number
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assert variance(X + Y, numsamples=10).is_number
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raises(TypeError, lambda: P(Y > z, numsamples=5))
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assert P(sin(Y) <= 1, numsamples=10) == 1.0
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assert P(sin(Y) <= 1, cos(Y) < 1, numsamples=10) == 1.0
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assert all(i in range(1, 7) for i in density(X, numsamples=10))
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assert all(i in range(4, 7) for i in density(X, X>3, numsamples=10))
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numpy = import_module('numpy')
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if not numpy:
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skip('Numpy is not installed. Abort tests')
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#Test Issue #21563: Output of sample must be a float or array
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assert isinstance(sample(X), (numpy.int32, numpy.int64))
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assert isinstance(sample(Y), numpy.float64)
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assert isinstance(sample(X, size=2), numpy.ndarray)
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with warns_deprecated_sympy():
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sample(X, numsamples=2)
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@XFAIL
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def test_samplingE():
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scipy = import_module('scipy')
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if not scipy:
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skip('Scipy is not installed. Abort tests')
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Y = Normal('Y', 0, 1)
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z = Symbol('z', integer=True)
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assert E(Sum(1/z**Y, (z, 1, oo)), Y > 2, numsamples=3).is_number
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def test_given():
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X = Normal('X', 0, 1)
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Y = Normal('Y', 0, 1)
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A = given(X, True)
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B = given(X, Y > 2)
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assert X == A == B
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def test_factorial_moment():
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X = Poisson('X', 2)
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Y = Binomial('Y', 2, S.Half)
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Z = Hypergeometric('Z', 4, 2, 2)
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assert factorial_moment(X, 2) == 4
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assert factorial_moment(Y, 2) == S.Half
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assert factorial_moment(Z, 2) == Rational(1, 3)
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x, y, z, l = symbols('x y z l')
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Y = Binomial('Y', 2, y)
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Z = Hypergeometric('Z', 10, 2, 3)
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assert factorial_moment(Y, l) == y**2*FallingFactorial(
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2, l) + 2*y*(1 - y)*FallingFactorial(1, l) + (1 - y)**2*\
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FallingFactorial(0, l)
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assert factorial_moment(Z, l) == 7*FallingFactorial(0, l)/\
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15 + 7*FallingFactorial(1, l)/15 + FallingFactorial(2, l)/15
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def test_dependence():
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X, Y = Die('X'), Die('Y')
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assert independent(X, 2*Y)
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assert not dependent(X, 2*Y)
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X, Y = Normal('X', 0, 1), Normal('Y', 0, 1)
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assert independent(X, Y)
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assert dependent(X, 2*X)
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# Create a dependency
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XX, YY = given(Tuple(X, Y), Eq(X + Y, 3))
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assert dependent(XX, YY)
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def test_dependent_finite():
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X, Y = Die('X'), Die('Y')
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# Dependence testing requires symbolic conditions which currently break
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# finite random variables
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assert dependent(X, Y + X)
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XX, YY = given(Tuple(X, Y), X + Y > 5) # Create a dependency
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assert dependent(XX, YY)
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def test_normality():
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X, Y = Normal('X', 0, 1), Normal('Y', 0, 1)
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x = Symbol('x', real=True)
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z = Symbol('z', real=True)
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dens = density(X - Y, Eq(X + Y, z))
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assert integrate(dens(x), (x, -oo, oo)) == 1
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def test_Density():
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X = Die('X', 6)
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d = Density(X)
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assert d.doit() == density(X)
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def test_NamedArgsMixin():
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class Foo(Basic, NamedArgsMixin):
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_argnames = 'foo', 'bar'
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a = Foo(S(1), S(2))
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assert a.foo == 1
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assert a.bar == 2
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raises(AttributeError, lambda: a.baz)
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class Bar(Basic, NamedArgsMixin):
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pass
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raises(AttributeError, lambda: Bar(S(1), S(2)).foo)
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def test_density_constant():
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assert density(3)(2) == 0
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assert density(3)(3) == DiracDelta(0)
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def test_cmoment_constant():
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assert variance(3) == 0
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assert cmoment(3, 3) == 0
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assert cmoment(3, 4) == 0
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x = Symbol('x')
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assert variance(x) == 0
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assert cmoment(x, 15) == 0
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assert cmoment(x, 0) == 1
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def test_moment_constant():
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assert moment(3, 0) == 1
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assert moment(3, 1) == 3
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assert moment(3, 2) == 9
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x = Symbol('x')
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assert moment(x, 2) == x**2
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def test_median_constant():
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assert median(3) == 3
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x = Symbol('x')
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assert median(x) == x
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def test_real():
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x = Normal('x', 0, 1)
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assert x.is_real
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def test_issue_10052():
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X = Exponential('X', 3)
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assert P(X < oo) == 1
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assert P(X > oo) == 0
|
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assert P(X < 2, X > oo) == 0
|
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|
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assert P(X < oo, X > oo) == 0
|
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|
|
assert P(X < oo, X > 2) == 1
|
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|
|
assert P(X < 3, X == 2) == 0
|
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|
|
raises(ValueError, lambda: P(1))
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|
|
raises(ValueError, lambda: P(X < 1, 2))
|
||
|
|
|
||
|
|
def test_issue_11934():
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|
|
density = {0: .5, 1: .5}
|
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|
|
X = FiniteRV('X', density)
|
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|
|
assert E(X) == 0.5
|
||
|
|
assert P( X>= 2) == 0
|
||
|
|
|
||
|
|
def test_issue_8129():
|
||
|
|
X = Exponential('X', 4)
|
||
|
|
assert P(X >= X) == 1
|
||
|
|
assert P(X > X) == 0
|
||
|
|
assert P(X > X+1) == 0
|
||
|
|
|
||
|
|
def test_issue_12237():
|
||
|
|
X = Normal('X', 0, 1)
|
||
|
|
Y = Normal('Y', 0, 1)
|
||
|
|
U = P(X > 0, X)
|
||
|
|
V = P(Y < 0, X)
|
||
|
|
W = P(X + Y > 0, X)
|
||
|
|
assert W == P(X + Y > 0, X)
|
||
|
|
assert U == BernoulliDistribution(S.Half, S.Zero, S.One)
|
||
|
|
assert V == S.Half
|
||
|
|
|
||
|
|
def test_is_random():
|
||
|
|
X = Normal('X', 0, 1)
|
||
|
|
Y = Normal('Y', 0, 1)
|
||
|
|
a, b = symbols('a, b')
|
||
|
|
G = GaussianUnitaryEnsemble('U', 2)
|
||
|
|
B = BernoulliProcess('B', 0.9)
|
||
|
|
assert not is_random(a)
|
||
|
|
assert not is_random(a + b)
|
||
|
|
assert not is_random(a * b)
|
||
|
|
assert not is_random(Matrix([a**2, b**2]))
|
||
|
|
assert is_random(X)
|
||
|
|
assert is_random(X**2 + Y)
|
||
|
|
assert is_random(Y + b**2)
|
||
|
|
assert is_random(Y > 5)
|
||
|
|
assert is_random(B[3] < 1)
|
||
|
|
assert is_random(G)
|
||
|
|
assert is_random(X * Y * B[1])
|
||
|
|
assert is_random(Matrix([[X, B[2]], [G, Y]]))
|
||
|
|
assert is_random(Eq(X, 4))
|
||
|
|
|
||
|
|
def test_issue_12283():
|
||
|
|
x = symbols('x')
|
||
|
|
X = RandomSymbol(x)
|
||
|
|
Y = RandomSymbol('Y')
|
||
|
|
Z = RandomMatrixSymbol('Z', 2, 1)
|
||
|
|
W = RandomMatrixSymbol('W', 2, 1)
|
||
|
|
RI = RandomIndexedSymbol(Indexed('RI', 3))
|
||
|
|
assert pspace(Z) == PSpace()
|
||
|
|
assert pspace(RI) == PSpace()
|
||
|
|
assert pspace(X) == PSpace()
|
||
|
|
assert E(X) == Expectation(X)
|
||
|
|
assert P(Y > 3) == Probability(Y > 3)
|
||
|
|
assert variance(X) == Variance(X)
|
||
|
|
assert variance(RI) == Variance(RI)
|
||
|
|
assert covariance(X, Y) == Covariance(X, Y)
|
||
|
|
assert covariance(W, Z) == Covariance(W, Z)
|
||
|
|
|
||
|
|
def test_issue_6810():
|
||
|
|
X = Die('X', 6)
|
||
|
|
Y = Normal('Y', 0, 1)
|
||
|
|
assert P(Eq(X, 2)) == S(1)/6
|
||
|
|
assert P(Eq(Y, 0)) == 0
|
||
|
|
assert P(Or(X > 2, X < 3)) == 1
|
||
|
|
assert P(And(X > 3, X > 2)) == S(1)/2
|
||
|
|
|
||
|
|
def test_issue_20286():
|
||
|
|
n, p = symbols('n p')
|
||
|
|
B = Binomial('B', n, p)
|
||
|
|
k = Dummy('k', integer = True)
|
||
|
|
eq = Sum(Piecewise((-p**k*(1 - p)**(-k + n)*log(p**k*(1 - p)**(-k + n)*binomial(n, k))*binomial(n, k), (k >= 0) & (k <= n)), (nan, True)), (k, 0, n))
|
||
|
|
assert eq.dummy_eq(H(B))
|