def test_ProductPSpace(): X = Normal('X', 0, 1) Y = Normal('Y', 0, 1) px = X.pspace py = Y.pspace assert pspace(X + Y) == ProductPSpace(px, py) assert pspace(X + Y) == ProductPSpace(py, px)
def test_domains(): X, Y = Die('x', 6), Die('y', 6) x, y = X.symbol, Y.symbol # Domains d = where(X > Y) assert d.condition == (x > y) d = where(And(X > Y, Y > 3)) assert d.as_boolean() == Or(And(Eq(x, 5), Eq(y, 4)), And(Eq(x, 6), Eq(y, 5)), And(Eq(x, 6), Eq(y, 4))) assert len(d.elements) == 3 assert len(pspace(X + Y).domain.elements) == 36 Z = Die('x', 4) pytest.raises(ValueError, lambda: P(X > Z)) # Two domains with same internal symbol assert pspace(X + Y).domain.set == FiniteSet(1, 2, 3, 4, 5, 6)**2 assert where(X > 3).set == FiniteSet(4, 5, 6) assert X.pspace.domain.dict == FiniteSet( *[Dict({X.symbol: i}) for i in range(1, 7)]) assert where(X > Y).dict == FiniteSet(*[Dict({X.symbol: i, Y.symbol: j}) for i in range(1, 7) for j in range(1, 7) if i > j]) X, Y = Die('x', 7), Die('y', 3) x, y = X.symbol, Y.symbol pytest.raises(ValueError, lambda: X.pspace.where(Y < 3)) cset = X.pspace.where(X < 3) assert ((x, 1),) in cset assert ((x, 3),) not in cset assert X.pspace.where(True) == X.pspace.domain
def test_domains(): X, Y = Die('x', 6), Die('y', 6) x, y = X.symbol, Y.symbol # Domains d = where(X > Y) assert d.condition == (x > y) d = where(And(X > Y, Y > 3)) assert d.as_boolean() == Or(And(Eq(x, 5), Eq(y, 4)), And(Eq(x, 6), Eq(y, 5)), And(Eq(x, 6), Eq(y, 4))) assert len(d.elements) == 3 assert len(pspace(X + Y).domain.elements) == 36 Z = Die('x', 4) pytest.raises(ValueError, lambda: P(X > Z)) # Two domains with same internal symbol assert pspace(X + Y).domain.set == FiniteSet(1, 2, 3, 4, 5, 6)**2 assert where(X > 3).set == FiniteSet(4, 5, 6) assert X.pspace.domain.dict == FiniteSet( *[Dict({X.symbol: i}) for i in range(1, 7)]) assert where(X > Y).dict == FiniteSet(*[ Dict({ X.symbol: i, Y.symbol: j }) for i in range(1, 7) for j in range(1, 7) if i > j ])
def test_pspace(): X, Y = Normal('X', 0, 1), Normal('Y', 0, 1) pytest.raises(ValueError, lambda: pspace(5 + 3)) pytest.raises(ValueError, lambda: pspace(x < 1)) assert pspace(X) == X.pspace assert pspace(2*X + 1) == X.pspace assert pspace(2*X + Y) == ProductPSpace(Y.pspace, X.pspace)
def test_FiniteRV(): F = FiniteRV('F', {1: S.Half, 2: S.One/4, 3: S.One/4}) assert dict(density(F).items()) == {Integer(1): S.Half, Integer(2): S.One/4, Integer(3): S.One/4} assert P(F >= 2) == S.Half assert pspace(F).domain.as_boolean() == Or( *[Eq(F.symbol, i) for i in [1, 2, 3]])
def test_FiniteRV(): F = FiniteRV('F', {1: Rational(1, 2), 2: Rational(1, 4), 3: Rational(1, 4)}) assert dict(density(F).items()) == {1: Rational(1, 2), 2: Rational(1, 4), 3: Rational(1, 4)} assert P(F >= 2) == Rational(1, 2) assert pspace(F).domain.as_boolean() == Or( *[Eq(F.symbol, i) for i in [1, 2, 3]])
def test_dice(): # TODO: Make iid method! X, Y, Z = Die('X', 6), Die('Y', 6), Die('Z', 6) a, b = symbols('a b') assert E(X) == 3 + Rational(1, 2) assert variance(X) == Rational(35, 12) assert E(X + Y) == 7 assert E(X + X) == 7 assert E(a * X + b) == a * E(X) + b assert variance(X + Y) == variance(X) + variance(Y) == cmoment(X + Y, 2) assert variance(X + X) == 4 * variance(X) == cmoment(X + X, 2) assert cmoment(X, 0) == 1 assert cmoment(4 * X, 3) == 64 * cmoment(X, 3) assert covariance(X, Y) == 0 assert covariance(X, X + Y) == variance(X) assert density(Eq(cos(X * pi), 1))[True] == Rational(1, 2) assert correlation(X, Y) == 0 assert correlation(X, Y) == correlation(Y, X) assert smoment(X + Y, 3) == skewness(X + Y) assert smoment(X, 0) == 1 assert P(X > 3) == Rational(1, 2) assert P(2 * X > 6) == Rational(1, 2) assert P(X > Y) == Rational(5, 12) assert P(Eq(X, Y)) == P(Eq(X, 1)) assert E(X, X > 3) == 5 == moment(X, 1, 0, X > 3) assert E(X, Y > 3) == E(X) == moment(X, 1, 0, Y > 3) assert E(X + Y, Eq(X, Y)) == E(2 * X) assert moment(X, 0) == 1 assert moment(5 * X, 2) == 25 * moment(X, 2) assert P(X > 3, X > 3) == 1 assert P(X > Y, Eq(Y, 6)) == 0 assert P(Eq(X + Y, 12)) == Rational(1, 36) assert P(Eq(X + Y, 12), Eq(X, 6)) == Rational(1, 6) assert density(X + Y) == density(Y + Z) != density(X + X) d = density(2 * X + Y**Z) assert d[22] == Rational(1, 108) and d[4100] == Rational( 1, 216) and 3130 not in d assert pspace(X).domain.as_boolean() == Or( *[Eq(X.symbol, i) for i in [1, 2, 3, 4, 5, 6]]) assert where(X > 3).set == FiniteSet(4, 5, 6) X = Die('X', 2) x = X.symbol assert X.pspace.compute_cdf(X) == {1: Rational(1, 2), 2: 1} assert X.pspace.sorted_cdf(X) == [(1, Rational(1, 2)), (2, 1)] assert X.pspace.compute_density(X)(1) == Rational(1, 2) assert X.pspace.compute_density(X)(0) == 0 assert X.pspace.compute_density(X)(8) == 0 assert X.pspace.density == x
def test_dice(): # TODO: Make iid method! X, Y, Z = Die('X', 6), Die('Y', 6), Die('Z', 6) a, b = symbols('a b') assert E(X) == 3 + Rational(1, 2) assert variance(X) == Rational(35, 12) assert E(X + Y) == 7 assert E(X + X) == 7 assert E(a*X + b) == a*E(X) + b assert variance(X + Y) == variance(X) + variance(Y) == cmoment(X + Y, 2) assert variance(X + X) == 4 * variance(X) == cmoment(X + X, 2) assert cmoment(X, 0) == 1 assert cmoment(4*X, 3) == 64*cmoment(X, 3) assert covariance(X, Y) == 0 assert covariance(X, X + Y) == variance(X) assert density(Eq(cos(X*pi), 1))[True] == Rational(1, 2) assert correlation(X, Y) == 0 assert correlation(X, Y) == correlation(Y, X) assert smoment(X + Y, 3) == skewness(X + Y) assert smoment(X, 0) == 1 assert P(X > 3) == Rational(1, 2) assert P(2*X > 6) == Rational(1, 2) assert P(X > Y) == Rational(5, 12) assert P(Eq(X, Y)) == P(Eq(X, 1)) assert E(X, X > 3) == 5 == moment(X, 1, 0, X > 3) assert E(X, Y > 3) == E(X) == moment(X, 1, 0, Y > 3) assert E(X + Y, Eq(X, Y)) == E(2*X) assert moment(X, 0) == 1 assert moment(5*X, 2) == 25*moment(X, 2) assert P(X > 3, X > 3) == 1 assert P(X > Y, Eq(Y, 6)) == 0 assert P(Eq(X + Y, 12)) == Rational(1, 36) assert P(Eq(X + Y, 12), Eq(X, 6)) == Rational(1, 6) assert density(X + Y) == density(Y + Z) != density(X + X) d = density(2*X + Y**Z) assert d[22] == Rational(1, 108) and d[4100] == Rational(1, 216) and 3130 not in d assert pspace(X).domain.as_boolean() == Or( *[Eq(X.symbol, i) for i in [1, 2, 3, 4, 5, 6]]) assert where(X > 3).set == FiniteSet(4, 5, 6) X = Die('X', 2) x = X.symbol assert X.pspace.compute_cdf(X) == {1: Rational(1, 2), 2: 1} assert X.pspace.sorted_cdf(X) == [(1, Rational(1, 2)), (2, 1)] assert X.pspace.compute_density(X)(1) == Rational(1, 2) assert X.pspace.compute_density(X)(0) == 0 assert X.pspace.compute_density(X)(8) == 0 assert X.pspace.density == x
def test_RandomDomain(): X = Normal('x1', 0, 1) assert str(where(X > 0)) == "Domain: And(0 < x1, x1 < oo)" D = Die('d1', 6) assert str(where(D > 4)) == "Domain: Or(Eq(d1, 5), Eq(d1, 6))" A = Exponential('a', 1) B = Exponential('b', 1) assert str(pspace(Tuple(A, B)).domain) == "Domain: And(0 <= a, 0 <= b, a < oo, b < oo)"
def test_RandomDomain(): X = Normal('x1', 0, 1) assert str(where(X > 0)) == "Domain: (0 < x1) & (x1 < oo)" D = Die('d1', 6) assert str(where(D > 4)) == "Domain: (Eq(d1, 5)) | (Eq(d1, 6))" A = Exponential('a', 1) B = Exponential('b', 1) assert str(pspace(Tuple(A, B)).domain) == "Domain: (0 <= a) & (0 <= b) & (a < oo) & (b < oo)"
def test_RandomDomain(): X = Normal('x1', 0, 1) assert str(where(X > 0)) == "Domain: And(0 < x1, x1 < oo)" D = Die('d1', 6) assert str(where(D > 4)) == "Domain: Or(Eq(d1, 5), Eq(d1, 6))" A = Exponential('a', 1) B = Exponential('b', 1) assert str(pspace(Tuple( A, B)).domain) == "Domain: And(0 <= a, 0 <= b, a < oo, b < oo)"
def test_coins(): C, D = Coin('C'), Coin('D') H, T = symbols('H, T') assert P(Eq(C, D)) == Rational(1, 2) assert density(Tuple(C, D)) == {(H, H): Rational(1, 4), (H, T): Rational(1, 4), (T, H): Rational(1, 4), (T, T): Rational(1, 4)} assert dict(density(C).items()) == {H: Rational(1, 2), T: Rational(1, 2)} F = Coin('F', Rational(1, 10)) assert P(Eq(F, H)) == Rational(1, 10) d = pspace(C).domain assert d.as_boolean() == Or(Eq(C.symbol, H), Eq(C.symbol, T)) pytest.raises(ValueError, lambda: P(C > D)) # Can't intelligently compare H to T
def test_dice(): # TODO: Make iid method! X, Y, Z = Die('X', 6), Die('Y', 6), Die('Z', 6) a, b = symbols('a b') assert E(X) == 3 + S.Half assert variance(X) == Rational(35, 12) assert E(X + Y) == 7 assert E(X + X) == 7 assert E(a * X + b) == a * E(X) + b assert variance(X + Y) == variance(X) + variance(Y) == cmoment(X + Y, 2) assert variance(X + X) == 4 * variance(X) == cmoment(X + X, 2) assert cmoment(X, 0) == 1 assert cmoment(4 * X, 3) == 64 * cmoment(X, 3) assert covariance(X, Y) == S.Zero assert covariance(X, X + Y) == variance(X) assert density(Eq(cos(X * S.Pi), 1))[True] == S.Half assert correlation(X, Y) == 0 assert correlation(X, Y) == correlation(Y, X) assert smoment(X + Y, 3) == skewness(X + Y) assert smoment(X, 0) == 1 assert P(X > 3) == S.Half assert P(2 * X > 6) == S.Half assert P(X > Y) == Rational(5, 12) assert P(Eq(X, Y)) == P(Eq(X, 1)) assert E(X, X > 3) == 5 == moment(X, 1, 0, X > 3) assert E(X, Y > 3) == E(X) == moment(X, 1, 0, Y > 3) assert E(X + Y, Eq(X, Y)) == E(2 * X) assert moment(X, 0) == 1 assert moment(5 * X, 2) == 25 * moment(X, 2) assert P(X > 3, X > 3) == S.One assert P(X > Y, Eq(Y, 6)) == S.Zero assert P(Eq(X + Y, 12)) == S.One / 36 assert P(Eq(X + Y, 12), Eq(X, 6)) == S.One / 6 assert density(X + Y) == density(Y + Z) != density(X + X) d = density(2 * X + Y**Z) assert d[Integer(22)] == S.One / 108 and d[Integer( 4100)] == S.One / 216 and Integer(3130) not in d assert pspace(X).domain.as_boolean() == Or( *[Eq(X.symbol, i) for i in [1, 2, 3, 4, 5, 6]]) assert where(X > 3).set == FiniteSet(4, 5, 6)
def test_beta(): a, b = symbols('alpha beta', positive=True) B = Beta('x', a, b) assert pspace(B).domain.set == Interval(0, 1) dens = density(B) x = Symbol('x') assert dens(x) == x**(a - 1)*(1 - x)**(b - 1) / beta(a, b) # This is too slow # assert E(B) == a / (a + b) # assert variance(B) == (a*b) / ((a+b)**2 * (a+b+1)) # Full symbolic solution is too much, test with numeric version a, b = Integer(1), Integer(2) B = Beta('x', a, b) assert expand_func(E(B)) == a/(a + b) assert expand_func(variance(B)) == (a*b)/(a + b)**2/(a + b + 1)
def test_ProductPSpace(): X = Normal('X', 0, 1) Y = Normal('Y', 0, 1) px = X.pspace py = Y.pspace assert pspace(X + Y) == ProductPSpace(px, py) assert pspace(X + Y) == ProductPSpace(py, px) X = Die("X", 2) Y = Die("Y", 2) assert (pspace(X + Y).density == Dict((frozenset({('X', 1), ('Y', 2)}), Rational(1, 4)), (frozenset({('X', 1), ('Y', 1)}), Rational(1, 4)), (frozenset({('X', 2), ('Y', 1)}), Rational(1, 4)), (frozenset({('X', 2), ('Y', 2)}), Rational(1, 4)))) d = pspace(X + Y).domain assert ((X.symbol, 1), (Y.symbol, 2)) in d assert ((X.symbol, 0), (Y.symbol, 2)) not in d Z = Die("Z", 2) d1 = pspace(X + Y).domain assert ProductDomain(d1, Z.pspace.domain) == pspace(X + Y + Z).domain
def test_ProductPSpace(): X = Normal('X', 0, 1) Y = Normal('Y', 0, 1) px = X.pspace py = Y.pspace assert pspace(X + Y) == ProductPSpace(px, py) assert pspace(X + Y) == ProductPSpace(py, px) X = Die('X', 2) Y = Die('Y', 2) assert (pspace(X + Y).density == Dict((frozenset({('X', 1), ('Y', 2)}), Rational(1, 4)), (frozenset({('X', 1), ('Y', 1)}), Rational(1, 4)), (frozenset({('X', 2), ('Y', 1)}), Rational(1, 4)), (frozenset({('X', 2), ('Y', 2)}), Rational(1, 4)))) d = pspace(X + Y).domain assert ((X.symbol, 1), (Y.symbol, 2)) in d assert ((X.symbol, 0), (Y.symbol, 2)) not in d Z = Die('Z', 2) d1 = pspace(X + Y).domain assert ProductDomain(d1, Z.pspace.domain) == pspace(X + Y + Z).domain
def test_random_parameters(): mu = Normal('mu', 2, 3) meas = Normal('T', mu, 1) assert density(meas, evaluate=False)(z) assert isinstance(pspace(meas), ProductPSpace)