def test_uniform_P():
""" This stopped working because SingleContinuousPSpace.compute_density no
longer calls integrate on a DiracDelta but rather just solves directly.
integrate used to call UniformDistribution.expectation which special-cased
subsed out the Min and Max terms that Uniform produces
I decided to regress on this class for general cleanliness (and I suspect
speed) of the algorithm.
"""
l = Symbol('l', real=True)
w = Symbol('w', positive=True)
X = Uniform('x', l, l + w)
assert P(X < l) == 0 and P(X > l + w) == 0
def test_uniform():
l = Symbol('l', real=True, finite=True)
w = Symbol('w', positive=True, finite=True)
X = Uniform('x', l, l + w)
assert simplify(E(X)) == l + w/2
assert simplify(variance(X)) == w**2/12
# With numbers all is well
X = Uniform('x', 3, 5)
assert P(X < 3) == 0 and P(X > 5) == 0
assert P(X < 4) == P(X > 4) == S.Half
z = Symbol('z')
p = density(X)(z)
assert p.subs(z, 3.7) == S(1)/2
assert p.subs(z, -1) == 0
assert p.subs(z, 6) == 0
c = cdf(X)
assert c(2) == 0 and c(3) == 0
assert c(S(7)/2) == S(1)/4
assert c(5) == 1 and c(6) == 1
def test_uniform():
l = Symbol('l', real=True)
w = Symbol('w', positive=True)
X = Uniform('x', l, l + w)
assert E(X) == l + w / 2
assert variance(X).expand() == w**2 / 12
# With numbers all is well
X = Uniform('x', 3, 5)
assert P(X < 3) == 0 and P(X > 5) == 0
assert P(X < 4) == P(X > 4) == S.Half
z = Symbol('z')
p = density(X)(z)
assert p.subs(z, 3.7) == S.Half
assert p.subs(z, -1) == 0
assert p.subs(z, 6) == 0
c = cdf(X)
assert c(2) == 0 and c(3) == 0
assert c(Rational(7, 2)) == Rational(1, 4)
assert c(5) == 1 and c(6) == 1
def test_prefab_sampling():
N = Normal('X', 0, 1)
L = LogNormal('L', 0, 1)
E = Exponential('Ex', 1)
P = Pareto('P', 1, 3)
W = Weibull('W', 1, 1)
U = Uniform('U', 0, 1)
B = Beta('B', 2, 5)
G = Gamma('G', 1, 3)
variables = [N, L, E, P, W, U, B, G]
niter = 10
for var in variables:
for i in range(niter):
assert sample(var) in var.pspace.domain.set
def test_characteristic_function():
X = Uniform('x', 0, 1)
cf = characteristic_function(X)
assert cf(1) == -I*(-1 + exp(I))
Y = Normal('y', 1, 1)
cf = characteristic_function(Y)
assert cf(0) == 1
assert simplify(cf(1)) == exp(I - S(1)/2)
Z = Exponential('z', 5)
cf = characteristic_function(Z)
assert cf(0) == 1
assert simplify(cf(1)) == S(25)/26 + 5*I/26
def test_prefab_sampling():
N = Normal(0, 1)
L = LogNormal(0, 1)
E = Exponential(1)
P = Pareto(1, 3)
W = Weibull(1, 1)
U = Uniform(0, 1)
B = Beta(2,5)
G = Gamma(1,3)
variables = [N,L,E,P,W,U,B,G]
niter = 10
for var in variables:
for i in xrange(niter):
assert Sample(var) in var.pspace.domain.set
def test_bernoulli_CompoundDist():
X = Beta('X', 1, 2)
Y = Bernoulli('Y', X)
assert density(Y).dict == {0: S(2)/3, 1: S(1)/3}
assert E(Y) == P(Eq(Y, 1)) == S(1)/3
assert variance(Y) == S(2)/9
assert cdf(Y) == {0: S(2)/3, 1: 1}
# test issue 8128
a = Bernoulli('a', S(1)/2)
b = Bernoulli('b', a)
assert density(b).dict == {0: S(1)/2, 1: S(1)/2}
assert P(b > 0.5) == S(1)/2
X = Uniform('X', 0, 1)
Y = Bernoulli('Y', X)
assert E(Y) == S(1)/2
assert P(Eq(Y, 1)) == E(Y)
def generate_all_turnip_patterns(previous_pattern_prior):
assert(previous_pattern_prior.shape == (4,))
assert(np.allclose(np.sum(previous_pattern_prior), 1.))
all_rollouts = []
# Random integer base price on [90, 110]
base_price = Uniform("base_price", 90., 110.)
# Probability of being in each pattern:
pattern_probs = np.dot(pattern_transition_matrix, previous_pattern_prior)
for next_pattern_k in range(4):
all_rollouts += pattern_rollout_generators[next_pattern_k](
base_price=base_price,
rollout_probability=pattern_probs[next_pattern_k])
return all_rollouts
def test_characteristic_function():
X = Uniform('x', 0, 1)
cf = characteristic_function(X)
assert cf(1) == -I * (-1 + exp(I))
Y = Normal('y', 1, 1)
cf = characteristic_function(Y)
assert cf(0) == 1
assert cf(1) == exp(I - S(1) / 2)
Z = Exponential('z', 5)
cf = characteristic_function(Z)
assert cf(0) == 1
assert cf(1).expand() == S(25) / 26 + 5 * I / 26
X = GaussianInverse('x', 1, 1)
cf = characteristic_function(X)
assert cf(0) == 1
assert cf(1) == exp(1 - sqrt(1 - 2 * I))
def test_prefab_sampling():
scipy = import_module('scipy')
if not scipy:
skip('Scipy is not installed. Abort tests')
N = Normal('X', 0, 1)
L = LogNormal('L', 0, 1)
E = Exponential('Ex', 1)
P = Pareto('P', 1, 3)
W = Weibull('W', 1, 1)
U = Uniform('U', 0, 1)
B = Beta('B', 2, 5)
G = Gamma('G', 1, 3)
variables = [N, L, E, P, W, U, B, G]
niter = 10
size = 5
for var in variables:
for _ in range(niter):
assert sample(var) in var.pspace.domain.set
samps = sample(var, size=size)
for samp in samps:
assert samp in var.pspace.domain.set
def test_sample_scipy():
distribs_scipy = [
Beta("B", 1, 1),
BetaPrime("BP", 1, 1),
Cauchy("C", 1, 1),
Chi("C", 1),
Normal("N", 0, 1),
Gamma("G", 2, 7),
GammaInverse("GI", 1, 1),
GaussianInverse("GUI", 1, 1),
Exponential("E", 2),
LogNormal("LN", 0, 1),
Pareto("P", 1, 1),
StudentT("S", 2),
ChiSquared("CS", 2),
Uniform("U", 0, 1)
]
size = 3
numsamples = 5
scipy = import_module('scipy')
if not scipy:
skip('Scipy is not installed. Abort tests for _sample_scipy.')
else:
with ignore_warnings(
UserWarning
): ### TODO: Restore tests once warnings are removed
g_sample = list(
sample(Gamma("G", 2, 7), size=size, numsamples=numsamples))
assert len(g_sample) == numsamples
for X in distribs_scipy:
samps = next(sample(X, size=size, library='scipy'))
samps2 = next(sample(X, size=(2, 2), library='scipy'))
for sam in samps:
assert sam in X.pspace.domain.set
for i in range(2):
for j in range(2):
assert samps2[i][j] in X.pspace.domain.set
def test_sample_pymc3():
distribs_pymc3 = [
Beta("B", 1, 1),
Cauchy("C", 1, 1),
Normal("N", 0, 1),
Gamma("G", 2, 7),
GaussianInverse("GI", 1, 1),
Exponential("E", 2),
LogNormal("LN", 0, 1),
Pareto("P", 1, 1),
ChiSquared("CS", 2),
Uniform("U", 0, 1)
]
size = 3
pymc3 = import_module('pymc3')
if not pymc3:
skip('PyMC3 is not installed. Abort tests for _sample_pymc3.')
else:
for X in distribs_pymc3:
samps = sample(X, size=size, library='pymc3')
for sam in samps:
assert sam in X.pspace.domain.set
raises(NotImplementedError,
lambda: sample(Chi("C", 1), library='pymc3'))
def test_sample_numpy():
distribs_numpy = [
Beta("B", 1, 1),
Normal("N", 0, 1),
Gamma("G", 2, 7),
Exponential("E", 2),
LogNormal("LN", 0, 1),
Pareto("P", 1, 1),
ChiSquared("CS", 2),
Uniform("U", 0, 1)
]
size = 3
numpy = import_module('numpy')
if not numpy:
skip('Numpy is not installed. Abort tests for _sample_numpy.')
else:
for X in distribs_numpy:
samps = sample(X, size=size, library='numpy')
for sam in samps:
assert sam in X.pspace.domain.set
raises(NotImplementedError,
lambda: sample(Chi("C", 1), library='numpy'))
raises(NotImplementedError,
lambda: Chi("C", 1).pspace.distribution.sample(library='tensorflow'))
def test_issue_13324():
X = Uniform('X', 0, 1)
assert E(X, X > Rational(1, 2)) == Rational(3, 4)
assert E(X, X > 0) == Rational(1, 2)
def test_moment_generating_function():
t = symbols('t', positive=True)
# Symbolic tests
a, b, c = symbols('a b c')
mgf = moment_generating_function(Beta('x', a, b))(t)
assert mgf == hyper((a, ), (a + b, ), t)
mgf = moment_generating_function(Chi('x', a))(t)
assert mgf == sqrt(2)*t*gamma(a/2 + S.Half)*\
hyper((a/2 + S.Half,), (Rational(3, 2),), t**2/2)/gamma(a/2) +\
hyper((a/2,), (S.Half,), t**2/2)
mgf = moment_generating_function(ChiSquared('x', a))(t)
assert mgf == (1 - 2 * t)**(-a / 2)
mgf = moment_generating_function(Erlang('x', a, b))(t)
assert mgf == (1 - t / b)**(-a)
mgf = moment_generating_function(ExGaussian("x", a, b, c))(t)
assert mgf == exp(a * t + b**2 * t**2 / 2) / (1 - t / c)
mgf = moment_generating_function(Exponential('x', a))(t)
assert mgf == a / (a - t)
mgf = moment_generating_function(Gamma('x', a, b))(t)
assert mgf == (-b * t + 1)**(-a)
mgf = moment_generating_function(Gumbel('x', a, b))(t)
assert mgf == exp(b * t) * gamma(-a * t + 1)
mgf = moment_generating_function(Gompertz('x', a, b))(t)
assert mgf == b * exp(b) * expint(t / a, b)
mgf = moment_generating_function(Laplace('x', a, b))(t)
assert mgf == exp(a * t) / (-b**2 * t**2 + 1)
mgf = moment_generating_function(Logistic('x', a, b))(t)
assert mgf == exp(a * t) * beta(-b * t + 1, b * t + 1)
mgf = moment_generating_function(Normal('x', a, b))(t)
assert mgf == exp(a * t + b**2 * t**2 / 2)
mgf = moment_generating_function(Pareto('x', a, b))(t)
assert mgf == b * (-a * t)**b * uppergamma(-b, -a * t)
mgf = moment_generating_function(QuadraticU('x', a, b))(t)
assert str(mgf) == (
"(3*(t*(-4*b + (a + b)**2) + 4)*exp(b*t) - "
"3*(t*(a**2 + 2*a*(b - 2) + b**2) + 4)*exp(a*t))/(t**2*(a - b)**3)")
mgf = moment_generating_function(RaisedCosine('x', a, b))(t)
assert mgf == pi**2 * exp(a * t) * sinh(b * t) / (b * t *
(b**2 * t**2 + pi**2))
mgf = moment_generating_function(Rayleigh('x', a))(t)
assert mgf == sqrt(2)*sqrt(pi)*a*t*(erf(sqrt(2)*a*t/2) + 1)\
*exp(a**2*t**2/2)/2 + 1
mgf = moment_generating_function(Triangular('x', a, b, c))(t)
assert str(mgf) == ("(-2*(-a + b)*exp(c*t) + 2*(-a + c)*exp(b*t) + "
"2*(b - c)*exp(a*t))/(t**2*(-a + b)*(-a + c)*(b - c))")
mgf = moment_generating_function(Uniform('x', a, b))(t)
assert mgf == (-exp(a * t) + exp(b * t)) / (t * (-a + b))
mgf = moment_generating_function(UniformSum('x', a))(t)
assert mgf == ((exp(t) - 1) / t)**a
mgf = moment_generating_function(WignerSemicircle('x', a))(t)
assert mgf == 2 * besseli(1, a * t) / (a * t)
# Numeric tests
mgf = moment_generating_function(Beta('x', 1, 1))(t)
assert mgf.diff(t).subs(t, 1) == hyper((2, ), (3, ), 1) / 2
mgf = moment_generating_function(Chi('x', 1))(t)
assert mgf.diff(t).subs(t, 1) == sqrt(2) * hyper(
(1, ), (Rational(3, 2), ), S.Half) / sqrt(pi) + hyper(
(Rational(3, 2), ),
(Rational(3, 2), ), S.Half) + 2 * sqrt(2) * hyper(
(2, ), (Rational(5, 2), ), S.Half) / (3 * sqrt(pi))
mgf = moment_generating_function(ChiSquared('x', 1))(t)
assert mgf.diff(t).subs(t, 1) == I
mgf = moment_generating_function(Erlang('x', 1, 1))(t)
assert mgf.diff(t).subs(t, 0) == 1
mgf = moment_generating_function(ExGaussian("x", 0, 1, 1))(t)
assert mgf.diff(t).subs(t, 2) == -exp(2)
mgf = moment_generating_function(Exponential('x', 1))(t)
assert mgf.diff(t).subs(t, 0) == 1
mgf = moment_generating_function(Gamma('x', 1, 1))(t)
assert mgf.diff(t).subs(t, 0) == 1
mgf = moment_generating_function(Gumbel('x', 1, 1))(t)
assert mgf.diff(t).subs(t, 0) == EulerGamma + 1
mgf = moment_generating_function(Gompertz('x', 1, 1))(t)
assert mgf.diff(t).subs(t, 1) == -e * meijerg(((), (1, 1)),
((0, 0, 0), ()), 1)
mgf = moment_generating_function(Laplace('x', 1, 1))(t)
assert mgf.diff(t).subs(t, 0) == 1
mgf = moment_generating_function(Logistic('x', 1, 1))(t)
assert mgf.diff(t).subs(t, 0) == beta(1, 1)
mgf = moment_generating_function(Normal('x', 0, 1))(t)
assert mgf.diff(t).subs(t, 1) == exp(S.Half)
mgf = moment_generating_function(Pareto('x', 1, 1))(t)
assert mgf.diff(t).subs(t, 0) == expint(1, 0)
mgf = moment_generating_function(QuadraticU('x', 1, 2))(t)
assert mgf.diff(t).subs(t, 1) == -12 * e - 3 * exp(2)
mgf = moment_generating_function(RaisedCosine('x', 1, 1))(t)
assert mgf.diff(t).subs(t, 1) == -2*e*pi**2*sinh(1)/\
(1 + pi**2)**2 + e*pi**2*cosh(1)/(1 + pi**2)
mgf = moment_generating_function(Rayleigh('x', 1))(t)
assert mgf.diff(t).subs(t, 0) == sqrt(2) * sqrt(pi) / 2
mgf = moment_generating_function(Triangular('x', 1, 3, 2))(t)
assert mgf.diff(t).subs(t, 1) == -e + exp(3)
mgf = moment_generating_function(Uniform('x', 0, 1))(t)
assert mgf.diff(t).subs(t, 1) == 1
mgf = moment_generating_function(UniformSum('x', 1))(t)
assert mgf.diff(t).subs(t, 1) == 1
mgf = moment_generating_function(WignerSemicircle('x', 1))(t)
assert mgf.diff(t).subs(t, 1) == -2*besseli(1, 1) + besseli(2, 1) +\
besseli(0, 1)
def test_issue_13324():
X = Uniform('X', 0, 1)
assert E(X, X > S.Half) == Rational(3, 4)
assert E(X, X > 0) == S.Half
