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from sympy.core.function import Function
from sympy.core.symbol import symbols
from sympy.functions.elementary.exponential import exp
from sympy.stats.error_prop import variance_prop
from sympy.stats.symbolic_probability import (RandomSymbol, Variance,
Covariance)
def test_variance_prop():
x, y, z = symbols('x y z')
phi, t = consts = symbols('phi t')
a = RandomSymbol(x)
var_x = Variance(a)
var_y = Variance(RandomSymbol(y))
var_z = Variance(RandomSymbol(z))
f = Function('f')(x)
cases = {
x + y: var_x + var_y,
a + y: var_x + var_y,
x + y + z: var_x + var_y + var_z,
2*x: 4*var_x,
x*y: var_x*y**2 + var_y*x**2,
1/x: var_x/x**4,
x/y: (var_x*y**2 + var_y*x**2)/y**4,
exp(x): var_x*exp(2*x),
exp(2*x): 4*var_x*exp(4*x),
exp(-x*t): t**2*var_x*exp(-2*t*x),
f: Variance(f),
}
for inp, out in cases.items():
obs = variance_prop(inp, consts=consts)
assert out == obs
def test_variance_prop_with_covar():
x, y, z = symbols('x y z')
phi, t = consts = symbols('phi t')
a = RandomSymbol(x)
var_x = Variance(a)
b = RandomSymbol(y)
var_y = Variance(b)
c = RandomSymbol(z)
var_z = Variance(c)
covar_x_y = Covariance(a, b)
covar_x_z = Covariance(a, c)
covar_y_z = Covariance(b, c)
cases = {
x + y: var_x + var_y + 2*covar_x_y,
a + y: var_x + var_y + 2*covar_x_y,
x + y + z: var_x + var_y + var_z + \
2*covar_x_y + 2*covar_x_z + 2*covar_y_z,
2*x: 4*var_x,
x*y: var_x*y**2 + var_y*x**2 + 2*covar_x_y/(x*y),
1/x: var_x/x**4,
exp(x): var_x*exp(2*x),
exp(2*x): 4*var_x*exp(4*x),
exp(-x*t): t**2*var_x*exp(-2*t*x),
}
for inp, out in cases.items():
obs = variance_prop(inp, consts=consts, include_covar=True)
assert out == obs
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