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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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