+ i Rt^RIHtHt^RIHt^RIHt^RIH t ^RI H t ^RI H t ^RIHt^RIHt^R IHtHtHt^R IHtR tRR ltR #)z'Tools for arithmetic error propagation.)repeat combinations)Add)Mul)Pow)S)Symbol)exp)simplify) RandomSymbolVariance Covariance) is_randomc`\VP4^8dVP^,#T#))lenargs)vars&T/var/www/html/photoedit/myenv/lib/python3.14/site-packages/sympy/stats/error_prop.pyrs##chh-!*;388A;DDc VPp\V4^8XdW9d\P#\ V4'd\ V4P 4#\V\4'd#\ \V44P 4#\P#\V4p\\\V\W4\W$444p\V\4'dt\V!pV'da\V^4UUu.uF8wrx^\!\#V4\#V44P%4,NK: p ppV\V !, pV#\V\&4'd\)W54U U u.uFwrW^,, NK p p p \+V^,\V !,4pV'd\)\V^4\V^44U U UUu.uFJwwrwrx^\!\#V4\#V44P%4,W,, NKL p pp p pV\V !, pV#\V\,4'dBV^,p V^,W ,V^,, ^,,p \+V 4pV#\V\.4'd#\+V^,V^,,4pV#\ V4pV#uuppiuup p iuuppp p i)a8Symbolically propagates variance (`\sigma^2`) for expressions. This is computed as as seen in [1]_. Parameters ========== expr : Expr A SymPy expression to compute the variance for. consts : sequence of Symbols, optional Represents symbols that are known constants in the expr, and thus have zero variance. All symbols not in consts are assumed to be variant. include_covar : bool, optional Flag for whether or not to include covariances, default=False. Returns ======= var_expr : Expr An expression for the total variance of the expr. The variance for the original symbols (e.g. x) are represented via instance of the Variance symbol (e.g. Variance(x)). Examples ======== >>> from sympy import symbols, exp >>> from sympy.stats.error_prop import variance_prop >>> x, y = symbols('x y') >>> variance_prop(x + y) Variance(x) + Variance(y) >>> variance_prop(x * y) x**2*Variance(y) + y**2*Variance(x) >>> variance_prop(exp(2*x)) 4*exp(4*x)*Variance(x) References ========== .. [1] https://en.wikipedia.org/wiki/Propagation_of_uncertainty )rrrZerorr doit isinstancerr listmap variance_proprrrr _arg0_or_varexpandrzipr rr ) exprconsts include_covarrnargsvar_argsvar_exprxytermsavbs &&& rrrs~\ 99D 4yA~ >66M t__D>&&( ( f % %L./446 666M IEC tVF-B}467H$> !-h!: O)<9Ks>K7 K=4AL N)F)__doc__ itertoolsrrsympy.core.addrsympy.core.mulrsympy.core.powerrsympy.core.singletonrsympy.core.symbolr&sympy.functions.elementary.exponentialr sympy.simplify.simplifyr sympy.stats.symbolic_probabilityr r r sympy.stats.rvrrrr-rrr9s4-* "$6,OO$D Rr