\h SrSSKJrJr SSKJr SSKJr SSKJ r SSK J r SSK J r SSKJr SS KJr SS KJrJrJr SS KJr S rSS jrg)z'Tools for arithmetic error propagation.)repeat combinations)Add)Mul)Pow)S)Symbol)exp)simplify) RandomSymbolVariance Covariance) is_randomcV[UR5S:aURS$U$)Nr)lenargs)vars N/var/www/auris/envauris/lib/python3.13/site-packages/sympy/stats/error_prop.pyrs##chh-!*;388A;DDc `URn[U5S:XaX;a[R$[ U5(a[ U5R 5$[U[5(a"[ [U55R 5$[R$[U5n[[[U[X5[X$555n[U[5(ai[U6nU(aX[US5VVs/sH4upxS[![#U5[#U55R%5-PM6 n nnU[U 6- nU$[U[&5(a[)X55V V s/sH upXS-- PM n n n [+US-[U 6-5nU(az[)[US5[US55V V VVs/sH>uupupxS[![#U5[#U55R%5-X-- PM@ n nn n nU[U 6- nU$[U[,5(a%USn USX -US- S--n [+U 5nU$[U[.5(a[+USUS--5nU$[ U5nU$s snnfs sn n fs snnn n f)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 r)rrrZerorr doit isinstancer r listmap variance_proprrrr _arg0_or_varexpandrzipr rr ) exprconsts include_covarrnargsvar_argsvar_exprxytermsavbs rrrsv\ 99D 4yA~ >66M t__D>&&( ( f % %L./446 666M IEC tVF-B}467H$> !-h!: O)<9Ks ;J:J"AJ( 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 rsympy.stats.rvrr rr/rrr;s4-* "$6,OO$D Rr