ó ¡¼™\c@ sAddlmZmZddlmZmZmZmZmZm Z m Z m Z m Z m Z mZmZmZmZmZmZmZmZddlmZddlmZddlmZddlmZmZmZm Z m!Z!m"Z"m#Z#m$Z$ddl%m&Z&ddl'm(Z(dd l)m*Z*m+Z+dd l,m-Z-dd l.m/Z/dd l0m1Z1dd l2Z2defd„ƒYZ3de3efd„ƒYZ4de4fd„ƒYZ5de#fd„ƒYZ6de6efd„ƒYZ7de6e"fd„ƒYZ8de!fd„ƒYZ9de$e6fd„ƒYZ:de9efd„ƒYZ;d S( iÿÿÿÿ(tprint_functiontdivision(tBasictsympifytsymbolstDummytLambdat summationt PiecewisetStcacheittSumtexptItNetEqtpolytseriest factorialtAnd(tPolynomialError(tsolveset(t!reduce_rational_inequalities_wrap(tNamedArgsMixint SinglePSpacet SingleDomaintrandom_symbolstPSpacetConditionalDomaint RandomDomaint ProductDomain(t Probability(tfloor(tRanget FiniteSet(tUnion(tContains(t filldedentNtDiscreteDistributioncB seZd„ZRS(cG s |j|ŒS(N(tpdf(tselftargs((s.lib/python2.7/site-packages/sympy/stats/drv.pyt__call__s(t__name__t __module__R*(((s.lib/python2.7/site-packages/sympy/stats/drv.pyR&stSingleDiscreteDistributioncB s¿eZdZejZd„Zed„ƒZd„Z e d„ƒZ e d„ƒZ d„Z d„Ze d„ƒZd „Zd „Ze d „ƒZd „Zd „Zed„Zd„ZRS(sÊ Discrete distribution of a single variable Serves as superclass for PoissonDistribution etc.... Provides methods for pdf, cdf, and sampling See Also: sympy.stats.crv_types.* cG s%ttt|ƒƒ}tj||ŒS(N(tlisttmapRRt__new__(tclsR)((s.lib/python2.7/site-packages/sympy/stats/drv.pyR0(scG sdS(N((R)((s.lib/python2.7/site-packages/sympy/stats/drv.pytcheck,scC s[|jƒ}xHtrVtt|tjddƒƒƒdƒ}||jjkr|SqWdS(s, A random realization from the distribution iiN(t_inverse_cdf_expressiontTrueR R.trandomtuniformtsettinf(R(ticdftsample_((s.lib/python2.7/site-packages/sympy/stats/drv.pytsample0s   (cC s·tddtdtdtƒ}tddtdtƒ}|j|ƒ}y t|||dtjƒ}Wntk r~d }nX| s›t |j ƒdkrªtdƒ‚nt ||ƒS( s4 Inverse of the CDF Used by sample txtpositivetintegerR1tztdomainisCould not invert CDFN( RR4RtcdfRR tRealstNotImplementedErrortNonetlent free_symbolsR(R(R<R?tcdf_tempt inverse_cdf((s.lib/python2.7/site-packages/sympy/stats/drv.pyR38s   cK sˆtddtdtdtƒ\}}|jj}|j|ƒ}t||||f|}t|||kfdtfƒ}t||ƒS(s@ Compute the CDF from the PDF Returns a Lambda sx, zR>tfiniteR1i( RR4RR7R8R'RRR(R(tkwargsR<R?t left_boundR'RA((s.lib/python2.7/site-packages/sympy/stats/drv.pyt compute_cdfKs $ !cC sdS(N(RD(R(R<((s.lib/python2.7/site-packages/sympy/stats/drv.pyt_cdf[scK s;|s(|j|ƒ}|dk r(|Sn|j||ƒS(s Cumulative density function N(RMRDRL(R(R<RJRA((s.lib/python2.7/site-packages/sympy/stats/drv.pyRA^s  cK svtddtdtdtƒ\}}|j|ƒ}ttt||ƒ|||jj|jj fƒ}t ||ƒS(sT Compute the characteristic function from the PDF Returns a Lambda sx, ttrealRIR1( RR4RR'RR R R7R8tsupR(R(RJR<ttR'tcf((s.lib/python2.7/site-packages/sympy/stats/drv.pytcompute_characteristic_functionfs$6cC sdS(N(RD(R(RP((s.lib/python2.7/site-packages/sympy/stats/drv.pyt_characteristic_functionqscK s;|s(|j|ƒ}|dk r(|Sn|j||ƒS(s Characteristic function N(RSRDRR(R(RPRJRQ((s.lib/python2.7/site-packages/sympy/stats/drv.pytcharacteristic_functionts  cK srtddtdtdtƒ\}}|j|ƒ}tt||ƒ|||jj|jjfƒ}t ||ƒS(Nsx, tRNRIR1( RR4RR'RR R7R8ROR(R(RJR<RPR'tmgf((s.lib/python2.7/site-packages/sympy/stats/drv.pyt"compute_moment_generating_function|s$2cC sdS(N(RD(R(RP((s.lib/python2.7/site-packages/sympy/stats/drv.pyt_moment_generating_functionƒscK s;|s(|j|ƒ}|dk r(|Sn|j||ƒS(N(RWRDRV(R(RPRJRU((s.lib/python2.7/site-packages/sympy/stats/drv.pytmoment_generating_function†s  c K sA|r y¿t||ƒ}tddtƒ}|j|ƒ}|jƒ}tt||d|dƒjƒ|ƒ} d} xJt|dƒD]8} | |j|| ƒ| j|| ƒt | ƒ7} q„W| SWq=t k rt ||j |ƒ||j j|j jf|SXn2t||j |ƒ||j j|j jf|SdS(s- Expectation of expression over distribution RPRNiiN(RRR4RXtdegreeRtremoveOtrangetcoeff_monomialRRRR'R7R8ROR ( R(texprtvartevaluateRJtpRPRUtdegttaylortresulttk((s.lib/python2.7/site-packages/sympy/stats/drv.pyt expectations  (6 #cG s |j|ŒS(N(R'(R(R)((s.lib/python2.7/site-packages/sympy/stats/drv.pyR*¨s(R+R,t__doc__R tIntegersR7R0t staticmethodR2R;R R3RLRMRARRRSRTRVRWRXR4ReR*(((s.lib/python2.7/site-packages/sympy/stats/drv.pyR-s"           tDiscreteDistributionHandmadecB s,eZdZed„ƒZejd„ZRS(R'cC s |jdS(Ni(R)(R(((s.lib/python2.7/site-packages/sympy/stats/drv.pyR7¯scC stj|||ƒS(N(RR0(R1R'R7((s.lib/python2.7/site-packages/sympy/stats/drv.pyR0³s(R'(R+R,t _argnamestpropertyR7R RgR0(((s.lib/python2.7/site-packages/sympy/stats/drv.pyRi¬stDiscreteDomaincB seZdZeZRS(se A domain with discrete support with step size one. Represented using symbols and Range. (R+R,RfR4t is_Discrete(((s.lib/python2.7/site-packages/sympy/stats/drv.pyRl¶stSingleDiscreteDomaincB seZd„ZRS(cC st|j|jƒS(N(R$tsymbolR7(R(((s.lib/python2.7/site-packages/sympy/stats/drv.pyt as_boolean¾s(R+R,Rp(((s.lib/python2.7/site-packages/sympy/stats/drv.pyRn½stConditionalDiscreteDomaincB seZdZed„ƒZRS(sb Domain with discrete support of step size one, that is restricted by some condition. cC sb|j}t|jƒdkr3ttdƒƒ‚nt|ƒd}t|j|ƒj|jj ƒS(NisI Multivariate condtional domains are not yet implemented.i( RRERCR%R.Rt conditiont intersectt fulldomainR7(R(trv((s.lib/python2.7/site-packages/sympy/stats/drv.pyR7Çs  (R+R,RfRkR7(((s.lib/python2.7/site-packages/sympy/stats/drv.pyRqÂstDiscretePSpacecB sGeZeZeZed„ƒZd„Zd„Zd„Z d„Z RS(cC s|j|jŒS(N(tdensityR(R(((s.lib/python2.7/site-packages/sympy/stats/drv.pyR'Ösc s‘t|ƒ}t‡fd†|Dƒƒs.t‚t|ƒdkrUttdƒƒ‚nt||dƒ}|jˆjj ƒ}t |dj |ƒS(Nc3 s!|]}|jˆjkVqdS(N(RoR(t.0tr(R((s.lib/python2.7/site-packages/sympy/stats/drv.pys ÜsisIMultivariate discrete random variables are not yet supported.i( RtalltAssertionErrorRERCR%RRsR@R7RnRo(R(Rrtrvstconditional_domain((R(s.lib/python2.7/site-packages/sympy/stats/drv.pytwhereÚs " c C snt|tƒ}|r5t|jd|jdƒ}nyl|j|ƒj}|tkse|tjkrltj S|t ksŠ||j jkr‘tj S|j |ƒ}Wnštk r=ddlm}|j|j}||ƒ}t|tƒsût|ƒ}ntddt ƒ}t||ƒ} | j|j| jdƒƒ}nX|dkrYt|ƒ}n|sc|Stj |S(Niiiÿÿÿÿ(RwR?RN(t isinstanceRRR)R~R7tFalseR tEmptySettZeroR4R@tOnet eval_probRCtsympy.stats.rvRwtlhstrhsR&RiRtSingleDiscretePSpacet probabilityt __class__tvalueRDR( R(Rrt complementt_domaintprobRwR]tdensR?tspace((s.lib/python2.7/site-packages/sympy/stats/drv.pyR‰ås,   " c  stˆjƒd}t|tƒrtddtdtƒ}d„|jDƒ\}}}ˆjj|||ƒ}t||||||dfƒj ƒ}|St|t ƒrÞt |ˆjƒ‰t ‡fd†|Dƒƒ}|St|t ƒrt ‡fd†|jDƒƒ}|SdS( NitnR>RIcs s|] }|VqdS(N((RxRy((s.lib/python2.7/site-packages/sympy/stats/drv.pys sic3 s|]}ˆ|ƒVqdS(N((RxR<(R'(s.lib/python2.7/site-packages/sympy/stats/drv.pys sc3 s|]}ˆj|ƒVqdS(N(R„(RxR<(R((s.lib/python2.7/site-packages/sympy/stats/drv.pys s(R.RRR!R4R)R'treplaceRtdoitR"RtsumR#( R(RtsymR‘R8ROtsteptsummandRu((R'R(s.lib/python2.7/site-packages/sympy/stats/drv.pyR„ýs  $cC sct|j|j|j|ƒƒ}|jtd„|jDƒƒƒ}t|j|ƒ}t ||ƒS(Ncs s|]}||jfVqdS(N(Ro(RxRu((s.lib/python2.7/site-packages/sympy/stats/drv.pys s( RRR'R‰txreplacetdicttvaluesRqR@Rv(R(RrRwR@((s.lib/python2.7/site-packages/sympy/stats/drv.pytconditional_spaces""( R+R,R4tis_realRmRkR'R~R‰R„R›(((s.lib/python2.7/site-packages/sympy/stats/drv.pyRvÒs  tProductDiscreteDomaincB seZd„ZRS(cC s#tg|jD]}|j^q ŒS(N(RtdomainsRp(R(R@((s.lib/python2.7/site-packages/sympy/stats/drv.pyRps(R+R,Rp(((s.lib/python2.7/site-packages/sympy/stats/drv.pyRsRˆcB sneZdZeZed„ƒZed„ƒZd„Zd ed„Z d„Z d„Z d„Z d„ZRS( s> Discrete probability space over a single univariate variable cC s |jjS(N(t distributionR7(R(((s.lib/python2.7/site-packages/sympy/stats/drv.pyR7scC st|j|jƒS(N(RnRoR7(R(((s.lib/python2.7/site-packages/sympy/stats/drv.pyR@!scC si|jjƒ|j6S(so Internal sample method Returns dictionary mapping RandomSymbol to realization value. 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