ó 9­\c@ sÂdZddlmZmZddlmZmZmZmZm Z m Z m Z m Z ddl mZmZddlmZddlmZddlmZmZddlmZdd lmZmZmZdd lmZmZm Z dd l!m"Z"m#Z#m$Z$m%Z%m&Z&m'Z'dd l(m)Z)d e"fd„ƒYZ*dee#fd„ƒYZ+de%fd„ƒYZ,de+e#fd„ƒYZ-d„Z.dee#fd„ƒYZ/defd„ƒYZ0dS(sq Joint Random Variables Module See Also ======== sympy.stats.rv sympy.stats.frv sympy.stats.crv sympy.stats.drv iÿÿÿÿ(tprint_functiontdivision(tBasictLambdatsympifytIndexedtSymbolt ProductSettStDummy(tSumt summation(t string_types(tTuple(tIntegralt integrate(tImmutableMatrix(tContinuousDistributiontSingleContinuousDistributiontSingleContinuousPSpace(tDiscreteDistributiontSingleDiscreteDistributiontSingleDiscretePSpace(t ProductPSpacetNamedArgsMixint ProductDomaint RandomSymboltrandom_symbolst SingleDomain(t filldedentt JointPSpacecB sÔeZdZd„Zed„ƒZed„ƒZed„ƒZed„ƒZed„ƒZ ed„ƒZ ed„ƒZ d „Z ed „ƒZ d „Zded „Zd „Zd„Zd„Zd„ZRS(st Represents a joint probability space. Represented using symbols for each component and a distribution. cC s‡t|tƒrt||ƒSt|tƒr8t||ƒSt|tƒrVt|ƒ}nt|tƒsttdƒ‚ntj |||ƒS(Ns#s should have been string or Symbol( t isinstanceRRRRR Rt TypeErrorRt__new__(tclstsymtdist((s3lib/python2.7/site-packages/sympy/stats/joint_rv.pyR!%s  cC s |jjS(N(tdomaintset(tself((s3lib/python2.7/site-packages/sympy/stats/joint_rv.pyR&0scC s |jdS(Ni(targs(R'((s3lib/python2.7/site-packages/sympy/stats/joint_rv.pytsymbol4scC s |jdS(Ni(R((R'((s3lib/python2.7/site-packages/sympy/stats/joint_rv.pyt distribution8scC st|j|ƒS(N(tJointRandomSymbolR)(R'((s3lib/python2.7/site-packages/sympy/stats/joint_rv.pytvalue<scC s,|jj}t|tƒr(t|jƒSdS(Ni(R*R&RRtlenR((R't_set((s3lib/python2.7/site-packages/sympy/stats/joint_rv.pytcomponent_count@s cC s;gt|jƒD]}t|j|ƒ^q}|j|ŒS(N(trangeR/RR)R*(R'tiR#((s3lib/python2.7/site-packages/sympy/stats/joint_rv.pytpdfEs.cC sWt|jƒ}t|ƒdkr4t|j|jƒStg|D]}|jj^q>ŒS(Ni( RR*R-RR)R&RtpspaceR%(R'trvstrv((s3lib/python2.7/site-packages/sympy/stats/joint_rv.pyR%JscC s|jj|S(N(R&R((R'tindex((s3lib/python2.7/site-packages/sympy/stats/joint_rv.pytcomponent_domainQscC s |jjS(N(R%tsymbols(R'((s3lib/python2.7/site-packages/sympy/stats/joint_rv.pyR8Tsc  sœ|j}gt|ƒD]}t|j|ƒ^q}g|D]}tt|ƒƒ^q;}tt||ƒƒ}g|D]$}ttt|j|ƒƒƒ^qu‰t‡fd†|Dƒƒ}d}x_t|ƒD]Q}||krÎ||j |j j j |ƒt ||ƒ||<|d7}qÎqÎWt |ƒ}|j jr_tˆt|j |Œ|ƒƒ} n0|j jrtˆt|j |ƒ|ƒƒ} n| j|ƒS(Nc3 s$|]}|ˆkr|gVqdS(N((t.0R1(R#(s3lib/python2.7/site-packages/sympy/stats/joint_rv.pys ^sii(R/R0RR)RtstrtdicttziptlisttappendR*R&R(ttuplet is_ContinuousRRt is_DiscreteR txreplace( R'tindicestcountR1torigtall_symst replace_dicttlimitsR6tf((R#s3lib/python2.7/site-packages/sympy/stats/joint_rv.pytmarginal_distributionXs$ +%1   $ $c  s7t‡fd†tˆjƒDƒƒ}|p.|}tg|D]}||k^q;ƒsZ|S|ˆj}xz|D]r}t|tƒrµ|jitt|j ƒ|j dƒ|6ƒ}qnt|t ƒrn|ji|j |6ƒ}qnqnWˆj t|ƒkrttdƒƒ‚nt‡fd†|Dƒƒ}t||ŒS(Nc3 s|]}ˆj|VqdS(N(R,(R9R1(R'(s3lib/python2.7/site-packages/sympy/stats/joint_rv.pys msisq Expectations of expression with unindexed joint random symbols cannot be calculated yet.c3 sH|]>}tt|jƒ|jdƒˆjjj|jdfVqdS(iN(RR:tbaseR(R*R&(R9R5(R'(s3lib/python2.7/site-packages/sympy/stats/joint_rv.pys {s(R?R0R/tanyR2RRRBR:RKR(RR)R,RtNotImplementedErrorRR( R'texprR4tevaluatetkwargstsymsR1R5RH((R's3lib/python2.7/site-packages/sympy/stats/joint_rv.pytcompute_expectationls % %  2  cC s tƒ‚dS(N(RM(R't condition((s3lib/python2.7/site-packages/sympy/stats/joint_rv.pytwherescC s tƒ‚dS(N(RM(R'RN((s3lib/python2.7/site-packages/sympy/stats/joint_rv.pytcompute_density‚scC s tƒ‚dS(N(RM(R'((s3lib/python2.7/site-packages/sympy/stats/joint_rv.pytsample…scC s tƒ‚dS(N(RM(R'RS((s3lib/python2.7/site-packages/sympy/stats/joint_rv.pyt probabilityˆsN(t__name__t __module__t__doc__R!tpropertyR&R)R*R,R/R2R%R7R8RJtNonetFalseRRRTRURVRW(((s3lib/python2.7/site-packages/sympy/stats/joint_rv.pyR s"      tJointDistributioncB sMeZdZdZd„Zed„ƒZed„ƒZd„Zd„Z RS(s“ Represented by the random variables part of the joint distribution. Contains methods for PDF, CDF, sampling, marginal densities, etc. R2cG slttt|ƒƒ}xDtt|ƒƒD]0}t||tƒr(t||ƒ||¦s(RR;tAssertionErrortkeysR%R&R2R?R8R0R-R@RtinfRAR (R'totherR4R.RNR1R`((s3lib/python2.7/site-packages/sympy/stats/joint_rv.pytcdf¢s  "  cG s |j|ŒS(N(R2(R'R(((s3lib/python2.7/site-packages/sympy/stats/joint_rv.pyt__call__°s(R2( RXRYRZt _argnamesR!R[R%R2ReRf(((s3lib/python2.7/site-packages/sympy/stats/joint_rv.pyR^‹s  R+cB seZdZd„ZRS(sg Representation of random symbols with joint probability distributions to allow indexing." cC s[t|jtƒrW|jj|krJtd|j|jjdfƒ‚nt||ƒSdS(Ns$Index keys for %s can only up to %s.i(RR3RR/t ValueErrortnameR(R'tkey((s3lib/python2.7/site-packages/sympy/stats/joint_rv.pyt __getitem__¸s  (RXRYRZRk(((s3lib/python2.7/site-packages/sympy/stats/joint_rv.pyR+³stJointDistributionHandmadecB s#eZdZeZed„ƒZRS(R2cC s |jdS(Ni(R((R'((s3lib/python2.7/site-packages/sympy/stats/joint_rv.pyR&Äs(R2(RXRYRgtTrueR@R[R&(((s3lib/python2.7/site-packages/sympy/stats/joint_rv.pyRl¿scG s­t|ƒ}xEtt|ƒƒD]1}t||tƒr||jd||>> from sympy.stats.crv_types import Normal >>> from sympy.stats.joint_rv import marginal_distribution >>> m = Normal('X', [1, 2], [[2, 1], [1, 2]]) >>> marginal_distribution(m, m[0])(1) 1/(2*sqrt(pi)) is6At least one component for marginal density is needed.RJ(( R=R0R-RRR(R3RhthasattrR*RJR)(R5RCR1t prob_space((s3lib/python2.7/site-packages/sympy/stats/joint_rv.pyRJÈs    tCompoundDistributioncB sAeZdZd„Zed„ƒZd„Zd„Zd„ZRS(s¹ Represents a compound probability distribution. Constructed using a single probability distribution with a parameter distributed according to some given distribution. cC sot|ttfƒs*ttdƒƒ‚n|j}tg|D]}t|tƒ^q=ƒs_|Stj ||ƒS(Ns{CompoundDistribution can only be initialized from ContinuousDistribution or DiscreteDistribution ( RRRRhRR(RLRRR!(R"R$t_argsR1((s3lib/python2.7/site-packages/sympy/stats/joint_rv.pyR!ös (cC st|jdƒS(Ni(RR((R'((s3lib/python2.7/site-packages/sympy/stats/joint_rv.pytlatent_distributionsscG sz|jd}tdƒ}t|tƒr=t||ƒj}n$t|tƒrat||ƒj}nt||fƒj |ŒS(Nitz( R(R RRRR,RRtMarginalDistributionR2(R'txR$RsR5((s3lib/python2.7/site-packages/sympy/stats/joint_rv.pyR2s  cC s|jdjS(Ni(R(R&(R'((s3lib/python2.7/site-packages/sympy/stats/joint_rv.pyR& scG s |j|ŒS(N(R2(R'R(((s3lib/python2.7/site-packages/sympy/stats/joint_rv.pyRfs( RXRYRZR!R[RrR2R&Rf(((s3lib/python2.7/site-packages/sympy/stats/joint_rv.pyRpïs   RtcB sbeZdZd„Zd„Zed„ƒZed„ƒZd„Zd„Z d„Z d„Z RS( sî Represents the marginal distribution of a joint probability space. Initialised using a probability distribution and random variables(or their indexed components) which should be a part of the resultant distribution. cC sƒtd„|Dƒƒs+ttdƒƒ‚ntjd„|Dƒƒ}t|tƒ rptt|ƒƒdkrp|St j |||ƒS(Ncs s'|]}t|ttfƒgVqdS(N(RRR(R9R5((s3lib/python2.7/site-packages/sympy/stats/joint_rv.pys ssMarginal distribution can be intitialised only in terms of random variables or indexed random variablescs s|] }|VqdS(N((R9R5((s3lib/python2.7/site-packages/sympy/stats/joint_rv.pys "si( tallRhRR tfromiterRR^R-RRR!(R"R$R4((s3lib/python2.7/site-packages/sympy/stats/joint_rv.pyR!s(cC sdS(N((R'((s3lib/python2.7/site-packages/sympy/stats/joint_rv.pytcheck'scC s gt|jdƒD] }|^q}gt|jdƒD]}||jdkr:|^q:}x*|D]"}||krf|j|ƒqfqfWtd„|DƒƒS(Nics s|]}|jjVqdS(N(R3R&(R9R1((s3lib/python2.7/site-packages/sympy/stats/joint_rv.pys 2s(RR(tremoveR(R'R1R4tmarginalise_out((s3lib/python2.7/site-packages/sympy/stats/joint_rv.pyR&*s&  cC s0|jd}tg|D]}|jj^qƒS(Ni(R(R&R3R)(R'R4R5((s3lib/python2.7/site-packages/sympy/stats/joint_rv.pyR84s cG s|jd|jd}}gt|ƒD]}||jdkr(|^q(}g|jdD]}|jj^q[}xT|jtƒD]C}t|tƒrƒt|jtƒrƒ||krƒ|j |ƒqƒqƒWt|t ƒrt ddt ƒ}|jdj |ƒ}nmt|tƒrqt|jjƒ}t ddt dt ƒ}g|D]}t||ƒ^qD}tj |ƒ}nt||j||ƒƒ|ŒS(NiiRutrealtfinite(R(RR3R)tatomsRRRKRR>RpR RmR2R^R-R%t expressionRt compute_pdf(R'RuRNR4R1RzRQRD((s3lib/python2.7/site-packages/sympy/stats/joint_rv.pyR29s 2&! 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