B [_/@sJdZddlmZmZddlmZmZmZmZm Z m Z m Z m Z m Z ddlmZmZddlmZmZddlmZmZmZmZmZmZddlmZmZmZddlm Z m!Z!m"Z"dd l#m$Z$dd l%m&Z&dd l'm(Z(dd l)m*Z*Gd ddeZ+GdddeeZ,GdddeZ-Gddde,eZ.ddZ/GdddeeZ0GdddeZ1dS)zq Joint Random Variables Module See Also ======== sympy.stats.rv sympy.stats.frv sympy.stats.crv sympy.stats.drv )print_functiondivision) BasicLambdasympifyIndexedSymbol ProductSetSDummyMul)Sum summation)Integral integrate) ProductPSpaceNamedArgsMixin ProductDomain RandomSymbolrandom_symbols SingleDomain)ContinuousDistributionSingleContinuousDistributionSingleContinuousPSpace)DiscreteDistributionSingleDiscreteDistributionSingleDiscretePSpace) string_types)ImmutableMatrix)Tuple) filldedentc@seZdZdZddZeddZeddZedd Zed d Z ed d Z eddZ eddZ ddZ eddZddZd$ddZddZddZd d!Zd"d#ZdS)% JointPSpacezt Represents a joint probability space. Represented using symbols for each component and a distribution. cCsZt|trt||St|tr(t||St|tr:t|}t|tsLtdt |||S)Nz#s should have been string or Symbol) isinstancerrrrrr TypeErrorr__new__)clssymdistr(3lib/python3.7/site-packages/sympy/stats/joint_rv.pyr$%s      zJointPSpace.__new__cCs|jjS)N)domainset)selfr(r(r)r+0szJointPSpace.setcCs |jdS)Nr)args)r,r(r(r)symbol4szJointPSpace.symbolcCs |jdS)N)r-)r,r(r(r) distribution8szJointPSpace.distributioncCs t|j|S)N)JointRandomSymbolr.)r,r(r(r)value<szJointPSpace.valuecCs |jj}t|trt|jSdS)Nr/)r0r+r"r lenr-)r,_setr(r(r)component_count@szJointPSpace.component_countcs"fddtjD}j|S)Ncsg|]}tj|qSr()rr.).0i)r,r(r) Gsz#JointPSpace.pdf..)ranger5r0)r,r&r()r,r)pdfEszJointPSpace.pdfcCs6t|j}t|dkr$t|j|jStdd|DS)NrcSsg|] }|jjqSr()pspacer*)r6rvr(r(r)r8Osz&JointPSpace.domain..)rr0r3rr.r+r)r,rvsr(r(r)r*Js  zJointPSpace.domaincCs |jj|S)N)r+r-)r,indexr(r(r)component_domainQszJointPSpace.component_domaincCs|jjS)N)r*symbols)r,r(r(r)r@TszJointPSpace.symbolsc sj}fddt|D}dd|D}tt||}fdd|Dtfdd|D}d}xHt|D]<}||krn||jjj|t ||||<|d7}qnWt |}jj rt t j||} njj rt t||} | |S) Ncsg|]}tj|qSr()rr.)r6r7)r,r(r)r8Zsz5JointPSpace.marginal_distribution..cSsg|]}tt|qSr()rstr)r6r7r(r(r)r8[scs g|]}tttj|qSr()rrArr.)r6r7)r,r(r)r8]sc3s|]}|kr|gVqdS)Nr()r6r7)r&r(r) ^sz4JointPSpace.marginal_distribution..rr/)r5r9dictziplistappendr0r+r-tuple is_Continuousrr is_Discreterxreplace) r,indicescountZorigZall_symsZ replace_dictlimitsr>r7fr()r,r&r)marginal_distributionXs$ z!JointPSpace.marginal_distributionNFc stfddtjD}p"|tfdd|Ds>|S|j}xRD]J}t|tr~||tt|j |j di}qNt|t rN|||j i}qNWj t|krttdtfdd|D}t|f|S)Nc3s|]}j|VqdS)N)r2)r6r7)r,r(r)rBmsz2JointPSpace.compute_expectation..csg|] }|kqSr(r()r6r7)r=r(r)r8osz3JointPSpace.compute_expectation..r/zq Expectations of expression with unindexed joint random symbols cannot be calculated yet.c3s8|]0}tt|j|jdjjj|jdfVqdS)r/N)rrAbaser-r0r+)r6r<)r,r(r)rB{s)rGr9r5anyr:r"rrJrArPr-rr.r2rNotImplementedErrorr r)r,exprr=Zevaluatekwargssymsr<rMr()r=r,r)compute_expectationls    "   zJointPSpace.compute_expectationcCs tdS)N)rR)r, conditionr(r(r)whereszJointPSpace.wherecCs tdS)N)rR)r,rSr(r(r)compute_densityszJointPSpace.compute_densitycCs tdS)N)rR)r,r(r(r)sampleszJointPSpace.samplecCs tdS)N)rR)r,rWr(r(r) probabilityszJointPSpace.probability)NF)__name__ __module__ __qualname____doc__r$propertyr+r.r0r2r5r:r*r?r@rOrVrXrYrZr[r(r(r(r)r! s"         r!c@sDeZdZdZdZddZeddZeddZd d Z d d Z d S)JointDistributionz Represented by the random variables part of the joint distribution. Contains methods for PDF, CDF, sampling, marginal densities, etc. )r:cGsRttt|}x2tt|D]"}t||trt||||<qWtj|f|S)N) rEmaprr9r3r"rrr$)r%r-r7r(r(r)r$s zJointDistribution.__new__cCs t|jS)N)rr@)r,r(r(r)r*szJointDistribution.domaincGs |jjdS)Nr/)densityr-)r,r-r(r(r)r:szJointDistribution.pdfcCst|tst|}|jj}|tdd|jD}xjt |D]^}||j rtt |||||j |||f}qB||j rBt|||||j |||f}qBW|S)Ncss|]}|jdVqdS)rN)r-)r6r7r(r(r)rBsz(JointDistribution.cdf..)r"rCAssertionErrorkeysr*r+r:rGr@r3rHrinfrIr )r,otherr=r4rSr7rcr(r(r)cdfs  zJointDistribution.cdfcGs |j|S)N)r:)r,r-r(r(r)__call__szJointDistribution.__call__N) r\r]r^r_ _argnamesr$r`r*r:rhrir(r(r(r)ras  rac@seZdZdZddZdS)r1zg Representation of random symbols with joint probability distributions to allow indexing." cCsLddlm}t|j|rH|jj|kr>td|j|jjdft||SdS)Nr)r!z$Index keys for %s can only up to %s.r/)Zsympy.stats.joint_rvr!r"r;r5 ValueErrornamer)r,keyr!r(r(r) __getitem__s    zJointRandomSymbol.__getitem__N)r\r]r^r_rnr(r(r(r)r1sr1c@s eZdZdZdZeddZdS)JointDistributionHandmade)r:TcCs |jdS)Nr/)r-)r,r(r(r)r+szJointDistributionHandmade.setN)r\r]r^rjrHr`r+r(r(r(r)rosrocGszt|}x4tt|D]$}t||tr||jd||<qW|j}|dkrTtdt|j drp|j ||j S|j |S)aR Marginal distribution function of a joint random variable. Parameters ========== rv: A random variable with a joint probability distribution. indices: component indices or the indexed random symbol for whom the joint distribution is to be calculated Returns ======= A Lambda expression n `sym`. Examples ======== >>> 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)) r/r(z6At least one component for marginal density is needed.rO) rEr9r3r"rr-r;rkhasattrr0rOr.)r<rKr7Z prob_spacer(r(r)rOs rOc@s<eZdZdZddZeddZddZdd Zd d Z d S) CompoundDistributionz Represents a compound probability distribution. 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Initialised using a probability distribution and random variables(or their indexed components) which should be a part of the resultant distribution. cCs^tdd|Dsttdtdd|D}t|tsPtt|dkrP|St |||S)Ncss|]}t|ttfgVqdS)N)r"rr)r6r<r(r(r)rBsz/MarginalDistribution.__new__..zMarginal distribution can be intitialised only in terms of random variables or indexed random variablescss|] }|VqdS)Nr()r6r<r(r(r)rB!sr) allrkr rZfromiterr"rar3rrr$)r%r'r=r(r(r)r$szMarginalDistribution.__new__cCsdS)Nr()r,r(r(r)check&szMarginalDistribution.checkcsfddtjdD}fddtjdD}x|D]}||kr:||q:Wtdd|DS)NcSsg|]}|qSr(r()r6r7r(r(r)r8+sz,MarginalDistribution.set..r/csg|]}|jdkr|qS)r/)r-)r6r7)r,r(r)r8,scss|]}|jjVqdS)N)r;r+)r6r7r(r(r)rB1sz+MarginalDistribution.set..)rr-remover )r,r=marginalise_outr7r()r,r)r+)s  zMarginalDistribution.setcCs|jd}tdd|DS)Nr/cSsg|] }|jjqSr()r;r.)r6r<r(r(r)r86sz0MarginalDistribution.symbols..)r-r+)r,r=r(r(r)r@3s zMarginalDistribution.symbolscsjdjd}}fddt|D}ddjdD}x:|tD],}t|trLt|jtrL||krL||qLWt|trt ddd}|jd |}n@t|t rt |j j}t dddd fd d|D}t |}t|||S) Nrr/csg|]}|jdkr|qS)r/)r-)r6r7)r,r(r)r8:sz,MarginalDistribution.pdf..cSsg|] }|jjqSr()r;r.)r6r7r(r(r)r8;sruT)real)rzZfinitecsg|]}t|qSr()r)r6r7)rur(r)r8Fs)r-rZatomsrr"rPrrFrqr r:rar3r*Z expressionr compute_pdf)r,rurSr=ryrUr7rLr()r,rur)r:8s      zMarginalDistribution.pdfcCs8x2|D]*}d}t|tr |jj}||||}qW|S)Nr/)r"rr;r:ry)r,rSr=r<Zlpdfr(r(r)r{Js   z MarginalDistribution.compute_pdfcCsddlm}t|tr |jj}n$t|trD|j|j|j d}| ||jj i}|jj rrt ||jj |f}n:|jjr|tjtjtjfkr|j|jf}|||jj |f}|S)Nr)r r/)sympy.concrete.summationsr r"rr;r+rrPr?r-rJr.rHrrIr ZIntegersZNaturalsZ Naturals0rfZsup)r,rSr<r Zdomr(r(r)ryRs     z$MarginalDistribution.marginalise_outcGs |j|S)N)r:)r,r-r(r(r)rieszMarginalDistribution.__call__N) r\r]r^r_r$rwr`r+r@r:r{ryrir(r(r(r)rts  rtN)2r_Z __future__rrZsympyrrrrrr r r r r|r rZsympy.integrals.integralsrrZsympy.stats.rvrrrrrrZsympy.stats.crvrrrZsympy.stats.drvrrrZsympy.core.compatibilityrZsympy.matricesrZsympy.core.containersrZsympy.utilities.miscr r!rar1rorOrqrtr(r(r(r) s$,     k(  %%