a амZ>GddДde5ГZ?GddДde?e6ГZ@GddДde9e?ГZAGddДde?e7ГZBGdd Дd e>ГZCGd!d"Дd"eCe=ГZDGd#d$Дd$e:ГZEGd%d&Дd&eEe;ГZFd'd(ДZGd)d*ДZHd+S),zl Continuous Random Variables Module See Also ======== sympy.stats.crv_types sympy.stats.rv sympy.stats.frv щ)┌Basic)┌cacheit)┌Lambda┌ PoleError)┌I┌nan┌oo)┌Eq┌Ne)┌S)┌Dummy┌symbols)┌_sympify┌sympify)┌ factorial)┌exp)┌ Piecewise)┌ DiracDelta)┌Integral┌ integrate)┌And┌Or)┌PolynomialError)┌poly)┌series)┌ FiniteSet┌Intersection┌Interval┌Union)┌solveset)┌reduce_rational_inequalities) ┌RandomDomain┌SingleDomain┌ConditionalDomain┌ is_random┌ ProductDomain┌PSpace┌SinglePSpace┌random_symbols┌NamedArgsMixin┌Distributionc@seZdZdZdZddДZdS)┌ContinuousDomainzX A domain with continuous support Represented using symbols and Intervals. TcCstdГВdS)Nz#Not Implemented for generic Domains)┌NotImplementedErrorй┌selfйr/·_/Users/vegardjervell/Documents/master/model/venv/lib/python3.9/site-packages/sympy/stats/crv.py┌ as_boolean,szContinuousDomain.as_booleanN)┌__name__┌ __module__┌__qualname__┌__doc__┌ is_Continuousr1r/r/r/r0r+$sr+c@s"eZdZdZdddДZddДZdS)┌SingleContinuousDomainzj A univariate domain with continuous support Represented using a single symbol and interval. NcKsJ|dur|j}|s|St|Гt|jГkr0tdГВt||j|jffi|дОS)NzValues should be equal)r ┌ frozenset┌ ValueErrorr┌symbol┌set)r.┌expr┌ variables┌kwargsr/r/r0┌compute_expectation6sz*SingleContinuousDomain.compute_expectationcCs|jа|jбSйN)r;Z as_relationalr:r-r/r/r0r1@sz!SingleContinuousDomain.as_boolean)Nйr2r3r4r5r?r1r/r/r/r0r70s r7c@s"eZdZdZdddДZddДZdS)┌ProductContinuousDomainzE A collection of independent domains with continuous support NcKsH|dur|j}|jD].}t|Гt|jГ@}|r|j||fi|дО}q|Sr@)r ┌domainsr8r?)r.r<r=r>┌domainZdomain_varsr/r/r0r?Is z+ProductContinuousDomain.compute_expectationcCstddД|jDГОS)NcSsg|]}|абСqSr/)r1)┌.0rDr/r/r0┌ Sєz6ProductContinuousDomain.as_boolean..)rrCr-r/r/r0r1Rsz"ProductContinuousDomain.as_boolean)NrAr/r/r/r0rBDs rBc@s.eZdZdZd ddДZddДZeddДГZdS) ┌ConditionalContinuousDomainzo A domain with continuous support that has been further restricted by a condition such as $x > 3$. NcKsJ|dur|j}|s|S|jа||б}|jt|jГ}}|jg}|Рr4|аб}|jr~t |t Гrj|а|jбnt |t Гr|tdГВq>|jРr&|jrв|t|j|jГ9}nВ|jt|jГ@} t| Гdkr╞tdГВ| аб} t|ГD]L\}}|d| kr╓t|| Г} t|d|dГ}| а|б}| |j|jf||<q╓q>td|ГВq>t|g|вRi|дОS)NzOr not implemented hereщz-Multivariate Inequalities not yet implementedrщz+Condition %s is not a relational or Boolean)r ┌ fulldomainr?┌function┌list┌limits┌ condition┌popZ is_Boolean┌ isinstancer┌extend┌argsrr,┌ is_RelationalZis_Equalityr┌lhs┌rhsZfree_symbolsr;┌len┌ enumerate┌!reduce_rational_inequalities_wrapr┌ intersect┌left┌right┌ TypeErrorr)r.r<r=r>Z fullintgrlZ integrandrN┌ conditionsZcondr r:┌i┌limitZcintvlZlintvlZintvlr/r/r0r?\sF z/ConditionalContinuousDomain.compute_expectationcCst|jаб|jГSr@)rrKr1rOr-r/r/r0r1Лsz&ConditionalContinuousDomain.as_booleancCs8t|jГdkr,|jjt|jt|jГdГ@StdГВdS)NrIrz)Set of Conditional Domain not Implemented)rWr rKr;rYrO┌tupler,r-r/r/r0r;Оs zConditionalContinuousDomain.set)N)r2r3r4r5r?r1┌propertyr;r/r/r/r0rHVs /rHc@seZdZddДZdS)┌ContinuousDistributioncGs |j|ОSr@)┌pdf)r.rSr/r/r0┌__call__ЩszContinuousDistribution.__call__N)r2r3r4rer/r/r/r0rcШsrcc@sкeZdZdZeeeГZddДZeddДГZ e ddДГZdd ДZd dДZ e dd ДГZddДZddДZe ddДГZddДZddДZd"ddДZe ddДГZddДZdd ДZd!S)#┌SingleContinuousDistributionaЩ Continuous distribution of a single variable. Explanation =========== Serves as superclass for Normal/Exponential/UniformDistribution etc.... Represented by parameters for each of the specific classes. E.g NormalDistribution is represented by a mean and standard deviation. Provides methods for pdf, cdf, and sampling. See Also ======== sympy.stats.crv_types.* cGs ttt|ГГ}tj|g|вRОSr@)rM┌maprr┌__new__)┌clsrSr/r/r0rh▓sz$SingleContinuousDistribution.__new__cGsdSr@r/)rSr/r/r0┌check╢sz"SingleContinuousDistribution.checkcKs\tddtdН\}}|jj}|а|б}t|аб|||ffi|дО}t|||kfdГ}t||ГS)zB Compute the CDF from the PDF. Returns a Lambda. ·x, zTй┌realriйrT) r rr;┌startrdrZdoitrr)r.r>┌x┌z┌ left_boundrd┌cdfr/r/r0┌compute_cdf║s z(SingleContinuousDistribution.compute_cdfcCsdSr@r/йr.rpr/r/r0┌_cdf╩sz!SingleContinuousDistribution._cdfcKs6t|Гdkr"|а|б}|dur"|S|jfi|дО|ГSйz Cumulative density function rN)rWrvrt)r.rpr>rsr/r/r0rs═s z SingleContinuousDistribution.cdfcKsFtddtdН\}}|а|б}ttt||Г|||jfГ}t||ГS)zV Compute the characteristic function from the PDF. Returns a Lambda. ·x, tTrl)r rrdrrrr;r)r.r>rp┌trd┌cfr/r/r0┌compute_characteristic_function╒s zrzr/r/r0┌characteristic_functionуs z4SingleContinuousDistribution.characteristic_functioncKsBtddtdН\}}|а|б}tt||Г|||jfГ}t||ГS)zY Compute the moment generating function from the PDF. Returns a Lambda. rxTrl)r rrdrrr;r)r.r>rpryrd┌mgfr/r/r0┌"compute_moment_generating_functionыs z?SingleContinuousDistribution.compute_moment_generating_functioncCsdSr@r/r|r/r/r0┌_moment_generating_functionЎsz8SingleContinuousDistribution._moment_generating_functioncKs.|s|а|б}|dur|S|jfi|дО|ГS)z Moment generating function N)rБrА)r.ryr>rr/r/r0┌moment_generating_function∙s z7SingleContinuousDistribution.moment_generating_functionTcKs(|Рrz┬t||Г}|jr tjWStdddН}|а|б}|durbt||а|б||jffi|дОWS|а б}tt ||d|dГаб|Г} d} t|dГD],}| |а ||б| а ||бt|Г7} qЦ| WStРy■t||а|б||jffi|дОYS0n"t||а|б||jffi|дОSdS)z- Expectation of expression over distribution ryTйrmNrrI)r┌is_zeror┌ZerorrБrrdr;ZdegreerZremoveO┌rangeZcoeff_monomialrrr)r.r<┌var┌evaluater>┌pryr┌degZtaylor┌result┌kr/r/r0┌expectations$ $**z(SingleContinuousDistribution.expectationcKsrtddtdН\}}|jj}|а|б}t||||ffi|дО}t||||jГ}t|t||dk|dk@ft dfГГS)zG Compute the Quantile from the PDF. Returns a Lambda. zx, pTrlrrI) r rr;rordrrrrr)r.r>rprЙrrrdrs┌quantiler/r/r0┌compute_quantiles z-SingleContinuousDistribution.compute_quantilecCsdSr@r/rur/r/r0┌ _quantile%sz&SingleContinuousDistribution._quantilecKs6t|Гdkr"|а|б}|dur"|S|jfi|дО|ГSrw)rWrРrП)r.rpr>rОr/r/r0rО(s z%SingleContinuousDistribution.quantileN)T)r2r3r4r5rrr;rh┌staticmethodrjrrtrvrsr{r}r~rАrБrВrНrПrРrОr/r/r/r0rfЭs, rfc@sАeZdZdZdZdZeddДГZdddДZd d ДZ e ddДГZe d dДГZe ddДГZ e ddДГZddДZddДZdddДZdS)┌ContinuousPSpacezо Continuous Probability Space Represents the likelihood of an event space defined over a continuum. Represented with a ContinuousDomain and a PDF (Lambda-Like) TcCs|j|jjОSr@)┌densityrDr r-r/r/r0rd<szContinuousPSpace.pdfNFcKsZ|dur|j}nt|Г}|аddД|DГб}tddД|DГГ}|jj|j||fi|дОS)NcSsi|]}||jУqSr/йr:йrE┌rvr/r/r0┌ FrGz8ContinuousPSpace.compute_expectation..css|]}|jVqdSr@rФrХr/r/r0┌ HrGz7ContinuousPSpace.compute_expectation..)┌valuesr8┌xreplacerDr?rd)r.r<┌rvsrИr>Zdomain_symbolsr/r/r0r?@s z$ContinuousPSpace.compute_expectationcKsД||jvrXtt|jГt|gГГ}tddД|DГГ}|jj|j|fi|дО}t|j|ГSt dddН}t||jt ||Гfi|дОГS)Ncss|]}|jVqdSr@rФ)rE┌rsr/r/r0rШRrGz3ContinuousPSpace.compute_density..rqTrГ)rЩrar;r8rDr?rdrr:rr)r.r<r>Z randomsymbolsr rdrqr/r/r0┌compute_densityMs z ContinuousPSpace.compute_densitycKsx|jjjstdГВ|j|fi|дО}tddtdН\}}|jjj}t||Г|||ffi|дО}t |||kfdГ}t ||ГS)Nz0CDF not well defined on multivariate expressionsrkTrlrn)rDr;┌is_Intervalr9rЭr rrorrr)r.r<r>┌drprqrrrsr/r/r0rtYs zContinuousPSpace.compute_cdfcKsn|jjjstdГВ|j|fi|дО}tddtdН\}}ttt ||Г||Г|t t ffi|дО}t||ГS)NzCCharacteristic function of multivariate expressions not implementedrxTrl)rDr;rЮr,rЭr rrrrrr)r.r<r>rЯrpryrzr/r/r0r{is .z0ContinuousPSpace.compute_characteristic_functioncKsj|jjjstdГВ|j|fi|дО}tddtdН\}}tt||Г||Г|t t ffi|дО}t ||ГS)NzFMoment generating function of multivariate expressions not implementedrxTrl)rDr;rЮr,rЭr rrrrr)r.r<r>rЯrpryrr/r/r0rАss *z3ContinuousPSpace.compute_moment_generating_functioncKs\|jjjstdГВ|j|fi|дО}tdddН}tdddН}t||Г|||jГ}t||ГS)Nz5Quantile not well defined on multivariate expressionsrpTrГrЙ)Zpositive)rDr;rЮr9rtrrr)r.r<r>rЯrprЙrОr/r/r0rП}s z!ContinuousPSpace.compute_quantilec sФtdddНЙd}t|tГr4t|jd|jdГ}d}zи|а|бЙЗfddД|jDГd}|j|fiИдОЙИjt j usВtИjtГrФ|sМt jnt j WStИjtГr└tЗЗЗfd d ДИjjDГГWStИИГИИjffiИдОWStРyОddlm}|j|j}t|ГРs|j}|j}n||fiИдО}d}t|tГРsXddlm} | ||jjd Н}tИ|Г} | а|а| j|бб}|РsА|nt j |YS0dS)NrqTrГFrrIcsg|]}|jИjkr|СqSr/rФrХ)rDr/r0rFФrGz0ContinuousPSpace.probability..c3s2|]*}t|tГrtИИГИ|ffiИдОVqdSr@)rQrr)rEZsubset)r>rdrqr/r0rШЫs z/ContinuousPSpace.probability..)rУ)┌ContinuousDistributionHandmade)r;)rrQr r rS┌whererЩrЭr;rZEmptySetrrЕZOner┌sumrr,┌sympy.stats.rvrУrUrVr$rcZsympy.stats.crv_typesrаrD┌SingleContinuousPSpace┌probability┌ __class__┌value)r.rOr>Zcond_invrЦrУr<Zdens┌comprа┌spacerЛr/)rDr>rdrqr0rеЛs< ■ zContinuousPSpace.probabilitycCs\tt|ГГ}t|Гdkr$|а|jбs,tdГВt|Гd}t||Г}|а|j j б}t|j|ГS)NrIz2Multiple continuous random variables not supportedr) r8r(rW┌issubsetrЩr,rarYrZrDr;r7r:)r.rOrЫrЦ┌intervalr/r/r0rб┤s zContinuousPSpace.wherec Kst|аddД|jDГб}t|j|Г}|rjddД|jDГ}|j|jfi|дО}|j|а|б}tt|jГ|Г}t ||ГS)NcSsi|]}||jУqSr/rФrХr/r/r0rЧ┐rGz6ContinuousPSpace.conditional_space..cSsi|]}|tt|ГГУqSr/)r┌strrХr/r/r0rЧ╟rG) rЪrЩrHrDr r?rdrrarТ) r.rO┌ normalizer>rD┌replacementZnormrdrУr/r/r0┌conditional_space╛sz"ContinuousPSpace.conditional_space)NF)T)r2r3r4r5r6Zis_realrbrdr?rЭrrtr{rАrПrеrбrпr/r/r/r0rТ1s$ ) rТc@sdeZdZdZeddДГZeddДГZdd d ДZddd ДZddДZ ddДZ ddДZddДZddДZ dS)rдa A continuous probability space over a single univariate variable. 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