EdUddlmZddlmZddlmZddlmZddlm Z ddl m Z ddl m Z mZddlmZmZmZmZmZmZmZmZmZdd lmZmZmZmZmZmZm Z dd l!m"Z"Gd d eZ#d Z$GddZ%GddZ&GddZ'e%e'e'e&dZ(Gdde eZ)Gdde)Z*dZ+Gdde)Z,dZ-Gdde)Z.dZ/Gd d!e)Z0d"Z1d#S)$)prod)Basic)pi)S)exp) multigamma)sympify_sympify) ImmutableMatrixInverseTrace Determinant MatrixSymbol MatrixBase Transpose MatrixSet matrix2numpy) _value_checkRandomMatrixSymbolNamedArgsMixinPSpace_symbol_converter MatrixDomain Distribution) import_moduleceZdZdZdZedZedZedZedZ edZ dZ d d Z d S) MatrixPSpacezD Represents probability space for Matrix Distributions. ct|}t|t|}}|jr|jstdt j|||||S)NzDimensions should be integers)rr is_integer ValueErrorr__new__)clssym distributiondim_ndim_ms @lib/python3.11/site-packages/sympy/stats/matrix_distributions.pyr!zMatrixPSpace.__new__s`$$u  >U%5 ><== =}S#|UEBBBc|jdS)Nargsselfs r'zMatrixPSpace. s 1r(c|jdSNrr+r-s r'r/zMatrixPSpace.!s 49Q<r(c@t|j|jjSN)rsymbolr$setr-s r'domainzMatrixPSpace.domain#sDK):)>???r(c\t|j|jd|jd|S)N)rr4r,r-s r'valuezMatrixPSpace.value's$!$+ty|TYq\4PPPr(c|jhSr3)r:r-s r'valueszMatrixPSpace.values+s  |r(c|t}t|dkst|tst d|j|S)Nr*ztCurrently, no algorithm has been implemented to handle general expressions containing multiple matrix distributions.)atomsrlen isinstanceNotImplementedErrorr$pdf)r.exprr,rmss r'compute_densityzMatrixPSpace.compute_density/shjj+,, s88a< 6 41C D D 6%'566 6 $$T***r(scipyNcJ|j|j|||iS)zu Internal sample method Returns dictionary mapping RandomMatrixSymbol to realization value. )libraryseed)r:r$sample)r.sizerIrJs r'rKzMatrixPSpace.sample7s*  D-44T7QU4VVWWr(rFrGN) __name__ __module__ __qualname____doc__r!propertyr$r4r6r:r<rErKrFr(r'rrsCCC85566L X// 0 0F @@X@QQXQX+++XXXXXXr(rcttt|}||}|j||j}t |||d|d}|jS)Nrr*)listmapr check dimensionrr:)r4r"r,distdimpspaces r'rvr[@s] GT"" # #D 3:DDJ .C &$AA 7 7F <r(c0eZdZdZddZedZdS)SampleMatrixScipyz7Returns the sample from scipy of the given distributionNc0||||Sr3) _sample_scipyr"rXrLrJs r'r!zSampleMatrixScipy.__new__K  tT222r(c ddlm ddl} fd fdd}ddd}|}|jj|vrdS|t |tr|j | }n|}||jj|t||} | |||jj|zS) zSample from SciPy.r)statsNcjt|jt |jt |S)N)dfscalerL)wishartrvsintnr scale_matrixfloatrXrL rand_state scipy_statss r'r/z1SampleMatrixScipy._sample_scipy..UsB+BUBYBYtv;;l43De&L&LSWCZCYCYr(cjt|jtt|jtt|jt||S)N)meanrowcovcolcovrL random_state) matrix_normalrhrlocation_matrixrlscale_matrix_1scale_matrix_2rms r'r/z1SampleMatrixScipy._sample_scipy..WsZ{G`GdGd!$"6>>#D$7??#D$7??dYcHeHeHer(WishartDistributionMatrixNormalDistributionc|jjSr3rkshaperXs r'r/z1SampleMatrixScipy._sample_scipy..^ 0A0Gr(c|jjSr3rvr~rs r'r/z1SampleMatrixScipy._sample_scipy.._ d6J6Pr(rJ) rGrcnumpykeys __class__rNr@rirandom default_rngrreshape) r"rXrLrJr scipy_rv_map sample_shape dist_listrnsampros @r'r_zSampleMatrixScipy._sample_scipyNs( /..... $Y$Y$Y$Y)e)e)e)e  $H#G)P)P  !%%'' > ") 3 4  :dC00 11t1< ") 3 4  :dC00 11t1<.sXT5F5Fs 4e<<#D$7??#D$7??*0 6G6262r(cdt|jt|jt S)Nr)nur)WishartBartlettrirjrrkrlrs r'r/z/SampleMatrixPymc._sample_pymc..s;0D0DStv;;,t/@%"H"H1E1J1Jr()r{rzc|jjSr3r}rs r'r/z/SampleMatrixPymc._sample_pymc..rr(c|jjSr3rrs r'r/z/SampleMatrixPymc._sample_pymc..rr(ryrr*F)drawschains progressbar random_seedreturn_inferencedatacompute_convergence_checksr)r ImportErrorpymc3rrrNlogging getLoggersetLevelERRORModelrKrr) r"rXrLrJ pymc_rv_maprrrsampsrs @r'rzSampleMatrixPymc._sample_pymcs ! KKKK ! ! !  !)2)2)2)2 $J$J$J$J   $H#G)P)P   $$&& > ") 3 4&!!**7=999 ZZ\\ d d 0K/ 0 6 6 6KKd4jj[_v{Y^K__`cdE d d d d d d d d d d d d d d d}}T$IL1H$I$$O$OOPPPsA C--C14C1r3)rNrOrPrQr!rrrFr(r'rrsN@@2222QQ[QQQr(r)rGrrrc<eZdZdZdZedZdZd dZdS) MatrixDistributionz1 Abstract class for Matrix Distribution. c>d|D}tj|g|RS)Nctg|]5}t|trt|nt|6SrF)r@rTr r ).0args r' z.MatrixDistribution.__new__..sM444'*)33(=(=#$$$c]]444r()rr!)r"r,s r'r!zMatrixDistribution.__new__s844.2444}S(4((((r(cdSr3rFr+s r'rVzMatrixDistribution.checks r(ctt|trt|}||Sr3)r@rTr rB)r.rCs r'__call__zMatrixDistribution.__call__s1 dD ! ! )"4((Dxx~~r(rFrGNcgd}||vrtdt|zt|std|zt ||||}||Std|jjd|)zo Internal sample method Returns dictionary mapping RandomSymbol to realization value. )rGrrrz&Sampling from %s is not supported yet.zFailed to import %sNz Sampling for z# is not currently implemented from )rAstrrr _get_sample_class_matrixrvrrN)r.rLrIrJ librariesrs r'rKzMatrixDistribution.samples877 ) # 8%&N*-g,,'788 8W%% >2W<== =*73D$EE  L!!>***GG5 r(rM) rNrOrPrQr! staticmethodrVrrKrFr(r'rrsk)))   \  r(rcZeZdZdZedZedZedZdZ dS)MatrixGammaDistributionalphabetarkct|tst|jdt|jdt|jdt|jddS)N+The shape matrix must be positive definite.Should be square matrix#Shape parameter should be positive.z#Scale parameter should be positive.r@rris_positive_definite is_square is_positivers r'rVzMatrixGammaDistribution.checksz, 55 5 :=4 5 5 5\+.   U&(MNNNT%'LMMMMMr(c\|jjd}t||tjSr1rkr~rrRealsr.ks r'r5zMatrixGammaDistribution.set&   #A &Aqw'''r(c|jjSr3r}r-s r'rWz!MatrixGammaDistribution.dimension &&r(c"|j|j|j}}}|jd}t |t rt |}t |ttfstdt|zt| |z|z }tt||||zzt||zz }t|| z}t||t!|dzdz z z} ||z| zS)Nr4%s should be an isinstance of Matrix or MatrixSymbolr*r8)rrrkr~r@rTr rrr rr rr rrr) r.xrrrkp sigma_inv_xterm1term2term3s r'rBzMatrixGammaDistribution.pdfs$(J 4;L\t  q ! a   #""A!j,788 0&(+A/00 0 ---a/$6 E+&&''$5/Zq=Q=Q)QR\**uf5Q51QU88A:#56u}u$$r(N rNrOrP _argnamesrrVrRr5rWrBrFr(r'rrsz1INN\N((X(''X' % % % % %r(rc|t|trt|}t|t|||fS)a  Creates a random variable with Matrix Gamma Distribution. The density of the said distribution can be found at [1]. Parameters ========== alpha: Positive Real number Shape Parameter beta: Positive Real number Scale Parameter scale_matrix: Positive definite real square matrix Scale Matrix Returns ======= RandomSymbol Examples ======== >>> from sympy.stats import density, MatrixGamma >>> from sympy import MatrixSymbol, symbols >>> a, b = symbols('a b', positive=True) >>> M = MatrixGamma('M', a, b, [[2, 1], [1, 2]]) >>> X = MatrixSymbol('X', 2, 2) >>> density(M)(X).doit() exp(Trace(Matrix([ [-2/3, 1/3], [ 1/3, -2/3]])*X)/b)*Determinant(X)**(a - 3/2)/(3**a*sqrt(pi)*b**(2*a)*gamma(a)*gamma(a - 1/2)) >>> density(M)([[1, 0], [0, 1]]).doit() exp(-4/(3*b))/(3**a*sqrt(pi)*b**(2*a)*gamma(a)*gamma(a - 1/2)) References ========== .. [1] https://en.wikipedia.org/wiki/Matrix_gamma_distribution )r@rTr r[r)r4rrrks r' MatrixGammars>V,%%5&|44 f-t\/J K KKr(cZeZdZdZedZedZedZdZ dS)rzrjrkct|tst|jdt|jdt|jddS)Nrrrrrs r'rVzWishartDistribution.checkLse, 55 5 :=4 5 5 5\+.   Q]$IJJJJJr(c\|jjd}t||tjSr1rrs r'r5zWishartDistribution.setUrr(c|jjSr3r}r-s r'rWzWishartDistribution.dimensionZrr(c|j|j}}|jd}t|trt |}t|t tfstdt|zt| |ztdz }tt|d||ztdz zt|tdz |zz }t|| tdz z}t|t||z dz dz z}||z|zS)Nrrr8r*)rjrkr~r@rTr rrr rr rrr rr) r.rrjrkrrrrrs r'rBzWishartDistribution.pdf^s,&$"3<  q ! a   #""A!j,788 0&(+A/00 0 ---a/!A$$6 E+&&''!ac!A$$h-:a!fa;P;P)PQ\**qb1g6Q1QUQY<<>2u}u$$r(NrrFr(r'rzrzHsz%IKK\K((X(''X' % % % % %r(rzczt|trt|}t|t||fS)a Creates a random variable with Wishart Distribution. The density of the said distribution can be found at [1]. Parameters ========== n: Positive Real number Represents degrees of freedom scale_matrix: Positive definite real square matrix Scale Matrix Returns ======= RandomSymbol Examples ======== >>> from sympy.stats import density, Wishart >>> from sympy import MatrixSymbol, symbols >>> n = symbols('n', positive=True) >>> W = Wishart('W', n, [[2, 1], [1, 2]]) >>> X = MatrixSymbol('X', 2, 2) >>> density(W)(X).doit() exp(Trace(Matrix([ [-1/3, 1/6], [ 1/6, -1/3]])*X))*Determinant(X)**(n/2 - 3/2)/(2**n*3**(n/2)*sqrt(pi)*gamma(n/2)*gamma(n/2 - 1/2)) >>> density(W)([[1, 0], [0, 1]]).doit() exp(-2/3)/(2**n*3**(n/2)*sqrt(pi)*gamma(n/2)*gamma(n/2 - 1/2)) References ========== .. [1] https://en.wikipedia.org/wiki/Wishart_distribution )r@rTr r[rz)r4rjrks r'Wishartrls<P,%%5&|44 f)A|+< = ==r(cZeZdZdZedZedZedZdZ dS)r{)rvrwrxc 2t|tst|jdt|tst|jdt|jdt|jd|jd}|jd}t|jd|kdt |dt |t|jd|kdt |dt |dS) Nr)Scale matrix 1 should be be square matrix)Scale matrix 2 should be be square matrixrr*"Scale matrix 1 should be of shape  x "Scale matrix 2 should be of shape )r@rrrrr~r)rvrwrxrjrs r'rVzMatrixNormalDistribution.checks:.,77 5 <?4 5 5 5.,77 5 <?4 5 5 5^-0   ^-0     !! $  !! $^)!,11!!ffffc!fff4. / / /^)!,11!!ffffc!fff4. / / / / /r(cV|jj\}}t||tjSr3rvr~rrrr.rjrs r'r5zMatrixNormalDistribution.set%#)1Aqw'''r(c|jjSr3rr-s r'rWz"MatrixNormalDistribution.dimension#))r(c|j|j|j}}}|j\}}t |t rt |}t |ttfstdt|zt|t||z zt|z||z z}tt| tdz }dt zt||zdz zt#|t|zzdz t#|t|zzdz } || z S)Nrr8)rvrwrxr~r@rTr rrr rr rrr rrr) r.rMUVrjrrnumdens r'rBzMatrixNormalDistribution.pdfs*&(;T=Pa1w1 a   #""A!j,788 0&(+A/00 0 9QU+++GAJJ6A>5<<-!$%%tq1vvax ;q>>1Q44#779KNNAaDD>> from sympy import MatrixSymbol >>> from sympy.stats import density, MatrixNormal >>> M = MatrixNormal('M', [[1, 2]], [1], [[1, 0], [0, 1]]) >>> X = MatrixSymbol('X', 1, 2) >>> density(M)(X).doit() 2*exp(-Trace((Matrix([ [-1], [-2]]) + X.T)*(Matrix([[-1, -2]]) + X))/2)/pi >>> density(M)([[3, 4]]).doit() 2*exp(-4)/pi References ========== .. [1] https://en.wikipedia.org/wiki/Matrix_normal_distribution )r@rTr r[r{)r4rvrwrxr,s r'rrsR/4((;)/::.$''9(88.$''9(88 ^^ KAQ)?)NyYZ]^Y^O_O_)_ _``FQJM"1$&& &r(NrrFr(r'rrszMIUU\U&((X(**X* & & & & &r(rct|trt|}t|trt|}t|trt|}||||f}t|t|S)a Creates a random variable with Matrix Gamma Distribution. The density of the said distribution can be found at [1]. Parameters ========== nu: Positive Real number degrees of freedom location_matrix: Positive definite real square matrix Location Matrix of shape ``n x p`` scale_matrix_1: Positive definite real square matrix Scale Matrix of shape ``p x p`` scale_matrix_2: Positive definite real square matrix Scale Matrix of shape ``n x n`` Returns ======= RandomSymbol Examples ======== >>> from sympy import MatrixSymbol,symbols >>> from sympy.stats import density, MatrixStudentT >>> v = symbols('v',positive=True) >>> M = MatrixStudentT('M', v, [[1, 2]], [[1, 0], [0, 1]], [1]) >>> X = MatrixSymbol('X', 1, 2) >>> density(M)(X) gamma(v/2 + 1)*Determinant((Matrix([[-1, -2]]) + X)*(Matrix([ [-1], [-2]]) + X.T) + Matrix([[1]]))**(-v/2 - 1)/(pi**1.0*gamma(v/2)*Determinant(Matrix([[1]]))**1.0*Determinant(Matrix([ [1, 0], [0, 1]]))**0.5) References ========== .. [1] https://en.wikipedia.org/wiki/Matrix_t-distribution )r@rTr r[r)r4rrvrwrxr,s r'MatrixStudentTr /sX/4((;)/::.$''9(88.$''9(88  @D f0$ 7 77r(N)2mathrsympy.core.basicrsympy.core.numbersrsympy.core.singletonr&sympy.functions.elementary.exponentialr'sympy.functions.special.gamma_functionsrsympy.core.sympifyr r sympy.matricesr r r rrrrrrsympy.stats.rvrrrrrrrsympy.externalrrr[r]rrrrrrrzrr{rrr rFr(r'rs""""""!!!!!!""""""666666>>>>>>00000000**********************KKKKKKKKKKKKKKKKKK(((((( )X)X)X)X)X6)X)X)XX#P#P#P#P#P#P#P#PLPPPPPPPP>&Q&Q&Q&Q&Q&Q&Q&QR    '''''~'''`#%#%#%#%#%0#%#%#%J-L-L-Ld"%"%"%"%"%,"%"%"%H*>*>*>^+++++1+++Z060606j.&.&.&.&.&!3.&.&.&d3838383838r(