U ZʹjU@szddlmZddlmZddlmZddlmZddlm Z ddl m Z ddl m Z mZddlmZmZmZmZmZmZmZmZmZdd lmZmZmZmZmZmZm Z dd l!m"Z"Gd d d eZ#d dZ$GdddZ%GdddZ&GdddZ'e%e'e'e&dZ(Gddde eZ)Gddde)Z*ddZ+Gddde)Z,ddZ-Gd d!d!e)Z.d"d#Z/Gd$d%d%e)Z0d&d'Z1d(S)))prod)Basic)pi)S)exp) multigamma)sympify_sympify) ImmutableMatrixInverseTrace Determinant MatrixSymbol MatrixBase Transpose MatrixSet matrix2numpy) _value_checkRandomMatrixSymbolNamedArgsMixinPSpace_symbol_converter MatrixDomain Distribution) import_modulec@sfeZdZdZddZeddZeddZeddZed d Z ed d Z d dZ dddZ dS) MatrixPSpacezD Represents probability space for Matrix Distributions. cCs@t|}t|t|}}|jr&|js.tdt|||||S)NzDimensions should be integers)rr is_integer ValueErrorr__new__)clssym distributionZdim_nZdim_mr"_/var/www/html/bwave/python/venv/lib/python3.8/site-packages/sympy/stats/matrix_distributions.pyrs  zMatrixPSpace.__new__cCs |jdS)Nargsselfr"r"r# zMatrixPSpace.cCs 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dd}|}|jj|krXdS|dksjt|trz|jj |d }n|}||jj|t ||} | |||jj|S) zSample from SciPy.r)statsNcs jjt|jt|jt|dS)N)Zdfscaler>)Zwishartrvsintnr scale_matrixfloatrHr> rand_stateZ scipy_statsr"r#r)Us z1SampleMatrixScipy._sample_scipy..cs.jjt|jtt|jtt|jt||dS)N)Zmeanrowcovcolcovr>Z random_state)Z matrix_normalrPrlocation_matrixrTscale_matrix_1scale_matrix_2rUrWr"r#r)Ws    WishartDistributionMatrixNormalDistributioncSs|jjSr,rSshaperHr"r"r#r)^r*cSs|jjSr,rZrarbr"r"r#r)_r*r<) r:rNnumpykeys __class__r?r5rQrandom default_rngrreshape) rrHr>r<reZ scipy_rv_map sample_shape dist_listrVsampr"rWr#rLNs      zSampleMatrixScipy._sample_scipy)N)r?r@rArBr classmethodrLr"r"r"r#rKIs rKc@s&eZdZdZdddZeddZdS)SampleMatrixNumpyz7Returns the sample from numpy of the given distributionNcCs||||Sr,) _sample_numpyrMr"r"r#rsszSampleMatrixNumpy.__new__c Csi}i}|}|jj|kr dSddl}|dks:t|trJ|jj|d}n|}||jj|t||} | |||jj|S)zSample from NumPy.Nrrd) rfrgr?rer5rQrhrirrj) rrHr>r<Z numpy_rv_maprkrlrerVrmr"r"r#rpvs 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sz.MatrixDistribution.__new__..)rr)rr&r"r"r#rszMatrixDistribution.__new__cGsdSr,r"r%r"r"r#rFszMatrixDistribution.checkcCst|trt|}||Sr,)r5rDr r7)r(r8r"r"r#__call__s zMatrixDistribution.__call__r"r:NcCslddddg}||kr$tdt|t|s8td|t||||}|dk rT|Std|jj|fdS) zo Internal sample method Returns dictionary mapping RandomSymbol to realization value. r:rer{rwz&Sampling from %s is not supported yet.zFailed to import %sNz4Sampling for %s is not currently implemented from %s)r6strrr_get_sample_class_matrixrvrgr?)r(r>r;r< librariesrr"r"r#r=s   zMatrixDistribution.sample)r"r:N) r?r@rArBr staticmethodrFrr=r"r"r"r#rs  rc@s<eZdZdZeddZeddZeddZdd Z d S) MatrixGammaDistributionalphabetarScCs>t|tst|jdt|jdt|jdt|jddS)N+The shape matrix must be positive definite.Should be square matrix#Shape parameter should be positive.z#Scale parameter should be positive.r5rris_positive_definite is_square is_positiverr"r"r#rFs     zMatrixGammaDistribution.checkcCs|jjd}t||tjSr+rSrarrRealsr(kr"r"r#r.s zMatrixGammaDistribution.setcCs|jjSr,r`r'r"r"r#rGsz!MatrixGammaDistribution.dimensionc Cs|j|j|j}}}|jd}t|tr2t|}t|ttfsPt dt |t | ||}t t ||||t||}t|| }t||t|dd} ||| S)Nr4%s should be an isinstance of Matrix or MatrixSymbolr$r0)rrrSrar5rDr rrrrr rr rr r) r(xrrrSp sigma_inv_xterm1term2term3r"r"r#r7s  "zMatrixGammaDistribution.pdfN r?r@rAZ _argnamesrrFrCr.rGr7r"r"r"r#rs   rcCs$t|trt|}t|t|||fS)a  Creates a random variable with Matrix Gamma Distribution. The density of the said distribution can be found at [1]. Parameters ========== alpha: Positive Real number Shape Parameter beta: Positive Real number Scale Parameter scale_matrix: Positive definite real square matrix Scale Matrix Returns ======= RandomSymbol Examples ======== >>> from sympy.stats import density, MatrixGamma >>> from sympy import MatrixSymbol, symbols >>> a, b = symbols('a b', positive=True) >>> M = MatrixGamma('M', a, b, [[2, 1], [1, 2]]) >>> X = MatrixSymbol('X', 2, 2) >>> density(M)(X).doit() exp(Trace(Matrix([ [-2/3, 1/3], [ 1/3, -2/3]])*X)/b)*Determinant(X)**(a - 3/2)/(3**a*sqrt(pi)*b**(2*a)*gamma(a)*gamma(a - 1/2)) >>> density(M)([[1, 0], [0, 1]]).doit() exp(-4/(3*b))/(3**a*sqrt(pi)*b**(2*a)*gamma(a)*gamma(a - 1/2)) References ========== .. [1] https://en.wikipedia.org/wiki/Matrix_gamma_distribution )r5rDr rJr)r-rrrSr"r"r# MatrixGammas+ rc@s<eZdZdZeddZeddZeddZdd Z d S) r^rRrScCs2t|tst|jdt|jdt|jddS)Nrrrrrr"r"r#rFLs   zWishartDistribution.checkcCs|jjd}t||tjSr+rrr"r"r#r.Us zWishartDistribution.setcCs|jjSr,r`r'r"r"r#rGZszWishartDistribution.dimensionc Cs|j|j}}|jd}t|tr*t|}t|ttfsHtdt |t | |t d}t t |d||t dt|t d|}t|| t d}t|t ||dd}|||S)Nrrr0r$)rRrSrar5rDr rrrrr rrr rr ) r(rrRrSrrrrrr"r"r#r7^s  2zWishartDistribution.pdfNrr"r"r"r#r^Hs   r^cCs"t|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 )r5rDr rJr^)r-rRrSr"r"r#Wishartls( rc@s<eZdZdZeddZeddZeddZdd Z d S) r_)rZr[r\cCst|tst|jdt|ts,t|jdt|jdt|jd|jd}|jd}t|jd|kdt|t|ft|jd|kdt|t|fdS)Nr)Scale matrix 1 should be be square matrix)Scale matrix 2 should be be square matrixrr$)Scale matrix 1 should be of shape %s x %s)Scale matrix 2 should be of shape %s x %s)r5rrrrrar)rZr[r\rRrr"r"r#rFs        zMatrixNormalDistribution.checkcCs|jj\}}t||tjSr,rZrarrrr(rRrr"r"r#r.s zMatrixNormalDistribution.setcCs|jjSr,rcr'r"r"r#rGsz"MatrixNormalDistribution.dimensionc Cs|j|j|j}}}|j\}}t|tr2t|}t|ttfsPt dt |t |t ||t |||}t t| td}dtt||dt|t|dt|t|d} || S)Nrr0)rZr[r\rar5rDr rrrrr rrr rrr ) r(rMUVrRrrnumZdenr"r"r#r7s  $@zMatrixNormalDistribution.pdfNrr"r"r"r#r_s   r_cCsLt|trt|}t|tr$t|}t|tr6t|}|||f}t|t|S)a Creates a random variable with Matrix Normal Distribution. The density of the said distribution can be found at [1]. Parameters ========== location_matrix: Real ``n x p`` matrix Represents degrees of freedom scale_matrix_1: Positive definite matrix Scale Matrix of shape ``n x n`` scale_matrix_2: Positive definite matrix Scale Matrix of shape ``p x p`` Returns ======= RandomSymbol Examples ======== >>> 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() exp(-Trace((Matrix([ [-1], [-2]]) + X.T)*(Matrix([[-1, -2]]) + X))/2)/(2*pi) >>> density(M)([[3, 4]]).doit() exp(-4)/(2*pi) References ========== .. [1] https://en.wikipedia.org/wiki/Matrix_normal_distribution )r5rDr rJr_)r-rZr[r\r&r"r"r#rus)    ruc@s<eZdZdZeddZeddZeddZdd Z d S) MatrixStudentTDistribution)rxrZr[r\cCst|tst|jdkdt|ts4t|jdkdt|jdkdt|jdkd|jd}|jd}t|jd|kdt|t|ft|jd|kdt|t|ft|jdkd dS) NFrrrrr$rrz#Degrees of freedom must be positive)r5rrrrrarr)rxrZr[r\rRrr"r"r#rFs    z MatrixStudentTDistribution.checkcCs|jj\}}t||tjSr,rrr"r"r#r.s zMatrixStudentTDistribution.setcCs|jjSr,rcr'r"r"r#rGsz$MatrixStudentTDistribution.dimensionc Csddlm}t|trt|}t|ttfs>> 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 )r5rDr rJr)r-rxrZr[r\r&r"r"r#MatrixStudentT/s,    rN)2mathrZsympy.core.basicrZsympy.core.numbersrZsympy.core.singletonrZ&sympy.functions.elementary.exponentialrZ'sympy.functions.special.gamma_functionsrZsympy.core.sympifyrr Zsympy.matricesr r r r rrrrrZsympy.stats.rvrrrrrrrZsympy.externalrrrJrKrorqrrrrr^rr_rurrr"r"r"r#s8      ,$ , &) 0%2$/-52