o GZhU@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|jstdt|||||S)NzDimensions should be integers)rr is_integer ValueErrorr__new__)clssym distributionZdim_nZdim_mr"O/var/www/auris/lib/python3.10/site-packages/sympy/stats/matrix_distributions.pyrs  zMatrixPSpace.__new__cC |jdS)Nargsselfr"r"r#  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z.MatrixDistribution.__new__..)rr)rr'r"r"r#rszMatrixDistribution.__new__cGsdSr-r"r&r"r"r#rIszMatrixDistribution.checkcCst|tr t|}||Sr-)r7rGr r9)r)r:r"r"r#__call__s  zMatrixDistribution.__call__r"r<NcCsdgd}||vrtdt|t|std|t||||}|dur(|Std|jj|f)zo Internal sample method Returns dictionary mapping RandomSymbol to realization value. )r<rnrrz&Sampling from %s is not supported yet.zFailed to import %sNz4Sampling for %s is not currently implemented from %s)r8strrr_get_sample_class_matrixrvrprB)r)r@r=r>Z librariesrr"r"r#r?s  zMatrixDistribution.samplerA) rBrCrDrEr staticmethodrIrr?r"r"r"r#rs rc@<eZdZdZeddZeddZeddZdd Z d S) MatrixGammaDistributionalphabetarYcCs>t|ts t|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.r7rris_positive_definite is_square is_positiverr"r"r#rIs    zMatrixGammaDistribution.checkcC|jjd}t||tjSr,rYrirrRealsr)kr"r"r#r/ 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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 )r7rGr rMr)r.rrrYr"r"r# MatrixGammas +rc@r) rerXrYcCs2t|ts t|jdt|jdt|jddS)Nrrrrrr"r"r#rILs   zWishartDistribution.checkcCrr,rrr"r"r#r/UrzWishartDistribution.setcCrgr-rhr(r"r"r#rJZr5zWishartDistribution.dimensionc Cs|j|j}}|jd}t|trt|}t|ttfs$tdt |t | |t d}t t |d||t dt|t d|}t|| t d}t|t ||dd}|||S)Nrrr1r%)rXrYrir7rGr rrrrr rrr rr ) r)rrXrYrrrrrr"r"r#r9^s  2 zWishartDistribution.pdfNrr"r"r"r#reHs    recCs"t|tr t|}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 )r7rGr rMre)r.rXrYr"r"r#Wishartls (rc@r) rf)rarbrccCst|ts t|jdt|tst|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)r7rrrrrir)rarbrcrXrr"r"r#rIs         zMatrixNormalDistribution.checkcC|jj\}}t||tjSr-rarirrrr)rXrr"r"r#r/rzMatrixNormalDistribution.setcCrgr-rlr(r"r"r#rJr5z"MatrixNormalDistribution.dimensionc Cs|j|j|j}}}|j\}}t|trt|}t|ttfs(t dt |t |t ||t |||}t t| td}dtt||dt|t|dt|t|d} || S)Nrr1)rarbrcrir7rGr rrrrr rrr rrr ) r)rMUVrXrrnumZdenr"r"r#r9s  $@zMatrixNormalDistribution.pdfNrr"r"r"r#rfs    rfcCsLt|tr t|}t|trt|}t|trt|}|||f}t|t|S)a Creates a random variable with Matrix Normal Distribution. The density of the said distribution can be found at [1]. Parameters ========== location_matrix: Real ``n x p`` matrix Represents degrees of freedom scale_matrix_1: Positive definite matrix Scale Matrix of shape ``n x n`` scale_matrix_2: Positive definite matrix Scale Matrix of shape ``p x p`` Returns ======= RandomSymbol Examples ======== >>> from sympy import MatrixSymbol >>> from sympy.stats import density, MatrixNormal >>> M = MatrixNormal('M', [[1, 2]], [1], [[1, 0], [0, 1]]) >>> X = MatrixSymbol('X', 1, 2) >>> density(M)(X).doit() exp(-Trace((Matrix([ [-1], [-2]]) + X.T)*(Matrix([[-1, -2]]) + X))/2)/(2*pi) >>> density(M)([[3, 4]]).doit() exp(-4)/(2*pi) References ========== .. [1] https://en.wikipedia.org/wiki/Matrix_normal_distribution )r7rGr rMrf)r.rarbrcr'r"r"r#r~s )    r~c@r) MatrixStudentTDistribution)rrarbrccCst|ts t|jdkdt|tst|jdkdt|jdkdt|jdkd|jd}|jd}t|jd|kdt|t|ft|jd|kdt|t|ft|jdkd dS) NFrrrrr%rrz#Degrees of freedom must be positive)r7rrrrrirr)rrarbrcrXrr"r"r#rIs    z MatrixStudentTDistribution.checkcCrr-rrr"r"r#r/rzMatrixStudentTDistribution.setcCrgr-rlr(r"r"r#rJr5z$MatrixStudentTDistribution.dimensionc Csddlm}t|trt|}t|ttfstdt||j |j |j |j f\}}}}|j \}}t|||dd|t|| dt|| dt||dt||dd|} | t||t|||t|t|||||d dS)Nr)eyerr%r1)Zsympy.matrices.denserr7rGr rrrrrrarbrcrirr rr r) r)rrrrOmegaSigmarXrKr"r"r#r9s   <$0zMatrixStudentTDistribution.pdfNrr"r"r"r#rs    rcCsNt|tr t|}t|trt|}t|trt|}||||f}t|t|S)a Creates a random variable with Matrix Gamma Distribution. The density of the said distribution can be found at [1]. Parameters ========== nu: Positive Real number degrees of freedom location_matrix: Positive definite real square matrix Location Matrix of shape ``n x p`` scale_matrix_1: Positive definite real square matrix Scale Matrix of shape ``p x p`` scale_matrix_2: Positive definite real square matrix Scale Matrix of shape ``n x n`` Returns ======= RandomSymbol Examples ======== >>> from sympy import MatrixSymbol,symbols >>> from sympy.stats import density, MatrixStudentT >>> v = symbols('v',positive=True) >>> M = MatrixStudentT('M', v, [[1, 2]], [[1, 0], [0, 1]], [1]) >>> X = MatrixSymbol('X', 1, 2) >>> density(M)(X) gamma(v/2 + 1)*Determinant((Matrix([[-1, -2]]) + X)*(Matrix([ [-1], [-2]]) + X.T) + Matrix([[1]]))**(-v/2 - 1)/(pi**1.0*gamma(v/2)*Determinant(Matrix([[1]]))**1.0*Determinant(Matrix([ [1, 0], [0, 1]]))**0.5) References ========== .. [1] https://en.wikipedia.org/wiki/Matrix_t-distribution )r7rGr rMr)r.rrarbrcr'r"r"r#MatrixStudentT/s ,    rN)2mathrZsympy.core.basicrZsympy.core.numbersrZsympy.core.singletonrZ&sympy.functions.elementary.exponentialrZ'sympy.functions.special.gamma_functionsrZsympy.core.sympifyrr Zsympy.matricesr r r r rrrrrZsympy.stats.rvrrrrrrrZsympy.externalrrrMrOrxrzrrrrrerrfr~rrr"r"r"r#s:     ,$ , &) 0%2$/-5 2