a zMatrixPSpace.cCs |jdSNrr%r'r"r"r#r) r*cCst|j|jjSN)rsymbolr!setr'r"r"r#domain"szMatrixPSpace.domaincCst|j|jd|jd|S)N)rr-r&r'r"r"r#value&szMatrixPSpace.valuecCs|jhSr,)r2r'r"r"r#values*szMatrixPSpace.valuescGs4|t}t|dks t|ts(td|j|S)Nr$ztCurrently, no algorithm has been implemented to handle general expressions containing multiple matrix distributions.)Zatomsrlen isinstanceNotImplementedErrorr!pdf)r(exprr&Zrmsr"r"r#compute_density.s zMatrixPSpace.compute_densityr"scipyNcCs|j|jj|||diS)zu Internal sample method Returns dictionary mapping RandomMatrixSymbol to realization value. )libraryseed)r2r!sample)r(sizer;r<r"r"r#r=6szMatrixPSpace.sample)r"r:N) __name__ __module__ __qualname____doc__rpropertyr!r-r/r2r3r9r=r"r"r"r#rs     rcCsBttt|}||}|j||j}t|||d|d}|jS)Nrr$)listmaprcheck dimensionrr2)r-rr&distZdimZpspacer"r"r#rv?s  rIc@s&eZdZdZdddZeddZdS)SampleMatrixScipyz7Returns the sample from scipy of the given distributionNcCs||||Sr,) _sample_scipyrrHr>r<r"r"r#rJszSampleMatrixScipy.__new__c sddlmddl}fddfddd}ddd dd}|}|jj|vrXdS|dusjt|trz|jj |d }n|}||jj|t ||} | |||jj|S) zSample from SciPy.r)statsNcs jjt|jt|jt|dS)N)ZdfZscaler>)Zwishartrvsintnr scale_matrixfloatrHr> rand_stateZ scipy_statsr"r#r)Tsz1SampleMatrixScipy._sample_scipy..cs.jjt|jtt|jtt|jt||dS)N)meanrowcovcolcovr>Z random_state)Z matrix_normalrNrlocation_matrixrRscale_matrix_1scale_matrix_2rSrUr"r#r)Vs  WishartDistributionMatrixNormalDistributioncSs|jjSr,rQshaperHr"r"r#r)]r*cSs|jjSr,rYr`rar"r"r#r)^r*r<) r:rMnumpykeys __class__r?r5rOrandom default_rngrreshape) rrHr>r<rdZ scipy_rv_map sample_shape dist_listrTsampr"rUr#rKMs      zSampleMatrixScipy._sample_scipy)N)r?r@rArBr classmethodrKr"r"r"r#rJHs rJc@s&eZdZdZdddZeddZdS)SampleMatrixNumpyz7Returns the sample from numpy of the given distributionNcCs||||Sr,) _sample_numpyrLr"r"r#rrszSampleMatrixNumpy.__new__c Csi}i}|}|jj|vr dSddl}|dus:t|trJ|jj|d}n|}||jj|t||} | |||jj|S)zSample from NumPy.Nrrc) rerfr?rdr5rOrgrhrri) rrHr>r<Z numpy_rv_maprjrkrdrTrlr"r"r#rous zSampleMatrixNumpy._sample_numpy)N)r?r@rArBrrmror"r"r"r#rnns rnc@s&eZdZdZdddZeddZdS)SampleMatrixPymcz7Returns the sample from pymc3 of the given distributionNcCs||||Sr,) _sample_pymc3rLr"r"r#rszSampleMatrixPymc.__new__c sddlfddfddd}ddddd }|}|jj|vrLdSddl}|d |j>||jj|j t |d d |d d d d}Wdn1s0Y| |||jj|S)zSample from PyMC3.rNcs0jdt|jtt|jtt|jt|jjdS)NX)murWrXr`) MatrixNormalrrYrRrZr[r`rapymc3r"r#r)s    z0SampleMatrixPymc._sample_pymc3..csjdt|jt|jtdS)Nrr)nur)ZWishartBartlettrOrPrrQrRrarur"r#r)s)r^r]cSs|jjSr,r_rar"r"r#r)r*cSs|jjSr,rbrar"r"r#r)r*r\rvr$F)ZdrawsZchainsZ progressbarZ random_seedZreturn_inferencedataZcompute_convergence_checksrr) rvrerfr?logging getLoggersetLevelERRORZModelr=rri) rrHr>r<Z pymc3_rv_maprjrkrxsampsr"rur#rqs      <zSampleMatrixPymc._sample_pymc3)N)r?r@rArBrrmrqr"r"r"r#rps rp)r:rvrdc@s6eZdZdZddZeddZddZd d d Zd S)MatrixDistributionz1 Abstract class for Matrix Distribution. cGs dd|D}tj|g|RS)NcSs&g|]}t|trt|nt|qSr")r5rDr r ).0argr"r"r# sz.MatrixDistribution.__new__..)rr)rr&r"r"r#rszMatrixDistribution.__new__cGsdSr,r"r%r"r"r#rFszMatrixDistribution.checkcCst|trt|}||Sr,)r5rDr r7)r(r8r"r"r#__call__s zMatrixDistribution.__call__r"r:NcCshgd}||vr tdt|t|s4td|t||||}|durP|Std|jj|fdS)zo Internal sample method Returns dictionary mapping RandomSymbol to realization value. )r:rdrvz&Sampling from %s is not supported yet.zFailed to import %sNz4Sampling for %s is not currently implemented from %s)r6strrr_get_sample_class_matrixrvrfr?)r(r>r;r< librariesr|r"r"r#r=s  zMatrixDistribution.sample)r"r:N) r?r@rArBr staticmethodrFrr=r"r"r"r#r}s  r}c@s<eZdZdZeddZeddZeddZdd Z d S) MatrixGammaDistributionalphabetarQcCs>t|tst|jdt|jdt|jdt|jddS)N+The shape matrix must be positive definite.Should be square matrix#Shape parameter should be positive.z#Scale parameter should be positive.r5rris_positive_definite is_square is_positiverr"r"r#rFs     zMatrixGammaDistribution.checkcCs|jjd}t||tjSr+rQr`rrRealsr(kr"r"r#r.s zMatrixGammaDistribution.setcCs|jjSr,r_r'r"r"r#rGsz!MatrixGammaDistribution.dimensionc Cs|j|j|j}}}|jd}t|tr2t|}t|ttfsPt dt |t | ||}t t ||||t||}t|| }t||t|dd} ||| S)Nr4%s should be an isinstance of Matrix or MatrixSymbolr$r0)rrrQr`r5rDr rrrrr rr rr r) r(xrrrQp sigma_inv_xterm1term2term3r"r"r#r7s  "zMatrixGammaDistribution.pdfN r?r@rAZ _argnamesrrFrCr.rGr7r"r"r"r#rs   rcCs$t|trt|}t|t|||fS)a  Creates a random variable with Matrix Gamma Distribution. The density of the said distribution can be found at [1]. Parameters ========== alpha: Positive Real number Shape Parameter beta: Positive Real number Scale Parameter scale_matrix: Positive definite real square matrix Scale Matrix Returns ======= RandomSymbol Examples ======== >>> from sympy.stats import density, MatrixGamma >>> from sympy import MatrixSymbol, symbols >>> a, b = symbols('a b', positive=True) >>> M = MatrixGamma('M', a, b, [[2, 1], [1, 2]]) >>> X = MatrixSymbol('X', 2, 2) >>> density(M)(X).doit() exp(Trace(Matrix([ [-2/3, 1/3], [ 1/3, -2/3]])*X)/b)*Determinant(X)**(a - 3/2)/(3**a*sqrt(pi)*b**(2*a)*gamma(a)*gamma(a - 1/2)) >>> density(M)([[1, 0], [0, 1]]).doit() exp(-4/(3*b))/(3**a*sqrt(pi)*b**(2*a)*gamma(a)*gamma(a - 1/2)) References ========== .. [1] https://en.wikipedia.org/wiki/Matrix_gamma_distribution )r5rDr rIr)r-rrrQr"r"r# MatrixGammas+ rc@s<eZdZdZeddZeddZeddZdd Z d S) r]rPrQcCs2t|tst|jdt|jdt|jddS)Nrrrrrr"r"r#rFGs   zWishartDistribution.checkcCs|jjd}t||tjSr+rrr"r"r#r.Ps zWishartDistribution.setcCs|jjSr,r_r'r"r"r#rGUszWishartDistribution.dimensionc Cs|j|j}}|jd}t|tr*t|}t|ttfsHtdt |t | |t d}t t |d||t dt|t d|}t|| t d}t|t ||dd}|||S)Nrrr0r$)rPrQr`r5rDr rrrrr rrr rr ) r(rrPrQrrrrrr"r"r#r7Ys  2zWishartDistribution.pdfNrr"r"r"r#r]Cs   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 rIr])r-rPrQr"r"r#Wishartgs( rc@s<eZdZdZeddZeddZeddZdd Z d S) r^)rYrZr[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)r5rrrrr`r)rYrZr[rPrr"r"r#rFs        zMatrixNormalDistribution.checkcCs|jj\}}t||tjSr,rYr`rrrr(rPrr"r"r#r.s zMatrixNormalDistribution.setcCs|jjSr,rbr'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)rYrZr[r`r5rDr rrrrr rrr rrr ) r(rMUVrPrrnumZdenr"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() 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 )r5rDr rIr^)r-rYrZr[r&r"r"r#rts)    rtc@s<eZdZdZeddZeddZeddZdd Z d S) MatrixStudentTDistribution)rwrYrZr[cCst|tst|jdkdt|ts4t|jdkdt|jdkdt|jdkd|jd}|jd}t|jd|kdt|t|ft|jd|kdt|t|ft|jdkd dS) NFrrrrr$rrz#Degrees of freedom must be positive)r5rrrrr`rr)rwrYrZr[rPrr"r"r#rFs    z MatrixStudentTDistribution.checkcCs|jj\}}t||tjSr,rrr"r"r#r.s zMatrixStudentTDistribution.setcCs|jjSr,rbr'r"r"r#rGsz$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 rIr)r-rwrYrZr[r&r"r"r#MatrixStudentT*s,    rN)2Zsympy.core.basicrZsympy.core.mulrZsympy.core.numbersrZsympy.core.singletonrZ&sympy.functions.elementary.exponentialrZ'sympy.functions.special.gamma_functionsrZsympy.core.sympifyrr Zsympy.matricesr r r r rrrrrZsympy.stats.rvrrrrrrrZsympy.externalrrrIrJrnrprr}rrr]rr^rtrrr"r"r"r#s6      ,$ , && 0%2$/-52