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| from sympy.concrete.products import Product | |
| from sympy.core.numbers import pi | |
| from sympy.core.singleton import S | |
| from sympy.core.symbol import (Dummy, symbols) | |
| from sympy.functions.elementary.exponential import exp | |
| from sympy.functions.elementary.miscellaneous import sqrt | |
| from sympy.functions.special.gamma_functions import gamma | |
| from sympy.matrices import Determinant, Matrix, Trace, MatrixSymbol, MatrixSet | |
| from sympy.stats import density, sample | |
| from sympy.stats.matrix_distributions import (MatrixGammaDistribution, | |
| MatrixGamma, MatrixPSpace, Wishart, MatrixNormal, MatrixStudentT) | |
| from sympy.testing.pytest import raises, skip | |
| from sympy.external import import_module | |
| def test_MatrixPSpace(): | |
| M = MatrixGammaDistribution(1, 2, [[2, 1], [1, 2]]) | |
| MP = MatrixPSpace('M', M, 2, 2) | |
| assert MP.distribution == M | |
| raises(ValueError, lambda: MatrixPSpace('M', M, 1.2, 2)) | |
| def test_MatrixGamma(): | |
| M = MatrixGamma('M', 1, 2, [[1, 0], [0, 1]]) | |
| assert M.pspace.distribution.set == MatrixSet(2, 2, S.Reals) | |
| assert isinstance(density(M), MatrixGammaDistribution) | |
| X = MatrixSymbol('X', 2, 2) | |
| num = exp(Trace(Matrix([[-S(1)/2, 0], [0, -S(1)/2]])*X)) | |
| assert density(M)(X).doit() == num/(4*pi*sqrt(Determinant(X))) | |
| assert density(M)([[2, 1], [1, 2]]).doit() == sqrt(3)*exp(-2)/(12*pi) | |
| X = MatrixSymbol('X', 1, 2) | |
| Y = MatrixSymbol('Y', 1, 2) | |
| assert density(M)([X, Y]).doit() == exp(-X[0, 0]/2 - Y[0, 1]/2)/(4*pi*sqrt( | |
| X[0, 0]*Y[0, 1] - X[0, 1]*Y[0, 0])) | |
| # symbolic | |
| a, b = symbols('a b', positive=True) | |
| d = symbols('d', positive=True, integer=True) | |
| Y = MatrixSymbol('Y', d, d) | |
| Z = MatrixSymbol('Z', 2, 2) | |
| SM = MatrixSymbol('SM', d, d) | |
| M2 = MatrixGamma('M2', a, b, SM) | |
| M3 = MatrixGamma('M3', 2, 3, [[2, 1], [1, 2]]) | |
| k = Dummy('k') | |
| exprd = pi**(-d*(d - 1)/4)*b**(-a*d)*exp(Trace((-1/b)*SM**(-1)*Y) | |
| )*Determinant(SM)**(-a)*Determinant(Y)**(a - d/2 - S(1)/2)/Product( | |
| gamma(-k/2 + a + S(1)/2), (k, 1, d)) | |
| assert density(M2)(Y).dummy_eq(exprd) | |
| raises(NotImplementedError, lambda: density(M3 + M)(Z)) | |
| raises(ValueError, lambda: density(M)(1)) | |
| raises(ValueError, lambda: MatrixGamma('M', -1, 2, [[1, 0], [0, 1]])) | |
| raises(ValueError, lambda: MatrixGamma('M', -1, -2, [[1, 0], [0, 1]])) | |
| raises(ValueError, lambda: MatrixGamma('M', -1, 2, [[1, 0], [2, 1]])) | |
| raises(ValueError, lambda: MatrixGamma('M', -1, 2, [[1, 0], [0]])) | |
| def test_Wishart(): | |
| W = Wishart('W', 5, [[1, 0], [0, 1]]) | |
| assert W.pspace.distribution.set == MatrixSet(2, 2, S.Reals) | |
| X = MatrixSymbol('X', 2, 2) | |
| term1 = exp(Trace(Matrix([[-S(1)/2, 0], [0, -S(1)/2]])*X)) | |
| assert density(W)(X).doit() == term1 * Determinant(X)/(24*pi) | |
| assert density(W)([[2, 1], [1, 2]]).doit() == exp(-2)/(8*pi) | |
| n = symbols('n', positive=True) | |
| d = symbols('d', positive=True, integer=True) | |
| Y = MatrixSymbol('Y', d, d) | |
| SM = MatrixSymbol('SM', d, d) | |
| W = Wishart('W', n, SM) | |
| k = Dummy('k') | |
| exprd = 2**(-d*n/2)*pi**(-d*(d - 1)/4)*exp(Trace(-(S(1)/2)*SM**(-1)*Y) | |
| )*Determinant(SM)**(-n/2)*Determinant(Y)**( | |
| -d/2 + n/2 - S(1)/2)/Product(gamma(-k/2 + n/2 + S(1)/2), (k, 1, d)) | |
| assert density(W)(Y).dummy_eq(exprd) | |
| raises(ValueError, lambda: density(W)(1)) | |
| raises(ValueError, lambda: Wishart('W', -1, [[1, 0], [0, 1]])) | |
| raises(ValueError, lambda: Wishart('W', -1, [[1, 0], [2, 1]])) | |
| raises(ValueError, lambda: Wishart('W', 2, [[1, 0], [0]])) | |
| def test_MatrixNormal(): | |
| M = MatrixNormal('M', [[5, 6]], [4], [[2, 1], [1, 2]]) | |
| assert M.pspace.distribution.set == MatrixSet(1, 2, S.Reals) | |
| X = MatrixSymbol('X', 1, 2) | |
| term1 = exp(-Trace(Matrix([[ S(2)/3, -S(1)/3], [-S(1)/3, S(2)/3]])*( | |
| Matrix([[-5], [-6]]) + X.T)*Matrix([[S(1)/4]])*(Matrix([[-5, -6]]) + X))/2) | |
| assert density(M)(X).doit() == (sqrt(3)) * term1/(24*pi) | |
| assert density(M)([[7, 8]]).doit() == sqrt(3)*exp(-S(1)/3)/(24*pi) | |
| d, n = symbols('d n', positive=True, integer=True) | |
| SM2 = MatrixSymbol('SM2', d, d) | |
| SM1 = MatrixSymbol('SM1', n, n) | |
| LM = MatrixSymbol('LM', n, d) | |
| Y = MatrixSymbol('Y', n, d) | |
| M = MatrixNormal('M', LM, SM1, SM2) | |
| exprd = (2*pi)**(-d*n/2)*exp(-Trace(SM2**(-1)*(-LM.T + Y.T)*SM1**(-1)*(-LM + Y) | |
| )/2)*Determinant(SM1)**(-d/2)*Determinant(SM2)**(-n/2) | |
| assert density(M)(Y).doit() == exprd | |
| raises(ValueError, lambda: density(M)(1)) | |
| raises(ValueError, lambda: MatrixNormal('M', [1, 2], [[1, 0], [0, 1]], [[1, 0], [2, 1]])) | |
| raises(ValueError, lambda: MatrixNormal('M', [1, 2], [[1, 0], [2, 1]], [[1, 0], [0, 1]])) | |
| raises(ValueError, lambda: MatrixNormal('M', [1, 2], [[1, 0], [0, 1]], [[1, 0], [0, 1]])) | |
| raises(ValueError, lambda: MatrixNormal('M', [1, 2], [[1, 0], [2]], [[1, 0], [0, 1]])) | |
| raises(ValueError, lambda: MatrixNormal('M', [1, 2], [[1, 0], [2, 1]], [[1, 0], [0]])) | |
| raises(ValueError, lambda: MatrixNormal('M', [[1, 2]], [[1, 0], [0, 1]], [[1, 0]])) | |
| raises(ValueError, lambda: MatrixNormal('M', [[1, 2]], [1], [[1, 0]])) | |
| def test_MatrixStudentT(): | |
| M = MatrixStudentT('M', 2, [[5, 6]], [[2, 1], [1, 2]], [4]) | |
| assert M.pspace.distribution.set == MatrixSet(1, 2, S.Reals) | |
| X = MatrixSymbol('X', 1, 2) | |
| D = pi ** (-1.0) * Determinant(Matrix([[4]])) ** (-1.0) * Determinant(Matrix([[2, 1], [1, 2]])) \ | |
| ** (-0.5) / Determinant(Matrix([[S(1) / 4]]) * (Matrix([[-5, -6]]) + X) | |
| * Matrix([[S(2) / 3, -S(1) / 3], [-S(1) / 3, S(2) / 3]]) * ( | |
| Matrix([[-5], [-6]]) + X.T) + Matrix([[1]])) ** 2 | |
| assert density(M)(X) == D | |
| v = symbols('v', positive=True) | |
| n, p = 1, 2 | |
| Omega = MatrixSymbol('Omega', p, p) | |
| Sigma = MatrixSymbol('Sigma', n, n) | |
| Location = MatrixSymbol('Location', n, p) | |
| Y = MatrixSymbol('Y', n, p) | |
| M = MatrixStudentT('M', v, Location, Omega, Sigma) | |
| exprd = gamma(v/2 + 1)*Determinant(Matrix([[1]]) + Sigma**(-1)*(-Location + Y)*Omega**(-1)*(-Location.T + Y.T))**(-v/2 - 1) / \ | |
| (pi*gamma(v/2)*sqrt(Determinant(Omega))*Determinant(Sigma)) | |
| assert density(M)(Y) == exprd | |
| raises(ValueError, lambda: density(M)(1)) | |
| raises(ValueError, lambda: MatrixStudentT('M', 1, [1, 2], [[1, 0], [0, 1]], [[1, 0], [2, 1]])) | |
| raises(ValueError, lambda: MatrixStudentT('M', 1, [1, 2], [[1, 0], [2, 1]], [[1, 0], [0, 1]])) | |
| raises(ValueError, lambda: MatrixStudentT('M', 1, [1, 2], [[1, 0], [0, 1]], [[1, 0], [0, 1]])) | |
| raises(ValueError, lambda: MatrixStudentT('M', 1, [1, 2], [[1, 0], [2]], [[1, 0], [0, 1]])) | |
| raises(ValueError, lambda: MatrixStudentT('M', 1, [1, 2], [[1, 0], [2, 1]], [[1], [2]])) | |
| raises(ValueError, lambda: MatrixStudentT('M', 1, [[1, 2]], [[1, 0], [0, 1]], [[1, 0]])) | |
| raises(ValueError, lambda: MatrixStudentT('M', 1, [[1, 2]], [1], [[1, 0]])) | |
| raises(ValueError, lambda: MatrixStudentT('M', -1, [1, 2], [[1, 0], [0, 1]], [4])) | |
| def test_sample_scipy(): | |
| distribs_scipy = [ | |
| MatrixNormal('M', [[5, 6]], [4], [[2, 1], [1, 2]]), | |
| Wishart('W', 5, [[1, 0], [0, 1]]) | |
| ] | |
| size = 5 | |
| scipy = import_module('scipy') | |
| if not scipy: | |
| skip('Scipy not installed. Abort tests for _sample_scipy.') | |
| else: | |
| for X in distribs_scipy: | |
| samps = sample(X, size=size) | |
| for sam in samps: | |
| assert Matrix(sam) in X.pspace.distribution.set | |
| M = MatrixGamma('M', 1, 2, [[1, 0], [0, 1]]) | |
| raises(NotImplementedError, lambda: sample(M, size=3)) | |
| def test_sample_pymc(): | |
| distribs_pymc = [ | |
| MatrixNormal('M', [[5, 6], [3, 4]], [[1, 0], [0, 1]], [[2, 1], [1, 2]]), | |
| Wishart('W', 7, [[2, 1], [1, 2]]) | |
| ] | |
| size = 3 | |
| pymc = import_module('pymc') | |
| if not pymc: | |
| skip('PyMC is not installed. Abort tests for _sample_pymc.') | |
| else: | |
| for X in distribs_pymc: | |
| samps = sample(X, size=size, library='pymc') | |
| for sam in samps: | |
| assert Matrix(sam) in X.pspace.distribution.set | |
| M = MatrixGamma('M', 1, 2, [[1, 0], [0, 1]]) | |
| raises(NotImplementedError, lambda: sample(M, size=3)) | |
| def test_sample_seed(): | |
| X = MatrixNormal('M', [[5, 6], [3, 4]], [[1, 0], [0, 1]], [[2, 1], [1, 2]]) | |
| libraries = ['scipy', 'numpy', 'pymc'] | |
| for lib in libraries: | |
| try: | |
| imported_lib = import_module(lib) | |
| if imported_lib: | |
| s0, s1, s2 = [], [], [] | |
| s0 = sample(X, size=10, library=lib, seed=0) | |
| s1 = sample(X, size=10, library=lib, seed=0) | |
| s2 = sample(X, size=10, library=lib, seed=1) | |
| for i in range(10): | |
| assert (s0[i] == s1[i]).all() | |
| assert (s1[i] != s2[i]).all() | |
| except NotImplementedError: | |
| continue | |