<s> """<STR_LIT>""" <EOL> from kameleon_mcmc . distribution . Distribution import Distribution , Sample <EOL> from kameleon_mcmc . tools . MatrixTools import MatrixTools <EOL> from numpy . lib . twodim_base import eye , diag <EOL> from numpy . linalg import cholesky , norm , eig <EOL> from numpy import array , shape , log , zeros , arange , mean <EOL> from numpy . random import randn <EOL> from scipy . constants . constants import pi <EOL> from scipy . linalg . basic import solve_triangular <EOL> from scipy . stats . distributions import chi2 <EOL> from numpy . linalg . linalg import LinAlgError <EOL> class Gaussian ( Distribution ) : <EOL> def __init__ ( self , mu = array ( [ <NUM_LIT:0> , <NUM_LIT:0> ] ) , Sigma = eye ( <NUM_LIT:2> ) , is_cholesky = False , ell = None ) : <EOL> Distribution . __init__ ( self , len ( Sigma ) ) <EOL> assert ( len ( shape ( mu ) ) == <NUM_LIT:1> ) <EOL> assert ( max ( shape ( Sigma ) ) == len ( mu ) ) <EOL> self . mu = mu <EOL> self . ell = ell <EOL> if is_cholesky : <EOL> self . L = Sigma <EOL> if ell == None : <EOL> assert ( shape ( Sigma ) [ <NUM_LIT:0> ] == shape ( Sigma ) [ <NUM_LIT:1> ] ) <EOL> else : <EOL> assert ( shape ( Sigma ) [ <NUM_LIT:1> ] == ell ) <EOL> else : <EOL> assert ( shape ( Sigma ) [ <NUM_LIT:0> ] == shape ( Sigma ) [ <NUM_LIT:1> ] ) <EOL> if ell is not None : <EOL> self . L , _ , _ = MatrixTools . low_rank_approx ( Sigma , ell ) <EOL> self . L = self . L . T <EOL> assert ( shape ( self . L ) [ <NUM_LIT:1> ] == ell ) <EOL> else : <EOL> try : <EOL> self . L = cholesky ( Sigma ) <EOL> except LinAlgError : <EOL> self . L = cholesky ( Sigma + eye ( len ( Sigma ) ) * <NUM_LIT> ) <EOL> def __str__ ( self ) : <EOL> s = self . __class__ . __name__ + "<STR_LIT>" <EOL> s += "<STR_LIT>" + str ( self . mu ) <EOL> s += "<STR_LIT>" + str ( self . L ) <EOL> s += "<STR_LIT:U+002CU+0020>" + Distribution . __str__ ( self ) <EOL> s += "<STR_LIT:]>" <EOL> return s <EOL> def sample ( self , n = <NUM_LIT:1> ) : <EOL> if self . ell is None : <EOL> V = randn ( self . dimension , n ) <EOL> else : <EOL> V = randn ( self . ell , n ) <EOL> return Sample ( self . L . dot ( V ) . T + self . mu ) <EOL> def log_pdf ( self , X ) : <EOL> assert ( len ( shape ( X ) ) == <NUM_LIT:2> ) <EOL> assert ( shape ( X ) [ <NUM_LIT:1> ] == self . dimension ) <EOL> log_determinant_part = - sum ( log ( diag ( self . L ) ) ) <EOL> quadratic_parts = zeros ( len ( X ) ) <EOL> for i in range ( len ( X ) ) : <EOL> x = X [ i ] - self . mu <EOL> y = solve_triangular ( self . L , x . T , lower = True ) <EOL> y = solve_triangular ( self . L . T , y , lower = False ) <EOL> quadratic_parts [ i ] = - <NUM_LIT:0.5> * x . dot ( y ) <EOL> const_part = - <NUM_LIT:0.5> * len ( self . L ) * log ( <NUM_LIT:2> * pi ) <EOL> return const_part + log_determinant_part + quadratic_parts <EOL> def log_pdf_at_quantile ( self , alphas ) : <EOL> """<STR_LIT>""" <EOL> chi2_instance = chi2 ( self . dimension ) <EOL> cuttoffs = chi2_instance . isf ( <NUM_LIT:1> - alphas ) <EOL> log_determinant_part = - sum ( log ( diag ( self . L ) ) ) <EOL> quadratic_part = - <NUM_LIT:0.5> * cuttoffs <EOL> const_part = - <NUM_LIT:0.5> * len ( self . L ) * log ( <NUM_LIT:2> * pi ) <EOL> return const_part + log_determinant_part + quadratic_part <EOL> def emp_quantiles ( self , X , quantiles = arange ( <NUM_LIT:0.1> , <NUM_LIT:1> , <NUM_LIT:0.1> ) ) : <EOL> chi2_instance = chi2 ( self . dimension ) <EOL> cutoffs = chi2_instance . isf ( <NUM_LIT:1> - quantiles ) <EOL> D , U = eig ( self . L . dot ( self . L . T ) ) <EOL> D = D ** ( - <NUM_LIT:0.5> ) <EOL> W = ( diag ( D ) . dot ( U . T ) . dot ( ( X - self . mu ) . T ) ) . T <EOL> norms_squared = array ( [ norm ( w ) ** <NUM_LIT:2> for w in W ] ) <EOL> results = zeros ( [ len ( quantiles ) ] ) <EOL> for jj in range ( <NUM_LIT:0> , len ( quantiles ) ) : <EOL> results [ jj ] = mean ( norms_squared < cutoffs [ jj ] ) <EOL> return results </s>
