<s> import itertools <EOL> from sympy . core . sympify import _sympify <EOL> from sympy . core . compatibility import default_sort_key <EOL> from sympy import Expr , Add , Mul , S <EOL> from sympy . core . evaluate import global_evaluate <EOL> from sympy . stats import variance , covariance <EOL> from sympy . stats . rv import RandomSymbol , probability , expectation <EOL> class Probability ( Expr ) : <EOL> """<STR_LIT>""" <EOL> def __new__ ( cls , prob , condition = None , ** kwargs ) : <EOL> prob = _sympify ( prob ) <EOL> if condition is None : <EOL> obj = Expr . __new__ ( cls , prob ) <EOL> else : <EOL> condition = _sympify ( condition ) <EOL> obj = Expr . __new__ ( cls , prob , condition ) <EOL> obj . _condition = condition <EOL> return obj <EOL> def doit ( self , ** kwargs ) : <EOL> return probability ( self . args [ <NUM_LIT:0> ] , given_condition = self . _condition , ** kwargs ) <EOL> class Expectation ( Expr ) : <EOL> """<STR_LIT>""" <EOL> def __new__ ( cls , expr , condition = None , ** kwargs ) : <EOL> expr = _sympify ( expr ) <EOL> if not kwargs . pop ( '<STR_LIT>' , global_evaluate [ <NUM_LIT:0> ] ) : <EOL> if condition is None : <EOL> obj = Expr . __new__ ( cls , expr ) <EOL> else : <EOL> condition = _sympify ( condition ) <EOL> obj = Expr . __new__ ( cls , expr , condition ) <EOL> obj . _condition = condition <EOL> return obj <EOL> if not expr . has ( RandomSymbol ) : <EOL> return expr <EOL> if condition is not None : <EOL> condition = _sympify ( condition ) <EOL> if isinstance ( expr , Add ) : <EOL> return Add ( * [ Expectation ( a , condition = condition ) for a in expr . args ] ) <EOL> elif isinstance ( expr , Mul ) : <EOL> rv = [ ] <EOL> nonrv = [ ] <EOL> for a in expr . args : <EOL> if isinstance ( a , RandomSymbol ) or a . has ( RandomSymbol ) : <EOL> rv . append ( a ) <EOL> else : <EOL> nonrv . append ( a ) <EOL> return Mul ( * nonrv ) * Expectation ( Mul ( * rv ) , condition = condition , evaluate = False ) <EOL> else : <EOL> if condition is None : <EOL> obj = Expr . __new__ ( cls , expr ) <EOL> else : <EOL> obj = Expr . __new__ ( cls , expr , condition ) <EOL> obj . _condition = condition <EOL> return obj <EOL> def doit ( self , ** kwargs ) : <EOL> return expectation ( self . args [ <NUM_LIT:0> ] , condition = self . _condition , ** kwargs ) <EOL> class Variance ( Expr ) : <EOL> """<STR_LIT>""" <EOL> def __new__ ( cls , arg , condition = None , ** kwargs ) : <EOL> arg = _sympify ( arg ) <EOL> if not kwargs . pop ( '<STR_LIT>' , global_evaluate [ <NUM_LIT:0> ] ) : <EOL> if condition is None : <EOL> obj = Expr . __new__ ( cls , arg ) <EOL> else : <EOL> condition = _sympify ( condition ) <EOL> obj = Expr . __new__ ( cls , arg , condition ) <EOL> obj . _condition = condition <EOL> return obj <EOL> if not arg . has ( RandomSymbol ) : <EOL> return S . Zero <EOL> if condition is not None : <EOL> condition = _sympify ( condition ) <EOL> if isinstance ( arg , RandomSymbol ) : <EOL> if condition is None : <EOL> obj = Expr . __new__ ( cls , arg ) <EOL> else : <EOL> obj = Expr . __new__ ( cls , arg , condition ) <EOL> obj . _condition = condition <EOL> return obj <EOL> elif isinstance ( arg , Add ) : <EOL> rv = [ ] <EOL> for a in arg . args : <EOL> if a . has ( RandomSymbol ) : <EOL> rv . append ( a ) <EOL> variances = Add ( * map ( lambda xv : Variance ( xv , condition ) , rv ) ) <EOL> map_to_covar = lambda x : <NUM_LIT:2> * Covariance ( * x , condition = condition ) <EOL> covariances = Add ( * map ( map_to_covar , itertools . combinations ( rv , <NUM_LIT:2> ) ) ) <EOL> return variances + covariances <EOL> elif isinstance ( arg , Mul ) : <EOL> nonrv = [ ] <EOL> rv = [ ] <EOL> for a in arg . args : <EOL> if a . has ( RandomSymbol ) : <EOL> rv . append ( a ) <EOL> else : <EOL> nonrv . append ( a ** <NUM_LIT:2> ) <EOL> if len ( rv ) == <NUM_LIT:0> : <EOL> return S . Zero <EOL> if condition is None : <EOL> obj = Expr . __new__ ( cls , Mul ( * rv ) ) <EOL> else : <EOL> obj = Expr . __new__ ( cls , Mul ( * rv ) , condition ) <EOL> obj . _condition = condition <EOL> return Mul ( * nonrv ) * obj <EOL> else : <EOL> return Variance ( arg , condition , evaluate = False ) <EOL> def doit ( self , ** kwargs ) : <EOL> return variance ( self . args [ <NUM_LIT:0> ] , self . _condition , ** kwargs ) <EOL> class Covariance ( Expr ) : <EOL> """<STR_LIT>""" <EOL> def __new__ ( cls , arg1 , arg2 , condition = None , ** kwargs ) : <EOL> arg1 = _sympify ( arg1 ) <EOL> arg2 = _sympify ( arg2 ) <EOL> if not kwargs . pop ( '<STR_LIT>' , global_evaluate [ <NUM_LIT:0> ] ) : <EOL> if condition is None : <EOL> obj = Expr . __new__ ( cls , arg1 , arg2 ) <EOL> else : <EOL> condition = _sympify ( condition ) <EOL> obj = Expr . __new__ ( cls , arg1 , arg2 , condition ) <EOL> obj . _condition = condition <EOL> return obj <EOL> if condition is not None : <EOL> condition = _sympify ( condition ) <EOL> if arg1 == arg2 : <EOL> return Variance ( arg1 , condition ) <EOL> if not arg1 . has ( RandomSymbol ) : <EOL> return S . Zero <EOL> if not arg2 . has ( RandomSymbol ) : <EOL> return S . Zero <EOL> arg1 , arg2 = sorted ( [ arg1 , arg2 ] , key = default_sort_key ) <EOL> if isinstance ( arg1 , RandomSymbol ) and isinstance ( arg2 , RandomSymbol ) : <EOL> return Expr . __new__ ( cls , arg1 , arg2 ) <EOL> coeff_rv_list1 = cls . _expand_single_argument ( arg1 . expand ( ) ) <EOL> coeff_rv_list2 = cls . _expand_single_argument ( arg2 . expand ( ) ) <EOL> addends = [ a * b * Covariance ( * sorted ( [ r1 , r2 ] , key = default_sort_key ) , evaluate = False ) <EOL> for ( a , r1 ) in coeff_rv_list1 for ( b , r2 ) in coeff_rv_list2 ] <EOL> return Add ( * addends ) <EOL> @ classmethod <EOL> def _expand_single_argument ( cls , expr ) : <EOL> if isinstance ( expr , RandomSymbol ) : <EOL> return [ ( S . One , expr ) ] <EOL> elif isinstance ( expr , Add ) : <EOL> outval = [ ] <EOL> for a in expr . args : <EOL> if isinstance ( a , Mul ) : <EOL> outval . append ( cls . _get_mul_nonrv_rv_tuple ( a ) ) <EOL> elif isinstance ( a , RandomSymbol ) : <EOL> outval . append ( ( S . One , a ) ) <EOL> return outval <EOL> elif isinstance ( expr , Mul ) : <EOL> return [ cls . _get_mul_nonrv_rv_tuple ( expr ) ] <EOL> elif expr . has ( RandomSymbol ) : <EOL> return [ ( S . One , expr ) ] <EOL> @ classmethod <EOL> def _get_mul_nonrv_rv_tuple ( cls , m ) : <EOL> rv = [ ] <EOL> nonrv = [ ] <EOL> for a in m . args : <EOL> if a . has ( RandomSymbol ) : <EOL> rv . append ( a ) <EOL> else : <EOL> nonrv . append ( a ) <EOL> return ( Mul ( * nonrv ) , Mul ( * rv ) ) <EOL> def doit ( self , ** kwargs ) : <EOL> return covariance ( self . args [ <NUM_LIT:0> ] , self . args [ <NUM_LIT:1> ] , self . _condition , ** kwargs ) </s>
