Module ImportFrom alias alias alias Import alias Import alias identifier Import alias ImportFrom alias ImportFrom alias alias alias ImportFrom alias ImportFrom alias Assign NameStore ListLoad Str Str Str Str Str Str Str Str Assign NameStore Call AttributeLoad NameLoad attr BinOpMult Num AttributeLoad NameLoad attr Assign NameStore Call AttributeLoad NameLoad attr Num Assign NameStore Call AttributeLoad NameLoad attr AttributeLoad NameLoad attr Assign NameStore Str FunctionDef arguments args NameParam defaults body Expr Str Assign NameStore Call AttributeLoad NameLoad attr If CompareEq AttributeLoad NameLoad attr Num body Assign NameStore SubscriptLoad NameLoad Index TupleLoad Return NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam defaults NameLoad NameLoad body Expr Str If CompareIsNot NameLoad NameLoad body Assign NameStore NameLoad If CompareIn NameLoad ListLoad NameLoad Num body Assign NameStore Call AttributeLoad AttributeLoad AttributeLoad NameLoad attr attr attr Assign NameStore Dict Str Str Num Num Assign NameStore BinOpMult SubscriptLoad NameLoad Index NameLoad AttributeLoad Call AttributeLoad NameLoad attr NameLoad attr Assign NameStore BinOpMult NameLoad Call AttributeLoad NameLoad attr Call NameLoad NameLoad Return NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults Num body Expr Str Return Call AttributeLoad NameLoad attr ListComp IfExp CompareLtE Call NameLoad NameLoad NameLoad Num BinOpDiv Num NameLoad comprehension NameStore NameLoad keyword NameLoad decorator_list ClassDef bases NameLoad body Expr Str FunctionDef arguments args NameParam NameParam NameParam NameParam NameParam NameParam NameParam defaults NameLoad NameLoad NameLoad NameLoad NameLoad body Assign TupleStore NameStore NameStore Call AttributeLoad AttributeLoad NameLoad attr attr NameLoad keyword NameLoad keyword NameLoad Assign NameStore Call NameLoad NameLoad NameLoad NameLoad If CompareLt Call AttributeLoad NameLoad attr NameLoad UnaryOpUSub NameLoad body Raise Call NameLoad Str Assign NameStore SubscriptLoad NameLoad Index CompareGt NameLoad NameLoad If BoolOpAnd CompareLt Call NameLoad NameLoad Call NameLoad NameLoad UnaryOpNot NameLoad body Raise Call AttributeLoad AttributeLoad NameLoad attr attr Str Assign NameStore Call NameLoad NameLoad NameLoad Assign NameStore Call AttributeLoad NameLoad attr NameLoad Call AttributeLoad NameLoad attr NameLoad Assign AttributeStore NameLoad attr Call NameLoad NameLoad Assign AttributeStore NameLoad attr NameLoad Assign AttributeStore NameLoad attr Call AttributeLoad NameLoad attr Call AttributeLoad NameLoad attr NameLoad Assign AttributeStore NameLoad attr NameLoad decorator_list FunctionDef arguments args NameParam defaults body If CompareIs AttributeLoad NameLoad attr NameLoad body Assign AttributeStore NameLoad attr Call AttributeLoad NameLoad attr AttributeLoad NameLoad attr AttributeLoad AttributeLoad NameLoad attr attr Return AttributeLoad NameLoad attr decorator_list NameLoad decorator_list ClassDef bases NameLoad body Expr Str FunctionDef arguments args NameParam NameParam defaults NameLoad body Expr Call AttributeLoad Call NameLoad NameLoad NameLoad attr Assign AttributeStore NameLoad attr Call NameLoad NameLoad decorator_list FunctionDef arguments args NameParam defaults body Expr Str Return AttributeLoad NameLoad attr decorator_list NameLoad FunctionDef arguments args NameParam NameParam defaults body Assign AttributeStore NameLoad attr Call NameLoad NameLoad decorator_list AttributeLoad NameLoad attr FunctionDef arguments args NameParam NameParam defaults body If CompareIsNot NameLoad NameLoad body Return Call NameLoad NameLoad orelse Return AttributeLoad NameLoad attr decorator_list decorator_list ClassDef bases NameLoad body Expr Str FunctionDef arguments args NameParam defaults body Return AttributeLoad AttributeLoad NameLoad attr attr decorator_list NameLoad FunctionDef arguments args NameParam NameParam defaults body Assign AttributeStore AttributeLoad NameLoad attr attr Call NameLoad NameLoad decorator_list AttributeLoad NameLoad attr decorator_list Assign NameStore Str Assign NameStore Str Assign NameStore Str Assign NameStore Str Assign NameStore Dict Str Str Str NameLoad NameLoad NameLoad Assign NameStore Dict Str Str Str NameLoad NameLoad NameLoad ClassDef bases NameLoad body Expr Str FunctionDef arguments args NameParam NameParam defaults NameLoad body Expr Call AttributeLoad Call NameLoad NameLoad NameLoad attr NameLoad Assign AttributeStore NameLoad attr Call AttributeLoad NameLoad attr AttributeLoad NameLoad attr NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam NameParam NameParam defaults NameLoad Num NameLoad NameLoad body Expr Str Return Call NameLoad NameLoad NameLoad keyword NameLoad keyword NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam NameParam defaults body Expr Str If CompareIs NameLoad NameLoad body If CompareIs NameLoad NameLoad body If CompareIs NameLoad NameLoad body Assign NameStore Num orelse Assign NameStore Call AttributeLoad NameLoad attr NameLoad keyword NameLoad If CompareLt AttributeLoad NameLoad attr Num body Assign NameStore Num orelse Assign NameStore SubscriptLoad AttributeLoad NameLoad attr Index Num orelse Assign NameStore Call AttributeLoad NameLoad attr NameLoad keyword NameLoad Assign NameStore AttributeLoad NameLoad attr orelse If UnaryOpNot Call AttributeLoad NameLoad attr NameLoad body Raise Call NameLoad Str If CompareIs NameLoad NameLoad body Assign NameStore Call AttributeLoad NameLoad attr NameLoad Assign NameStore Call AttributeLoad NameLoad attr NameLoad keyword NameLoad If CompareIs NameLoad NameLoad body Assign NameStore Num Assign NameStore Call AttributeLoad NameLoad attr NameLoad keyword NameLoad If CompareEq NameLoad Num body Assign AttributeStore NameLoad attr TupleLoad Num Assign AttributeStore NameLoad attr TupleLoad Num Num If BoolOpOr CompareNotEq AttributeLoad NameLoad attr Num CompareNotEq SubscriptLoad AttributeLoad NameLoad attr Index Num NameLoad body Raise Call NameLoad BinOpMod Str NameLoad If CompareEq AttributeLoad NameLoad attr Num body Assign NameStore BinOpMult NameLoad Call AttributeLoad NameLoad attr NameLoad orelse If CompareEq AttributeLoad NameLoad attr Num body Assign NameStore Call AttributeLoad NameLoad attr NameLoad orelse If BoolOpAnd CompareEq AttributeLoad NameLoad attr Num CompareNotEq AttributeLoad NameLoad attr TupleLoad NameLoad NameLoad body Assign TupleStore NameStore NameStore AttributeLoad NameLoad attr If CompareNotEq NameLoad NameLoad body Assign NameStore BinOpMod Str Call NameLoad AttributeLoad NameLoad attr orelse Assign NameStore Str Assign NameStore BinOpMod NameLoad TupleLoad Call NameLoad AttributeLoad NameLoad attr Call NameLoad NameLoad Raise Call NameLoad NameLoad orelse If CompareGt AttributeLoad NameLoad attr Num body Raise Call NameLoad BinOpMod Str AttributeLoad NameLoad attr Return TupleLoad NameLoad NameLoad NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam defaults body Expr Str Assign NameStore Call AttributeLoad NameLoad attr NameLoad keyword NameLoad If CompareEq AttributeLoad NameLoad attr Num body Assign NameStore SubscriptLoad NameLoad Index AttributeLoad NameLoad attr orelse If CompareEq AttributeLoad NameLoad attr Num body If CompareEq NameLoad Num body Assign NameStore SubscriptLoad NameLoad ExtSlice Slice Index AttributeLoad NameLoad attr orelse Assign NameStore SubscriptLoad NameLoad ExtSlice Index AttributeLoad NameLoad attr Slice Return NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam NameParam NameParam NameParam defaults body Expr Str Assign NameStore BinOpSub NameLoad NameLoad Assign NameStore Call AttributeLoad NameLoad attr Call AttributeLoad NameLoad attr Call AttributeLoad NameLoad attr NameLoad NameLoad keyword Num Return BinOpMult Num BinOpAdd BinOpAdd BinOpMult NameLoad NameLoad NameLoad NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam NameParam NameParam defaults NameLoad body Expr Str Assign TupleStore NameStore NameStore NameStore Call AttributeLoad NameLoad attr NameLoad NameLoad NameLoad Assign NameStore Call AttributeLoad NameLoad attr NameLoad NameLoad Assign NameStore Call NameLoad NameLoad keyword NameLoad Assign NameStore Call AttributeLoad NameLoad attr NameLoad NameLoad AttributeLoad NameLoad attr AttributeLoad NameLoad attr AttributeLoad NameLoad attr Return Call NameLoad NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam NameParam NameParam defaults NameLoad body Expr Str Assign TupleStore NameStore NameStore NameStore Call AttributeLoad NameLoad attr NameLoad NameLoad NameLoad Assign NameStore Call AttributeLoad NameLoad attr NameLoad NameLoad Assign NameStore Call NameLoad NameLoad keyword NameLoad Assign NameStore Call AttributeLoad NameLoad attr Call AttributeLoad NameLoad attr NameLoad NameLoad AttributeLoad NameLoad attr AttributeLoad NameLoad attr AttributeLoad NameLoad attr Return Call NameLoad NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam NameParam NameParam defaults NameLoad Num Num NameLoad body Expr Str Assign TupleStore NameStore NameStore NameStore Call AttributeLoad NameLoad attr NameLoad NameLoad NameLoad Assign NameStore Call AttributeLoad NameLoad attr NameLoad Assign NameStore Call AttributeLoad NameLoad attr NameLoad NameLoad NameLoad Return Call NameLoad NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam defaults NameLoad Num body Expr Str Assign TupleStore NameStore NameStore NameStore Call AttributeLoad NameLoad attr NameLoad NameLoad NameLoad Assign TupleStore NameStore NameStore Call AttributeLoad AttributeLoad NameLoad attr attr BinOpMult BinOpMult BinOpMult Num AttributeLoad NameLoad attr AttributeLoad NameLoad attr NameLoad Return BinOpMult Num NameLoad decorator_list decorator_list Assign NameStore Call NameLoad ClassDef bases NameLoad body FunctionDef arguments args NameParam NameParam NameParam NameParam NameParam defaults NameLoad Num NameLoad NameLoad body Expr Str Assign AttributeStore NameLoad attr Call NameLoad NameLoad Assign TupleStore AttributeStore NameLoad attr AttributeStore NameLoad attr AttributeStore NameLoad attr Call AttributeLoad AttributeLoad NameLoad attr attr NameLoad NameLoad NameLoad Assign AttributeStore NameLoad attr Call NameLoad AttributeLoad NameLoad attr keyword NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults body Assign NameStore Call AttributeLoad AttributeLoad NameLoad attr attr NameLoad AttributeLoad NameLoad attr Assign NameStore Call AttributeLoad AttributeLoad NameLoad attr attr NameLoad AttributeLoad NameLoad attr AttributeLoad AttributeLoad NameLoad attr attr AttributeLoad AttributeLoad NameLoad attr attr AttributeLoad AttributeLoad NameLoad attr attr Return Call NameLoad NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults body Return Call AttributeLoad NameLoad attr Call AttributeLoad NameLoad attr NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam defaults Num NameLoad body Return Call AttributeLoad AttributeLoad NameLoad attr attr AttributeLoad NameLoad attr AttributeLoad NameLoad attr NameLoad NameLoad decorator_list FunctionDef arguments args NameParam defaults body Expr Str Assign NameStore AttributeLoad AttributeLoad NameLoad attr attr Assign NameStore AttributeLoad AttributeLoad NameLoad attr attr Return BinOpMult Num BinOpAdd BinOpMult NameLoad BinOpAdd NameLoad Num NameLoad decorator_list decorator_list For NameStore ListLoad Str Str Str body Assign NameStore SubscriptLoad AttributeLoad NameLoad attr Index NameLoad Assign NameStore SubscriptLoad AttributeLoad NameLoad attr Index NameLoad Assign AttributeStore NameLoad attr Call AttributeLoad NameLoad attr AttributeLoad NameLoad attr NameLoad Assign AttributeStore NameLoad attr Call AttributeLoad NameLoad attr AttributeLoad NameLoad attr NameLoad Assign NameStore Str Assign NameStore Str Assign NameStore Str Assign NameStore Str Assign NameStore Dict Str Str Str NameLoad NameLoad NameLoad Assign NameStore Dict Str Str Str NameLoad NameLoad NameLoad ClassDef bases NameLoad body Expr Str FunctionDef arguments args NameParam NameParam defaults NameLoad body Expr Call AttributeLoad Call NameLoad NameLoad NameLoad attr NameLoad Assign AttributeStore NameLoad attr Call AttributeLoad NameLoad attr AttributeLoad NameLoad attr NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam NameParam NameParam defaults NameLoad Num Num NameLoad body Expr Str Return Call NameLoad NameLoad NameLoad NameLoad keyword NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam NameParam defaults body Expr Str If CompareIsNot NameLoad NameLoad body Assign NameStore Call AttributeLoad NameLoad attr NameLoad keyword NameLoad Assign NameStore AttributeLoad NameLoad attr If CompareNotEq Call NameLoad NameLoad Num body Raise Call NameLoad Str If Call AttributeLoad NameLoad attr CompareEq NameLoad Num body Raise Call NameLoad Str Assign NameStore Call AttributeLoad NameLoad attr NameLoad keyword NameLoad If CompareEq AttributeLoad NameLoad attr Num body If CompareIsNot NameLoad NameLoad body Assign NameStore BinOpMult NameLoad Call AttributeLoad NameLoad attr SubscriptLoad NameLoad Index Num orelse Assign NameStore BinOpMult NameLoad Call AttributeLoad NameLoad attr Num orelse If CompareEq AttributeLoad NameLoad attr Num body Assign NameStore Call AttributeLoad NameLoad attr NameLoad Assign NameStore AttributeLoad NameLoad attr If CompareNotEq Call NameLoad NameLoad Num body Raise Call NameLoad Str If CompareNotEq SubscriptLoad NameLoad Index Num SubscriptLoad NameLoad Index Num body Raise Call NameLoad Str If CompareEq SubscriptLoad NameLoad Index Num Num body Raise Call NameLoad Str Assign NameStore SubscriptLoad NameLoad Index Num Assign NameStore Call AttributeLoad NameLoad attr NameLoad keyword NameLoad If CompareEq AttributeLoad NameLoad attr Num body If CompareIsNot NameLoad NameLoad body Assign NameStore BinOpMult NameLoad Call AttributeLoad NameLoad attr SubscriptLoad NameLoad Index Num orelse Assign NameStore BinOpMult NameLoad Call AttributeLoad NameLoad attr Num orelse If CompareEq AttributeLoad NameLoad attr Num body Assign NameStore Call AttributeLoad NameLoad attr NameLoad Assign NameStore AttributeLoad NameLoad attr If CompareNotEq Call NameLoad NameLoad Num body Raise Call NameLoad Str If CompareNotEq SubscriptLoad NameLoad Index Num SubscriptLoad NameLoad Index Num body Raise Call NameLoad Str If CompareEq SubscriptLoad NameLoad Index Num Num body Raise Call NameLoad Str Assign NameStore SubscriptLoad NameLoad Index Num If CompareIsNot NameLoad NameLoad body If CompareNotEq SubscriptLoad NameLoad Index Num NameLoad body Raise Call NameLoad Str If CompareNotEq SubscriptLoad NameLoad Index Num NameLoad body Raise Call NameLoad Str orelse Assign NameStore Call AttributeLoad NameLoad attr TupleLoad NameLoad NameLoad Assign NameStore TupleLoad NameLoad NameLoad Return TupleLoad NameLoad NameLoad NameLoad NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam defaults body Expr Str Assign NameStore Call AttributeLoad NameLoad attr NameLoad keyword NameLoad If CompareEq AttributeLoad NameLoad attr Num body Assign NameStore SubscriptLoad NameLoad ExtSlice Index AttributeLoad NameLoad attr Slice If CompareNotEq SubscriptLoad AttributeLoad NameLoad attr Slice Num NameLoad body Raise Call NameLoad Str Return NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam NameParam NameParam NameParam NameParam NameParam defaults body Expr Str Assign TupleStore NameStore NameStore NameLoad Assign NameStore Call AttributeLoad NameLoad attr BinOpSub NameLoad NameLoad keyword Num keyword Num Assign NameStore Call AttributeLoad NameLoad attr AttributeLoad NameLoad attr Call AttributeLoad NameLoad attr NameLoad NameLoad Num Assign NameStore Call AttributeLoad NameLoad attr Call AttributeLoad NameLoad attr Call AttributeLoad NameLoad attr NameLoad keyword Num keyword Num Return BinOpMult Num BinOpAdd BinOpAdd BinOpAdd BinOpMult BinOpMult NameLoad NameLoad NameLoad BinOpMult NameLoad NameLoad BinOpMult NameLoad NameLoad NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam NameParam NameParam defaults NameLoad Num Num body Expr Str Assign TupleStore NameStore NameStore NameStore NameStore Call AttributeLoad NameLoad attr NameLoad NameLoad NameLoad Assign NameStore Call AttributeLoad NameLoad attr NameLoad NameLoad Assign NameStore Call NameLoad NameLoad keyword NameLoad Assign NameStore Call NameLoad NameLoad keyword NameLoad Assign NameStore Call AttributeLoad NameLoad attr NameLoad NameLoad NameLoad AttributeLoad NameLoad attr AttributeLoad NameLoad attr AttributeLoad NameLoad attr AttributeLoad NameLoad attr Return Call NameLoad NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam NameParam NameParam defaults NameLoad Num Num body Expr Str Return Call AttributeLoad NameLoad attr Call AttributeLoad NameLoad attr NameLoad NameLoad NameLoad NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam NameParam NameParam NameParam defaults NameLoad Num Num Num NameLoad body Expr Str Assign NameStore Call NameLoad NameLoad Assign TupleStore NameStore NameStore NameStore NameStore Call AttributeLoad NameLoad attr NameLoad NameLoad NameLoad Assign NameStore Call AttributeLoad AttributeLoad NameLoad attr attr NameLoad keyword NameLoad Assign NameStore Call AttributeLoad AttributeLoad NameLoad attr attr NameLoad keyword NameLoad Assign NameStore Call AttributeLoad NameLoad attr NameLoad Assign NameStore Call AttributeLoad NameLoad attr keyword TupleLoad SubscriptLoad NameLoad Index Num NameLoad SubscriptLoad NameLoad Index Num Assign NameStore Call AttributeLoad NameLoad attr NameLoad Call AttributeLoad NameLoad attr NameLoad AttributeLoad NameLoad attr Num Assign NameStore BinOpAdd Call AttributeLoad NameLoad attr AttributeLoad NameLoad attr keyword Num keyword Num SubscriptLoad NameLoad ExtSlice Index AttributeLoad NameLoad attr Slice Slice If CompareEq NameLoad Num body Assign NameStore Call AttributeLoad NameLoad attr AttributeLoad NameLoad attr Return NameLoad decorator_list decorator_list Assign NameStore Call NameLoad ClassDef bases NameLoad body FunctionDef arguments args NameParam NameParam NameParam NameParam NameParam defaults NameLoad Num Num NameLoad body Expr Str Assign AttributeStore NameLoad attr Call NameLoad NameLoad Assign TupleStore AttributeStore NameLoad attr AttributeStore NameLoad attr AttributeStore NameLoad attr AttributeStore NameLoad attr Call AttributeLoad AttributeLoad NameLoad attr attr NameLoad NameLoad NameLoad Assign AttributeStore NameLoad attr Call NameLoad AttributeLoad NameLoad attr keyword NameLoad Assign AttributeStore NameLoad attr Call NameLoad AttributeLoad NameLoad attr keyword NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults body Assign NameStore Call AttributeLoad AttributeLoad NameLoad attr attr NameLoad AttributeLoad NameLoad attr Assign NameStore Call AttributeLoad AttributeLoad NameLoad attr attr AttributeLoad NameLoad attr NameLoad AttributeLoad NameLoad attr AttributeLoad AttributeLoad NameLoad attr attr AttributeLoad AttributeLoad NameLoad attr attr AttributeLoad AttributeLoad NameLoad attr attr AttributeLoad AttributeLoad NameLoad attr attr Return Call NameLoad NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults body Return Call AttributeLoad NameLoad attr Call AttributeLoad NameLoad attr NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam defaults Num NameLoad body Return Call AttributeLoad AttributeLoad NameLoad attr attr AttributeLoad NameLoad attr AttributeLoad NameLoad attr AttributeLoad NameLoad attr NameLoad NameLoad decorator_list decorator_list For NameStore ListLoad Str Str Str body Assign NameStore SubscriptLoad AttributeLoad NameLoad attr Index NameLoad Assign NameStore SubscriptLoad AttributeLoad NameLoad attr Index NameLoad Assign AttributeStore NameLoad attr Call AttributeLoad NameLoad attr AttributeLoad NameLoad attr NameLoad Assign AttributeStore NameLoad attr Call AttributeLoad NameLoad attr AttributeLoad NameLoad attr NameLoad Assign NameStore Str Assign NameStore Str Assign NameStore Str Assign NameStore Dict Str Str NameLoad NameLoad Assign NameStore Dict Str Str NameLoad NameLoad FunctionDef arguments args NameParam defaults body Assign NameStore Call AttributeLoad NameLoad attr NameLoad If CompareLtE Call AttributeLoad NameLoad attr NameLoad Num body Raise Call NameLoad Str orelse If CompareNotEq AttributeLoad NameLoad attr Num body Raise Call NameLoad BinOpMod Str TupleLoad AttributeLoad NameLoad attr Return NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults body Assign NameStore Call AttributeLoad NameLoad attr NameLoad If BoolOpAnd CompareNotEq BinOpAdd SubscriptLoad AttributeLoad NameLoad attr Index Num Num SubscriptLoad AttributeLoad NameLoad attr Index Num CompareNotEq SubscriptLoad AttributeLoad NameLoad attr Index Num SubscriptLoad AttributeLoad NameLoad attr Index Num body Raise Call NameLoad BinOpMod Str TupleLoad AttributeLoad NameLoad attr AttributeLoad NameLoad attr If CompareNotEq SubscriptLoad AttributeLoad NameLoad attr Index Num SubscriptLoad AttributeLoad NameLoad attr Index Num body Assign NameStore Call AttributeLoad NameLoad attr ListLoad BinOpSub Num Call AttributeLoad NameLoad attr NameLoad Num If CompareEq AttributeLoad NameLoad attr Num body Assign NameStore Call AttributeLoad NameLoad attr NameLoad NameLoad orelse If CompareEq AttributeLoad NameLoad attr Num body Assign NameStore Call AttributeLoad NameLoad attr TupleLoad NameLoad NameLoad orelse Raise Call NameLoad Str If CompareLtE Call AttributeLoad NameLoad attr NameLoad Num body Raise Call NameLoad Str If CompareGt Call AttributeLoad NameLoad attr NameLoad Num body Raise Call NameLoad Str If Call AttributeLoad CompareGt Call AttributeLoad NameLoad attr BinOpSub Call AttributeLoad NameLoad attr NameLoad Num Num Num attr body Raise Call NameLoad BinOpMod Str Call AttributeLoad NameLoad attr NameLoad Num Return NameLoad decorator_list FunctionDef arguments args NameParam defaults body Expr Str Return BinOpSub Call AttributeLoad NameLoad attr Call NameLoad NameLoad Call NameLoad Call AttributeLoad NameLoad attr NameLoad decorator_list ClassDef bases NameLoad body Expr Str FunctionDef arguments args NameParam NameParam defaults NameLoad body Expr Call AttributeLoad Call NameLoad NameLoad NameLoad attr NameLoad Assign AttributeStore NameLoad attr Call AttributeLoad NameLoad attr AttributeLoad NameLoad attr NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam defaults NameLoad body Return Call NameLoad NameLoad keyword NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam defaults body Expr Str Assign NameStore Call NameLoad NameLoad Return BinOpAdd UnaryOpUSub NameLoad Call AttributeLoad NameLoad attr AttributeLoad BinOpMult Call AttributeLoad NameLoad attr AttributeLoad NameLoad attr BinOpSub NameLoad Num attr Num decorator_list FunctionDef arguments args NameParam NameParam NameParam defaults body Expr Str Assign NameStore Call NameLoad NameLoad Assign NameStore Call NameLoad NameLoad NameLoad Assign NameStore Call AttributeLoad NameLoad attr NameLoad NameLoad Return Call NameLoad NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam defaults body Expr Str Assign NameStore Call NameLoad NameLoad Assign NameStore Call NameLoad NameLoad NameLoad Assign NameStore Call AttributeLoad NameLoad attr Call AttributeLoad NameLoad attr NameLoad NameLoad Return Call NameLoad NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults body Expr Str Assign NameStore Call NameLoad NameLoad Assign NameStore BinOpDiv NameLoad Call AttributeLoad NameLoad attr NameLoad Return Call NameLoad NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults body Expr Str Assign NameStore Call NameLoad NameLoad Assign NameStore Call AttributeLoad NameLoad attr NameLoad Assign NameStore BinOpDiv BinOpMult NameLoad BinOpSub NameLoad NameLoad BinOpMult BinOpMult NameLoad NameLoad BinOpAdd NameLoad Num Return NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults body Expr Str Assign NameStore Call NameLoad NameLoad Assign NameStore Call AttributeLoad NameLoad attr NameLoad Assign NameStore Call NameLoad NameLoad Assign NameStore SubscriptLoad AttributeLoad NameLoad attr Index Num Assign NameStore BinOpSub BinOpAdd NameLoad BinOpMult BinOpSub NameLoad NameLoad Call AttributeLoad AttributeLoad NameLoad attr attr NameLoad Call AttributeLoad NameLoad attr BinOpMult BinOpSub NameLoad Num Call AttributeLoad AttributeLoad NameLoad attr attr NameLoad Return Call NameLoad NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam NameParam defaults Num NameLoad body Expr Str Assign NameStore Call NameLoad NameLoad Assign NameStore Call AttributeLoad NameLoad attr NameLoad Return Call AttributeLoad NameLoad attr NameLoad keyword NameLoad decorator_list decorator_list Assign NameStore Call NameLoad ClassDef bases NameLoad body FunctionDef arguments args NameParam NameParam NameParam defaults NameLoad body Assign AttributeStore NameLoad attr Call NameLoad NameLoad Assign AttributeStore NameLoad attr Call NameLoad NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults body Return Call AttributeLoad AttributeLoad NameLoad attr attr NameLoad AttributeLoad NameLoad attr decorator_list FunctionDef arguments args NameParam NameParam defaults body Return Call AttributeLoad AttributeLoad NameLoad attr attr NameLoad AttributeLoad NameLoad attr decorator_list FunctionDef arguments args NameParam defaults body Return Call AttributeLoad AttributeLoad NameLoad attr attr AttributeLoad NameLoad attr decorator_list FunctionDef arguments args NameParam defaults body Return Call AttributeLoad AttributeLoad NameLoad attr attr AttributeLoad NameLoad attr decorator_list FunctionDef arguments args NameParam defaults body Return Call AttributeLoad AttributeLoad NameLoad attr attr AttributeLoad NameLoad attr decorator_list FunctionDef arguments args NameParam NameParam NameParam defaults Num NameLoad body Return Call AttributeLoad AttributeLoad NameLoad attr attr AttributeLoad NameLoad attr NameLoad NameLoad decorator_list decorator_list For NameStore ListLoad Str Str Str Str Str Str body Assign NameStore SubscriptLoad AttributeLoad NameLoad attr Index NameLoad Assign NameStore SubscriptLoad AttributeLoad NameLoad attr Index NameLoad Assign AttributeStore NameLoad attr Call AttributeLoad NameLoad attr AttributeLoad NameLoad attr NameLoad Assign AttributeStore NameLoad attr Call AttributeLoad NameLoad attr AttributeLoad NameLoad attr NameLoad Assign NameStore Str Assign NameStore Str Assign NameStore Str Assign NameStore Str Assign NameStore Dict Str Str Str NameLoad NameLoad NameLoad Assign NameStore Dict Str Str Str NameLoad NameLoad NameLoad ClassDef bases NameLoad body Expr Str FunctionDef arguments args NameParam NameParam defaults NameLoad body Expr Call AttributeLoad Call NameLoad NameLoad NameLoad attr NameLoad Assign AttributeStore NameLoad attr Call AttributeLoad NameLoad attr AttributeLoad NameLoad attr NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam NameParam defaults NameLoad NameLoad NameLoad body Expr Str Return Call NameLoad NameLoad NameLoad NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam defaults body If CompareIs NameLoad NameLoad body Assign NameStore Num Assign NameStore Call AttributeLoad NameLoad attr NameLoad keyword NameLoad If CompareEq AttributeLoad NameLoad attr Num body Assign NameStore SubscriptLoad NameLoad Index TupleLoad AttributeLoad NameLoad attr AttributeLoad NameLoad attr orelse If CompareEq AttributeLoad NameLoad attr Num body Assign NameStore Call AttributeLoad NameLoad attr NameLoad orelse If BoolOpAnd CompareEq AttributeLoad NameLoad attr Num UnaryOpNot CompareEq SubscriptLoad AttributeLoad NameLoad attr Index Num SubscriptLoad AttributeLoad NameLoad attr Index Num body Raise Call NameLoad BinOpMod Str Call NameLoad AttributeLoad NameLoad attr orelse If CompareGt AttributeLoad NameLoad attr Num body Raise Call NameLoad BinOpMod Str AttributeLoad NameLoad attr Assign NameStore SubscriptLoad AttributeLoad NameLoad attr Index Num If CompareIs NameLoad NameLoad body Assign NameStore NameLoad orelse If UnaryOpNot Call AttributeLoad NameLoad attr NameLoad body Raise Call NameLoad Str orelse If CompareLt NameLoad NameLoad body Raise Call NameLoad BinOpMod Str NameLoad Return TupleLoad NameLoad NameLoad NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam defaults body Expr Str Assign NameStore Call AttributeLoad NameLoad attr NameLoad keyword NameLoad If CompareEq AttributeLoad NameLoad attr Num body Assign NameStore BinOpMult NameLoad SubscriptLoad Call AttributeLoad NameLoad attr NameLoad ExtSlice Slice Slice Index AttributeLoad NameLoad attr If CompareEq AttributeLoad NameLoad attr Num body If CompareEq NameLoad Num body Assign NameStore SubscriptLoad NameLoad ExtSlice Index AttributeLoad NameLoad attr Index AttributeLoad NameLoad attr Slice orelse Assign NameStore SubscriptLoad Call AttributeLoad NameLoad attr NameLoad ExtSlice Slice Slice Index AttributeLoad NameLoad attr orelse If CompareEq AttributeLoad NameLoad attr Num body If UnaryOpNot CompareEq SubscriptLoad AttributeLoad NameLoad attr Index Num SubscriptLoad AttributeLoad NameLoad attr Index Num body Raise Call NameLoad BinOpMod Str Call NameLoad AttributeLoad NameLoad attr Assign NameStore SubscriptLoad NameLoad ExtSlice Slice Slice Index AttributeLoad NameLoad attr orelse If CompareEq AttributeLoad NameLoad attr Num body If UnaryOpNot CompareEq SubscriptLoad AttributeLoad NameLoad attr Index Num SubscriptLoad AttributeLoad NameLoad attr Index Num body Raise Call NameLoad BinOpMod Str Call NameLoad AttributeLoad NameLoad attr orelse If CompareGt AttributeLoad NameLoad attr Num body Raise Call NameLoad BinOpMod Str AttributeLoad NameLoad attr If UnaryOpNot CompareEq SubscriptLoad AttributeLoad NameLoad attr Slice Num Num TupleLoad NameLoad NameLoad body Raise Call NameLoad BinOpMod Str TupleLoad TupleLoad NameLoad NameLoad SubscriptLoad AttributeLoad NameLoad attr Slice Num Num Return NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults body Assign NameStore Call AttributeLoad NameLoad attr NameLoad If CompareEq AttributeLoad NameLoad attr Num body Assign NameStore SubscriptLoad NameLoad Index AttributeLoad NameLoad attr orelse If CompareGt AttributeLoad NameLoad attr Num body Raise Call NameLoad BinOpMod Str Call NameLoad Call NameLoad NameLoad Assign NameStore Call AttributeLoad NameLoad attr Assign NameStore Call NameLoad NameLoad Return TupleLoad NameLoad NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam NameParam NameParam NameParam NameParam defaults body Expr Str Assign NameStore Call AttributeLoad NameLoad attr SubscriptLoad AttributeLoad NameLoad attr Index Num Assign NameStore Call AttributeLoad NameLoad attr AttributeLoad NameLoad attr Assign NameStore Call AttributeLoad NameLoad attr SubscriptLoad AttributeLoad NameLoad attr Index Num For NameStore Call NameLoad SubscriptLoad AttributeLoad NameLoad attr Index Num body Assign TupleStore NameStore SubscriptStore NameLoad Index NameLoad Call AttributeLoad NameLoad attr SubscriptLoad NameLoad ExtSlice Slice Slice Index NameLoad Assign SubscriptStore NameLoad ExtSlice Slice Slice Index NameLoad Call AttributeLoad AttributeLoad NameLoad attr attr TupleLoad NameLoad NameLoad SubscriptLoad NameLoad ExtSlice Slice Slice Index NameLoad Assign SubscriptStore NameLoad Index NameLoad Call AttributeLoad SubscriptLoad NameLoad ExtSlice Slice Slice Index NameLoad attr Assign NameStore BinOpSub BinOpSub BinOpMult BinOpMult Num BinOpSub BinOpSub NameLoad NameLoad Num NameLoad BinOpMult Num NameLoad BinOpAdd BinOpAdd BinOpMult BinOpMult BinOpMult Num NameLoad NameLoad NameLoad BinOpMult BinOpMult Num NameLoad NameLoad Call NameLoad BinOpMult Num NameLoad NameLoad Return NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam NameParam defaults body Expr Str Assign TupleStore NameStore NameStore NameStore Call AttributeLoad NameLoad attr NameLoad NameLoad Assign NameStore Call AttributeLoad NameLoad attr NameLoad NameLoad Assign TupleStore NameStore NameStore Call AttributeLoad NameLoad attr NameLoad Assign NameStore Call AttributeLoad NameLoad attr NameLoad NameLoad NameLoad NameLoad NameLoad NameLoad Return Call NameLoad NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam NameParam defaults body Expr Str Return Call AttributeLoad NameLoad attr Call AttributeLoad NameLoad attr NameLoad NameLoad NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam NameParam defaults body Expr Str Return BinOpMult NameLoad NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam defaults body Expr Str Assign TupleStore NameStore NameStore NameStore Call AttributeLoad NameLoad attr NameLoad NameLoad Assign NameStore Call AttributeLoad NameLoad attr NameLoad NameLoad NameLoad Return Call NameLoad NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam NameParam defaults body Expr Str If CompareGtE NameLoad BinOpAdd NameLoad Num body Assign NameStore BinOpMult BinOpSub BinOpSub NameLoad NameLoad Num NameLoad orelse Assign NameStore NameLoad Return NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam defaults body Expr Str Assign TupleStore NameStore NameStore NameStore Call AttributeLoad NameLoad attr NameLoad NameLoad Assign NameStore Call AttributeLoad NameLoad attr NameLoad NameLoad NameLoad Return IfExp CompareIsNot NameLoad NameLoad Call NameLoad NameLoad NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam NameParam defaults body Expr Str Assign NameStore BinOpPow NameLoad Num Assign NameStore Call AttributeLoad NameLoad attr AugAssignAdd NameStore Call AttributeLoad NameLoad attr NameLoad NameLoad AugAssignMult NameStore NameLoad Return NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam defaults body Expr Str Assign TupleStore NameStore NameStore NameStore Call AttributeLoad NameLoad attr NameLoad NameLoad Assign NameStore Call AttributeLoad NameLoad attr NameLoad NameLoad NameLoad Return Call NameLoad NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam NameParam NameParam NameParam defaults body Expr Str Assign NameStore BinOpFloorDiv BinOpMult NameLoad BinOpSub NameLoad Num Num Assign NameStore Call AttributeLoad Call AttributeLoad NameLoad attr keyword BinOpMult NameLoad NameLoad attr BinOpAdd NameLoad TupleLoad NameLoad Assign NameStore AttributeLoad Call AttributeLoad SubscriptLoad AttributeLoad NameLoad attr Index ListComp BinOpPow Call AttributeLoad NameLoad attr BinOpAdd BinOpSub NameLoad BinOpAdd NameLoad Num Num keyword NameLoad Num comprehension NameStore Call NameLoad NameLoad attr BinOpAdd TupleLoad NameLoad SubscriptLoad NameLoad Slice Num attr Assign NameStore Call AttributeLoad NameLoad attr BinOpAdd NameLoad TupleLoad NameLoad NameLoad Assign NameStore Call NameLoad BinOpMult ListLoad Call NameLoad NameLoad NameLoad NameLoad Call NameLoad NameLoad Assign NameStore Call AttributeLoad NameLoad attr NameLoad keyword Num Assign SubscriptStore NameLoad Index BinOpAdd NameLoad NameLoad NameLoad Assign NameStore Call AttributeLoad NameLoad attr NameLoad Assign SubscriptStore NameLoad Index BinOpAdd NameLoad NameLoad NameLoad Return NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam NameParam NameParam NameParam NameParam defaults body Expr Str Assign NameStore Call AttributeLoad NameLoad attr NameLoad Assign NameStore Call AttributeLoad NameLoad attr NameLoad NameLoad NameLoad NameLoad NameLoad For NameStore Call AttributeLoad NameLoad attr NameLoad body Assign NameStore Call AttributeLoad NameLoad attr NameLoad SubscriptLoad NameLoad Index NameLoad Assign SubscriptStore NameLoad Index NameLoad Call AttributeLoad NameLoad attr NameLoad AttributeLoad NameLoad attr Return NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam NameParam NameParam defaults Num NameLoad body Expr Str Assign TupleStore NameStore NameStore Call AttributeLoad NameLoad attr NameLoad Assign TupleStore NameStore NameStore NameStore Call AttributeLoad NameLoad attr NameLoad NameLoad Assign NameStore Call AttributeLoad AttributeLoad NameLoad attr attr NameLoad keyword NameLoad Assign NameStore Call AttributeLoad NameLoad attr NameLoad NameLoad NameLoad NameLoad NameLoad NameLoad Return Call NameLoad NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam NameParam defaults body Expr Str Return BinOpAdd BinOpSub BinOpAdd BinOpAdd BinOpMult BinOpMult Num BinOpAdd NameLoad Num NameLoad BinOpMult BinOpMult BinOpMult Num NameLoad BinOpAdd NameLoad Num NameLoad Call NameLoad BinOpMult Num NameLoad NameLoad BinOpMult BinOpMult Num BinOpSub BinOpSub NameLoad NameLoad Num Call AttributeLoad NameLoad attr ListComp Call NameLoad BinOpMult Num BinOpSub BinOpAdd NameLoad Num BinOpAdd NameLoad Num comprehension NameStore Call NameLoad NameLoad BinOpMult BinOpMult Num NameLoad NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam defaults body Expr Str Assign TupleStore NameStore NameStore NameStore Call AttributeLoad NameLoad attr NameLoad NameLoad Assign TupleStore NameStore NameStore Call AttributeLoad NameLoad attr NameLoad Return Call AttributeLoad NameLoad attr NameLoad NameLoad NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults body Expr Str Assign NameStore Call AttributeLoad AttributeLoad NameLoad attr attr NameLoad keyword NameLoad Assign NameStore BinOpMult Num Call AttributeLoad NameLoad attr Call AttributeLoad NameLoad attr Call AttributeLoad NameLoad attr Return TupleLoad NameLoad NameLoad decorator_list decorator_list Assign NameStore Call NameLoad ClassDef bases NameLoad body Expr Str FunctionDef arguments args NameParam NameParam NameParam NameParam defaults NameLoad body Assign AttributeStore NameLoad attr Call NameLoad NameLoad Assign TupleStore AttributeStore NameLoad attr AttributeStore NameLoad attr AttributeStore NameLoad attr Call AttributeLoad AttributeLoad NameLoad attr attr NameLoad NameLoad Assign TupleStore AttributeStore NameLoad attr AttributeStore NameLoad attr Call AttributeLoad AttributeLoad NameLoad attr attr AttributeLoad NameLoad attr decorator_list FunctionDef arguments args NameParam NameParam defaults body Assign NameStore Call AttributeLoad AttributeLoad NameLoad attr attr NameLoad AttributeLoad NameLoad attr Assign NameStore Call AttributeLoad AttributeLoad NameLoad attr attr NameLoad AttributeLoad NameLoad attr AttributeLoad NameLoad attr AttributeLoad NameLoad attr AttributeLoad NameLoad attr AttributeLoad NameLoad attr Return Call NameLoad NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults body Return Call AttributeLoad NameLoad attr Call AttributeLoad NameLoad attr NameLoad decorator_list FunctionDef arguments args NameParam defaults body Assign NameStore Call AttributeLoad AttributeLoad NameLoad attr attr AttributeLoad NameLoad attr AttributeLoad NameLoad attr AttributeLoad NameLoad attr Return Call NameLoad NameLoad decorator_list FunctionDef arguments args NameParam defaults body Assign NameStore Call AttributeLoad AttributeLoad NameLoad attr attr AttributeLoad NameLoad attr AttributeLoad NameLoad attr AttributeLoad NameLoad attr Return IfExp CompareIsNot NameLoad NameLoad Call NameLoad NameLoad NameLoad decorator_list FunctionDef arguments args NameParam defaults body Assign NameStore Call AttributeLoad AttributeLoad NameLoad attr attr AttributeLoad NameLoad attr AttributeLoad NameLoad attr AttributeLoad NameLoad attr Return Call NameLoad NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam defaults Num NameLoad body Assign TupleStore NameStore NameStore Call AttributeLoad AttributeLoad NameLoad attr attr NameLoad Assign NameStore Call AttributeLoad AttributeLoad NameLoad attr attr NameLoad NameLoad AttributeLoad NameLoad attr AttributeLoad NameLoad attr AttributeLoad NameLoad attr NameLoad Return Call NameLoad NameLoad decorator_list FunctionDef arguments args NameParam defaults body Return Call AttributeLoad AttributeLoad NameLoad attr attr AttributeLoad NameLoad attr AttributeLoad NameLoad attr AttributeLoad NameLoad attr decorator_list decorator_list For NameStore ListLoad Str Str Str Str Str Str Str body Assign NameStore SubscriptLoad AttributeLoad NameLoad attr Index NameLoad Assign NameStore SubscriptLoad AttributeLoad NameLoad attr Index NameLoad Assign AttributeStore NameLoad attr Call AttributeLoad NameLoad attr AttributeLoad NameLoad attr NameLoad Assign AttributeStore NameLoad attr Call AttributeLoad NameLoad attr AttributeLoad NameLoad attr NameLoad ImportFrom alias alias ImportFrom alias ImportFrom alias FunctionDef arguments args NameParam NameParam defaults NameLoad body Expr Str If NameLoad body Assign NameStore Call NameLoad NameLoad orelse Assign NameStore Call NameLoad NameLoad If BoolOpOr CompareLt Call NameLoad AttributeLoad NameLoad attr Num CompareNotEq SubscriptLoad AttributeLoad NameLoad attr Index Num SubscriptLoad AttributeLoad NameLoad attr Index Num body Raise Call NameLoad Str Assign TupleStore NameStore NameStore Call NameLoad TupleLoad Str Str TupleLoad NameLoad Assign NameStore Call AttributeLoad NameLoad attr SubscriptLoad AttributeLoad NameLoad attr Index Num keyword Num Assign NameStore Call AttributeLoad NameLoad attr SubscriptLoad AttributeLoad NameLoad attr Index Num keyword Num For NameStore Call AttributeLoad NameLoad attr SubscriptLoad AttributeLoad NameLoad attr Slice Num body Assign TupleStore SubscriptStore NameLoad Index NameLoad NameStore Call NameLoad SubscriptLoad NameLoad Index NameLoad keyword NameLoad keyword NameLoad keyword NameLoad If CompareGt NameLoad Num body Raise Call NameLoad BinOpMod Str NameLoad If CompareLt NameLoad Num body Raise Call NameLoad BinOpMod Str UnaryOpUSub NameLoad Assign TupleStore SubscriptStore NameLoad Index NameLoad NameStore Call NameLoad SubscriptLoad NameLoad Index NameLoad keyword NameLoad keyword NameLoad If CompareGt NameLoad Num body Raise Call NameLoad Str If CompareLt NameLoad Num body Raise Call NameLoad BinOpMod Str UnaryOpUSub NameLoad Assign SubscriptStore SubscriptLoad NameLoad Index NameLoad Index NameLoad SubscriptLoad SubscriptLoad NameLoad Index NameLoad Index NameLoad Return NameLoad decorator_list ClassDef bases NameLoad body Expr Str FunctionDef arguments args NameParam NameParam defaults NameLoad body Expr Call AttributeLoad Call NameLoad NameLoad NameLoad attr NameLoad Assign AttributeStore NameLoad attr Call AttributeLoad NameLoad attr AttributeLoad NameLoad attr NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam NameParam defaults NameLoad NameLoad NameLoad body Expr Str Return Call NameLoad NameLoad NameLoad NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam NameParam NameParam NameParam 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BinOpSub BinOpSub BinOpMult BinOpMult Num NameLoad NameLoad BinOpMult Num NameLoad BinOpAdd BinOpMult BinOpMult BinOpMult Num NameLoad NameLoad NameLoad BinOpMult BinOpMult Num BinOpAdd BinOpAdd NameLoad NameLoad Num NameLoad Call NameLoad BinOpMult Num NameLoad NameLoad Return NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam NameParam defaults body Expr Str Assign TupleStore NameStore NameStore NameStore Call AttributeLoad NameLoad attr NameLoad NameLoad Assign NameStore Call AttributeLoad NameLoad attr NameLoad NameLoad Assign TupleStore NameStore NameStore Call AttributeLoad NameLoad attr NameLoad Assign NameStore Call AttributeLoad NameLoad attr NameLoad NameLoad NameLoad NameLoad NameLoad Return Call NameLoad NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam NameParam defaults body Expr Str Return Call AttributeLoad NameLoad attr Call AttributeLoad NameLoad attr NameLoad NameLoad NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam NameParam defaults body Expr Str If CompareGt NameLoad BinOpAdd NameLoad Num body Assign NameStore BinOpDiv NameLoad BinOpSub BinOpSub NameLoad NameLoad Num orelse Assign NameStore NameLoad Return NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam defaults body Expr Str Assign TupleStore NameStore NameStore NameStore Call AttributeLoad NameLoad attr NameLoad NameLoad Assign NameStore Call AttributeLoad NameLoad attr NameLoad NameLoad NameLoad Return IfExp CompareIsNot NameLoad NameLoad Call NameLoad NameLoad NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam NameParam defaults body Expr Str Return BinOpDiv NameLoad BinOpAdd BinOpAdd NameLoad NameLoad Num decorator_list FunctionDef arguments args NameParam NameParam NameParam defaults body Expr Str Assign TupleStore NameStore NameStore NameStore Call AttributeLoad NameLoad attr NameLoad NameLoad Assign NameStore Call AttributeLoad NameLoad attr NameLoad NameLoad NameLoad Return Call NameLoad NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam NameParam defaults body Expr Str If CompareGt NameLoad BinOpAdd NameLoad Num body Assign NameStore BinOpMult BinOpAdd BinOpSub NameLoad NameLoad Num BinOpPow NameLoad Num Assign NameStore Call AttributeLoad NameLoad attr AugAssignAdd NameStore BinOpMult BinOpSub BinOpSub NameLoad NameLoad Num Call AttributeLoad NameLoad attr NameLoad NameLoad AugAssignDiv NameStore BinOpMult BinOpMult BinOpSub NameLoad NameLoad BinOpPow BinOpSub BinOpSub NameLoad NameLoad Num Num BinOpSub BinOpSub NameLoad NameLoad Num orelse Assign NameStore NameLoad Return NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam defaults body Expr Str Assign TupleStore NameStore NameStore NameStore Call AttributeLoad NameLoad attr NameLoad NameLoad Assign NameStore Call AttributeLoad NameLoad attr NameLoad NameLoad NameLoad Return IfExp CompareIsNot NameLoad NameLoad Call NameLoad NameLoad NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam NameParam NameParam NameParam NameParam defaults body Expr Str Assign NameStore Call AttributeLoad NameLoad attr NameLoad Assign NameStore Call AttributeLoad Call NameLoad NameLoad NameLoad attr NameLoad NameLoad NameLoad NameLoad NameLoad Assign NameStore Call AttributeLoad NameLoad attr NameLoad Assign NameStore Call NameLoad Str TupleLoad NameLoad For NameStore Call AttributeLoad NameLoad attr SubscriptLoad AttributeLoad NameLoad attr Slice Num body Assign NameStore Call AttributeLoad NameLoad attr NameLoad SubscriptLoad NameLoad Index NameLoad If CompareGt NameLoad Num body Assign TupleStore NameStore NameStore Call NameLoad NameLoad NameLoad keyword NameLoad If CompareGt NameLoad Num body Raise Call NameLoad Str If CompareLt NameLoad Num body Raise Call NameLoad BinOpMod Str UnaryOpUSub NameLoad orelse Assign NameStore BinOpDiv Num NameLoad Assign SubscriptStore NameLoad Index NameLoad Call AttributeLoad NameLoad attr AttributeLoad NameLoad attr NameLoad Return NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam NameParam NameParam defaults Num NameLoad body Expr Str Assign TupleStore NameStore NameStore Call AttributeLoad NameLoad attr NameLoad Assign TupleStore NameStore NameStore NameStore Call AttributeLoad NameLoad attr NameLoad NameLoad Assign NameStore Call AttributeLoad NameLoad attr NameLoad Assign TupleStore NameStore NameStore Call AttributeLoad AttributeLoad NameLoad attr attr NameLoad keyword NameLoad Assign NameStore Call AttributeLoad AttributeLoad NameLoad attr attr TupleLoad NameLoad NameLoad NameLoad Assign NameStore Call AttributeLoad AttributeLoad NameLoad attr attr NameLoad keyword NameLoad Assign NameStore Call AttributeLoad NameLoad attr NameLoad NameLoad NameLoad NameLoad NameLoad NameLoad Return Call NameLoad NameLoad decorator_list FunctionDef arguments args NameParam 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AttributeLoad NameLoad attr attr AttributeLoad NameLoad attr keyword NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults body Assign NameStore Call AttributeLoad AttributeLoad NameLoad attr attr NameLoad AttributeLoad NameLoad attr Assign NameStore Call AttributeLoad AttributeLoad NameLoad attr attr NameLoad AttributeLoad NameLoad attr AttributeLoad NameLoad attr AttributeLoad NameLoad attr AttributeLoad NameLoad attr Return Call NameLoad NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults body Return Call AttributeLoad NameLoad attr Call AttributeLoad NameLoad attr NameLoad decorator_list FunctionDef arguments args NameParam defaults body Assign NameStore Call AttributeLoad AttributeLoad NameLoad attr attr AttributeLoad NameLoad attr AttributeLoad NameLoad attr AttributeLoad NameLoad attr Return IfExp CompareIsNot NameLoad NameLoad Call NameLoad NameLoad NameLoad decorator_list FunctionDef arguments args NameParam defaults body Assign NameStore Call AttributeLoad AttributeLoad NameLoad attr attr AttributeLoad NameLoad attr AttributeLoad NameLoad attr AttributeLoad NameLoad attr Return Call NameLoad NameLoad decorator_list FunctionDef arguments args NameParam defaults body Assign NameStore Call AttributeLoad AttributeLoad NameLoad attr attr AttributeLoad NameLoad attr AttributeLoad NameLoad attr AttributeLoad NameLoad attr Return IfExp CompareIsNot NameLoad NameLoad Call NameLoad NameLoad NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam defaults Num NameLoad body Assign TupleStore NameStore NameStore Call AttributeLoad AttributeLoad NameLoad attr attr NameLoad Assign NameStore Call AttributeLoad AttributeLoad NameLoad attr attr NameLoad NameLoad AttributeLoad NameLoad attr AttributeLoad NameLoad attr AttributeLoad NameLoad attr NameLoad Return Call NameLoad NameLoad decorator_list FunctionDef arguments args NameParam defaults body Raise NameLoad decorator_list decorator_list For NameStore ListLoad Str Str Str Str Str Str body Assign NameStore SubscriptLoad AttributeLoad NameLoad attr Index NameLoad Assign NameStore SubscriptLoad AttributeLoad NameLoad attr Index NameLoad Assign AttributeStore NameLoad attr Call AttributeLoad NameLoad attr AttributeLoad NameLoad attr NameLoad Assign AttributeStore NameLoad attr Call AttributeLoad NameLoad attr AttributeLoad NameLoad attr NameLoad ClassDef bases NameLoad body Expr Str FunctionDef arguments args NameParam NameParam defaults NameLoad body Expr Call AttributeLoad Call NameLoad NameLoad NameLoad attr NameLoad Assign AttributeStore NameLoad attr Call AttributeLoad NameLoad attr AttributeLoad NameLoad attr decorator_list FunctionDef arguments args NameParam NameParam NameParam defaults NameLoad NameLoad body Expr Str Return Call NameLoad NameLoad keyword NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults body Expr Str If BoolOpOr CompareIs NameLoad NameLoad UnaryOpNot Call AttributeLoad NameLoad attr NameLoad CompareLtE NameLoad Num CompareNotEq NameLoad Call NameLoad NameLoad body Raise Call NameLoad Str Return NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam NameParam defaults Num NameLoad body Expr Str Assign NameStore Call NameLoad NameLoad If CompareGt NameLoad Num body Return Call AttributeLoad NameLoad attr ListComp Call AttributeLoad NameLoad attr NameLoad keyword Num keyword NameLoad comprehension NameStore Call NameLoad NameLoad Assign NameStore Call AttributeLoad NameLoad attr NameLoad Assign NameStore Call AttributeLoad NameLoad attr NameLoad Assign NameStore Call AttributeLoad NameLoad attr NameLoad Assign NameStore Call AttributeLoad NameLoad attr TupleLoad NameLoad For NameStore Call NameLoad Num NameLoad body Assign NameStore Call AttributeLoad NameLoad attr keyword TupleLoad BinOpAdd BinOpSub NameLoad NameLoad Num Assign SubscriptStore NameLoad Index BinOpSub NameLoad Num Call AttributeLoad NameLoad attr SubscriptLoad NameLoad Index Num AugAssignSub SubscriptStore NameLoad Index Num BinOpMult SubscriptLoad NameLoad Index BinOpSub NameLoad Num Call AttributeLoad NameLoad attr Call AttributeLoad BinOpMult NameLoad NameLoad attr Assign NameStore BinOpSub Call AttributeLoad NameLoad attr BinOpAdd BinOpSub NameLoad NameLoad Num BinOpDiv BinOpMult Num Call AttributeLoad NameLoad attr NameLoad NameLoad Call AttributeLoad BinOpMult NameLoad NameLoad attr Assign NameStore Call AttributeLoad NameLoad attr NameLoad Assign SubscriptStore NameLoad ExtSlice Slice BinOpSub NameLoad Num Slice BinOpSub NameLoad Num NameLoad Assign NameStore Call AttributeLoad NameLoad attr NameLoad NameLoad Assign SubscriptStore NameLoad Index Num BinOpMult BinOpPow Num BinOpSub Num BinOpMod NameLoad Num Call AttributeLoad NameLoad attr Assign NameStore AttributeLoad BinOpMult NameLoad AttributeLoad NameLoad attr attr Return NameLoad decorator_list decorator_list Assign NameStore Call NameLoad ClassDef bases NameLoad body FunctionDef arguments args NameParam NameParam NameParam defaults NameLoad NameLoad body Expr Str Assign AttributeStore NameLoad attr Call NameLoad NameLoad Assign AttributeStore NameLoad attr Call AttributeLoad AttributeLoad NameLoad attr attr NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam defaults Num NameLoad body Return Call AttributeLoad AttributeLoad NameLoad attr attr AttributeLoad NameLoad attr NameLoad NameLoad decorator_list decorator_list ClassDef bases NameLoad body Expr Str FunctionDef arguments args NameParam NameParam defaults NameLoad body Expr Call AttributeLoad Call NameLoad NameLoad NameLoad attr NameLoad Assign AttributeStore NameLoad attr Call AttributeLoad NameLoad attr AttributeLoad NameLoad attr decorator_list FunctionDef arguments args NameParam NameParam defaults body Expr Str If BoolOpOr CompareIs NameLoad NameLoad UnaryOpNot Call AttributeLoad NameLoad attr NameLoad CompareLtE NameLoad Num CompareNotEq NameLoad Call NameLoad NameLoad body Raise Call NameLoad Str Return NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam NameParam defaults Num NameLoad body Expr Str Assign NameStore Call NameLoad NameLoad If CompareGt NameLoad Num body Return Call AttributeLoad NameLoad attr ListComp Call AttributeLoad NameLoad attr NameLoad keyword Num keyword NameLoad comprehension NameStore Call NameLoad NameLoad Assign NameStore Call AttributeLoad NameLoad attr NameLoad Assign NameStore Call AttributeLoad NameLoad attr NameLoad Assign NameStore Call AttributeLoad NameLoad attr NameLoad For NameStore Call NameLoad Num NameLoad body Assign NameStore Call AttributeLoad NameLoad attr keyword TupleLoad BinOpAdd BinOpSub NameLoad NameLoad Num Assign NameStore Call AttributeLoad NameLoad attr SubscriptLoad NameLoad Index Num AugAssignAdd SubscriptStore NameLoad Index Num BinOpMult NameLoad Call AttributeLoad NameLoad attr Call AttributeLoad BinOpMult NameLoad NameLoad attr Assign NameStore BinOpMult UnaryOpUSub NameLoad BinOpSub Call AttributeLoad NameLoad attr BinOpAdd BinOpSub NameLoad NameLoad Num BinOpDiv BinOpMult Num Call AttributeLoad NameLoad attr NameLoad NameLoad Call AttributeLoad BinOpMult NameLoad NameLoad attr Assign NameStore Call AttributeLoad NameLoad attr NameLoad Assign SubscriptStore NameLoad ExtSlice Slice BinOpSub NameLoad Num Slice BinOpSub NameLoad Num NameLoad Assign NameStore Call AttributeLoad NameLoad attr NameLoad NameLoad Return NameLoad decorator_list decorator_list Assign NameStore Call NameLoad ClassDef bases NameLoad body Expr Str FunctionDef arguments args NameParam NameParam defaults NameLoad body Expr Call AttributeLoad Call NameLoad NameLoad NameLoad attr NameLoad Assign AttributeStore NameLoad attr Call AttributeLoad NameLoad attr AttributeLoad NameLoad attr decorator_list FunctionDef arguments args NameParam NameParam NameParam defaults body Assign NameStore Call AttributeLoad NameLoad attr NameLoad keyword NameLoad Assign NameStore AttributeLoad NameLoad attr If BoolOpOr CompareNotEq AttributeLoad NameLoad attr Num CompareNotEq SubscriptLoad AttributeLoad NameLoad attr Index Num NameLoad CompareLtE NameLoad Num body Raise Call NameLoad Str If CompareGt Call AttributeLoad NameLoad attr BinOpSub Call AttributeLoad NameLoad attr NameLoad NameLoad NameLoad body Raise Call NameLoad Str For NameStore NameLoad body If CompareLt NameLoad UnaryOpUSub NameLoad body Raise Call NameLoad Str Return TupleLoad NameLoad NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam NameParam defaults body Expr Str Assign NameStore BinOpSub NameLoad Num Assign NameStore BinOpSub NameLoad Num If CompareEq NameLoad Num body Return TupleLoad Num Num Assign NameStore Call AttributeLoad NameLoad attr Call NameLoad BinOpSub BinOpPow NameLoad Num BinOpMult NameLoad NameLoad Num Assign NameStore BinOpDiv BinOpAdd NameLoad Call AttributeLoad NameLoad attr NameLoad NameLoad NameLoad Assign NameStore BinOpDiv Num Call AttributeLoad NameLoad attr BinOpAdd Num BinOpMult NameLoad NameLoad If CompareEq NameLoad Num body Assign NameStore Num orelse Assign NameStore BinOpMult NameLoad NameLoad Return TupleLoad NameLoad NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults body Expr Str If UnaryOpNot BoolOpAnd AttributeLoad AttributeLoad NameLoad attr attr CompareEq AttributeLoad NameLoad attr AttributeLoad NameLoad attr CompareEq SubscriptLoad AttributeLoad NameLoad attr Index Num SubscriptLoad AttributeLoad NameLoad attr Index Num body Raise Call NameLoad Assign NameStore SubscriptLoad AttributeLoad NameLoad attr Index Num For NameStore Call NameLoad BinOpSub NameLoad Num body If CompareEq SubscriptLoad NameLoad Index TupleLoad NameLoad NameLoad Num body Continue orelse If CompareGt SubscriptLoad NameLoad Index TupleLoad NameLoad NameLoad Num body For NameStore Call NameLoad BinOpAdd NameLoad Num NameLoad body If CompareLt SubscriptLoad NameLoad Index TupleLoad NameLoad NameLoad Num body Break orelse For NameStore Call NameLoad BinOpAdd NameLoad Num NameLoad body If CompareGt SubscriptLoad NameLoad Index TupleLoad NameLoad NameLoad Num body Break Assign TupleStore NameStore NameStore Call AttributeLoad NameLoad attr SubscriptLoad NameLoad Index TupleLoad NameLoad NameLoad SubscriptLoad NameLoad Index TupleLoad NameLoad NameLoad SubscriptLoad NameLoad Index TupleLoad NameLoad NameLoad Assign NameStore Call AttributeLoad NameLoad attr Expr Call NameLoad NameLoad NameLoad NameLoad UnaryOpUSub NameLoad keyword NameLoad keyword BinOpMult NameLoad NameLoad keyword Num keyword BinOpMult NameLoad NameLoad keyword Num keyword NameLoad keyword NameLoad Expr Call NameLoad NameLoad NameLoad NameLoad UnaryOpUSub NameLoad keyword NameLoad keyword NameLoad keyword NameLoad keyword NameLoad keyword NameLoad keyword NameLoad keyword NameLoad Return NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam NameParam NameParam defaults NameLoad Num Num body Expr Str Assign TupleStore NameStore NameStore Call AttributeLoad NameLoad attr NameLoad keyword NameLoad Assign NameStore Call AttributeLoad NameLoad attr NameLoad Assign NameStore Call AttributeLoad NameLoad attr NameLoad keyword NameLoad Assign NameStore Call AttributeLoad NameLoad attr Call AttributeLoad NameLoad attr NameLoad Call AttributeLoad NameLoad attr NameLoad AttributeLoad NameLoad attr Assign NameStore Call AttributeLoad NameLoad attr NameLoad If CompareGt Call AttributeLoad Call NameLoad BinOpSub Call AttributeLoad NameLoad attr Num attr NameLoad body Raise Call NameLoad Str Return NameLoad decorator_list decorator_list Assign NameStore Call NameLoad
N/A __future__ division print_function absolute_import N/A math N/A numpy np N/A scipy.linalg scipy.misc doccer scipy.special gammaln psi multigammaln scipy._lib._util check_random_state scipy.linalg.blas drot N/A __all__ N/A multivariate_normal matrix_normal dirichlet wishart invwishart special_ortho_group ortho_group random_correlation N/A _LOG_2PI N/A N/A np log N/A 2 N/A np pi N/A _LOG_2 N/A N/A np log 2 N/A _LOG_PI N/A N/A np log N/A np pi N/A _doc_random_state random_state : None or int or np.random.RandomState instance, optional
    If int or RandomState, use it for drawing the random variates.
    If None (or np.random), the global np.random state is used.
    Default is None.
 _squeeze_output N/A N/A out N/A N/A N/A 
    Remove single-dimensional entries from array and convert to scalar,
    if necessary.

     N/A out N/A N/A out squeeze N/A N/A N/A out ndim 0 N/A N/A out N/A out N/A N/A N/A out N/A _eigvalsh_to_eps N/A N/A spectrum cond rcond N/A None None N/A N/A 
    Determine which eigenvalues are "small" given the spectrum.

    This is for compatibility across various linear algebra functions
    that should agree about whether or not a Hermitian matrix is numerically
    singular and what is its numerical matrix rank.
    This is designed to be compatible with scipy.linalg.pinvh.

    Parameters
    ----------
    spectrum : 1d ndarray
        Array of eigenvalues of a Hermitian matrix.
    cond, rcond : float, optional
        Cutoff for small eigenvalues.
        Singular values smaller than rcond * largest_eigenvalue are
        considered zero.
        If None or -1, suitable machine precision is used.

    Returns
    -------
    eps : float
        Magnitude cutoff for numerical negligibility.

     N/A N/A rcond None N/A N/A cond rcond N/A N/A cond N/A None -1 N/A N/A t N/A N/A N/A N/A spectrum dtype char lower N/A factor N/A f d 1000.0 1000000.0 N/A cond N/A N/A factor N/A t N/A N/A N/A np finfo t eps N/A eps N/A cond N/A N/A np max N/A abs spectrum N/A eps N/A _pinv_1d N/A N/A v eps N/A 1e-05 N/A N/A 
    A helper function for computing the pseudoinverse.

    Parameters
    ----------
    v : iterable of numbers
        This may be thought of as a vector of eigenvalues or singular values.
    eps : float
        Values with magnitude no greater than eps are considered negligible.

    Returns
    -------
    v_pinv : 1d float ndarray
        A vector of pseudo-inverted numbers.

     N/A N/A N/A np array N/A N/A N/A N/A abs x eps 0 N/A 1 x N/A x v dtype float N/A _PSD N/A object N/A N/A 
    Compute coordinated functions of a symmetric positive semidefinite matrix.

    This class addresses two issues.  Firstly it allows the pseudoinverse,
    the logarithm of the pseudo-determinant, and the rank of the matrix
    to be computed using one call to eigh instead of three.
    Secondly it allows these functions to be computed in a way
    that gives mutually compatible results.
    All of the functions are computed with a common understanding as to
    which of the eigenvalues are to be considered negligibly small.
    The functions are designed to coordinate with scipy.linalg.pinvh()
    but not necessarily with np.linalg.det() or with np.linalg.matrix_rank().

    Parameters
    ----------
    M : array_like
        Symmetric positive semidefinite matrix (2-D).
    cond, rcond : float, optional
        Cutoff for small eigenvalues.
        Singular values smaller than rcond * largest_eigenvalue are
        considered zero.
        If None or -1, suitable machine precision is used.
    lower : bool, optional
        Whether the pertinent array data is taken from the lower
        or upper triangle of M. (Default: lower)
    check_finite : bool, optional
        Whether to check that the input matrices contain only finite
        numbers. Disabling may give a performance gain, but may result
        in problems (crashes, non-termination) if the inputs do contain
        infinities or NaNs.
    allow_singular : bool, optional
        Whether to allow a singular matrix.  (Default: True)

    Notes
    -----
    The arguments are similar to those of scipy.linalg.pinvh().

     __init__ N/A N/A self M cond rcond lower check_finite allow_singular N/A None None True True True N/A N/A N/A s u N/A N/A N/A scipy linalg eigh M lower lower check_finite check_finite N/A eps N/A _eigvalsh_to_eps s cond rcond N/A N/A N/A N/A np min s N/A eps N/A N/A N/A ValueError the input matrix must be positive semidefinite N/A d N/A s N/A N/A s eps N/A N/A N/A N/A len d N/A len s N/A allow_singular N/A N/A N/A N/A N/A np linalg LinAlgError singular matrix N/A s_pinv N/A _pinv_1d s eps N/A U N/A N/A np multiply u N/A N/A np sqrt s_pinv N/A N/A self rank N/A len d N/A N/A self U U N/A N/A self log_pdet N/A N/A np sum N/A N/A np log d N/A N/A self _pinv None N/A pinv N/A N/A self N/A N/A N/A N/A N/A self _pinv None N/A N/A N/A self _pinv N/A N/A np dot N/A self U N/A N/A self U T N/A N/A self _pinv N/A property N/A multi_rv_generic N/A object N/A N/A 
    Class which encapsulates common functionality between all multivariate
    distributions.

     __init__ N/A N/A self seed N/A None N/A N/A N/A N/A N/A super multi_rv_generic self __init__ N/A N/A self _random_state N/A check_random_state seed N/A random_state N/A N/A self N/A N/A N/A  Get or set the RandomState object for generating random variates.

        This can be either None or an existing RandomState object.

        If None (or np.random), use the RandomState singleton used by np.random.
        If already a RandomState instance, use it.
        If an int, use a new RandomState instance seeded with seed.

         N/A N/A self _random_state N/A property random_state N/A N/A self seed N/A N/A N/A N/A self _random_state N/A check_random_state seed N/A N/A random_state setter _get_random_state N/A N/A self random_state N/A N/A N/A N/A random_state None N/A N/A N/A check_random_state random_state N/A N/A N/A self _random_state N/A N/A multi_rv_frozen N/A object N/A N/A 
    Class which encapsulates common functionality between all frozen
    multivariate distributions.
     random_state N/A N/A self N/A N/A N/A N/A N/A self _dist _random_state N/A property random_state N/A N/A self seed N/A N/A N/A N/A N/A self _dist _random_state N/A check_random_state seed N/A N/A random_state setter N/A N/A _mvn_doc_default_callparams mean : array_like, optional
    Mean of the distribution (default zero)
cov : array_like, optional
    Covariance matrix of the distribution (default one)
allow_singular : bool, optional
    Whether to allow a singular covariance matrix.  (Default: False)
 N/A _mvn_doc_callparams_note Setting the parameter `mean` to `None` is equivalent to having `mean`
    be the zero-vector. The parameter `cov` can be a scalar, in which case
    the covariance matrix is the identity times that value, a vector of
    diagonal entries for the covariance matrix, or a two-dimensional
    array_like.
     N/A _mvn_doc_frozen_callparams N/A _mvn_doc_frozen_callparams_note See class definition for a detailed description of parameters. N/A mvn_docdict_params N/A _mvn_doc_default_callparams _mvn_doc_callparams_note _doc_random_state _mvn_doc_default_callparams _mvn_doc_callparams_note _doc_random_state N/A mvn_docdict_noparams N/A _mvn_doc_default_callparams _mvn_doc_callparams_note _doc_random_state _mvn_doc_frozen_callparams _mvn_doc_frozen_callparams_note _doc_random_state multivariate_normal_gen N/A multi_rv_generic N/A N/A 
    A multivariate normal random variable.

    The `mean` keyword specifies the mean. The `cov` keyword specifies the
    covariance matrix.

    Methods
    -------
    ``pdf(x, mean=None, cov=1, allow_singular=False)``
        Probability density function.
    ``logpdf(x, mean=None, cov=1, allow_singular=False)``
        Log of the probability density function.
    ``rvs(mean=None, cov=1, size=1, random_state=None)``
        Draw random samples from a multivariate normal distribution.
    ``entropy()``
        Compute the differential entropy of the multivariate normal.

    Parameters
    ----------
    x : array_like
        Quantiles, with the last axis of `x` denoting the components.
    %(_mvn_doc_default_callparams)s
    %(_doc_random_state)s

    Alternatively, the object may be called (as a function) to fix the mean
    and covariance parameters, returning a "frozen" multivariate normal
    random variable:

    rv = multivariate_normal(mean=None, cov=1, allow_singular=False)
        - Frozen object with the same methods but holding the given
          mean and covariance fixed.

    Notes
    -----
    %(_mvn_doc_callparams_note)s

    The covariance matrix `cov` must be a (symmetric) positive
    semi-definite matrix. The determinant and inverse of `cov` are computed
    as the pseudo-determinant and pseudo-inverse, respectively, so
    that `cov` does not need to have full rank.

    The probability density function for `multivariate_normal` is

    .. math::

        f(x) = \frac{1}{\sqrt{(2 \pi)^k \det \Sigma}}
               \exp\left( -\frac{1}{2} (x - \mu)^T \Sigma^{-1} (x - \mu) \right),

    where :math:`\mu` is the mean, :math:`\Sigma` the covariance matrix,
    and :math:`k` is the dimension of the space where :math:`x` takes values.

    .. versionadded:: 0.14.0

    Examples
    --------
    >>> import matplotlib.pyplot as plt
    >>> from scipy.stats import multivariate_normal

    >>> x = np.linspace(0, 5, 10, endpoint=False)
    >>> y = multivariate_normal.pdf(x, mean=2.5, cov=0.5); y
    array([ 0.00108914,  0.01033349,  0.05946514,  0.20755375,  0.43939129,
            0.56418958,  0.43939129,  0.20755375,  0.05946514,  0.01033349])
    >>> fig1 = plt.figure()
    >>> ax = fig1.add_subplot(111)
    >>> ax.plot(x, y)

    The input quantiles can be any shape of array, as long as the last
    axis labels the components.  This allows us for instance to
    display the frozen pdf for a non-isotropic random variable in 2D as
    follows:

    >>> x, y = np.mgrid[-1:1:.01, -1:1:.01]
    >>> pos = np.dstack((x, y))
    >>> rv = multivariate_normal([0.5, -0.2], [[2.0, 0.3], [0.3, 0.5]])
    >>> fig2 = plt.figure()
    >>> ax2 = fig2.add_subplot(111)
    >>> ax2.contourf(x, y, rv.pdf(pos))

     __init__ N/A N/A self seed N/A None N/A N/A N/A N/A N/A super multivariate_normal_gen self __init__ seed N/A N/A self __doc__ N/A N/A doccer docformat N/A self __doc__ mvn_docdict_params N/A __call__ N/A N/A self mean cov allow_singular seed N/A None 1 False None N/A N/A 
        Create a frozen multivariate normal distribution.

        See `multivariate_normal_frozen` for more information.

         N/A N/A multivariate_normal_frozen mean cov allow_singular allow_singular seed seed N/A _process_parameters N/A N/A self dim mean cov N/A N/A N/A 
        Infer dimensionality from mean or covariance matrix, ensure that
        mean and covariance are full vector resp. matrix.

         N/A N/A dim None N/A N/A N/A mean None N/A N/A N/A cov None N/A N/A dim 1 N/A N/A cov N/A N/A np asarray cov dtype float N/A N/A N/A cov ndim 2 N/A N/A dim 1 N/A N/A dim N/A N/A cov shape N/A 0 N/A N/A mean N/A N/A np asarray mean dtype float N/A dim N/A mean size N/A N/A N/A N/A N/A np isscalar dim N/A N/A N/A ValueError Dimension of random variable must be a scalar. N/A N/A mean None N/A N/A mean N/A N/A np zeros dim N/A mean N/A N/A np asarray mean dtype float N/A N/A cov None N/A N/A cov 1.0 N/A cov N/A N/A np asarray cov dtype float N/A N/A dim 1 N/A N/A N/A mean shape N/A 1 N/A N/A cov shape N/A 1 1 N/A N/A N/A N/A mean ndim 1 N/A N/A N/A mean shape N/A 0 dim N/A N/A N/A ValueError N/A Array 'mean' must be a vector of length %d. dim N/A N/A N/A cov ndim 0 N/A N/A cov N/A cov N/A N/A np eye dim N/A N/A N/A N/A cov ndim 1 N/A N/A cov N/A N/A np diag cov N/A N/A N/A N/A N/A cov ndim 2 N/A N/A cov shape N/A dim dim N/A N/A N/A rows cols N/A cov shape N/A N/A rows cols N/A N/A msg N/A Array 'cov' must be square if it is two dimensional, but cov.shape = %s. N/A str N/A cov shape N/A N/A msg Dimension mismatch: array 'cov' is of shape %s, but 'mean' is a vector of length %d. N/A msg N/A msg N/A N/A str N/A cov shape N/A len mean N/A N/A ValueError msg N/A N/A N/A N/A cov ndim 2 N/A N/A N/A ValueError N/A Array 'cov' must be at most two-dimensional, but cov.ndim = %d N/A cov ndim N/A N/A dim mean cov N/A _process_quantiles N/A N/A self x dim N/A N/A N/A 
        Adjust quantiles array so that last axis labels the components of
        each data point.

         N/A x N/A N/A np asarray x dtype float N/A N/A N/A x ndim 0 N/A N/A x N/A x N/A N/A np newaxis N/A N/A N/A N/A x ndim 1 N/A N/A N/A dim 1 N/A N/A x N/A x N/A N/A N/A N/A np newaxis N/A N/A x N/A x N/A N/A N/A np newaxis N/A N/A x N/A _logpdf N/A N/A self x mean prec_U log_det_cov rank N/A N/A N/A 
        Parameters
        ----------
        x : ndarray
            Points at which to evaluate the log of the probability
            density function
        mean : ndarray
            Mean of the distribution
        prec_U : ndarray
            A decomposition such that np.dot(prec_U, prec_U.T)
            is the precision matrix, i.e. inverse of the covariance matrix.
        log_det_cov : float
            Logarithm of the determinant of the covariance matrix
        rank : int
            Rank of the covariance matrix.

        Notes
        -----
        As this function does no argument checking, it should not be
        called directly; use 'logpdf' instead.

         N/A dev N/A x mean N/A maha N/A N/A np sum N/A N/A np square N/A N/A np dot dev prec_U axis -1 N/A N/A -0.5 N/A N/A N/A rank _LOG_2PI log_det_cov maha N/A logpdf N/A N/A self x mean cov allow_singular N/A False N/A N/A 
        Log of the multivariate normal probability density function.

        Parameters
        ----------
        x : array_like
            Quantiles, with the last axis of `x` denoting the components.
        %(_mvn_doc_default_callparams)s

        Returns
        -------
        pdf : ndarray
            Log of the probability density function evaluated at `x`

        Notes
        -----
        %(_mvn_doc_callparams_note)s

         N/A N/A dim mean cov N/A N/A self _process_parameters None mean cov N/A x N/A N/A self _process_quantiles x dim N/A psd N/A _PSD cov allow_singular allow_singular N/A out N/A N/A self _logpdf x mean N/A psd U N/A psd log_pdet N/A psd rank N/A N/A _squeeze_output out N/A pdf N/A N/A self x mean cov allow_singular N/A False N/A N/A 
        Multivariate normal probability density function.

        Parameters
        ----------
        x : array_like
            Quantiles, with the last axis of `x` denoting the components.
        %(_mvn_doc_default_callparams)s

        Returns
        -------
        pdf : ndarray
            Probability density function evaluated at `x`

        Notes
        -----
        %(_mvn_doc_callparams_note)s

         N/A N/A dim mean cov N/A N/A self _process_parameters None mean cov N/A x N/A N/A self _process_quantiles x dim N/A psd N/A _PSD cov allow_singular allow_singular N/A out N/A N/A np exp N/A N/A self _logpdf x mean N/A psd U N/A psd log_pdet N/A psd rank N/A N/A _squeeze_output out N/A rvs N/A N/A self mean cov size random_state N/A None 1 1 None N/A N/A 
        Draw random samples from a multivariate normal distribution.

        Parameters
        ----------
        %(_mvn_doc_default_callparams)s
        size : integer, optional
            Number of samples to draw (default 1).
        %(_doc_random_state)s

        Returns
        -------
        rvs : ndarray or scalar
            Random variates of size (`size`, `N`), where `N` is the
            dimension of the random variable.

        Notes
        -----
        %(_mvn_doc_callparams_note)s

         N/A N/A dim mean cov N/A N/A self _process_parameters None mean cov N/A random_state N/A N/A self _get_random_state random_state N/A out N/A N/A random_state multivariate_normal mean cov size N/A N/A _squeeze_output out N/A entropy N/A N/A self mean cov N/A None 1 N/A N/A 
        Compute the differential entropy of the multivariate normal.

        Parameters
        ----------
        %(_mvn_doc_default_callparams)s

        Returns
        -------
        h : scalar
            Entropy of the multivariate normal distribution

        Notes
        -----
        %(_mvn_doc_callparams_note)s

         N/A N/A dim mean cov N/A N/A self _process_parameters None mean cov N/A N/A _ logdet N/A N/A N/A np linalg slogdet N/A N/A N/A 2 N/A np pi N/A np e cov N/A N/A 0.5 logdet N/A N/A N/A multivariate_normal N/A multivariate_normal_gen multivariate_normal_frozen N/A multi_rv_frozen N/A __init__ N/A N/A self mean cov allow_singular seed N/A None 1 False None N/A N/A 
        Create a frozen multivariate normal distribution.

        Parameters
        ----------
        mean : array_like, optional
            Mean of the distribution (default zero)
        cov : array_like, optional
            Covariance matrix of the distribution (default one)
        allow_singular : bool, optional
            If this flag is True then tolerate a singular
            covariance matrix (default False).
        seed : None or int or np.random.RandomState instance, optional
            This parameter defines the RandomState object to use for drawing
            random variates.
            If None (or np.random), the global np.random state is used.
            If integer, it is used to seed the local RandomState instance
            Default is None.

        Examples
        --------
        When called with the default parameters, this will create a 1D random
        variable with mean 0 and covariance 1:

        >>> from scipy.stats import multivariate_normal
        >>> r = multivariate_normal()
        >>> r.mean
        array([ 0.])
        >>> r.cov
        array([[1.]])

         N/A N/A self _dist N/A multivariate_normal_gen seed N/A N/A N/A self dim N/A self mean N/A self cov N/A N/A N/A self _dist _process_parameters None mean cov N/A N/A self cov_info N/A _PSD N/A self cov allow_singular allow_singular N/A logpdf N/A N/A self x N/A N/A N/A x N/A N/A N/A self _dist _process_quantiles x N/A self dim N/A out N/A N/A N/A self _dist _logpdf x N/A self mean N/A N/A self cov_info U N/A N/A self cov_info log_pdet N/A N/A self cov_info rank N/A N/A _squeeze_output out N/A pdf N/A N/A self x N/A N/A N/A N/A N/A np exp N/A N/A self logpdf x N/A rvs N/A N/A self size random_state N/A 1 None N/A N/A N/A N/A N/A self _dist rvs N/A self mean N/A self cov size random_state N/A entropy N/A N/A self N/A N/A N/A 
        Computes the differential entropy of the multivariate normal.

        Returns
        -------
        h : scalar
            Entropy of the multivariate normal distribution

         N/A log_pdet N/A N/A self cov_info log_pdet N/A rank N/A N/A self cov_info rank N/A N/A 0.5 N/A N/A rank N/A _LOG_2PI 1 log_pdet N/A N/A N/A name N/A logpdf pdf rvs N/A N/A method N/A N/A multivariate_normal_gen __dict__ N/A name N/A method_frozen N/A N/A multivariate_normal_frozen __dict__ N/A name N/A N/A method_frozen __doc__ N/A N/A doccer docformat N/A method __doc__ mvn_docdict_noparams N/A N/A method __doc__ N/A N/A doccer docformat N/A method __doc__ mvn_docdict_params N/A _matnorm_doc_default_callparams mean : array_like, optional
    Mean of the distribution (default: `None`)
rowcov : array_like, optional
    Among-row covariance matrix of the distribution (default: `1`)
colcov : array_like, optional
    Among-column covariance matrix of the distribution (default: `1`)
 N/A _matnorm_doc_callparams_note If `mean` is set to `None` then a matrix of zeros is used for the mean.
    The dimensions of this matrix are inferred from the shape of `rowcov` and
    `colcov`, if these are provided, or set to `1` if ambiguous.

    `rowcov` and `colcov` can be two-dimensional array_likes specifying the
    covariance matrices directly. Alternatively, a one-dimensional array will
    be be interpreted as the entries of a diagonal matrix, and a scalar or
    zero-dimensional array will be interpreted as this value times the
    identity matrix.
     N/A _matnorm_doc_frozen_callparams N/A _matnorm_doc_frozen_callparams_note See class definition for a detailed description of parameters. N/A matnorm_docdict_params N/A _matnorm_doc_default_callparams _matnorm_doc_callparams_note _doc_random_state _matnorm_doc_default_callparams _matnorm_doc_callparams_note _doc_random_state N/A matnorm_docdict_noparams N/A _matnorm_doc_default_callparams _matnorm_doc_callparams_note _doc_random_state _matnorm_doc_frozen_callparams _matnorm_doc_frozen_callparams_note _doc_random_state matrix_normal_gen N/A multi_rv_generic N/A N/A 
    A matrix normal random variable.

    The `mean` keyword specifies the mean. The `rowcov` keyword specifies the
    among-row covariance matrix. The 'colcov' keyword specifies the
    among-column covariance matrix.

    Methods
    -------
    ``pdf(X, mean=None, rowcov=1, colcov=1)``
        Probability density function.
    ``logpdf(X, mean=None, rowcov=1, colcov=1)``
        Log of the probability density function.
    ``rvs(mean=None, rowcov=1, colcov=1, size=1, random_state=None)``
        Draw random samples.

    Parameters
    ----------
    X : array_like
        Quantiles, with the last two axes of `X` denoting the components.
    %(_matnorm_doc_default_callparams)s
    %(_doc_random_state)s

    Alternatively, the object may be called (as a function) to fix the mean
    and covariance parameters, returning a "frozen" matrix normal
    random variable:

    rv = matrix_normal(mean=None, rowcov=1, colcov=1)
        - Frozen object with the same methods but holding the given
          mean and covariance fixed.

    Notes
    -----
    %(_matnorm_doc_callparams_note)s

    The covariance matrices specified by `rowcov` and `colcov` must be
    (symmetric) positive definite. If the samples in `X` are
    :math:`m \times n`, then `rowcov` must be :math:`m \times m` and
    `colcov` must be :math:`n \times n`. `mean` must be the same shape as `X`.

    The probability density function for `matrix_normal` is

    .. math::

        f(X) = (2 \pi)^{-\frac{mn}{2}}|U|^{-\frac{n}{2}} |V|^{-\frac{m}{2}}
               \exp\left( -\frac{1}{2} \mathrm{Tr}\left[ U^{-1} (X-M) V^{-1}
               (X-M)^T \right] \right),

    where :math:`M` is the mean, :math:`U` the among-row covariance matrix,
    :math:`V` the among-column covariance matrix.

    The `allow_singular` behaviour of the `multivariate_normal`
    distribution is not currently supported. Covariance matrices must be
    full rank.

    The `matrix_normal` distribution is closely related to the
    `multivariate_normal` distribution. Specifically, :math:`\mathrm{Vec}(X)`
    (the vector formed by concatenating the columns  of :math:`X`) has a
    multivariate normal distribution with mean :math:`\mathrm{Vec}(M)`
    and covariance :math:`V \otimes U` (where :math:`\otimes` is the Kronecker
    product). Sampling and pdf evaluation are
    :math:`\mathcal{O}(m^3 + n^3 + m^2 n + m n^2)` for the matrix normal, but
    :math:`\mathcal{O}(m^3 n^3)` for the equivalent multivariate normal,
    making this equivalent form algorithmically inefficient.

    .. versionadded:: 0.17.0

    Examples
    --------

    >>> from scipy.stats import matrix_normal

    >>> M = np.arange(6).reshape(3,2); M
    array([[0, 1],
           [2, 3],
           [4, 5]])
    >>> U = np.diag([1,2,3]); U
    array([[1, 0, 0],
           [0, 2, 0],
           [0, 0, 3]])
    >>> V = 0.3*np.identity(2); V
    array([[ 0.3,  0. ],
           [ 0. ,  0.3]])
    >>> X = M + 0.1; X
    array([[ 0.1,  1.1],
           [ 2.1,  3.1],
           [ 4.1,  5.1]])
    >>> matrix_normal.pdf(X, mean=M, rowcov=U, colcov=V)
    0.023410202050005054

    >>> # Equivalent multivariate normal
    >>> from scipy.stats import multivariate_normal
    >>> vectorised_X = X.T.flatten()
    >>> equiv_mean = M.T.flatten()
    >>> equiv_cov = np.kron(V,U)
    >>> multivariate_normal.pdf(vectorised_X, mean=equiv_mean, cov=equiv_cov)
    0.023410202050005054
     __init__ N/A N/A self seed N/A None N/A N/A N/A N/A N/A super matrix_normal_gen self __init__ seed N/A N/A self __doc__ N/A N/A doccer docformat N/A self __doc__ matnorm_docdict_params N/A __call__ N/A N/A self mean rowcov colcov seed N/A None 1 1 None N/A N/A 
        Create a frozen matrix normal distribution.

        See `matrix_normal_frozen` for more information.

         N/A N/A matrix_normal_frozen mean rowcov colcov seed seed N/A _process_parameters N/A N/A self mean rowcov colcov N/A N/A N/A 
        Infer dimensionality from mean or covariance matrices. Handle
        defaults. Ensure compatible dimensions.

         N/A N/A mean None N/A N/A mean N/A N/A np asarray mean dtype float N/A meanshape N/A mean shape N/A N/A N/A len meanshape 2 N/A N/A N/A ValueError Array `mean` must be two dimensional. N/A N/A N/A np any N/A meanshape 0 N/A N/A N/A ValueError Array `mean` has invalid shape. N/A rowcov N/A N/A np asarray rowcov dtype float N/A N/A N/A rowcov ndim 0 N/A N/A N/A mean None N/A N/A rowcov N/A rowcov N/A N/A np identity N/A meanshape N/A 0 N/A N/A rowcov N/A rowcov N/A N/A np identity 1 N/A N/A N/A N/A rowcov ndim 1 N/A N/A rowcov N/A N/A np diag rowcov N/A rowshape N/A rowcov shape N/A N/A N/A len rowshape 2 N/A N/A N/A ValueError `rowcov` must be a scalar or a 2D array. N/A N/A N/A rowshape N/A 0 N/A rowshape N/A 1 N/A N/A N/A ValueError Array `rowcov` must be square. N/A N/A N/A rowshape N/A 0 0 N/A N/A N/A ValueError Array `rowcov` has invalid shape. N/A numrows N/A rowshape N/A 0 N/A colcov N/A N/A np asarray colcov dtype float N/A N/A N/A colcov ndim 0 N/A N/A N/A mean None N/A N/A colcov N/A colcov N/A N/A np identity N/A meanshape N/A 1 N/A N/A colcov N/A colcov N/A N/A np identity 1 N/A N/A N/A N/A colcov ndim 1 N/A N/A colcov N/A N/A np diag colcov N/A colshape N/A colcov shape N/A N/A N/A len colshape 2 N/A N/A N/A ValueError `colcov` must be a scalar or a 2D array. N/A N/A N/A colshape N/A 0 N/A colshape N/A 1 N/A N/A N/A ValueError Array `colcov` must be square. N/A N/A N/A colshape N/A 0 0 N/A N/A N/A ValueError Array `colcov` has invalid shape. N/A numcols N/A colshape N/A 0 N/A N/A mean None N/A N/A N/A N/A meanshape N/A 0 numrows N/A N/A N/A ValueError Arrays `mean` and `rowcov` must have thesame number of rows. N/A N/A N/A meanshape N/A 1 numcols N/A N/A N/A ValueError Arrays `mean` and `colcov` must have thesame number of columns. N/A N/A mean N/A N/A np zeros N/A numrows numcols N/A dims N/A numrows numcols N/A N/A dims mean rowcov colcov N/A _process_quantiles N/A N/A self X dims N/A N/A N/A 
        Adjust quantiles array so that last two axes labels the components of
        each data point.

         N/A X N/A N/A np asarray X dtype float N/A N/A N/A X ndim 2 N/A N/A X N/A X N/A N/A N/A np newaxis N/A N/A N/A N/A N/A X shape N/A -2 dims N/A N/A N/A ValueError The shape of array `X` is not compatible with the distribution parameters. N/A X N/A _logpdf N/A N/A self dims X mean row_prec_rt log_det_rowcov col_prec_rt log_det_colcov N/A N/A N/A 
        Parameters
        ----------
        dims : tuple
            Dimensions of the matrix variates
        X : ndarray
            Points at which to evaluate the log of the probability
            density function
        mean : ndarray
            Mean of the distribution
        row_prec_rt : ndarray
            A decomposition such that np.dot(row_prec_rt, row_prec_rt.T)
            is the inverse of the among-row covariance matrix
        log_det_rowcov : float
            Logarithm of the determinant of the among-row covariance matrix
        col_prec_rt : ndarray
            A decomposition such that np.dot(col_prec_rt, col_prec_rt.T)
            is the inverse of the among-column covariance matrix
        log_det_colcov : float
            Logarithm of the determinant of the among-column covariance matrix

        Notes
        -----
        As this function does no argument checking, it should not be
        called directly; use 'logpdf' instead.

         N/A N/A numrows numcols dims N/A roll_dev N/A N/A np rollaxis N/A X mean axis -1 start 0 N/A scale_dev N/A N/A np tensordot N/A col_prec_rt T N/A N/A np dot roll_dev row_prec_rt 1 N/A maha N/A N/A np sum N/A N/A np sum N/A N/A np square scale_dev axis -1 axis 0 N/A N/A -0.5 N/A N/A N/A N/A N/A numrows numcols _LOG_2PI N/A numcols log_det_rowcov N/A numrows log_det_colcov maha N/A logpdf N/A N/A self X mean rowcov colcov N/A None 1 1 N/A N/A 
        Log of the matrix normal probability density function.

        Parameters
        ----------
        X : array_like
            Quantiles, with the last two axes of `X` denoting the components.
        %(_matnorm_doc_default_callparams)s

        Returns
        -------
        logpdf : ndarray
            Log of the probability density function evaluated at `X`

        Notes
        -----
        %(_matnorm_doc_callparams_note)s

         N/A N/A dims mean rowcov colcov N/A N/A self _process_parameters mean rowcov colcov N/A X N/A N/A self _process_quantiles X dims N/A rowpsd N/A _PSD rowcov allow_singular False N/A colpsd N/A _PSD colcov allow_singular False N/A out N/A N/A self _logpdf dims X mean N/A rowpsd U N/A rowpsd log_pdet N/A colpsd U N/A colpsd log_pdet N/A N/A _squeeze_output out N/A pdf N/A N/A self X mean rowcov colcov N/A None 1 1 N/A N/A 
        Matrix normal probability density function.

        Parameters
        ----------
        X : array_like
            Quantiles, with the last two axes of `X` denoting the components.
        %(_matnorm_doc_default_callparams)s

        Returns
        -------
        pdf : ndarray
            Probability density function evaluated at `X`

        Notes
        -----
        %(_matnorm_doc_callparams_note)s

         N/A N/A N/A np exp N/A N/A self logpdf X mean rowcov colcov N/A rvs N/A N/A self mean rowcov colcov size random_state N/A None 1 1 1 None N/A N/A 
        Draw random samples from a matrix normal distribution.

        Parameters
        ----------
        %(_matnorm_doc_default_callparams)s
        size : integer, optional
            Number of samples to draw (default 1).
        %(_doc_random_state)s

        Returns
        -------
        rvs : ndarray or scalar
            Random variates of size (`size`, `dims`), where `dims` is the
            dimension of the random matrices.

        Notes
        -----
        %(_matnorm_doc_callparams_note)s

         N/A size N/A int size N/A N/A dims mean rowcov colcov N/A N/A self _process_parameters mean rowcov colcov N/A rowchol N/A N/A N/A scipy linalg cholesky rowcov lower True N/A colchol N/A N/A N/A scipy linalg cholesky colcov lower True N/A random_state N/A N/A self _get_random_state random_state N/A std_norm N/A N/A random_state standard_normal size N/A N/A dims N/A 1 size N/A dims N/A 0 N/A roll_rvs N/A N/A np tensordot colchol N/A N/A np dot std_norm N/A rowchol T 1 N/A out N/A N/A N/A np rollaxis N/A roll_rvs T axis 1 start 0 N/A mean N/A N/A N/A np newaxis N/A N/A N/A N/A size 1 N/A N/A out N/A N/A out reshape N/A mean shape N/A out N/A N/A N/A matrix_normal N/A matrix_normal_gen matrix_normal_frozen N/A multi_rv_frozen N/A __init__ N/A N/A self mean rowcov colcov seed N/A None 1 1 None N/A N/A 
        Create a frozen matrix normal distribution.

        Parameters
        ----------
        %(_matnorm_doc_default_callparams)s
        seed : None or int or np.random.RandomState instance, optional
            If int or RandomState, use it for drawing the random variates.
            If None (or np.random), the global np.random state is used.
            Default is None.

        Examples
        --------
        >>> from scipy.stats import matrix_normal

        >>> distn = matrix_normal(mean=np.zeros((3,3)))
        >>> X = distn.rvs(); X
        array([[-0.02976962,  0.93339138, -0.09663178],
               [ 0.67405524,  0.28250467, -0.93308929],
               [-0.31144782,  0.74535536,  1.30412916]])
        >>> distn.pdf(X)
        2.5160642368346784e-05
        >>> distn.logpdf(X)
        -10.590229595124615
         N/A N/A self _dist N/A matrix_normal_gen seed N/A N/A N/A self dims N/A self mean N/A self rowcov N/A self colcov N/A N/A N/A self _dist _process_parameters mean rowcov colcov N/A N/A self rowpsd N/A _PSD N/A self rowcov allow_singular False N/A N/A self colpsd N/A _PSD N/A self colcov allow_singular False N/A logpdf N/A N/A self X N/A N/A N/A X N/A N/A N/A self _dist _process_quantiles X N/A self dims N/A out N/A N/A N/A self _dist _logpdf N/A self dims X N/A self mean N/A N/A self rowpsd U N/A N/A self rowpsd log_pdet N/A N/A self colpsd U N/A N/A self colpsd log_pdet N/A N/A _squeeze_output out N/A pdf N/A N/A self X N/A N/A N/A N/A N/A np exp N/A N/A self logpdf X N/A rvs N/A N/A self size random_state N/A 1 None N/A N/A N/A N/A N/A self _dist rvs N/A self mean N/A self rowcov N/A self colcov size random_state N/A N/A N/A name N/A logpdf pdf rvs N/A N/A method N/A N/A matrix_normal_gen __dict__ N/A name N/A method_frozen N/A N/A matrix_normal_frozen __dict__ N/A name N/A N/A method_frozen __doc__ N/A N/A doccer docformat N/A method __doc__ matnorm_docdict_noparams N/A N/A method __doc__ N/A N/A doccer docformat N/A method __doc__ matnorm_docdict_params N/A _dirichlet_doc_default_callparams alpha : array_like
    The concentration parameters. The number of entries determines the
    dimensionality of the distribution.
 N/A _dirichlet_doc_frozen_callparams N/A _dirichlet_doc_frozen_callparams_note See class definition for a detailed description of parameters. N/A dirichlet_docdict_params N/A _dirichlet_doc_default_callparams _doc_random_state _dirichlet_doc_default_callparams _doc_random_state N/A dirichlet_docdict_noparams N/A _dirichlet_doc_default_callparams _doc_random_state _dirichlet_doc_frozen_callparams _doc_random_state _dirichlet_check_parameters N/A N/A alpha N/A N/A N/A alpha N/A N/A np asarray alpha N/A N/A N/A N/A np min alpha 0 N/A N/A N/A ValueError All parameters must be greater than 0 N/A N/A N/A N/A alpha ndim 1 N/A N/A N/A ValueError N/A Parameter vector 'a' must be one dimensional, but a.shape = %s. N/A N/A alpha shape N/A alpha N/A _dirichlet_check_input N/A N/A alpha x N/A N/A N/A x N/A N/A np asarray x N/A N/A N/A N/A N/A N/A x shape N/A 0 1 N/A N/A alpha shape N/A 0 N/A N/A N/A x shape N/A 0 N/A N/A alpha shape N/A 0 N/A N/A N/A ValueError N/A Vector 'x' must have either the same number of entries as, or one entry fewer than, parameter vector 'a', but alpha.shape = %s and x.shape = %s. N/A N/A alpha shape N/A x shape N/A N/A N/A N/A x shape N/A 0 N/A N/A alpha shape N/A 0 N/A N/A xk N/A N/A np array N/A N/A 1 N/A N/A np sum x 0 N/A N/A N/A xk ndim 1 N/A N/A x N/A N/A np append x xk N/A N/A N/A N/A xk ndim 2 N/A N/A x N/A N/A np vstack N/A x xk N/A N/A N/A ValueError The input must be one dimensional or a two dimensional matrix containing the entries. N/A N/A N/A N/A np min x 0 N/A N/A N/A ValueError Each entry in 'x' must be greater than zero. N/A N/A N/A N/A np max x 1 N/A N/A N/A ValueError Each entry in 'x' must be smaller or equal one. N/A N/A N/A N/A N/A N/A np abs N/A N/A N/A np sum x 0 1.0 1e-09 any N/A N/A N/A ValueError N/A The input vector 'x' must lie within the normal simplex. but np.sum(x, 0) = %s. N/A N/A np sum x 0 N/A x N/A _lnB N/A N/A alpha N/A N/A N/A 
    Internal helper function to compute the log of the useful quotient

    .. math::

        B(\alpha) = \frac{\prod_{i=1}{K}\Gamma(\alpha_i)}{\Gamma\left(\sum_{i=1}^{K}\alpha_i\right)}

    Parameters
    ----------
    %(_dirichlet_doc_default_callparams)s

    Returns
    -------
    B : scalar
        Helper quotient, internal use only

     N/A N/A N/A N/A np sum N/A gammaln alpha N/A gammaln N/A N/A np sum alpha N/A dirichlet_gen N/A multi_rv_generic N/A N/A 
    A Dirichlet random variable.

    The `alpha` keyword specifies the concentration parameters of the
    distribution.

    .. versionadded:: 0.15.0

    Methods
    -------
    ``pdf(x, alpha)``
        Probability density function.
    ``logpdf(x, alpha)``
        Log of the probability density function.
    ``rvs(alpha, size=1, random_state=None)``
        Draw random samples from a Dirichlet distribution.
    ``mean(alpha)``
        The mean of the Dirichlet distribution
    ``var(alpha)``
        The variance of the Dirichlet distribution
    ``entropy(alpha)``
        Compute the differential entropy of the multivariate normal.

    Parameters
    ----------
    x : array_like
        Quantiles, with the last axis of `x` denoting the components.
    %(_dirichlet_doc_default_callparams)s
    %(_doc_random_state)s

    Alternatively, the object may be called (as a function) to fix
    concentration parameters, returning a "frozen" Dirichlet
    random variable:

    rv = dirichlet(alpha)
        - Frozen object with the same methods but holding the given
          concentration parameters fixed.

    Notes
    -----
    Each :math:`\alpha` entry must be positive. The distribution has only
    support on the simplex defined by

    .. math::
        \sum_{i=1}^{K} x_i \le 1


    The probability density function for `dirichlet` is

    .. math::

        f(x) = \frac{1}{\mathrm{B}(\boldsymbol\alpha)} \prod_{i=1}^K x_i^{\alpha_i - 1}

    where

    .. math::

        \mathrm{B}(\boldsymbol\alpha) = \frac{\prod_{i=1}^K \Gamma(\alpha_i)}
                                     {\Gamma\bigl(\sum_{i=1}^K \alpha_i\bigr)}

    and :math:`\boldsymbol\alpha=(\alpha_1,\ldots,\alpha_K)`, the
    concentration parameters and :math:`K` is the dimension of the space
    where :math:`x` takes values.

    Note that the dirichlet interface is somewhat inconsistent.
    The array returned by the rvs function is transposed
    with respect to the format expected by the pdf and logpdf.

     __init__ N/A N/A self seed N/A None N/A N/A N/A N/A N/A super dirichlet_gen self __init__ seed N/A N/A self __doc__ N/A N/A doccer docformat N/A self __doc__ dirichlet_docdict_params N/A __call__ N/A N/A self alpha seed N/A None N/A N/A N/A dirichlet_frozen alpha seed seed N/A _logpdf N/A N/A self x alpha N/A N/A N/A 
        Parameters
        ----------
        x : ndarray
            Points at which to evaluate the log of the probability
            density function
        %(_dirichlet_doc_default_callparams)s

        Notes
        -----
        As this function does no argument checking, it should not be
        called directly; use 'logpdf' instead.

         N/A lnB N/A _lnB alpha N/A N/A N/A lnB N/A N/A np sum N/A N/A N/A N/A np log N/A x T N/A alpha 1 T 0 N/A logpdf N/A N/A self x alpha N/A N/A N/A 
        Log of the Dirichlet probability density function.

        Parameters
        ----------
        x : array_like
            Quantiles, with the last axis of `x` denoting the components.
        %(_dirichlet_doc_default_callparams)s

        Returns
        -------
        pdf : ndarray
            Log of the probability density function evaluated at `x`.

         N/A alpha N/A _dirichlet_check_parameters alpha N/A x N/A _dirichlet_check_input alpha x N/A out N/A N/A self _logpdf x alpha N/A N/A _squeeze_output out N/A pdf N/A N/A self x alpha N/A N/A N/A 
        The Dirichlet probability density function.

        Parameters
        ----------
        x : array_like
            Quantiles, with the last axis of `x` denoting the components.
        %(_dirichlet_doc_default_callparams)s

        Returns
        -------
        pdf : ndarray
            The probability density function evaluated at `x`.

         N/A alpha N/A _dirichlet_check_parameters alpha N/A x N/A _dirichlet_check_input alpha x N/A out N/A N/A np exp N/A N/A self _logpdf x alpha N/A N/A _squeeze_output out N/A mean N/A N/A self alpha N/A N/A N/A 
        Compute the mean of the dirichlet distribution.

        Parameters
        ----------
        %(_dirichlet_doc_default_callparams)s

        Returns
        -------
        mu : scalar
            Mean of the Dirichlet distribution

         N/A alpha N/A _dirichlet_check_parameters alpha N/A out N/A alpha N/A N/A np sum alpha N/A N/A _squeeze_output out N/A var N/A N/A self alpha N/A N/A N/A 
        Compute the variance of the dirichlet distribution.

        Parameters
        ----------
        %(_dirichlet_doc_default_callparams)s

        Returns
        -------
        v : scalar
            Variance of the Dirichlet distribution

         N/A alpha N/A _dirichlet_check_parameters alpha N/A alpha0 N/A N/A np sum alpha N/A out N/A N/A alpha N/A alpha0 alpha N/A N/A alpha0 alpha0 N/A alpha0 1 N/A out N/A entropy N/A N/A self alpha N/A N/A N/A 
        Compute the differential entropy of the dirichlet distribution.

        Parameters
        ----------
        %(_dirichlet_doc_default_callparams)s

        Returns
        -------
        h : scalar
            Entropy of the Dirichlet distribution

         N/A alpha N/A _dirichlet_check_parameters alpha N/A alpha0 N/A N/A np sum alpha N/A lnB N/A _lnB alpha N/A K N/A N/A alpha shape N/A 0 N/A out N/A N/A lnB N/A N/A alpha0 K N/A N/A N/A scipy special psi alpha0 N/A N/A np sum N/A N/A alpha 1 N/A N/A N/A scipy special psi alpha N/A N/A _squeeze_output out N/A rvs N/A N/A self alpha size random_state N/A 1 None N/A N/A 
        Draw random samples from a Dirichlet distribution.

        Parameters
        ----------
        %(_dirichlet_doc_default_callparams)s
        size : int, optional
            Number of samples to draw (default 1).
        %(_doc_random_state)s

        Returns
        -------
        rvs : ndarray or scalar
            Random variates of size (`size`, `N`), where `N` is the
            dimension of the random variable.

         N/A alpha N/A _dirichlet_check_parameters alpha N/A random_state N/A N/A self _get_random_state random_state N/A N/A N/A random_state dirichlet alpha size size N/A N/A N/A dirichlet N/A dirichlet_gen dirichlet_frozen N/A multi_rv_frozen N/A __init__ N/A N/A self alpha seed N/A None N/A N/A N/A self alpha N/A _dirichlet_check_parameters alpha N/A N/A self _dist N/A dirichlet_gen seed N/A logpdf N/A N/A self x N/A N/A N/A N/A N/A N/A self _dist logpdf x N/A self alpha N/A pdf N/A N/A self x N/A N/A N/A N/A N/A N/A self _dist pdf x N/A self alpha N/A mean N/A N/A self N/A N/A N/A N/A N/A N/A self _dist mean N/A self alpha N/A var N/A N/A self N/A N/A N/A N/A N/A N/A self _dist var N/A self alpha N/A entropy N/A N/A self N/A N/A N/A N/A N/A N/A self _dist entropy N/A self alpha N/A rvs N/A N/A self size random_state N/A 1 None N/A N/A N/A N/A N/A self _dist rvs N/A self alpha size random_state N/A N/A N/A name N/A logpdf pdf rvs mean var entropy N/A N/A method N/A N/A dirichlet_gen __dict__ N/A name N/A method_frozen N/A N/A dirichlet_frozen __dict__ N/A name N/A N/A method_frozen __doc__ N/A N/A doccer docformat N/A method __doc__ dirichlet_docdict_noparams N/A N/A method __doc__ N/A N/A doccer docformat N/A method __doc__ dirichlet_docdict_params N/A _wishart_doc_default_callparams df : int
    Degrees of freedom, must be greater than or equal to dimension of the
    scale matrix
scale : array_like
    Symmetric positive definite scale matrix of the distribution
 N/A _wishart_doc_callparams_note N/A _wishart_doc_frozen_callparams N/A _wishart_doc_frozen_callparams_note See class definition for a detailed description of parameters. N/A wishart_docdict_params N/A _doc_default_callparams _doc_callparams_note _doc_random_state _wishart_doc_default_callparams _wishart_doc_callparams_note _doc_random_state N/A wishart_docdict_noparams N/A _doc_default_callparams _doc_callparams_note _doc_random_state _wishart_doc_frozen_callparams _wishart_doc_frozen_callparams_note _doc_random_state wishart_gen N/A multi_rv_generic N/A N/A 
    A Wishart random variable.

    The `df` keyword specifies the degrees of freedom. The `scale` keyword
    specifies the scale matrix, which must be symmetric and positive definite.
    In this context, the scale matrix is often interpreted in terms of a
    multivariate normal precision matrix (the inverse of the covariance
    matrix).

    Methods
    -------
    ``pdf(x, df, scale)``
        Probability density function.
    ``logpdf(x, df, scale)``
        Log of the probability density function.
    ``rvs(df, scale, size=1, random_state=None)``
        Draw random samples from a Wishart distribution.
    ``entropy()``
        Compute the differential entropy of the Wishart distribution.

    Parameters
    ----------
    x : array_like
        Quantiles, with the last axis of `x` denoting the components.
    %(_doc_default_callparams)s
    %(_doc_random_state)s

    Alternatively, the object may be called (as a function) to fix the degrees
    of freedom and scale parameters, returning a "frozen" Wishart random
    variable:

    rv = wishart(df=1, scale=1)
        - Frozen object with the same methods but holding the given
          degrees of freedom and scale fixed.

    See Also
    --------
    invwishart, chi2

    Notes
    -----
    %(_doc_callparams_note)s

    The scale matrix `scale` must be a symmetric positive definite
    matrix. Singular matrices, including the symmetric positive semi-definite
    case, are not supported.

    The Wishart distribution is often denoted

    .. math::

        W_p(\nu, \Sigma)

    where :math:`\nu` is the degrees of freedom and :math:`\Sigma` is the
    :math:`p \times p` scale matrix.

    The probability density function for `wishart` has support over positive
    definite matrices :math:`S`; if :math:`S \sim W_p(\nu, \Sigma)`, then
    its PDF is given by:

    .. math::

        f(S) = \frac{|S|^{\frac{\nu - p - 1}{2}}}{2^{ \frac{\nu p}{2} }
               |\Sigma|^\frac{\nu}{2} \Gamma_p \left ( \frac{\nu}{2} \right )}
               \exp\left( -tr(\Sigma^{-1} S) / 2 \right)

    If :math:`S \sim W_p(\nu, \Sigma)` (Wishart) then
    :math:`S^{-1} \sim W_p^{-1}(\nu, \Sigma^{-1})` (inverse Wishart).

    If the scale matrix is 1-dimensional and equal to one, then the Wishart
    distribution :math:`W_1(\nu, 1)` collapses to the :math:`\chi^2(\nu)`
    distribution.

    .. versionadded:: 0.16.0

    References
    ----------
    .. [1] M.L. Eaton, "Multivariate Statistics: A Vector Space Approach",
           Wiley, 1983.
    .. [2] W.B. Smith and R.R. Hocking, "Algorithm AS 53: Wishart Variate
           Generator", Applied Statistics, vol. 21, pp. 341-345, 1972.

    Examples
    --------
    >>> import matplotlib.pyplot as plt
    >>> from scipy.stats import wishart, chi2
    >>> x = np.linspace(1e-5, 8, 100)
    >>> w = wishart.pdf(x, df=3, scale=1); w[:5]
    array([ 0.00126156,  0.10892176,  0.14793434,  0.17400548,  0.1929669 ])
    >>> c = chi2.pdf(x, 3); c[:5]
    array([ 0.00126156,  0.10892176,  0.14793434,  0.17400548,  0.1929669 ])
    >>> plt.plot(x, w)

    The input quantiles can be any shape of array, as long as the last
    axis labels the components.

     __init__ N/A N/A self seed N/A None N/A N/A N/A N/A N/A super wishart_gen self __init__ seed N/A N/A self __doc__ N/A N/A doccer docformat N/A self __doc__ wishart_docdict_params N/A __call__ N/A N/A self df scale seed N/A None None None N/A N/A 
        Create a frozen Wishart distribution.

        See `wishart_frozen` for more information.

         N/A N/A wishart_frozen df scale seed N/A _process_parameters N/A N/A self df scale N/A N/A N/A N/A scale None N/A N/A scale 1.0 N/A scale N/A N/A np asarray scale dtype float N/A N/A N/A scale ndim 0 N/A N/A scale N/A scale N/A N/A N/A np newaxis N/A np newaxis N/A N/A N/A N/A scale ndim 1 N/A N/A scale N/A N/A np diag scale N/A N/A N/A N/A N/A scale ndim 2 N/A N/A N/A N/A scale shape N/A 0 N/A N/A scale shape N/A 1 N/A N/A N/A ValueError N/A Array 'scale' must be square if it is two dimensional, but scale.scale = %s. N/A str N/A scale shape N/A N/A N/A N/A scale ndim 2 N/A N/A N/A ValueError N/A Array 'scale' must be at most two-dimensional, but scale.ndim = %d N/A scale ndim N/A dim N/A N/A scale shape N/A 0 N/A N/A df None N/A N/A df dim N/A N/A N/A N/A N/A np isscalar df N/A N/A N/A ValueError Degrees of freedom must be a scalar. N/A N/A N/A df dim N/A N/A N/A ValueError N/A Degrees of freedom cannot be less than dimension of scale matrix, but df = %d df N/A N/A dim df scale N/A _process_quantiles N/A N/A self x dim N/A N/A N/A 
        Adjust quantiles array so that last axis labels the components of
        each data point.
         N/A x N/A N/A np asarray x dtype float N/A N/A N/A x ndim 0 N/A N/A x N/A x N/A N/A N/A np eye dim N/A N/A N/A N/A N/A np newaxis N/A N/A N/A x ndim 1 N/A N/A N/A dim 1 N/A N/A x N/A x N/A N/A N/A np newaxis N/A N/A np newaxis N/A N/A N/A x N/A N/A N/A np diag x N/A N/A N/A N/A N/A np newaxis N/A N/A N/A N/A x ndim 2 N/A N/A N/A N/A N/A N/A x shape N/A 0 N/A N/A x shape N/A 1 N/A N/A N/A ValueError N/A Quantiles must be square if they are two dimensional, but x.shape = %s. N/A str N/A x shape N/A x N/A x N/A N/A N/A N/A N/A np newaxis N/A N/A N/A N/A x ndim 3 N/A N/A N/A N/A N/A N/A x shape N/A 0 N/A N/A x shape N/A 1 N/A N/A N/A ValueError N/A Quantiles must be square in the first two dimensions if they are three dimensional, but x.shape = %s. N/A str N/A x shape N/A N/A N/A N/A x ndim 3 N/A N/A N/A ValueError N/A Quantiles must be at most two-dimensional with an additional dimension for multiplecomponents, but x.ndim = %d N/A x ndim N/A N/A N/A N/A N/A x shape N/A 0 2 N/A dim dim N/A N/A N/A ValueError N/A Quantiles have incompatible dimensions: should be %s, got %s. N/A N/A dim dim N/A N/A x shape N/A 0 2 N/A x N/A _process_size N/A N/A self size N/A N/A N/A size N/A N/A np asarray size N/A N/A N/A size ndim 0 N/A N/A size N/A size N/A N/A np newaxis N/A N/A N/A N/A size ndim 1 N/A N/A N/A ValueError N/A Size must be an integer or tuple of integers; thus must have dimension <= 1. Got size.ndim = %s N/A str N/A tuple size N/A n N/A N/A size prod N/A shape N/A tuple size N/A N/A n shape N/A _logpdf N/A N/A self x dim df scale log_det_scale C N/A N/A N/A 
        Parameters
        ----------
        x : ndarray
            Points at which to evaluate the log of the probability
            density function
        dim : int
            Dimension of the scale matrix
        df : int
            Degrees of freedom
        scale : ndarray
            Scale matrix
        log_det_scale : float
            Logarithm of the determinant of the scale matrix
        C : ndarray
            Cholesky factorization of the scale matrix, lower triagular.

        Notes
        -----
        As this function does no argument checking, it should not be
        called directly; use 'logpdf' instead.

         N/A log_det_x N/A N/A np zeros N/A N/A x shape N/A -1 N/A scale_inv_x N/A N/A np zeros N/A x shape N/A tr_scale_inv_x N/A N/A np zeros N/A N/A x shape N/A -1 N/A i N/A range N/A N/A x shape N/A -1 N/A N/A N/A _ N/A log_det_x N/A i N/A N/A self _cholesky_logdet N/A x N/A N/A N/A N/A i N/A N/A scale_inv_x N/A N/A N/A N/A i N/A N/A N/A scipy linalg cho_solve N/A C True N/A x N/A N/A N/A N/A i N/A N/A tr_scale_inv_x N/A i N/A N/A N/A scale_inv_x N/A N/A N/A N/A i trace N/A out N/A N/A N/A N/A 0.5 N/A N/A df dim 1 log_det_x N/A 0.5 tr_scale_inv_x N/A N/A N/A N/A N/A 0.5 df dim _LOG_2 N/A N/A 0.5 df log_det_scale N/A multigammaln N/A 0.5 df dim N/A out N/A logpdf N/A N/A self x df scale N/A N/A N/A 
        Log of the Wishart probability density function.

        Parameters
        ----------
        x : array_like
            Quantiles, with the last axis of `x` denoting the components.
            Each quantile must be a symmetric positive definite matrix.
        %(_doc_default_callparams)s

        Returns
        -------
        pdf : ndarray
            Log of the probability density function evaluated at `x`

        Notes
        -----
        %(_doc_callparams_note)s

         N/A N/A dim df scale N/A N/A self _process_parameters df scale N/A x N/A N/A self _process_quantiles x dim N/A N/A C log_det_scale N/A N/A self _cholesky_logdet scale N/A out N/A N/A self _logpdf x dim df scale log_det_scale C N/A N/A _squeeze_output out N/A pdf N/A N/A self x df scale N/A N/A N/A 
        Wishart probability density function.

        Parameters
        ----------
        x : array_like
            Quantiles, with the last axis of `x` denoting the components.
            Each quantile must be a symmetric positive definite matrix.
        %(_doc_default_callparams)s

        Returns
        -------
        pdf : ndarray
            Probability density function evaluated at `x`

        Notes
        -----
        %(_doc_callparams_note)s

         N/A N/A N/A np exp N/A N/A self logpdf x df scale N/A _mean N/A N/A self dim df scale N/A N/A N/A 
        Parameters
        ----------
        dim : int
            Dimension of the scale matrix
        %(_doc_default_callparams)s

        Notes
        -----
        As this function does no argument checking, it should not be
        called directly; use 'mean' instead.

         N/A N/A df scale N/A mean N/A N/A self df scale N/A N/A N/A 
        Mean of the Wishart distribution

        Parameters
        ----------
        %(_doc_default_callparams)s

        Returns
        -------
        mean : float
            The mean of the distribution
         N/A N/A dim df scale N/A N/A self _process_parameters df scale N/A out N/A N/A self _mean dim df scale N/A N/A _squeeze_output out N/A _mode N/A N/A self dim df scale N/A N/A N/A 
        Parameters
        ----------
        dim : int
            Dimension of the scale matrix
        %(_doc_default_callparams)s

        Notes
        -----
        As this function does no argument checking, it should not be
        called directly; use 'mode' instead.

         N/A N/A df N/A dim 1 N/A N/A out N/A N/A N/A df dim 1 scale N/A N/A out None N/A out N/A mode N/A N/A self df scale N/A N/A N/A 
        Mode of the Wishart distribution

        Only valid if the degrees of freedom are greater than the dimension of
        the scale matrix.

        Parameters
        ----------
        %(_doc_default_callparams)s

        Returns
        -------
        mode : float or None
            The Mode of the distribution
         N/A N/A dim df scale N/A N/A self _process_parameters df scale N/A out N/A N/A self _mode dim df scale N/A N/A N/A out None N/A _squeeze_output out out N/A _var N/A N/A self dim df scale N/A N/A N/A 
        Parameters
        ----------
        dim : int
            Dimension of the scale matrix
        %(_doc_default_callparams)s

        Notes
        -----
        As this function does no argument checking, it should not be
        called directly; use 'var' instead.

         N/A var N/A scale 2 N/A diag N/A N/A scale diagonal N/A var N/A N/A np outer diag diag N/A var df N/A var N/A var N/A N/A self df scale N/A N/A N/A 
        Variance of the Wishart distribution

        Parameters
        ----------
        %(_doc_default_callparams)s

        Returns
        -------
        var : float
            The variance of the distribution
         N/A N/A dim df scale N/A N/A self _process_parameters df scale N/A out N/A N/A self _var dim df scale N/A N/A _squeeze_output out N/A _standard_rvs N/A N/A self n shape dim df random_state N/A N/A N/A 
        Parameters
        ----------
        n : integer
            Number of variates to generate
        shape : iterable
            Shape of the variates to generate
        dim : int
            Dimension of the scale matrix
        df : int
            Degrees of freedom
        random_state : np.random.RandomState instance
            RandomState used for drawing the random variates.

        Notes
        -----
        As this function does no argument checking, it should not be
        called directly; use 'rvs' instead.

         N/A n_tril N/A N/A dim N/A dim 1 2 N/A covariances N/A N/A N/A N/A random_state normal size N/A n n_tril reshape N/A shape N/A n_tril N/A variances N/A N/A N/A N/A N/A np r_ N/A N/A N/A N/A N/A random_state chisquare N/A N/A df N/A i 1 1 size n 0.5 N/A i N/A range dim reshape N/A N/A dim N/A shape N/A -1 T N/A A N/A N/A np zeros N/A shape N/A dim dim N/A size_idx N/A tuple N/A N/A N/A slice None None None N/A len shape N/A tril_idx N/A N/A np tril_indices dim k -1 N/A N/A A N/A N/A size_idx tril_idx covariances N/A diag_idx N/A N/A np diag_indices dim N/A N/A A N/A N/A size_idx diag_idx variances N/A A N/A _rvs N/A N/A self n shape dim df C random_state N/A N/A N/A 
        Parameters
        ----------
        n : integer
            Number of variates to generate
        shape : iterable
            Shape of the variates to generate
        dim : int
            Dimension of the scale matrix
        df : int
            Degrees of freedom
        scale : ndarray
            Scale matrix
        C : ndarray
            Cholesky factorization of the scale matrix, lower triangular.
        %(_doc_random_state)s

        Notes
        -----
        As this function does no argument checking, it should not be
        called directly; use 'rvs' instead.

         N/A random_state N/A N/A self _get_random_state random_state N/A A N/A N/A self _standard_rvs n shape dim df random_state N/A index N/A N/A np ndindex shape N/A N/A CA N/A N/A np dot C N/A A N/A index N/A N/A A N/A index N/A N/A np dot CA N/A CA T N/A A N/A rvs N/A N/A self df scale size random_state N/A 1 None N/A N/A 
        Draw random samples from a Wishart distribution.

        Parameters
        ----------
        %(_doc_default_callparams)s
        size : integer or iterable of integers, optional
            Number of samples to draw (default 1).
        %(_doc_random_state)s

        Returns
        -------
        rvs : ndarray
            Random variates of shape (`size`) + (`dim`, `dim), where `dim` is
            the dimension of the scale matrix.

        Notes
        -----
        %(_doc_callparams_note)s

         N/A N/A n shape N/A N/A self _process_size size N/A N/A dim df scale N/A N/A self _process_parameters df scale N/A C N/A N/A N/A scipy linalg cholesky scale lower True N/A out N/A N/A self _rvs n shape dim df C random_state N/A N/A _squeeze_output out N/A _entropy N/A N/A self dim df log_det_scale N/A N/A N/A 
        Parameters
        ----------
        dim : int
            Dimension of the scale matrix
        df : int
            Degrees of freedom
        log_det_scale : float
            Logarithm of the determinant of the scale matrix

        Notes
        -----
        As this function does no argument checking, it should not be
        called directly; use 'entropy' instead.

         N/A N/A N/A N/A N/A N/A N/A 0.5 N/A dim 1 log_det_scale N/A N/A N/A 0.5 dim N/A dim 1 _LOG_2 N/A multigammaln N/A 0.5 df dim N/A N/A 0.5 N/A N/A df dim 1 N/A N/A np sum N/A N/A psi N/A 0.5 N/A N/A df 1 N/A i 1 N/A i N/A range dim N/A N/A 0.5 df dim N/A entropy N/A N/A self df scale N/A N/A N/A 
        Compute the differential entropy of the Wishart.

        Parameters
        ----------
        %(_doc_default_callparams)s

        Returns
        -------
        h : scalar
            Entropy of the Wishart distribution

        Notes
        -----
        %(_doc_callparams_note)s

         N/A N/A dim df scale N/A N/A self _process_parameters df scale N/A N/A _ log_det_scale N/A N/A self _cholesky_logdet scale N/A N/A N/A self _entropy dim df log_det_scale N/A _cholesky_logdet N/A N/A self scale N/A N/A N/A 
        Compute Cholesky decomposition and determine (log(det(scale)).

        Parameters
        ----------
        scale : ndarray
            Scale matrix.

        Returns
        -------
        c_decomp : ndarray
            The Cholesky decomposition of `scale`.
        logdet : scalar
            The log of the determinant of `scale`.

        Notes
        -----
        This computation of ``logdet`` is equivalent to
        ``np.linalg.slogdet(scale)``.  It is ~2x faster though.

         N/A c_decomp N/A N/A N/A scipy linalg cholesky scale lower True N/A logdet N/A 2 N/A N/A np sum N/A N/A np log N/A N/A c_decomp diagonal N/A N/A c_decomp logdet N/A N/A N/A wishart N/A wishart_gen wishart_frozen N/A multi_rv_frozen N/A N/A 
    Create a frozen Wishart distribution.

    Parameters
    ----------
    df : array_like
        Degrees of freedom of the distribution
    scale : array_like
        Scale matrix of the distribution
    seed : None or int or np.random.RandomState instance, optional
        This parameter defines the RandomState object to use for drawing
        random variates.
        If None (or np.random), the global np.random state is used.
        If integer, it is used to seed the local RandomState instance
        Default is None.

     __init__ N/A N/A self df scale seed N/A None N/A N/A N/A self _dist N/A wishart_gen seed N/A N/A N/A self dim N/A self df N/A self scale N/A N/A N/A self _dist _process_parameters df scale N/A N/A N/A self C N/A self log_det_scale N/A N/A N/A self _dist _cholesky_logdet N/A self scale N/A logpdf N/A N/A self x N/A N/A N/A x N/A N/A N/A self _dist _process_quantiles x N/A self dim N/A out N/A N/A N/A self _dist _logpdf x N/A self dim N/A self df N/A self scale N/A self log_det_scale N/A self C N/A N/A _squeeze_output out N/A pdf N/A N/A self x N/A N/A N/A N/A N/A np exp N/A N/A self logpdf x N/A mean N/A N/A self N/A N/A N/A out N/A N/A N/A self _dist _mean N/A self dim N/A self df N/A self scale N/A N/A _squeeze_output out N/A mode N/A N/A self N/A N/A N/A out N/A N/A N/A self _dist _mode N/A self dim N/A self df N/A self scale N/A N/A N/A out None N/A _squeeze_output out out N/A var N/A N/A self N/A N/A N/A out N/A N/A N/A self _dist _var N/A self dim N/A self df N/A self scale N/A N/A _squeeze_output out N/A rvs N/A N/A self size random_state N/A 1 None N/A N/A N/A n shape N/A N/A N/A self _dist _process_size size N/A out N/A N/A N/A self _dist _rvs n shape N/A self dim N/A self df N/A self C random_state N/A N/A _squeeze_output out N/A entropy N/A N/A self N/A N/A N/A N/A N/A N/A self _dist _entropy N/A self dim N/A self df N/A self log_det_scale N/A N/A N/A name N/A logpdf pdf mean mode var rvs entropy N/A N/A method N/A N/A wishart_gen __dict__ N/A name N/A method_frozen N/A N/A wishart_frozen __dict__ N/A name N/A N/A method_frozen __doc__ N/A N/A doccer docformat N/A method __doc__ wishart_docdict_noparams N/A N/A method __doc__ N/A N/A doccer docformat N/A method __doc__ wishart_docdict_params numpy asarray_chkfinite asarray scipy.linalg.misc LinAlgError scipy.linalg.lapack get_lapack_funcs _cho_inv_batch N/A N/A a check_finite N/A True N/A N/A 
    Invert the matrices a_i, using a Cholesky factorization of A, where
    a_i resides in the last two dimensions of a and the other indices describe
    the index i.

    Overwrites the data in a.

    Parameters
    ----------
    a : array
        Array of matrices to invert, where the matrices themselves are stored
        in the last two dimensions.
    check_finite : bool, optional
        Whether to check that the input matrices contain only finite numbers.
        Disabling may give a performance gain, but may result in problems
        (crashes, non-termination) if the inputs do contain infinities or NaNs.

    Returns
    -------
    x : array
        Array of inverses of the matrices ``a_i``.

    See also
    --------
    scipy.linalg.cholesky : Cholesky factorization of a matrix

     N/A check_finite N/A N/A a1 N/A asarray_chkfinite a N/A N/A a1 N/A asarray a N/A N/A N/A N/A len N/A a1 shape 2 N/A N/A N/A a1 shape N/A -2 N/A N/A a1 shape N/A -1 N/A N/A N/A ValueError expected square matrix in last two dimensions N/A N/A potrf potri N/A get_lapack_funcs N/A potrf potri N/A a1 N/A tril_idx N/A N/A np tril_indices N/A N/A a shape N/A -2 k -1 N/A triu_idx N/A N/A np triu_indices N/A N/A a shape N/A -2 k 1 N/A index N/A N/A np ndindex N/A N/A a1 shape N/A -2 N/A N/A N/A N/A a1 N/A index info N/A potrf N/A a1 N/A index lower True overwrite_a False clean False N/A N/A info 0 N/A N/A N/A LinAlgError N/A %d-th leading minor not positive definite info N/A N/A info 0 N/A N/A N/A ValueError N/A illegal value in %d-th argument of internal potrf N/A info N/A N/A N/A a1 N/A index info N/A potri N/A a1 N/A index lower True overwrite_c False N/A N/A info 0 N/A N/A N/A LinAlgError the inverse could not be computed N/A N/A info 0 N/A N/A N/A ValueError N/A illegal value in %d-th argument of internal potrf N/A info N/A N/A N/A a1 N/A index N/A triu_idx N/A N/A a1 N/A index N/A tril_idx N/A a1 N/A invwishart_gen N/A wishart_gen N/A N/A 
    An inverse Wishart random variable.

    The `df` keyword specifies the degrees of freedom. The `scale` keyword
    specifies the scale matrix, which must be symmetric and positive definite.
    In this context, the scale matrix is often interpreted in terms of a
    multivariate normal covariance matrix.

    Methods
    -------
    ``pdf(x, df, scale)``
        Probability density function.
    ``logpdf(x, df, scale)``
        Log of the probability density function.
    ``rvs(df, scale, size=1, random_state=None)``
        Draw random samples from an inverse Wishart distribution.

    Parameters
    ----------
    x : array_like
        Quantiles, with the last axis of `x` denoting the components.
    %(_doc_default_callparams)s
    %(_doc_random_state)s

    Alternatively, the object may be called (as a function) to fix the degrees
    of freedom and scale parameters, returning a "frozen" inverse Wishart
    random variable:

    rv = invwishart(df=1, scale=1)
        - Frozen object with the same methods but holding the given
          degrees of freedom and scale fixed.

    See Also
    --------
    wishart

    Notes
    -----
    %(_doc_callparams_note)s

    The scale matrix `scale` must be a symmetric positive definite
    matrix. Singular matrices, including the symmetric positive semi-definite
    case, are not supported.

    The inverse Wishart distribution is often denoted

    .. math::

        W_p^{-1}(\nu, \Psi)

    where :math:`\nu` is the degrees of freedom and :math:`\Psi` is the
    :math:`p \times p` scale matrix.

    The probability density function for `invwishart` has support over positive
    definite matrices :math:`S`; if :math:`S \sim W^{-1}_p(\nu, \Sigma)`,
    then its PDF is given by:

    .. math::

        f(S) = \frac{|\Sigma|^\frac{\nu}{2}}{2^{ \frac{\nu p}{2} }
               |S|^{\frac{\nu + p + 1}{2}} \Gamma_p \left(\frac{\nu}{2} \right)}
               \exp\left( -tr(\Sigma S^{-1}) / 2 \right)

    If :math:`S \sim W_p^{-1}(\nu, \Psi)` (inverse Wishart) then
    :math:`S^{-1} \sim W_p(\nu, \Psi^{-1})` (Wishart).

    If the scale matrix is 1-dimensional and equal to one, then the inverse
    Wishart distribution :math:`W_1(\nu, 1)` collapses to the
    inverse Gamma distribution with parameters shape = :math:`\frac{\nu}{2}`
    and scale = :math:`\frac{1}{2}`.

    .. versionadded:: 0.16.0

    References
    ----------
    .. [1] M.L. Eaton, "Multivariate Statistics: A Vector Space Approach",
           Wiley, 1983.
    .. [2] M.C. Jones, "Generating Inverse Wishart Matrices", Communications in
           Statistics - Simulation and Computation, vol. 14.2, pp.511-514, 1985.

    Examples
    --------
    >>> import matplotlib.pyplot as plt
    >>> from scipy.stats import invwishart, invgamma
    >>> x = np.linspace(0.01, 1, 100)
    >>> iw = invwishart.pdf(x, df=6, scale=1)
    >>> iw[:3]
    array([  1.20546865e-15,   5.42497807e-06,   4.45813929e-03])
    >>> ig = invgamma.pdf(x, 6/2., scale=1./2)
    >>> ig[:3]
    array([  1.20546865e-15,   5.42497807e-06,   4.45813929e-03])
    >>> plt.plot(x, iw)

    The input quantiles can be any shape of array, as long as the last
    axis labels the components.

     __init__ N/A N/A self seed N/A None N/A N/A N/A N/A N/A super invwishart_gen self __init__ seed N/A N/A self __doc__ N/A N/A doccer docformat N/A self __doc__ wishart_docdict_params N/A __call__ N/A N/A self df scale seed N/A None None None N/A N/A 
        Create a frozen inverse Wishart distribution.

        See `invwishart_frozen` for more information.

         N/A N/A invwishart_frozen df scale seed N/A _logpdf N/A N/A self x dim df scale log_det_scale N/A N/A N/A 
        Parameters
        ----------
        x : ndarray
            Points at which to evaluate the log of the probability
            density function.
        dim : int
            Dimension of the scale matrix
        df : int
            Degrees of freedom
        scale : ndarray
            Scale matrix
        log_det_scale : float
            Logarithm of the determinant of the scale matrix

        Notes
        -----
        As this function does no argument checking, it should not be
        called directly; use 'logpdf' instead.

         N/A log_det_x N/A N/A np zeros N/A N/A x shape N/A -1 N/A x_inv N/A N/A N/A np copy x T N/A N/A dim 1 N/A N/A N/A _cho_inv_batch x_inv N/A N/A x_inv N/A 1.0 x_inv N/A tr_scale_x_inv N/A N/A np zeros N/A N/A x shape N/A -1 N/A i N/A range N/A N/A x shape N/A -1 N/A N/A N/A C lower N/A N/A N/A scipy linalg cho_factor N/A x N/A N/A N/A N/A i lower True N/A N/A log_det_x N/A i N/A 2 N/A N/A np sum N/A N/A np log N/A N/A C diagonal N/A N/A tr_scale_x_inv N/A i N/A N/A N/A N/A np dot scale N/A x_inv N/A i trace N/A out N/A N/A N/A N/A N/A 0.5 df log_det_scale N/A 0.5 tr_scale_x_inv N/A N/A N/A N/A 0.5 df dim _LOG_2 N/A N/A 0.5 N/A N/A df dim 1 log_det_x N/A multigammaln N/A 0.5 df dim N/A out N/A logpdf N/A N/A self x df scale N/A N/A N/A 
        Log of the inverse Wishart probability density function.

        Parameters
        ----------
        x : array_like
            Quantiles, with the last axis of `x` denoting the components.
            Each quantile must be a symmetric positive definite matrix.
        %(_doc_default_callparams)s

        Returns
        -------
        pdf : ndarray
            Log of the probability density function evaluated at `x`

        Notes
        -----
        %(_doc_callparams_note)s

         N/A N/A dim df scale N/A N/A self _process_parameters df scale N/A x N/A N/A self _process_quantiles x dim N/A N/A _ log_det_scale N/A N/A self _cholesky_logdet scale N/A out N/A N/A self _logpdf x dim df scale log_det_scale N/A N/A _squeeze_output out N/A pdf N/A N/A self x df scale N/A N/A N/A 
        Inverse Wishart probability density function.

        Parameters
        ----------
        x : array_like
            Quantiles, with the last axis of `x` denoting the components.
            Each quantile must be a symmetric positive definite matrix.

        %(_doc_default_callparams)s

        Returns
        -------
        pdf : ndarray
            Probability density function evaluated at `x`

        Notes
        -----
        %(_doc_callparams_note)s

         N/A N/A N/A np exp N/A N/A self logpdf x df scale N/A _mean N/A N/A self dim df scale N/A N/A N/A 
        Parameters
        ----------
        dim : int
            Dimension of the scale matrix
        %(_doc_default_callparams)s

        Notes
        -----
        As this function does no argument checking, it should not be
        called directly; use 'mean' instead.

         N/A N/A df N/A dim 1 N/A N/A out N/A scale N/A N/A df dim 1 N/A N/A out None N/A out N/A mean N/A N/A self df scale N/A N/A N/A 
        Mean of the inverse Wishart distribution

        Only valid if the degrees of freedom are greater than the dimension of
        the scale matrix plus one.

        Parameters
        ----------
        %(_doc_default_callparams)s

        Returns
        -------
        mean : float or None
            The mean of the distribution

         N/A N/A dim df scale N/A N/A self _process_parameters df scale N/A out N/A N/A self _mean dim df scale N/A N/A N/A out None N/A _squeeze_output out out N/A _mode N/A N/A self dim df scale N/A N/A N/A 
        Parameters
        ----------
        dim : int
            Dimension of the scale matrix
        %(_doc_default_callparams)s

        Notes
        -----
        As this function does no argument checking, it should not be
        called directly; use 'mode' instead.

         N/A N/A scale N/A N/A df dim 1 N/A mode N/A N/A self df scale N/A N/A N/A 
        Mode of the inverse Wishart distribution

        Parameters
        ----------
        %(_doc_default_callparams)s

        Returns
        -------
        mode : float
            The Mode of the distribution

         N/A N/A dim df scale N/A N/A self _process_parameters df scale N/A out N/A N/A self _mode dim df scale N/A N/A _squeeze_output out N/A _var N/A N/A self dim df scale N/A N/A N/A 
        Parameters
        ----------
        dim : int
            Dimension of the scale matrix
        %(_doc_default_callparams)s

        Notes
        -----
        As this function does no argument checking, it should not be
        called directly; use 'var' instead.

         N/A N/A df N/A dim 3 N/A N/A var N/A N/A N/A df dim 1 N/A scale 2 N/A diag N/A N/A scale diagonal N/A var N/A N/A N/A df dim 1 N/A N/A np outer diag diag N/A var N/A N/A N/A df dim N/A N/A N/A df dim 1 2 N/A N/A df dim 3 N/A N/A var None N/A var N/A var N/A N/A self df scale N/A N/A N/A 
        Variance of the inverse Wishart distribution

        Only valid if the degrees of freedom are greater than the dimension of
        the scale matrix plus three.

        Parameters
        ----------
        %(_doc_default_callparams)s

        Returns
        -------
        var : float
            The variance of the distribution
         N/A N/A dim df scale N/A N/A self _process_parameters df scale N/A out N/A N/A self _var dim df scale N/A N/A N/A out None N/A _squeeze_output out out N/A _rvs N/A N/A self n shape dim df C random_state N/A N/A N/A 
        Parameters
        ----------
        n : integer
            Number of variates to generate
        shape : iterable
            Shape of the variates to generate
        dim : int
            Dimension of the scale matrix
        df : int
            Degrees of freedom
        C : ndarray
            Cholesky factorization of the scale matrix, lower triagular.
        %(_doc_random_state)s

        Notes
        -----
        As this function does no argument checking, it should not be
        called directly; use 'rvs' instead.

         N/A random_state N/A N/A self _get_random_state random_state N/A A N/A N/A N/A super invwishart_gen self _standard_rvs n shape dim df random_state N/A eye N/A N/A np eye dim N/A trtrs N/A get_lapack_funcs trtrs N/A A N/A index N/A N/A np ndindex N/A N/A A shape N/A -2 N/A N/A CA N/A N/A np dot C N/A A N/A index N/A N/A dim 1 N/A N/A N/A CA info N/A trtrs CA eye lower True N/A N/A info 0 N/A N/A N/A LinAlgError Singular matrix. N/A N/A info 0 N/A N/A N/A ValueError N/A Illegal value in %d-th argument of internal trtrs N/A info N/A N/A CA N/A 1.0 CA N/A N/A A N/A index N/A N/A np dot N/A CA T CA N/A A N/A rvs N/A N/A self df scale size random_state N/A 1 None N/A N/A 
        Draw random samples from an inverse Wishart distribution.

        Parameters
        ----------
        %(_doc_default_callparams)s
        size : integer or iterable of integers, optional
            Number of samples to draw (default 1).
        %(_doc_random_state)s

        Returns
        -------
        rvs : ndarray
            Random variates of shape (`size`) + (`dim`, `dim), where `dim` is
            the dimension of the scale matrix.

        Notes
        -----
        %(_doc_callparams_note)s

         N/A N/A n shape N/A N/A self _process_size size N/A N/A dim df scale N/A N/A self _process_parameters df scale N/A eye N/A N/A np eye dim N/A N/A L lower N/A N/A N/A scipy linalg cho_factor scale lower True N/A inv_scale N/A N/A N/A scipy linalg cho_solve N/A L lower eye N/A C N/A N/A N/A scipy linalg cholesky inv_scale lower True N/A out N/A N/A self _rvs n shape dim df C random_state N/A N/A _squeeze_output out N/A entropy N/A N/A self N/A N/A N/A AttributeError N/A N/A N/A invwishart N/A invwishart_gen invwishart_frozen N/A multi_rv_frozen N/A __init__ N/A N/A self df scale seed N/A None N/A N/A 
        Create a frozen inverse Wishart distribution.

        Parameters
        ----------
        df : array_like
            Degrees of freedom of the distribution
        scale : array_like
            Scale matrix of the distribution
        seed : None or int or np.random.RandomState instance, optional
            This parameter defines the RandomState object to use for drawing
            random variates.
            If None (or np.random), the global np.random state is used.
            If integer, it is used to seed the local RandomState instance
            Default is None.

         N/A N/A self _dist N/A invwishart_gen seed N/A N/A N/A self dim N/A self df N/A self scale N/A N/A N/A self _dist _process_parameters df scale N/A N/A C lower N/A N/A N/A scipy linalg cho_factor N/A self scale lower True N/A N/A self log_det_scale N/A 2 N/A N/A np sum N/A N/A np log N/A N/A C diagonal N/A eye N/A N/A np eye N/A self dim N/A N/A self inv_scale N/A N/A N/A scipy linalg cho_solve N/A C lower eye N/A N/A self C N/A N/A N/A scipy linalg cholesky N/A self inv_scale lower True N/A logpdf N/A N/A self x N/A N/A N/A x N/A N/A N/A self _dist _process_quantiles x N/A self dim N/A out N/A N/A N/A self _dist _logpdf x N/A self dim N/A self df N/A self scale N/A self log_det_scale N/A N/A _squeeze_output out N/A pdf N/A N/A self x N/A N/A N/A N/A N/A np exp N/A N/A self logpdf x N/A mean N/A N/A self N/A N/A N/A out N/A N/A N/A self _dist _mean N/A self dim N/A self df N/A self scale N/A N/A N/A out None N/A _squeeze_output out out N/A mode N/A N/A self N/A N/A N/A out N/A N/A N/A self _dist _mode N/A self dim N/A self df N/A self scale N/A N/A _squeeze_output out N/A var N/A N/A self N/A N/A N/A out N/A N/A N/A self _dist _var N/A self dim N/A self df N/A self scale N/A N/A N/A out None N/A _squeeze_output out out N/A rvs N/A N/A self size random_state N/A 1 None N/A N/A N/A n shape N/A N/A N/A self _dist _process_size size N/A out N/A N/A N/A self _dist _rvs n shape N/A self dim N/A self df N/A self C random_state N/A N/A _squeeze_output out N/A entropy N/A N/A self N/A N/A N/A AttributeError N/A N/A N/A name N/A logpdf pdf mean mode var rvs N/A N/A method N/A N/A invwishart_gen __dict__ N/A name N/A method_frozen N/A N/A wishart_frozen __dict__ N/A name N/A N/A method_frozen __doc__ N/A N/A doccer docformat N/A method __doc__ wishart_docdict_noparams N/A N/A method __doc__ N/A N/A doccer docformat N/A method __doc__ wishart_docdict_params special_ortho_group_gen N/A multi_rv_generic N/A N/A 
    A matrix-valued SO(N) random variable.

    Return a random rotation matrix, drawn from the Haar distribution
    (the only uniform distribution on SO(n)).

    The `dim` keyword specifies the dimension N.

    Methods
    -------
    ``rvs(dim=None, size=1, random_state=None)``
        Draw random samples from SO(N).

    Parameters
    ----------
    dim : scalar
        Dimension of matrices

    Notes
    ----------
    This class is wrapping the random_rot code from the MDP Toolkit,
    https://github.com/mdp-toolkit/mdp-toolkit

    Return a random rotation matrix, drawn from the Haar distribution
    (the only uniform distribution on SO(n)).
    The algorithm is described in the paper
    Stewart, G.W., "The efficient generation of random orthogonal
    matrices with an application to condition estimators", SIAM Journal
    on Numerical Analysis, 17(3), pp. 403-409, 1980.
    For more information see
    http://en.wikipedia.org/wiki/Orthogonal_matrix#Randomization

    See also the similar `ortho_group`.

    Examples
    --------
    >>> from scipy.stats import special_ortho_group
    >>> x = special_ortho_group.rvs(3)

    >>> np.dot(x, x.T)
    array([[  1.00000000e+00,   1.13231364e-17,  -2.86852790e-16],
           [  1.13231364e-17,   1.00000000e+00,  -1.46845020e-16],
           [ -2.86852790e-16,  -1.46845020e-16,   1.00000000e+00]])

    >>> import scipy.linalg
    >>> scipy.linalg.det(x)
    1.0

    This generates one random matrix from SO(3). It is orthogonal and
    has a determinant of 1.

     __init__ N/A N/A self seed N/A None N/A N/A N/A N/A N/A super special_ortho_group_gen self __init__ seed N/A N/A self __doc__ N/A N/A doccer docformat N/A self __doc__ N/A __call__ N/A N/A self dim seed N/A None None N/A N/A 
        Create a frozen SO(N) distribution.

        See `special_ortho_group_frozen` for more information.

         N/A N/A special_ortho_group_frozen dim seed seed N/A _process_parameters N/A N/A self dim N/A N/A N/A 
        Dimension N must be specified; it cannot be inferred.
         N/A N/A N/A dim None N/A N/A N/A np isscalar dim N/A dim 1 N/A dim N/A int dim N/A N/A N/A ValueError Dimension of rotation must be specified,
                                and must be a scalar greater than 1. N/A dim N/A rvs N/A N/A self dim size random_state N/A 1 None N/A N/A 
        Draw random samples from SO(N).

        Parameters
        ----------
        dim : integer
            Dimension of rotation space (N).
        size : integer, optional
            Number of samples to draw (default 1).

        Returns
        -------
        rvs : ndarray or scalar
            Random size N-dimensional matrices, dimension (size, dim, dim)

         N/A size N/A int size N/A N/A size 1 N/A N/A N/A N/A np array N/A N/A N/A self rvs dim size 1 random_state random_state N/A i N/A range size N/A dim N/A N/A self _process_parameters dim N/A random_state N/A N/A self _get_random_state random_state N/A H N/A N/A np eye dim N/A D N/A N/A np ones N/A dim N/A n N/A range 1 dim N/A N/A x N/A N/A random_state normal size N/A N/A N/A dim n 1 N/A N/A D N/A N/A n 1 N/A N/A np sign N/A x N/A 0 N/A N/A x N/A 0 N/A N/A D N/A N/A n 1 N/A N/A np sqrt N/A N/A N/A x x sum N/A Hx N/A N/A N/A np eye N/A N/A dim n 1 N/A N/A 2.0 N/A N/A np outer x x N/A N/A N/A x x sum N/A mat N/A N/A np eye dim N/A N/A mat N/A N/A N/A n 1 N/A N/A n 1 Hx N/A H N/A N/A np dot H mat N/A N/A D N/A -1 N/A N/A -1 N/A 1 N/A dim 2 N/A N/A D prod N/A H N/A N/A D N/A H T T N/A H N/A N/A N/A special_ortho_group N/A special_ortho_group_gen special_ortho_group_frozen N/A multi_rv_frozen N/A __init__ N/A N/A self dim seed N/A None None N/A N/A 
        Create a frozen SO(N) distribution.

        Parameters
        ----------
        dim : scalar
            Dimension of matrices
        seed : None or int or np.random.RandomState instance, optional
            This parameter defines the RandomState object to use for drawing
            random variates.
            If None (or np.random), the global np.random state is used.
            If integer, it is used to seed the local RandomState instance
            Default is None.

        Examples
        --------
        >>> from scipy.stats import special_ortho_group
        >>> g = special_ortho_group(5)
        >>> x = g.rvs()

         N/A N/A self _dist N/A special_ortho_group_gen seed N/A N/A self dim N/A N/A N/A self _dist _process_parameters dim N/A rvs N/A N/A self size random_state N/A 1 None N/A N/A N/A N/A N/A self _dist rvs N/A self dim size random_state N/A N/A ortho_group_gen N/A multi_rv_generic N/A N/A 
    A matrix-valued O(N) random variable.

    Return a random orthogonal matrix, drawn from the O(N) Haar
    distribution (the only uniform distribution on O(N)).

    The `dim` keyword specifies the dimension N.

    Methods
    -------
    ``rvs(dim=None, size=1, random_state=None)``
        Draw random samples from O(N).

    Parameters
    ----------
    dim : scalar
        Dimension of matrices

    Notes
    ----------
    This class is closely related to `special_ortho_group`.

    Some care is taken to avoid numerical error, as per the paper by Mezzadri.

    References
    ----------
    .. [1] F. Mezzadri, "How to generate random matrices from the classical
           compact groups", arXiv:math-ph/0609050v2.

    Examples
    --------
    >>> from scipy.stats import ortho_group
    >>> x = ortho_group.rvs(3)

    >>> np.dot(x, x.T)
    array([[  1.00000000e+00,   1.13231364e-17,  -2.86852790e-16],
           [  1.13231364e-17,   1.00000000e+00,  -1.46845020e-16],
           [ -2.86852790e-16,  -1.46845020e-16,   1.00000000e+00]])

    >>> import scipy.linalg
    >>> np.fabs(scipy.linalg.det(x))
    1.0

    This generates one random matrix from O(3). It is orthogonal and
    has a determinant of +1 or -1.

     __init__ N/A N/A self seed N/A None N/A N/A N/A N/A N/A super ortho_group_gen self __init__ seed N/A N/A self __doc__ N/A N/A doccer docformat N/A self __doc__ N/A _process_parameters N/A N/A self dim N/A N/A N/A 
        Dimension N must be specified; it cannot be inferred.
         N/A N/A N/A dim None N/A N/A N/A np isscalar dim N/A dim 1 N/A dim N/A int dim N/A N/A N/A ValueError Dimension of rotation must be specified,and must be a scalar greater than 1. N/A dim N/A rvs N/A N/A self dim size random_state N/A 1 None N/A N/A 
        Draw random samples from O(N).

        Parameters
        ----------
        dim : integer
            Dimension of rotation space (N).
        size : integer, optional
            Number of samples to draw (default 1).

        Returns
        -------
        rvs : ndarray or scalar
            Random size N-dimensional matrices, dimension (size, dim, dim)

         N/A size N/A int size N/A N/A size 1 N/A N/A N/A N/A np array N/A N/A N/A self rvs dim size 1 random_state random_state N/A i N/A range size N/A dim N/A N/A self _process_parameters dim N/A random_state N/A N/A self _get_random_state random_state N/A H N/A N/A np eye dim N/A n N/A range 1 dim N/A N/A x N/A N/A random_state normal size N/A N/A N/A dim n 1 N/A D N/A N/A np sign N/A x N/A 0 N/A N/A x N/A 0 N/A D N/A N/A np sqrt N/A N/A N/A x x sum N/A Hx N/A N/A D N/A N/A N/A np eye N/A N/A dim n 1 N/A N/A 2.0 N/A N/A np outer x x N/A N/A N/A x x sum N/A mat N/A N/A np eye dim N/A N/A mat N/A N/A N/A n 1 N/A N/A n 1 Hx N/A H N/A N/A np dot H mat N/A H N/A N/A N/A ortho_group N/A ortho_group_gen random_correlation_gen N/A multi_rv_generic N/A N/A 
    A random correlation matrix.

    Return a random correlation matrix, given a vector of eigenvalues.

    The `eigs` keyword specifies the eigenvalues of the correlation matrix,
    and implies the dimension.

    Methods
    -------
    ``rvs(eigs=None, random_state=None)``
        Draw random correlation matrices, all with eigenvalues eigs.

    Parameters
    ----------
    eigs : 1d ndarray
        Eigenvalues of correlation matrix.

    Notes
    ----------

    Generates a random correlation matrix following a numerically stable
    algorithm spelled out by Davies & Higham. This algorithm uses a single O(N)
    similarity transformation to construct a symmetric positive semi-definite
    matrix, and applies a series of Givens rotations to scale it to have ones
    on the diagonal.

    References
    ----------

    .. [1] Davies, Philip I; Higham, Nicholas J; "Numerically stable generation
           of correlation matrices and their factors", BIT 2000, Vol. 40,
           No. 4, pp. 640 651

    Examples
    --------
    >>> from scipy.stats import random_correlation
    >>> np.random.seed(514)
    >>> x = random_correlation.rvs((.5, .8, 1.2, 1.5))
    >>> x
    array([[ 1.        , -0.20387311,  0.18366501, -0.04953711],
           [-0.20387311,  1.        , -0.24351129,  0.06703474],
           [ 0.18366501, -0.24351129,  1.        ,  0.38530195],
           [-0.04953711,  0.06703474,  0.38530195,  1.        ]])

    >>> import scipy.linalg
    >>> e, v = scipy.linalg.eigh(x)
    >>> e
    array([ 0.5,  0.8,  1.2,  1.5])

     __init__ N/A N/A self seed N/A None N/A N/A N/A N/A N/A super random_correlation_gen self __init__ seed N/A N/A self __doc__ N/A N/A doccer docformat N/A self __doc__ N/A _process_parameters N/A N/A self eigs tol N/A N/A N/A eigs N/A N/A np asarray eigs dtype float N/A dim N/A eigs size N/A N/A N/A N/A eigs ndim 1 N/A N/A N/A eigs shape N/A 0 dim N/A dim 1 N/A N/A N/A ValueError Array 'eigs' must be a vector of length greater than 1. N/A N/A N/A N/A np fabs N/A N/A N/A np sum eigs dim tol N/A N/A N/A ValueError Sum of eigenvalues must equal dimensionality. N/A x eigs N/A N/A N/A x N/A tol N/A N/A N/A ValueError All eigenvalues must be non-negative. N/A N/A dim eigs N/A _givens_to_1 N/A N/A self aii ajj aij N/A N/A N/A Computes a 2x2 Givens matrix to put 1's on the diagonal for the input matrix.

        The input matrix is a 2x2 symmetric matrix M = [ aii aij ; aij ajj ].

        The output matrix g is a 2x2 anti-symmetric matrix of the form [ c s ; -s c ];
        the elements c and s are returned.

        Applying the output matrix to the input matrix (as b=g.T M g)
        results in a matrix with bii=1, provided tr(M) - det(M) >= 1
        and floating point issues do not occur. Otherwise, some other
        valid rotation is returned. When tr(M)==2, also bjj=1.

         N/A aiid N/A aii 1.0 N/A ajjd N/A ajj 1.0 N/A N/A ajjd 0 N/A N/A N/A 0.0 1.0 N/A dd N/A N/A math sqrt N/A max N/A N/A aij 2 N/A aiid ajjd 0 N/A t N/A N/A aij N/A N/A math copysign dd aij ajjd N/A c N/A 1.0 N/A N/A math sqrt N/A 1.0 N/A t t N/A N/A c 0 N/A N/A s 1.0 N/A N/A s N/A c t N/A N/A c s N/A _to_corr N/A N/A self m N/A N/A N/A 
        Given a psd matrix m, rotate to put one's on the diagonal, turning it
        into a correlation matrix.  This also requires the trace equal the
        dimensionality. Note: modifies input matrix
         N/A N/A N/A N/A N/A m flags c_contiguous N/A N/A m dtype N/A np float64 N/A N/A N/A m shape N/A 0 N/A N/A m shape N/A 1 N/A N/A N/A ValueError N/A d N/A N/A m shape N/A 0 N/A i N/A range N/A d 1 N/A N/A N/A N/A m N/A N/A i i 1 N/A N/A N/A N/A N/A N/A m N/A N/A i i 1 N/A N/A j N/A range N/A i 1 d N/A N/A N/A N/A m N/A N/A j j 1 N/A N/A N/A N/A j N/A range N/A i 1 d N/A N/A N/A N/A m N/A N/A j j 1 N/A N/A N/A N/A c s N/A N/A self _givens_to_1 N/A m N/A N/A i i N/A m N/A N/A j j N/A m N/A N/A i j N/A mv N/A N/A m ravel N/A N/A drot mv mv c N/A s n d offx N/A i d incx 1 offy N/A j d incy 1 overwrite_x True overwrite_y True N/A N/A drot mv mv c N/A s n d offx i incx d offy j incy d overwrite_x True overwrite_y True N/A m N/A rvs N/A N/A self eigs random_state tol diag_tol N/A None 1e-13 1e-07 N/A N/A 
        Draw random correlation matrices

        Parameters
        ----------
        eigs : 1d ndarray
            Eigenvalues of correlation matrix
        tol : float, optional
            Tolerance for input parameter checks
        diag_tol : float, optional
            Tolerance for deviation of the diagonal of the resulting
            matrix. Default: 1e-7

        Raises
        ------
        RuntimeError
            Floating point error prevented generating a valid correlation
            matrix.

        Returns
        -------
        rvs : ndarray or scalar
            Random size N-dimensional matrices, dimension (size, dim, dim),
            each having eigenvalues eigs.

         N/A N/A dim eigs N/A N/A self _process_parameters eigs tol tol N/A random_state N/A N/A self _get_random_state random_state N/A m N/A N/A ortho_group rvs dim random_state random_state N/A m N/A N/A np dot N/A N/A np dot m N/A N/A np diag eigs N/A m T N/A m N/A N/A self _to_corr m N/A N/A N/A N/A N/A abs N/A N/A N/A m diagonal 1 max diag_tol N/A N/A N/A RuntimeError Failed to generate a valid correlation matrix N/A m N/A N/A N/A random_correlation N/A random_correlation_gen