Module ImportFrom alias alias Import alias ImportFrom alias ImportFrom alias ImportFrom alias alias alias ImportFrom alias ImportFrom alias ImportFrom alias ImportFrom alias ImportFrom alias alias alias ImportFrom alias Import alias ClassDef bases NameLoad body Expr Str FunctionDef arguments args NameParam defaults vararg body If BoolOpAnd CompareEq Call NameLoad NameLoad Num Call NameLoad SubscriptLoad NameLoad Index Num NameLoad body Assign AttributeStore NameLoad attr AttributeLoad SubscriptLoad NameLoad Index Num attr Assign AttributeStore NameLoad attr AttributeLoad SubscriptLoad NameLoad Index Num attr Assign AttributeStore NameLoad attr Call NameLoad AttributeLoad SubscriptLoad NameLoad Index Num attr Return Assign AttributeStore NameLoad attr Dict If CompareEq Call NameLoad NameLoad Num body Assign AttributeStore NameLoad attr Call NameLoad SubscriptLoad NameLoad Index Num Assign AttributeStore NameLoad attr Call NameLoad SubscriptLoad NameLoad Index Num If Call NameLoad SubscriptLoad NameLoad Index Num AttributeLoad NameLoad attr body Assign NameStore SubscriptLoad NameLoad Index Num For NameStore Call NameLoad AttributeLoad NameLoad attr body For NameStore Call NameLoad AttributeLoad NameLoad attr body Assign NameStore Call AttributeLoad NameLoad attr Call NameLoad Call AttributeLoad NameLoad attr NameLoad Call AttributeLoad NameLoad attr NameLoad If NameLoad body Assign SubscriptStore AttributeLoad NameLoad attr Index TupleLoad NameLoad NameLoad NameLoad orelse If Call NameLoad SubscriptLoad NameLoad Index Num TupleLoad NameLoad NameLoad body For NameStore Call AttributeLoad SubscriptLoad NameLoad Index Num attr body Assign NameStore SubscriptLoad SubscriptLoad NameLoad Index Num Index NameLoad If NameLoad body Assign SubscriptStore AttributeLoad NameLoad attr Index NameLoad Call AttributeLoad NameLoad attr NameLoad orelse If Call NameLoad SubscriptLoad NameLoad Index Num body If CompareNotEq Call NameLoad SubscriptLoad NameLoad Index Num BinOpMult AttributeLoad NameLoad attr AttributeLoad NameLoad attr body Raise Call NameLoad BinOpMod Str TupleLoad Call NameLoad SubscriptLoad NameLoad Index Num BinOpMult AttributeLoad NameLoad attr AttributeLoad NameLoad attr Assign NameStore SubscriptLoad NameLoad Index Num For NameStore Call NameLoad AttributeLoad NameLoad attr body For NameStore Call NameLoad AttributeLoad NameLoad attr body Assign NameStore Call AttributeLoad NameLoad attr SubscriptLoad NameLoad Index BinOpAdd BinOpMult NameLoad AttributeLoad NameLoad attr NameLoad If NameLoad body Assign SubscriptStore AttributeLoad NameLoad attr Index TupleLoad NameLoad NameLoad NameLoad orelse Assign TupleStore NameStore NameStore NameStore Call AttributeLoad NameLoad attr NameLoad Assign AttributeStore NameLoad attr NameLoad Assign AttributeStore NameLoad attr NameLoad For NameStore Call NameLoad AttributeLoad NameLoad attr body For NameStore Call NameLoad AttributeLoad NameLoad attr body Assign NameStore SubscriptLoad NameLoad Index BinOpAdd BinOpMult AttributeLoad NameLoad attr NameLoad NameLoad If NameLoad body Assign SubscriptStore AttributeLoad NameLoad attr Index TupleLoad NameLoad NameLoad NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults body If Call NameLoad NameLoad NameLoad body Assign TupleStore NameStore NameStore NameLoad TryExcept body Assign TupleStore NameStore NameStore Call AttributeLoad NameLoad attr NameLoad Return Call AttributeLoad AttributeLoad NameLoad attr attr TupleLoad NameLoad NameLoad AttributeLoad NameLoad attr handlers ExceptHandler type TupleLoad NameLoad NameLoad body If Call NameLoad NameLoad NameLoad body Assign NameStore SubscriptLoad Call NameLoad Call NameLoad AttributeLoad NameLoad attr Index NameLoad orelse If Call NameLoad NameLoad body Pass orelse If CompareGtE NameLoad AttributeLoad NameLoad attr body Raise Call NameLoad Str Assign NameStore ListLoad NameLoad If Call NameLoad NameLoad NameLoad body Assign NameStore SubscriptLoad Call NameLoad Call NameLoad AttributeLoad NameLoad attr Index NameLoad orelse If Call NameLoad NameLoad body Pass orelse If CompareGtE NameLoad AttributeLoad NameLoad attr body Raise Call NameLoad Str Assign NameStore ListLoad NameLoad Return Call AttributeLoad NameLoad attr NameLoad NameLoad If Call NameLoad NameLoad NameLoad body Assign TupleStore NameStore NameStore SubscriptLoad Call AttributeLoad NameLoad attr Call NameLoad NameLoad Slice Num Assign NameStore ListLoad For NameStore Call NameLoad NameLoad NameLoad body Assign TupleStore NameStore NameStore Call NameLoad NameLoad AttributeLoad NameLoad attr Expr Call AttributeLoad NameLoad attr Call AttributeLoad AttributeLoad NameLoad attr attr TupleLoad NameLoad NameLoad AttributeLoad NameLoad attr Return NameLoad Assign TupleStore NameStore NameStore Call NameLoad Call NameLoad NameLoad Call NameLoad NameLoad AttributeLoad NameLoad attr Return Call AttributeLoad AttributeLoad NameLoad attr attr TupleLoad NameLoad NameLoad AttributeLoad NameLoad attr decorator_list FunctionDef arguments args NameParam NameParam NameParam defaults body Raise Call NameLoad decorator_list FunctionDef arguments args NameParam defaults body Return Call AttributeLoad NameLoad attr AttributeLoad NameLoad attr AttributeLoad NameLoad attr AttributeLoad NameLoad attr decorator_list FunctionDef arguments args NameParam defaults body If UnaryOpNot AttributeLoad NameLoad attr body Return NameLoad If UnaryOpNot Call NameLoad GeneratorExp CompareEq SubscriptLoad NameLoad Index TupleLoad NameLoad NameLoad Num comprehension NameStore Call NameLoad AttributeLoad NameLoad attr body Return NameLoad Return CompareEq Call NameLoad AttributeLoad NameLoad attr AttributeLoad NameLoad attr decorator_list NameLoad FunctionDef arguments args NameParam defaults body Expr Str If UnaryOpNot AttributeLoad NameLoad attr body Return ListLoad If UnaryOpNot AttributeLoad NameLoad attr body Return ListComp ListLoad comprehension NameStore Call NameLoad AttributeLoad NameLoad attr Assign TupleStore NameStore NameStore AttributeLoad NameLoad attr Return ListComp ListComp SubscriptLoad NameLoad Index TupleLoad NameLoad NameLoad comprehension NameStore Call NameLoad NameLoad comprehension NameStore Call NameLoad NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults body Expr Str Return SubscriptLoad NameLoad ExtSlice Index NameLoad Slice decorator_list FunctionDef arguments args NameParam NameParam defaults body Expr Str Return SubscriptLoad NameLoad ExtSlice Slice Index NameLoad decorator_list FunctionDef arguments args NameParam defaults body Expr Str Return ListComp Call NameLoad BinOpAdd NameLoad TupleLoad SubscriptLoad NameLoad Index NameLoad comprehension NameStore Call NameLoad Call NameLoad Call AttributeLoad AttributeLoad NameLoad attr attr keyword Lambda arguments args NameParam defaults Call NameLoad NameLoad decorator_list Assign NameStore Call NameLoad NameLoad NameLoad NameLoad Str FunctionDef arguments args NameParam defaults body Expr Str Return ListComp Call NameLoad BinOpAdd NameLoad TupleLoad SubscriptLoad NameLoad Index NameLoad comprehension NameStore Call NameLoad Call NameLoad Call AttributeLoad AttributeLoad NameLoad attr attr keyword Lambda arguments args NameParam defaults Call NameLoad Call NameLoad NameLoad decorator_list Assign NameStore Call NameLoad NameLoad NameLoad NameLoad Str FunctionDef arguments args NameParam defaults body Expr Str Assign NameStore AttributeLoad NameLoad attr For NameStore Call NameLoad AttributeLoad NameLoad attr body AugAssignAdd NameStore Call AttributeLoad AttributeLoad NameLoad attr attr TupleLoad NameLoad NameLoad Num Return NameLoad decorator_list FunctionDef arguments args NameParam defaults body Expr Str Assign NameStore Call AttributeLoad NameLoad attr AttributeLoad NameLoad attr AttributeLoad NameLoad attr For TupleStore NameStore NameStore Call AttributeLoad AttributeLoad NameLoad attr attr body Assign NameStore TupleLoad SubscriptLoad NameLoad Index Num SubscriptLoad NameLoad Index Num Assign SubscriptStore AttributeLoad NameLoad attr Index NameLoad NameLoad Return NameLoad decorator_list FunctionDef arguments args NameParam defaults body Expr Str Assign NameStore Call AttributeLoad NameLoad attr For TupleStore NameStore NameStore Call AttributeLoad AttributeLoad NameLoad attr attr body Assign SubscriptStore AttributeLoad NameLoad attr Index NameLoad Call AttributeLoad NameLoad attr Return NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults body Expr Str Assign NameStore NameLoad Assign NameStore NameLoad Assign NameStore ListComp ListLoad comprehension NameStore Call NameLoad AttributeLoad NameLoad attr For TupleStore NameStore NameStore NameStore Call AttributeLoad NameLoad attr body Expr Call AttributeLoad SubscriptLoad NameLoad Index NameLoad attr TupleLoad NameLoad NameLoad Assign NameStore Call NameLoad NameLoad For TupleStore NameStore NameStore NameStore Call AttributeLoad NameLoad attr body For TupleStore NameStore NameStore SubscriptLoad NameLoad Index NameLoad body Assign NameStore BinOpMult NameLoad NameLoad AugAssignAdd SubscriptStore NameLoad Index TupleLoad NameLoad NameLoad NameLoad Assign NameStore Call AttributeLoad NameLoad attr AttributeLoad NameLoad attr AttributeLoad NameLoad attr Assign AttributeStore NameLoad attr DictComp NameLoad NameLoad comprehension TupleStore NameStore NameStore Call AttributeLoad NameLoad attr NameLoad Return NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults body Expr Str Assign NameStore Call AttributeLoad NameLoad attr AttributeLoad NameLoad attr If NameLoad body For NameStore AttributeLoad NameLoad attr body Assign NameStore BinOpMult NameLoad SubscriptLoad AttributeLoad NameLoad attr Index NameLoad If NameLoad body Assign SubscriptStore AttributeLoad NameLoad attr Index NameLoad NameLoad orelse Expr Call AttributeLoad AttributeLoad NameLoad attr attr NameLoad NameLoad Return NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults body Expr Str If Call NameLoad NameLoad NameLoad body Return Call AttributeLoad NameLoad attr NameLoad If Call NameLoad NameLoad NameLoad body Return Call AttributeLoad NameLoad attr BinOpMult NameLoad Call AttributeLoad NameLoad attr NameLoad Return Call AttributeLoad NameLoad attr NameLoad decorator_list Assign NameStore NameLoad FunctionDef arguments args NameParam NameParam defaults body Expr Str If Call NameLoad NameLoad NameLoad body Return BinOpMult NameLoad Call AttributeLoad NameLoad attr NameLoad Return Call AttributeLoad NameLoad attr NameLoad decorator_list Assign NameStore NameLoad FunctionDef arguments args NameParam NameParam defaults body Expr Str If Call NameLoad NameLoad NameLoad body Return Call AttributeLoad NameLoad attr NameLoad orelse If Call NameLoad NameLoad NameLoad body Return Call AttributeLoad NameLoad attr BinOpAdd NameLoad NameLoad orelse Raise Call NameLoad BinOpMod Str Call NameLoad ListComp AttributeLoad AttributeLoad NameLoad attr attr comprehension NameStore TupleLoad NameLoad NameLoad decorator_list FunctionDef arguments args NameParam defaults body Expr Str Assign NameStore Call AttributeLoad NameLoad attr For TupleStore NameStore NameStore Call AttributeLoad AttributeLoad NameLoad attr attr body Assign SubscriptStore AttributeLoad NameLoad attr Index NameLoad UnaryOpUSub NameLoad Return NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults body Expr Str If UnaryOpNot Call NameLoad NameLoad NameLoad body Raise Call NameLoad BinOpMod Str Call NameLoad ListComp AttributeLoad AttributeLoad NameLoad attr attr comprehension NameStore TupleLoad NameLoad NameLoad If CompareNotEq AttributeLoad NameLoad attr AttributeLoad NameLoad attr body Raise Call NameLoad Assign NameStore Call AttributeLoad NameLoad attr For TupleStore NameStore NameStore Call AttributeLoad AttributeLoad NameLoad attr attr body Assign NameStore BinOpAdd SubscriptLoad NameLoad Index NameLoad NameLoad If NameLoad body Assign SubscriptStore AttributeLoad NameLoad attr Index NameLoad NameLoad orelse Expr Call AttributeLoad AttributeLoad NameLoad attr attr NameLoad NameLoad Return NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam defaults body Assign NameStore Call NameLoad Call NameLoad NameLoad Assign NameStore Call NameLoad Call NameLoad NameLoad Assign NameStore Dict If CompareLt BinOpMult Call NameLoad NameLoad Call NameLoad NameLoad Call NameLoad AttributeLoad NameLoad attr body For TupleStore NameStore NameStore Call NameLoad NameLoad body For TupleStore NameStore NameStore Call NameLoad NameLoad body Assign SubscriptStore NameLoad Index TupleLoad NameLoad NameLoad Call AttributeLoad AttributeLoad NameLoad attr attr TupleLoad NameLoad NameLoad Num orelse For TupleStore NameStore NameStore AttributeLoad NameLoad attr body If BoolOpAnd CompareIn NameLoad NameLoad CompareIn NameLoad NameLoad body Assign SubscriptStore NameLoad Index TupleLoad Call AttributeLoad NameLoad attr NameLoad Call AttributeLoad NameLoad attr NameLoad SubscriptLoad AttributeLoad NameLoad attr Index TupleLoad NameLoad NameLoad Assign NameStore Call AttributeLoad NameLoad attr Call NameLoad NameLoad Call NameLoad NameLoad NameLoad If CompareNotEq Call NameLoad NameLoad Call NameLoad NameLoad body For TupleStore NameStore NameStore Call NameLoad NameLoad body Assign NameStore Call AttributeLoad NameLoad attr NameLoad If CompareNotEq NameLoad NameLoad body Assign NameStore Call AttributeLoad NameLoad attr NameLoad Call AttributeLoad NameLoad attr NameLoad If CompareNotEq Call NameLoad NameLoad Call NameLoad NameLoad body For TupleStore NameStore NameStore Call NameLoad NameLoad body Assign NameStore Call AttributeLoad NameLoad attr NameLoad If CompareNotEq NameLoad NameLoad body Assign NameStore Call AttributeLoad NameLoad attr NameLoad Call AttributeLoad NameLoad attr NameLoad Return NameLoad decorator_list Assign AttributeStore NameLoad attr AttributeLoad AttributeLoad NameLoad attr attr FunctionDef arguments args NameParam defaults body Expr Str FunctionDef arguments args defaults body Assign NameStore AttributeLoad NameLoad attr Expr Yield AttributeLoad NameLoad attr If CompareLtE Call NameLoad NameLoad AttributeLoad NameLoad attr body Expr Yield Call NameLoad GeneratorExp AttributeLoad SubscriptLoad NameLoad Index TupleLoad NameLoad NameLoad attr comprehension TupleStore NameStore NameStore NameLoad CompareEq NameLoad NameLoad orelse Expr Yield Call NameLoad GeneratorExp AttributeLoad SubscriptLoad NameLoad Index TupleLoad NameLoad NameLoad attr comprehension NameStore Call NameLoad AttributeLoad NameLoad attr CompareIn TupleLoad NameLoad NameLoad NameLoad Expr Yield Call NameLoad GeneratorExp IfExp CompareIn TupleLoad NameLoad NameLoad NameLoad AttributeLoad BinOpSub SubscriptLoad NameLoad Index TupleLoad NameLoad NameLoad Call AttributeLoad SubscriptLoad NameLoad Index TupleLoad NameLoad NameLoad attr attr NameLoad comprehension TupleStore NameStore NameStore NameLoad decorator_list Return Call NameLoad GeneratorExp NameLoad comprehension NameStore Call NameLoad decorator_list NameLoad FunctionDef arguments args NameParam NameParam defaults NameLoad body Expr Str If NameLoad body Return Call NameLoad GeneratorExp BoolOpAnd CompareIn TupleLoad SubscriptLoad NameLoad Index Num SubscriptLoad NameLoad Index Num AttributeLoad NameLoad attr UnaryOpNot Call AttributeLoad BinOpSub SubscriptLoad NameLoad Index NameLoad SubscriptLoad NameLoad Index TupleLoad SubscriptLoad NameLoad Index Num SubscriptLoad NameLoad Index Num attr comprehension NameStore AttributeLoad NameLoad attr orelse Return Call NameLoad GeneratorExp BoolOpAnd CompareIn TupleLoad SubscriptLoad NameLoad Index Num SubscriptLoad NameLoad Index Num AttributeLoad NameLoad attr CompareEq SubscriptLoad NameLoad Index NameLoad SubscriptLoad NameLoad Index TupleLoad SubscriptLoad NameLoad Index Num SubscriptLoad NameLoad Index Num comprehension NameStore AttributeLoad NameLoad attr decorator_list FunctionDef arguments args NameParam defaults vararg body Expr Str Return Call NameLoad GeneratorExp Call AttributeLoad SubscriptLoad NameLoad Index NameLoad attr NameLoad comprehension NameStore AttributeLoad NameLoad attr decorator_list FunctionDef arguments args NameParam NameParam defaults body Expr Str If UnaryOpNot Call NameLoad NameLoad body Raise Call NameLoad Str Assign NameStore Call AttributeLoad NameLoad attr For TupleStore NameStore NameStore Call AttributeLoad AttributeLoad NameLoad attr attr body Assign NameStore Call NameLoad NameLoad If NameLoad body Assign SubscriptStore AttributeLoad NameLoad attr Index NameLoad NameLoad orelse Expr Call AttributeLoad AttributeLoad NameLoad attr attr NameLoad NameLoad Return NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam defaults body Expr Str If CompareNotEq Call NameLoad NameLoad BinOpMult NameLoad NameLoad body Raise Call NameLoad BinOpMod Str TupleLoad NameLoad NameLoad Assign NameStore Dict For TupleStore NameStore NameStore Call AttributeLoad AttributeLoad NameLoad attr attr body Assign TupleStore NameStore NameStore NameLoad Assign NameStore BinOpAdd BinOpMult NameLoad AttributeLoad NameLoad attr NameLoad Assign TupleStore NameStore NameStore Call NameLoad NameLoad NameLoad Assign SubscriptStore NameLoad Index TupleLoad NameLoad NameLoad SubscriptLoad AttributeLoad NameLoad attr Index TupleLoad NameLoad NameLoad Return Call AttributeLoad NameLoad attr NameLoad NameLoad NameLoad decorator_list FunctionDef arguments args NameParam defaults body Expr Str Assign NameStore ListComp ListLoad comprehension NameStore Call NameLoad AttributeLoad NameLoad attr For TupleStore NameStore NameStore NameStore Call AttributeLoad NameLoad attr body If CompareLtE NameLoad NameLoad body Expr Call AttributeLoad SubscriptLoad NameLoad Index NameLoad attr NameLoad Assign NameStore Call NameLoad NameLoad Assign NameStore BinOpMult ListLoad NameLoad AttributeLoad NameLoad attr Assign NameStore BinOpMult ListLoad NameLoad AttributeLoad NameLoad attr For NameStore Call NameLoad AttributeLoad NameLoad attr body For NameStore SubscriptLoad SubscriptLoad NameLoad Index NameLoad Slice Num body While CompareLt SubscriptLoad NameLoad Index NameLoad NameLoad body Assign NameStore SubscriptLoad NameLoad Index NameLoad Assign SubscriptStore NameLoad Index NameLoad NameLoad Assign NameStore NameLoad If CompareEq SubscriptLoad NameLoad Index NameLoad NameLoad body Assign SubscriptStore NameLoad Index NameLoad SubscriptStore NameLoad Index NameLoad NameLoad Return TupleLoad NameLoad NameLoad decorator_list FunctionDef arguments args NameParam defaults body Expr Str Assign TupleStore NameStore NameStore Call AttributeLoad NameLoad attr Assign NameStore Call NameLoad NameLoad Assign NameStore Call AttributeLoad NameLoad attr NameLoad For NameStore Call NameLoad AttributeLoad NameLoad attr body For NameStore SubscriptLoad NameLoad Index NameLoad body While BoolOpAnd CompareNotEq NameLoad NameLoad CompareNotEq NameLoad NameLoad body Expr Call AttributeLoad SubscriptLoad NameLoad Index NameLoad attr NameLoad Assign NameStore SubscriptLoad NameLoad Index NameLoad Assign SubscriptStore NameLoad Index NameLoad Call NameLoad Call NameLoad Call NameLoad SubscriptLoad NameLoad Index NameLoad Return NameLoad decorator_list FunctionDef arguments args NameParam defaults body Expr Str Assign NameStore Call AttributeLoad NameLoad attr Assign NameStore Call AttributeLoad NameLoad attr AttributeLoad NameLoad attr For NameStore Call NameLoad Call NameLoad NameLoad body For NameStore SubscriptLoad NameLoad Index NameLoad body If CompareNotEq NameLoad NameLoad body Assign SubscriptStore NameLoad Index TupleLoad NameLoad NameLoad SubscriptLoad NameLoad Index TupleLoad NameLoad NameLoad Assign NameStore Num For NameStore SubscriptLoad NameLoad Index NameLoad body If CompareLt NameLoad NameLoad body For NameStore SubscriptLoad NameLoad Index NameLoad body If CompareLt NameLoad NameLoad body If CompareEq NameLoad NameLoad body AugAssignAdd NameStore BinOpMult SubscriptLoad NameLoad Index TupleLoad NameLoad NameLoad SubscriptLoad NameLoad Index TupleLoad NameLoad NameLoad orelse Break orelse Break AugAssignSub SubscriptStore NameLoad Index TupleLoad NameLoad NameLoad NameLoad AugAssignDiv SubscriptStore NameLoad Index TupleLoad NameLoad NameLoad SubscriptLoad NameLoad Index TupleLoad NameLoad NameLoad orelse Assign SubscriptStore NameLoad Index TupleLoad NameLoad NameLoad SubscriptLoad NameLoad Index TupleLoad NameLoad NameLoad Assign NameStore Num For NameStore SubscriptLoad NameLoad Index NameLoad body If CompareLt NameLoad NameLoad body AugAssignAdd NameStore BinOpPow SubscriptLoad NameLoad Index TupleLoad NameLoad NameLoad Num orelse Break AugAssignSub SubscriptStore NameLoad Index TupleLoad NameLoad NameLoad NameLoad Assign SubscriptStore NameLoad Index TupleLoad NameLoad NameLoad Call NameLoad SubscriptLoad NameLoad Index TupleLoad NameLoad NameLoad Return NameLoad decorator_list FunctionDef arguments args NameParam defaults body Expr Str Assign NameStore Call AttributeLoad NameLoad attr Assign NameStore Call AttributeLoad NameLoad attr AttributeLoad NameLoad attr Assign NameStore Call AttributeLoad NameLoad attr AttributeLoad NameLoad attr AttributeLoad NameLoad attr For NameStore Call NameLoad Call NameLoad NameLoad body For NameStore SubscriptLoad NameLoad Index NameLoad body If CompareNotEq NameLoad NameLoad body Assign SubscriptStore NameLoad Index TupleLoad NameLoad NameLoad SubscriptLoad NameLoad Index TupleLoad NameLoad NameLoad Assign NameStore Num For NameStore SubscriptLoad NameLoad Index NameLoad body If CompareLt NameLoad NameLoad body For NameStore SubscriptLoad NameLoad Index NameLoad body If CompareLt NameLoad NameLoad body If CompareEq NameLoad NameLoad body AugAssignAdd NameStore BinOpMult BinOpMult SubscriptLoad NameLoad Index TupleLoad NameLoad NameLoad SubscriptLoad NameLoad Index TupleLoad NameLoad NameLoad SubscriptLoad NameLoad Index TupleLoad NameLoad NameLoad orelse Break orelse Break AugAssignSub SubscriptStore NameLoad Index TupleLoad NameLoad NameLoad NameLoad AugAssignDiv SubscriptStore NameLoad Index TupleLoad NameLoad NameLoad SubscriptLoad NameLoad Index TupleLoad NameLoad NameLoad orelse If CompareEq NameLoad NameLoad body Assign SubscriptStore NameLoad Index TupleLoad NameLoad NameLoad SubscriptLoad NameLoad Index TupleLoad NameLoad NameLoad Assign NameStore Num For NameStore SubscriptLoad NameLoad Index NameLoad body If CompareLt NameLoad NameLoad body AugAssignAdd NameStore BinOpMult BinOpPow SubscriptLoad NameLoad Index TupleLoad NameLoad NameLoad Num SubscriptLoad NameLoad Index TupleLoad NameLoad NameLoad orelse Break AugAssignSub SubscriptStore NameLoad Index TupleLoad NameLoad NameLoad NameLoad Return TupleLoad NameLoad NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults body Expr Str Assign NameStore ListComp ListLoad comprehension NameStore Call NameLoad AttributeLoad NameLoad attr For TupleStore NameStore NameStore NameStore Call AttributeLoad NameLoad attr body If CompareGt NameLoad NameLoad body Expr Call AttributeLoad SubscriptLoad NameLoad Index NameLoad attr TupleLoad NameLoad NameLoad Assign NameStore Call AttributeLoad NameLoad attr For NameStore Call NameLoad AttributeLoad NameLoad attr body For TupleStore NameStore NameStore SubscriptLoad NameLoad Index NameLoad body AugAssignSub SubscriptStore NameLoad Index TupleLoad NameLoad Num BinOpMult NameLoad SubscriptLoad NameLoad Index TupleLoad NameLoad Num AugAssignDiv SubscriptStore NameLoad Index TupleLoad NameLoad Num SubscriptLoad NameLoad Index TupleLoad NameLoad NameLoad Return Call AttributeLoad NameLoad attr NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults body Expr Str Assign NameStore ListComp ListLoad comprehension NameStore Call NameLoad AttributeLoad NameLoad attr For TupleStore NameStore NameStore NameStore Call AttributeLoad NameLoad attr body If CompareLt NameLoad NameLoad body Expr Call AttributeLoad SubscriptLoad NameLoad Index NameLoad attr TupleLoad NameLoad NameLoad Assign NameStore Call AttributeLoad NameLoad attr For NameStore Call NameLoad BinOpSub AttributeLoad NameLoad attr Num Num Num body Expr Call AttributeLoad SubscriptLoad NameLoad Index NameLoad attr For TupleStore NameStore NameStore SubscriptLoad NameLoad Index NameLoad body AugAssignSub SubscriptStore NameLoad Index TupleLoad NameLoad Num BinOpMult NameLoad SubscriptLoad NameLoad Index TupleLoad NameLoad Num AugAssignDiv SubscriptStore NameLoad Index TupleLoad NameLoad Num SubscriptLoad NameLoad Index TupleLoad NameLoad NameLoad Return Call AttributeLoad NameLoad attr NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults body Expr Str Return Call AttributeLoad NameLoad attr AttributeLoad NameLoad attr Num Lambda arguments args NameParam NameParam defaults BinOpDiv SubscriptLoad NameLoad Index TupleLoad NameLoad Num SubscriptLoad NameLoad Index TupleLoad NameLoad NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults body Assign NameStore Call AttributeLoad NameLoad attr Assign NameStore Call AttributeLoad NameLoad attr NameLoad Assign NameStore Call AttributeLoad AttributeLoad NameLoad attr attr NameLoad Return NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults body Assign TupleStore NameStore NameStore Call AttributeLoad NameLoad attr Assign NameStore Call AttributeLoad NameLoad attr NameLoad Assign NameStore Call AttributeLoad NameLoad attr NameLoad Return Call AttributeLoad AttributeLoad NameLoad attr attr NameLoad decorator_list FunctionDef arguments args NameParam defaults body Expr Str ImportFrom alias alias If UnaryOpNot Call AttributeLoad NameLoad attr body Raise Call NameLoad Str Assign NameStore Call AttributeLoad Call AttributeLoad NameLoad attr attr If BoolOpOr Call AttributeLoad NameLoad attr NameLoad Call AttributeLoad NameLoad attr NameLoad body Raise Call NameLoad Str Return Call AttributeLoad NameLoad attr NameLoad decorator_list FunctionDef arguments args NameParam defaults body Expr Str ImportFrom alias alias If UnaryOpNot Call AttributeLoad NameLoad attr body Raise Call NameLoad Str Assign TupleStore NameStore NameStore Call AttributeLoad Call AttributeLoad NameLoad attr attr If BoolOpOr Call AttributeLoad NameLoad attr NameLoad Call AttributeLoad NameLoad attr NameLoad Call AttributeLoad NameLoad attr NameLoad Call AttributeLoad NameLoad attr NameLoad body Raise Call NameLoad Str Return TupleLoad Call AttributeLoad NameLoad attr NameLoad Call AttributeLoad NameLoad attr NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam defaults Str body Expr Str Assign NameStore AttributeLoad NameLoad attr Return BinOpMult BinOpMult Call AttributeLoad BinOpMult NameLoad NameLoad attr keyword NameLoad NameLoad NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam defaults Str body Expr Str If UnaryOpNot AttributeLoad NameLoad attr body If CompareLt AttributeLoad NameLoad attr AttributeLoad NameLoad attr body Raise Call NameLoad Str orelse If CompareGt AttributeLoad NameLoad attr AttributeLoad NameLoad attr body Raise Call NameLoad Str orelse Return BinOpMult Call AttributeLoad NameLoad attr keyword NameLoad NameLoad decorator_list FunctionDef arguments args NameParam defaults kwarg body Expr Str Assign NameStore Call AttributeLoad NameLoad attr Assign NameStore Call AttributeLoad NameLoad attr Assign NameStore Call AttributeLoad NameLoad attr AttributeLoad NameLoad attr If UnaryOpNot NameLoad body Assign NameStore AttributeLoad NameLoad attr Assign NameStore SubscriptLoad NameLoad ExtSlice Index Num Slice Assign NameStore BinOpMult NameLoad NameLoad Assign NameStore BinOpMult NameLoad NameLoad Assign NameStore Call AttributeLoad NameLoad attr Str Str If CompareIn NameLoad Str body Assign NameStore AttributeLoad NameLoad attr orelse If CompareEq NameLoad Str body Assign NameStore AttributeLoad NameLoad attr orelse Raise Call NameLoad BinOpMod Str NameLoad Assign NameStore Call AttributeLoad NameLoad attr ListComp Call NameLoad SubscriptLoad NameLoad ExtSlice Slice Index NameLoad comprehension NameStore Call NameLoad AttributeLoad NameLoad attr If UnaryOpNot NameLoad body Assign NameStore SubscriptLoad BinOpMult NameLoad SubscriptLoad NameLoad ExtSlice Slice Index Num Index TupleLoad Num Num AugAssignDiv NameStore NameLoad Return Call AttributeLoad NameLoad attr NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults body TryExcept body If CompareNotEq AttributeLoad NameLoad attr AttributeLoad NameLoad attr body Return NameLoad If Call NameLoad NameLoad NameLoad body Return CompareEq AttributeLoad NameLoad attr AttributeLoad NameLoad attr orelse If Call NameLoad NameLoad NameLoad body Return CompareEq AttributeLoad NameLoad attr AttributeLoad Call NameLoad NameLoad attr handlers ExceptHandler type NameLoad body Return NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults body Return UnaryOpNot CompareEq NameLoad NameLoad decorator_list FunctionDef arguments args NameParam defaults body Expr Str Return Call NameLoad NameLoad decorator_list FunctionDef arguments args NameParam defaults body Expr Str ImportFrom alias Return Call NameLoad NameLoad decorator_list FunctionDef arguments args NameParam defaults body Expr Str Return Call NameLoad AttributeLoad NameLoad attr decorator_list FunctionDef arguments args NameParam NameParam NameParam defaults NameLoad body Expr Str Assign NameStore IfExp CompareIs NameLoad NameLoad NameLoad NameLoad Assign NameStore Call NameLoad NameLoad Assign NameStore Call NameLoad NameLoad Return Call NameLoad NameLoad NameLoad Dict decorator_list NameLoad FunctionDef arguments args NameParam NameParam defaults body Expr Str Assign NameStore Call NameLoad NameLoad Return Call NameLoad NameLoad NameLoad DictComp TupleLoad NameLoad NameLoad AttributeLoad NameLoad attr comprehension NameStore Call NameLoad NameLoad decorator_list NameLoad decorator_list ClassDef bases NameLoad NameLoad body FunctionDef arguments args NameParam defaults vararg kwarg body Return Call NameLoad NameLoad decorator_list NameLoad FunctionDef arguments args NameParam defaults body Return Call AttributeLoad NameLoad attr decorator_list FunctionDef arguments args NameParam NameParam NameParam defaults body Expr Str Assign NameStore Call AttributeLoad NameLoad attr NameLoad NameLoad If CompareIsNot NameLoad NameLoad body Assign TupleStore NameStore NameStore NameStore NameLoad If NameLoad body Assign SubscriptStore AttributeLoad NameLoad attr Index TupleLoad NameLoad NameLoad NameLoad orelse If CompareIn TupleLoad NameLoad NameLoad AttributeLoad NameLoad attr body Delete SubscriptDel AttributeLoad NameLoad attr Index TupleLoad NameLoad NameLoad decorator_list Assign NameStore NameLoad FunctionDef arguments args NameParam NameParam defaults body Expr Str Assign NameStore Dict Assign NameStore Call NameLoad NameLoad AttributeLoad NameLoad attr For TupleStore NameStore NameStore AttributeLoad NameLoad attr body If CompareEq NameLoad NameLoad body Pass orelse If CompareGt NameLoad NameLoad body Assign SubscriptStore NameLoad Index TupleLoad BinOpSub NameLoad Num NameLoad SubscriptLoad AttributeLoad NameLoad attr Index TupleLoad NameLoad NameLoad orelse Assign SubscriptStore NameLoad Index TupleLoad NameLoad NameLoad SubscriptLoad AttributeLoad NameLoad attr Index TupleLoad NameLoad NameLoad Assign AttributeStore NameLoad attr NameLoad AugAssignSub AttributeStore NameLoad attr Num decorator_list FunctionDef arguments args NameParam NameParam defaults body Expr Str Assign NameStore Dict Assign NameStore Call NameLoad NameLoad AttributeLoad NameLoad attr For TupleStore NameStore NameStore AttributeLoad NameLoad attr body If CompareEq NameLoad NameLoad body Pass orelse If CompareGt NameLoad NameLoad body Assign SubscriptStore NameLoad Index TupleLoad NameLoad BinOpSub NameLoad Num SubscriptLoad AttributeLoad NameLoad attr Index TupleLoad NameLoad NameLoad orelse Assign SubscriptStore NameLoad Index TupleLoad NameLoad NameLoad SubscriptLoad AttributeLoad NameLoad attr Index TupleLoad NameLoad NameLoad Assign AttributeStore NameLoad attr NameLoad AugAssignSub AttributeStore NameLoad attr Num decorator_list FunctionDef arguments args NameParam NameParam NameParam defaults body Expr Str If CompareGt NameLoad NameLoad body Assign TupleStore NameStore NameStore TupleLoad NameLoad NameLoad Assign NameStore Call AttributeLoad NameLoad attr Assign NameStore ListLoad For TupleStore NameStore NameStore NameStore NameLoad body If CompareEq NameLoad NameLoad body Expr Call AttributeLoad AttributeLoad NameLoad attr attr TupleLoad NameLoad NameLoad Expr Call AttributeLoad NameLoad attr TupleLoad NameLoad NameLoad orelse If CompareEq NameLoad NameLoad body Expr Call AttributeLoad AttributeLoad NameLoad attr attr TupleLoad NameLoad NameLoad Assign SubscriptStore AttributeLoad NameLoad attr Index TupleLoad NameLoad NameLoad NameLoad orelse If CompareGt NameLoad NameLoad body Break For TupleStore NameStore NameStore NameLoad body Assign SubscriptStore AttributeLoad NameLoad attr Index TupleLoad NameLoad NameLoad NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam defaults body Expr Str If CompareGt NameLoad NameLoad body Assign TupleStore NameStore NameStore TupleLoad NameLoad NameLoad Assign NameStore Call AttributeLoad NameLoad attr Assign NameStore ListLoad For TupleStore NameStore NameStore NameStore NameLoad body If CompareEq NameLoad NameLoad body Expr Call AttributeLoad AttributeLoad NameLoad attr attr TupleLoad NameLoad NameLoad Expr Call AttributeLoad NameLoad attr TupleLoad NameLoad NameLoad orelse If CompareEq NameLoad NameLoad body Expr Call AttributeLoad AttributeLoad NameLoad attr attr TupleLoad NameLoad NameLoad Assign SubscriptStore AttributeLoad NameLoad attr Index TupleLoad NameLoad NameLoad NameLoad orelse If CompareGt NameLoad NameLoad body Break For TupleStore NameStore NameStore NameLoad body Assign SubscriptStore AttributeLoad NameLoad attr Index TupleLoad NameLoad NameLoad NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults body Expr Str If UnaryOpNot NameLoad body Return Call Call NameLoad NameLoad NameLoad Assign TupleStore NameStore NameStore TupleLoad NameLoad NameLoad If UnaryOpNot CompareEq AttributeLoad NameLoad attr AttributeLoad NameLoad attr body Raise Call NameLoad Assign NameStore Call AttributeLoad NameLoad attr If UnaryOpNot Call NameLoad NameLoad NameLoad body Assign NameStore Num Assign NameStore AttributeLoad NameLoad attr For NameStore Call NameLoad AttributeLoad NameLoad attr body For NameStore Call NameLoad AttributeLoad NameLoad attr body Assign NameStore SubscriptLoad NameLoad Index NameLoad If NameLoad body Assign SubscriptStore AttributeLoad NameLoad attr Index TupleLoad NameLoad BinOpAdd NameLoad AttributeLoad NameLoad attr NameLoad AugAssignAdd NameStore Num orelse For TupleStore TupleStore NameStore NameStore NameStore Call AttributeLoad AttributeLoad NameLoad attr attr body Assign SubscriptStore AttributeLoad NameLoad attr Index TupleLoad NameLoad BinOpAdd NameLoad AttributeLoad NameLoad attr NameLoad AugAssignAdd AttributeStore NameLoad attr AttributeLoad NameLoad attr Return NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults body Expr Str If UnaryOpNot NameLoad body Return Call Call NameLoad NameLoad NameLoad Assign TupleStore NameStore NameStore TupleLoad NameLoad NameLoad If UnaryOpNot CompareEq AttributeLoad NameLoad attr AttributeLoad NameLoad attr body Raise Call NameLoad Assign NameStore Call AttributeLoad NameLoad attr If UnaryOpNot Call NameLoad NameLoad NameLoad body Assign NameStore Num Assign NameStore AttributeLoad NameLoad attr For NameStore Call NameLoad AttributeLoad NameLoad attr body For NameStore Call NameLoad AttributeLoad NameLoad attr body Assign NameStore SubscriptLoad NameLoad Index NameLoad If NameLoad body Assign SubscriptStore AttributeLoad NameLoad attr Index TupleLoad BinOpAdd NameLoad AttributeLoad NameLoad attr NameLoad NameLoad AugAssignAdd NameStore Num orelse For TupleStore TupleStore NameStore NameStore NameStore Call AttributeLoad AttributeLoad NameLoad attr attr body Assign SubscriptStore AttributeLoad NameLoad attr Index TupleLoad BinOpAdd NameLoad AttributeLoad NameLoad attr NameLoad NameLoad AugAssignAdd AttributeStore NameLoad attr AttributeLoad NameLoad attr Return NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam defaults body If UnaryOpNot Call NameLoad NameLoad body Raise Call NameLoad Str Expr Call AttributeLoad NameLoad attr NameLoad Call NameLoad NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam defaults body Assign TupleStore NameStore NameStore NameStore NameStore Call AttributeLoad NameLoad attr NameLoad Assign NameStore AttributeLoad NameLoad attr Assign TupleStore NameStore NameStore TupleLoad BinOpSub NameLoad NameLoad BinOpSub NameLoad NameLoad If CompareNotEq NameLoad TupleLoad NameLoad NameLoad body Raise Call NameLoad Str If UnaryOpNot Call NameLoad NameLoad NameLoad body For NameStore Call NameLoad AttributeLoad NameLoad attr body For NameStore Call NameLoad AttributeLoad NameLoad attr body Assign SubscriptStore NameLoad Index TupleLoad BinOpAdd NameLoad NameLoad BinOpAdd NameLoad NameLoad SubscriptLoad NameLoad Index TupleLoad NameLoad NameLoad orelse If CompareLt BinOpMult BinOpSub NameLoad NameLoad BinOpSub NameLoad NameLoad Call NameLoad NameLoad body For NameStore Call NameLoad NameLoad NameLoad body For NameStore Call NameLoad NameLoad NameLoad body Expr Call AttributeLoad AttributeLoad NameLoad attr attr TupleLoad NameLoad NameLoad NameLoad orelse For TupleStore NameStore NameStore NameStore Call AttributeLoad NameLoad attr body If BoolOpAnd CompareLtELt NameLoad NameLoad NameLoad CompareLtELt NameLoad NameLoad NameLoad body Expr Call AttributeLoad AttributeLoad NameLoad attr attr TupleLoad NameLoad NameLoad NameLoad For TupleStore NameStore NameStore Call AttributeLoad AttributeLoad NameLoad attr attr body Assign TupleStore NameStore NameStore NameLoad Assign SubscriptStore NameLoad Index TupleLoad BinOpAdd NameLoad NameLoad BinOpAdd NameLoad NameLoad SubscriptLoad NameLoad Index TupleLoad NameLoad NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam NameParam defaults body Expr Str Expr Call AttributeLoad NameLoad attr NameLoad Lambda arguments args NameParam NameParam defaults Call NameLoad NameLoad SubscriptLoad NameLoad Index TupleLoad NameLoad NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam defaults body Expr Str For NameStore Call NameLoad AttributeLoad NameLoad attr body Assign NameStore Call AttributeLoad AttributeLoad NameLoad attr attr TupleLoad NameLoad NameLoad AttributeLoad NameLoad attr Assign NameStore Call NameLoad NameLoad NameLoad If NameLoad body Assign SubscriptStore AttributeLoad NameLoad attr Index TupleLoad NameLoad NameLoad NameLoad orelse If NameLoad body Expr Call AttributeLoad AttributeLoad NameLoad attr attr TupleLoad NameLoad NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam defaults body Expr Str For NameStore Call NameLoad AttributeLoad NameLoad attr body Assign NameStore Call AttributeLoad AttributeLoad NameLoad attr attr TupleLoad NameLoad NameLoad AttributeLoad NameLoad attr Assign NameStore Call NameLoad NameLoad NameLoad If NameLoad body Assign SubscriptStore AttributeLoad NameLoad attr Index TupleLoad NameLoad NameLoad NameLoad orelse If NameLoad body Expr Call AttributeLoad AttributeLoad NameLoad attr attr TupleLoad NameLoad NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults body Expr Str If UnaryOpNot NameLoad body Assign AttributeStore NameLoad attr Dict orelse Assign NameStore Call AttributeLoad NameLoad attr NameLoad Assign AttributeStore NameLoad attr Call NameLoad ListComp TupleLoad TupleLoad NameLoad NameLoad NameLoad comprehension NameStore Call NameLoad AttributeLoad NameLoad attr comprehension NameStore Call NameLoad AttributeLoad NameLoad attr decorator_list decorator_list
N/A __future__ print_function division N/A copy collections defaultdict sympy.core.containers Dict sympy.core.compatibility is_sequence as_int range sympy.core.logic fuzzy_and sympy.core.singleton S sympy.functions.elementary.miscellaneous sqrt sympy.utilities.iterables uniq matrices MatrixBase ShapeError a2idx dense Matrix N/A collections SparseMatrix N/A MatrixBase N/A N/A 
    A sparse matrix (a matrix with a large number of zero elements).

    Examples
    ========

    >>> from sympy.matrices import SparseMatrix
    >>> SparseMatrix(2, 2, range(4))
    Matrix([
    [0, 1],
    [2, 3]])
    >>> SparseMatrix(2, 2, {(1, 1): 2})
    Matrix([
    [0, 0],
    [0, 2]])

    See Also
    ========
    sympy.matrices.dense.Matrix
     __init__ N/A N/A self N/A args N/A N/A N/A N/A N/A len args 1 N/A isinstance N/A args N/A 0 SparseMatrix N/A N/A N/A self rows N/A N/A args N/A 0 rows N/A N/A self cols N/A N/A args N/A 0 cols N/A N/A self _smat N/A dict N/A N/A args N/A 0 _smat N/A N/A N/A self _smat N/A N/A N/A N/A len args 3 N/A N/A N/A self rows N/A as_int N/A args N/A 0 N/A N/A self cols N/A as_int N/A args N/A 1 N/A N/A isinstance N/A args N/A 2 N/A collections Callable N/A N/A op N/A args N/A 2 N/A i N/A range N/A self rows N/A N/A j N/A range N/A self cols N/A N/A value N/A N/A self _sympify N/A op N/A N/A self _sympify i N/A N/A self _sympify j N/A value N/A N/A N/A N/A self _smat N/A N/A i j value N/A N/A N/A isinstance N/A args N/A 2 N/A dict Dict N/A N/A key N/A N/A N/A args N/A 2 keys N/A N/A v N/A N/A args N/A 2 N/A key N/A v N/A N/A N/A N/A self _smat N/A key N/A N/A self _sympify v N/A N/A N/A is_sequence N/A args N/A 2 N/A N/A N/A N/A len N/A args N/A 2 N/A N/A self rows N/A self cols N/A N/A N/A ValueError N/A List length (%s) != rows*columns (%s) N/A N/A len N/A args N/A 2 N/A N/A self rows N/A self cols N/A flat_list N/A args N/A 2 N/A i N/A range N/A self rows N/A N/A j N/A range N/A self cols N/A N/A value N/A N/A self _sympify N/A flat_list N/A N/A N/A i N/A self cols j N/A value N/A N/A N/A N/A self _smat N/A N/A i j value N/A N/A N/A r c _list N/A N/A Matrix _handle_creation_inputs args N/A N/A self rows r N/A N/A self cols c N/A i N/A range N/A self rows N/A N/A j N/A range N/A self cols N/A N/A value N/A _list N/A N/A N/A N/A self cols i j N/A value N/A N/A N/A N/A self _smat N/A N/A i j value N/A __getitem__ N/A N/A self key N/A N/A N/A N/A isinstance key tuple N/A N/A N/A i j key N/A N/A N/A N/A i j N/A N/A self key2ij key N/A N/A N/A N/A self _smat get N/A i j N/A S Zero N/A N/A N/A N/A TypeError IndexError N/A N/A N/A isinstance i slice N/A N/A i N/A N/A list N/A range N/A self rows N/A i N/A N/A N/A is_sequence i N/A N/A N/A N/A N/A i N/A self rows N/A N/A N/A IndexError Row index out of bounds N/A i N/A i N/A N/A isinstance j slice N/A N/A j N/A N/A list N/A range N/A self cols N/A j N/A N/A N/A is_sequence j N/A N/A N/A N/A N/A j N/A self cols N/A N/A N/A IndexError Col index out of bounds N/A j N/A j N/A N/A N/A self extract i j N/A N/A isinstance key slice N/A N/A N/A lo hi N/A N/A N/A key indices N/A len self N/A 2 N/A L N/A N/A i N/A range lo hi N/A N/A N/A m n N/A divmod i N/A self cols N/A N/A N/A L append N/A N/A N/A self _smat get N/A m n N/A S Zero N/A L N/A N/A i j N/A divmod N/A a2idx key N/A len self N/A self cols N/A N/A N/A N/A self _smat get N/A i j N/A S Zero N/A __setitem__ N/A N/A self key value N/A N/A N/A N/A NotImplementedError N/A copy N/A N/A self N/A N/A N/A N/A N/A self _new N/A self rows N/A self cols N/A self _smat N/A is_Identity N/A N/A self N/A N/A N/A N/A N/A self is_square N/A N/A False N/A N/A N/A all N/A N/A N/A self N/A N/A i i 1 N/A i N/A range N/A self rows N/A N/A False N/A N/A N/A len N/A self _smat N/A self rows N/A property tolist N/A N/A self N/A N/A N/A Convert this sparse matrix into a list of nested Python lists.

        Examples
        ========

        >>> from sympy.matrices import SparseMatrix, ones
        >>> a = SparseMatrix(((1, 2), (3, 4)))
        >>> a.tolist()
        [[1, 2], [3, 4]]

        When there are no rows then it will not be possible to tell how
        many columns were in the original matrix:

        >>> SparseMatrix(ones(0, 3)).tolist()
        []

         N/A N/A N/A self rows N/A N/A N/A N/A N/A N/A self cols N/A N/A N/A N/A N/A i N/A range N/A self rows N/A N/A I J N/A self shape N/A N/A N/A N/A self N/A N/A i j N/A j N/A range J N/A i N/A range I N/A row N/A N/A self i N/A N/A N/A Returns column i from self as a row vector.

        Examples
        ========

        >>> from sympy.matrices import SparseMatrix
        >>> a = SparseMatrix(((1, 2), (3, 4)))
        >>> a.row(0)
        Matrix([[1, 2]])

        See Also
        ========
        col
        row_list
         N/A N/A self N/A N/A i N/A N/A col N/A N/A self j N/A N/A N/A Returns column j from self as a column vector.

        Examples
        ========

        >>> from sympy.matrices import SparseMatrix
        >>> a = SparseMatrix(((1, 2), (3, 4)))
        >>> a.col(0)
        Matrix([
        [1],
        [3]])

        See Also
        ========
        row
        col_list
         N/A N/A self N/A N/A N/A j N/A row_list N/A N/A self N/A N/A N/A Returns a row-sorted list of non-zero elements of the matrix.

        Examples
        ========

        >>> from sympy.matrices import SparseMatrix
        >>> a = SparseMatrix(((1, 2), (3, 4)))
        >>> a
        Matrix([
        [1, 2],
        [3, 4]])
        >>> a.RL
        [(0, 0, 1), (0, 1, 2), (1, 0, 3), (1, 1, 4)]

        See Also
        ========
        row_op
        col_list
         N/A N/A N/A tuple N/A k N/A N/A self N/A k N/A k N/A sorted N/A list N/A N/A N/A self _smat keys key N/A N/A N/A k N/A N/A list k N/A N/A RL N/A property row_list None None Alternate faster representation col_list N/A N/A self N/A N/A N/A Returns a column-sorted list of non-zero elements of the matrix.

        Examples
        ========

        >>> from sympy.matrices import SparseMatrix
        >>> a=SparseMatrix(((1, 2), (3, 4)))
        >>> a
        Matrix([
        [1, 2],
        [3, 4]])
        >>> a.CL
        [(0, 0, 1), (1, 0, 3), (0, 1, 2), (1, 1, 4)]

        See Also
        ========
        col_op
        row_list
         N/A N/A N/A tuple N/A k N/A N/A self N/A k N/A k N/A sorted N/A list N/A N/A N/A self _smat keys key N/A N/A N/A k N/A N/A list N/A reversed k N/A N/A CL N/A property col_list None None Alternate faster representation _eval_trace N/A N/A self N/A N/A N/A Calculate the trace of a square matrix.

        Examples
        ========

        >>> from sympy.matrices import eye
        >>> eye(3).trace()
        3

         N/A trace N/A S Zero N/A i N/A range N/A self cols N/A N/A trace N/A N/A N/A self _smat get N/A i i 0 N/A trace N/A _eval_transpose N/A N/A self N/A N/A N/A Returns the transposed SparseMatrix of this SparseMatrix.

        Examples
        ========

        >>> from sympy.matrices import SparseMatrix
        >>> a = SparseMatrix(((1, 2), (3, 4)))
        >>> a
        Matrix([
        [1, 2],
        [3, 4]])
        >>> a.T
        Matrix([
        [1, 3],
        [2, 4]])
         N/A tran N/A N/A self zeros N/A self cols N/A self rows N/A N/A key value N/A N/A N/A self _smat items N/A N/A key N/A N/A key N/A 1 N/A key N/A 0 N/A N/A N/A tran _smat N/A key value N/A tran N/A _eval_conjugate N/A N/A self N/A N/A N/A Return the by-element conjugation.

        Examples
        ========

        >>> from sympy.matrices import SparseMatrix
        >>> from sympy import I
        >>> a = SparseMatrix(((1, 2 + I), (3, 4), (I, -I)))
        >>> a
        Matrix([
        [1, 2 + I],
        [3,     4],
        [I,    -I]])
        >>> a.C
        Matrix([
        [ 1, 2 - I],
        [ 3,     4],
        [-I,     I]])

        See Also
        ========

        transpose: Matrix transposition
        H: Hermite conjugation
        D: Dirac conjugation
         N/A conj N/A N/A self copy N/A N/A key value N/A N/A N/A self _smat items N/A N/A N/A N/A conj _smat N/A key N/A N/A value conjugate N/A conj N/A multiply N/A N/A self other N/A N/A N/A Fast multiplication exploiting the sparsity of the matrix.

        Examples
        ========

        >>> from sympy.matrices import SparseMatrix, ones
        >>> A, B = SparseMatrix(ones(4, 3)), SparseMatrix(ones(3, 4))
        >>> A.multiply(B) == 3*ones(4)
        True

        See Also
        ========

        add
         N/A A self N/A B other N/A Blist N/A N/A N/A i N/A range N/A B rows N/A N/A i j v N/A N/A B row_list N/A N/A N/A N/A N/A Blist N/A i append N/A j v N/A Cdict N/A defaultdict int N/A N/A k j Akj N/A N/A A row_list N/A N/A N/A n Bjn N/A Blist N/A j N/A N/A temp N/A Akj Bjn N/A N/A Cdict N/A N/A k n temp N/A rv N/A N/A self zeros N/A A rows N/A B cols N/A N/A rv _smat N/A k v N/A N/A k v N/A N/A Cdict items v N/A rv N/A scalar_multiply N/A N/A self scalar N/A N/A N/A Scalar element-wise multiplication N/A M N/A N/A self zeros N/A self shape N/A scalar N/A N/A i N/A self _smat N/A N/A v N/A scalar N/A N/A self _smat N/A i N/A v N/A N/A N/A N/A M _smat N/A i v N/A N/A N/A N/A N/A M _smat pop i None N/A M N/A __mul__ N/A N/A self other N/A N/A N/A Multiply self and other, watching for non-matrix entities.

        When multiplying be a non-sparse matrix, the result is no longer
        sparse.

        Examples
        ========

        >>> from sympy.matrices import SparseMatrix, eye, zeros
        >>> I = SparseMatrix(eye(3))
        >>> I*I == I
        True
        >>> Z = zeros(3)
        >>> I*Z
        Matrix([
        [0, 0, 0],
        [0, 0, 0],
        [0, 0, 0]])
        >>> I*2 == 2*I
        True
         N/A N/A isinstance other SparseMatrix N/A N/A N/A N/A self multiply other N/A N/A isinstance other MatrixBase N/A N/A N/A N/A other _new N/A self N/A N/A self _new other N/A N/A N/A self scalar_multiply other N/A N/A __matmul__ __mul__ __rmul__ N/A N/A self other N/A N/A N/A Return product the same type as other (if a Matrix).

        When multiplying be a non-sparse matrix, the result is no longer
        sparse.

        Examples
        ========

        >>> from sympy.matrices import Matrix, SparseMatrix
        >>> A = Matrix(2, 2, range(1, 5))
        >>> S = SparseMatrix(2, 2, range(2, 6))
        >>> A*S == S*A
        False
        >>> (isinstance(A*S, SparseMatrix) ==
        ...  isinstance(S*A, SparseMatrix) == False)
        True
         N/A N/A isinstance other MatrixBase N/A N/A N/A other N/A N/A other _new self N/A N/A N/A self scalar_multiply other N/A N/A __rmatmul__ __rmul__ __add__ N/A N/A self other N/A N/A N/A Add other to self, efficiently if possible.

        When adding a non-sparse matrix, the result is no longer
        sparse.

        Examples
        ========

        >>> from sympy.matrices import SparseMatrix, eye
        >>> A = SparseMatrix(eye(3)) + SparseMatrix(eye(3))
        >>> B = SparseMatrix(eye(3)) + eye(3)
        >>> A
        Matrix([
        [2, 0, 0],
        [0, 2, 0],
        [0, 0, 2]])
        >>> A == B
        True
        >>> isinstance(A, SparseMatrix) and isinstance(B, SparseMatrix)
        False

         N/A N/A isinstance other SparseMatrix N/A N/A N/A N/A self add other N/A N/A N/A isinstance other MatrixBase N/A N/A N/A N/A other _new N/A other self N/A N/A N/A NotImplementedError N/A Cannot add %s to %s N/A tuple N/A N/A N/A c __class__ __name__ N/A c N/A other self N/A __neg__ N/A N/A self N/A N/A N/A Negate all elements of self.

        Examples
        ========

        >>> from sympy.matrices import SparseMatrix, eye
        >>> -SparseMatrix(eye(3))
        Matrix([
        [-1,  0,  0],
        [ 0, -1,  0],
        [ 0,  0, -1]])

         N/A rv N/A N/A self copy N/A N/A k v N/A N/A N/A rv _smat items N/A N/A N/A N/A rv _smat N/A k N/A v N/A rv N/A add N/A N/A self other N/A N/A N/A Add two sparse matrices with dictionary representation.

        Examples
        ========

        >>> from sympy.matrices import SparseMatrix, eye, ones
        >>> SparseMatrix(eye(3)).add(SparseMatrix(ones(3)))
        Matrix([
        [2, 1, 1],
        [1, 2, 1],
        [1, 1, 2]])
        >>> SparseMatrix(eye(3)).add(-SparseMatrix(eye(3)))
        Matrix([
        [0, 0, 0],
        [0, 0, 0],
        [0, 0, 0]])

        Only the non-zero elements are stored, so the resulting dictionary
        that is used to represent the sparse matrix is empty:

        >>> _._smat
        {}

        See Also
        ========

        multiply
         N/A N/A N/A isinstance other SparseMatrix N/A N/A N/A ValueError N/A only use add with %s, not %s N/A tuple N/A N/A N/A c __class__ __name__ N/A c N/A self other N/A N/A N/A self shape N/A other shape N/A N/A N/A ShapeError N/A M N/A N/A self copy N/A N/A i v N/A N/A N/A other _smat items N/A N/A v N/A N/A M N/A i v N/A v N/A N/A N/A N/A M _smat N/A i v N/A N/A N/A N/A N/A M _smat pop i None N/A M N/A extract N/A N/A self rowsList colsList N/A N/A N/A urow N/A list N/A uniq rowsList N/A ucol N/A list N/A uniq colsList N/A smat N/A N/A N/A N/A N/A len urow N/A len ucol N/A len N/A self _smat N/A N/A N/A i r N/A enumerate urow N/A N/A N/A j c N/A enumerate ucol N/A N/A N/A smat N/A N/A i j N/A N/A N/A self _smat get N/A r c 0 N/A N/A N/A rk ck N/A self _smat N/A N/A N/A N/A rk urow N/A ck ucol N/A N/A N/A smat N/A N/A N/A N/A urow index rk N/A N/A ucol index ck N/A N/A self _smat N/A N/A rk ck N/A rv N/A N/A self _new N/A len urow N/A len ucol smat N/A N/A N/A len rowsList N/A len urow N/A N/A N/A i r N/A enumerate rowsList N/A N/A i_previous N/A N/A rowsList index r N/A N/A i_previous i N/A N/A rv N/A N/A rv row_insert i N/A N/A rv row i_previous N/A N/A N/A len colsList N/A len ucol N/A N/A N/A i c N/A enumerate colsList N/A N/A i_previous N/A N/A colsList index c N/A N/A i_previous i N/A N/A rv N/A N/A rv col_insert i N/A N/A rv col i_previous N/A rv N/A N/A N/A extract __doc__ N/A N/A MatrixBase extract __doc__ is_hermitian N/A N/A self N/A N/A N/A Checks if the matrix is Hermitian.

        In a Hermitian matrix element i,j is the complex conjugate of
        element j,i.

        Examples
        ========

        >>> from sympy.matrices import SparseMatrix
        >>> from sympy import I
        >>> from sympy.abc import x
        >>> a = SparseMatrix([[1, I], [-I, 1]])
        >>> a
        Matrix([
        [ 1, I],
        [-I, 1]])
        >>> a.is_hermitian
        True
        >>> a[0, 0] = 2*I
        >>> a.is_hermitian
        False
        >>> a[0, 0] = x
        >>> a.is_hermitian
        >>> a[0, 1] = a[1, 0]*I
        >>> a.is_hermitian
        False
         cond N/A N/A N/A N/A N/A d N/A self _smat N/A N/A N/A self is_square N/A N/A N/A len d N/A self rows N/A N/A N/A N/A fuzzy_and N/A N/A N/A d N/A N/A i i is_real N/A N/A i j d N/A i j N/A N/A N/A N/A fuzzy_and N/A N/A N/A d N/A N/A i i is_real N/A i N/A range N/A self rows N/A N/A i i d N/A N/A N/A fuzzy_and N/A N/A N/A N/A j i d N/A N/A N/A self N/A N/A i j N/A N/A N/A self N/A N/A j i conjugate is_zero False N/A N/A i j d N/A N/A N/A fuzzy_and N/A i N/A i N/A cond N/A property is_symmetric N/A N/A self simplify N/A True N/A N/A Return True if self is symmetric.

        Examples
        ========

        >>> from sympy.matrices import SparseMatrix, eye
        >>> M = SparseMatrix(eye(3))
        >>> M.is_symmetric()
        True
        >>> M[0, 2] = 1
        >>> M.is_symmetric()
        False
         N/A simplify N/A N/A N/A all N/A N/A N/A N/A N/A k N/A 1 N/A k N/A 0 N/A self _smat N/A N/A N/A N/A N/A self N/A k N/A self N/A N/A N/A k N/A 1 N/A k N/A 0 simplify N/A k N/A self _smat N/A N/A N/A all N/A N/A N/A N/A N/A k N/A 1 N/A k N/A 0 N/A self _smat N/A N/A self N/A k N/A self N/A N/A N/A k N/A 1 N/A k N/A 0 N/A k N/A self _smat N/A has N/A N/A self N/A patterns N/A N/A Test whether any subexpression matches any of the patterns.

        Examples
        ========

        >>> from sympy import SparseMatrix, Float
        >>> from sympy.abc import x, y
        >>> A = SparseMatrix(((1, x), (0.2, 3)))
        >>> A.has(x)
        True
        >>> A.has(y)
        False
        >>> A.has(Float)
        True
         N/A N/A any N/A N/A N/A N/A self N/A key has patterns N/A key N/A self _smat N/A applyfunc N/A N/A self f N/A N/A N/A Apply a function to each element of the matrix.

        Examples
        ========

        >>> from sympy.matrices import SparseMatrix
        >>> m = SparseMatrix(2, 2, lambda i, j: i*2+j)
        >>> m
        Matrix([
        [0, 1],
        [2, 3]])
        >>> m.applyfunc(lambda i: 2*i)
        Matrix([
        [0, 2],
        [4, 6]])

         N/A N/A N/A callable f N/A N/A N/A TypeError `f` must be callable. N/A out N/A N/A self copy N/A N/A k v N/A N/A N/A self _smat items N/A N/A fv N/A f v N/A fv N/A N/A N/A N/A out _smat N/A k fv N/A N/A N/A N/A N/A out _smat pop k None N/A out N/A reshape N/A N/A self rows cols N/A N/A N/A Reshape matrix while retaining original size.

        Examples
        ========

        >>> from sympy.matrices import SparseMatrix
        >>> S = SparseMatrix(4, 2, range(8))
        >>> S.reshape(2, 4)
        Matrix([
        [0, 1, 2, 3],
        [4, 5, 6, 7]])

         N/A N/A N/A len self N/A rows cols N/A N/A N/A ValueError N/A Invalid reshape parameters %d %d N/A rows cols N/A smat N/A N/A N/A k v N/A N/A N/A self _smat items N/A N/A N/A i j k N/A n N/A N/A i N/A self cols j N/A N/A ii jj N/A divmod n cols N/A N/A smat N/A N/A ii jj N/A N/A self _smat N/A N/A i j N/A N/A N/A self _new rows cols smat N/A liupc N/A N/A self N/A N/A N/A Liu's algorithm, for pre-determination of the Elimination Tree of
        the given matrix, used in row-based symbolic Cholesky factorization.

        Examples
        ========

        >>> from sympy.matrices import SparseMatrix
        >>> S = SparseMatrix([
        ... [1, 0, 3, 2],
        ... [0, 0, 1, 0],
        ... [4, 0, 0, 5],
        ... [0, 6, 7, 0]])
        >>> S.liupc()
        ([[0], [], [0], [1, 2]], [4, 3, 4, 4])

        References
        ==========

        Symbolic Sparse Cholesky Factorization using Elimination Trees,
        Jeroen Van Grondelle (1999)
        http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.39.7582
         N/A R N/A N/A N/A r N/A range N/A self rows N/A N/A r c _ N/A N/A self row_list N/A N/A N/A c r N/A N/A N/A N/A N/A R N/A r append c N/A inf N/A len R N/A parent N/A N/A inf N/A self rows N/A virtual N/A N/A inf N/A self rows N/A r N/A range N/A self rows N/A N/A c N/A N/A R N/A r N/A -1 N/A N/A N/A N/A virtual N/A c r N/A N/A t N/A virtual N/A c N/A N/A virtual N/A c r N/A c t N/A N/A N/A virtual N/A c inf N/A N/A N/A parent N/A c N/A virtual N/A c r N/A N/A R parent N/A row_structure_symbolic_cholesky N/A N/A self N/A N/A N/A Symbolic cholesky factorization, for pre-determination of the
        non-zero structure of the Cholesky factororization.

        Examples
        ========

        >>> from sympy.matrices import SparseMatrix
        >>> S = SparseMatrix([
        ... [1, 0, 3, 2],
        ... [0, 0, 1, 0],
        ... [4, 0, 0, 5],
        ... [0, 6, 7, 0]])
        >>> S.row_structure_symbolic_cholesky()
        [[0], [], [0], [1, 2]]

        References
        ==========

        Symbolic Sparse Cholesky Factorization using Elimination Trees,
        Jeroen Van Grondelle (1999)
        http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.39.7582
         N/A N/A R parent N/A N/A self liupc N/A inf N/A len R N/A Lrow N/A N/A copy deepcopy R N/A k N/A range N/A self rows N/A N/A j N/A R N/A k N/A N/A N/A N/A j inf N/A j k N/A N/A N/A N/A N/A Lrow N/A k append j N/A j N/A parent N/A j N/A N/A Lrow N/A k N/A list N/A sorted N/A set N/A Lrow N/A k N/A Lrow N/A _cholesky_sparse N/A N/A self N/A N/A N/A Algorithm for numeric Cholesky factorization of a sparse matrix. N/A Crowstruc N/A N/A self row_structure_symbolic_cholesky N/A C N/A N/A self zeros N/A self rows N/A i N/A range N/A len Crowstruc N/A N/A j N/A Crowstruc N/A i N/A N/A N/A i j N/A N/A N/A C N/A N/A i j N/A self N/A N/A i j N/A summ 0 N/A p1 N/A Crowstruc N/A i N/A N/A N/A p1 j N/A N/A p2 N/A Crowstruc N/A j N/A N/A N/A p2 j N/A N/A N/A p1 p2 N/A N/A summ N/A N/A C N/A N/A i p1 N/A C N/A N/A j p1 N/A N/A N/A N/A N/A N/A C N/A N/A i j summ N/A N/A C N/A N/A i j N/A C N/A N/A j j N/A N/A N/A C N/A N/A j j N/A self N/A N/A j j N/A summ 0 N/A k N/A Crowstruc N/A j N/A N/A N/A k j N/A N/A summ N/A N/A C N/A N/A j k 2 N/A N/A N/A N/A C N/A N/A j j summ N/A N/A C N/A N/A j j N/A sqrt N/A C N/A N/A j j N/A C N/A _LDL_sparse N/A N/A self N/A N/A N/A Algorithm for numeric LDL factization, exploiting sparse structure.
         N/A Lrowstruc N/A N/A self row_structure_symbolic_cholesky N/A L N/A N/A self eye N/A self rows N/A D N/A N/A self zeros N/A self rows N/A self cols N/A i N/A range N/A len Lrowstruc N/A N/A j N/A Lrowstruc N/A i N/A N/A N/A i j N/A N/A N/A L N/A N/A i j N/A self N/A N/A i j N/A summ 0 N/A p1 N/A Lrowstruc N/A i N/A N/A N/A p1 j N/A N/A p2 N/A Lrowstruc N/A j N/A N/A N/A p2 j N/A N/A N/A p1 p2 N/A N/A summ N/A N/A N/A L N/A N/A i p1 N/A L N/A N/A j p1 N/A D N/A N/A p1 p1 N/A N/A N/A N/A N/A N/A L N/A N/A i j summ N/A N/A L N/A N/A i j N/A D N/A N/A j j N/A N/A N/A i j N/A N/A N/A D N/A N/A i i N/A self N/A N/A i i N/A summ 0 N/A k N/A Lrowstruc N/A i N/A N/A N/A k i N/A N/A summ N/A N/A N/A L N/A N/A i k 2 N/A D N/A N/A k k N/A N/A N/A N/A D N/A N/A i i summ N/A N/A L D N/A _lower_triangular_solve N/A N/A self rhs N/A N/A N/A Fast algorithm for solving a lower-triangular system,
        exploiting the sparsity of the given matrix.
         N/A rows N/A N/A N/A i N/A range N/A self rows N/A N/A i j v N/A N/A self row_list N/A N/A N/A i j N/A N/A N/A N/A N/A rows N/A i append N/A j v N/A X N/A N/A rhs copy N/A i N/A range N/A self rows N/A N/A N/A j v N/A rows N/A i N/A N/A N/A X N/A N/A i 0 N/A v N/A X N/A N/A j 0 N/A N/A X N/A N/A i 0 N/A self N/A N/A i i N/A N/A N/A self _new X N/A _upper_triangular_solve N/A N/A self rhs N/A N/A N/A Fast algorithm for solving an upper-triangular system,
        exploiting the sparsity of the given matrix.
         N/A rows N/A N/A N/A i N/A range N/A self rows N/A N/A i j v N/A N/A self row_list N/A N/A N/A i j N/A N/A N/A N/A N/A rows N/A i append N/A j v N/A X N/A N/A rhs copy N/A i N/A range N/A N/A self rows 1 -1 -1 N/A N/A N/A N/A N/A rows N/A i reverse N/A N/A j v N/A rows N/A i N/A N/A N/A X N/A N/A i 0 N/A v N/A X N/A N/A j 0 N/A N/A X N/A N/A i 0 N/A self N/A N/A i i N/A N/A N/A self _new X N/A _diagonal_solve N/A N/A self rhs N/A N/A N/A Diagonal solve. N/A N/A N/A self _new N/A self rows 1 N/A N/A N/A i j N/A N/A N/A rhs N/A N/A i 0 N/A self N/A N/A i i N/A _cholesky_solve N/A N/A self rhs N/A N/A N/A L N/A N/A self _cholesky_sparse N/A Y N/A N/A L _lower_triangular_solve rhs N/A rv N/A N/A N/A L T _upper_triangular_solve Y N/A rv N/A _LDL_solve N/A N/A self rhs N/A N/A N/A N/A L D N/A N/A self _LDL_sparse N/A Z N/A N/A L _lower_triangular_solve rhs N/A Y N/A N/A D _diagonal_solve Z N/A N/A N/A N/A L T _upper_triangular_solve Y N/A cholesky N/A N/A self N/A N/A N/A 
        Returns the Cholesky decomposition L of a matrix A
        such that L * L.T = A

        A must be a square, symmetric, positive-definite
        and non-singular matrix

        Examples
        ========

        >>> from sympy.matrices import SparseMatrix
        >>> A = SparseMatrix(((25,15,-5),(15,18,0),(-5,0,11)))
        >>> A.cholesky()
        Matrix([
        [ 5, 0, 0],
        [ 3, 3, 0],
        [-1, 1, 3]])
        >>> A.cholesky() * A.cholesky().T == A
        True
         sympy.core.numbers nan oo N/A N/A N/A N/A self is_symmetric N/A N/A N/A ValueError Cholesky decomposition applies only to symmetric matrices. N/A M N/A N/A N/A N/A self as_mutable _cholesky_sparse N/A N/A N/A N/A M has nan N/A N/A M has oo N/A N/A N/A ValueError Cholesky decomposition applies only to positive-definite matrices N/A N/A N/A self _new M N/A LDLdecomposition N/A N/A self N/A N/A N/A 
        Returns the LDL Decomposition (matrices ``L`` and ``D``) of matrix
        ``A``, such that ``L * D * L.T == A``. ``A`` must be a square,
        symmetric, positive-definite and non-singular.

        This method eliminates the use of square root and ensures that all
        the diagonal entries of L are 1.

        Examples
        ========

        >>> from sympy.matrices import SparseMatrix
        >>> A = SparseMatrix(((25, 15, -5), (15, 18, 0), (-5, 0, 11)))
        >>> L, D = A.LDLdecomposition()
        >>> L
        Matrix([
        [   1,   0, 0],
        [ 3/5,   1, 0],
        [-1/5, 1/3, 1]])
        >>> D
        Matrix([
        [25, 0, 0],
        [ 0, 9, 0],
        [ 0, 0, 9]])
        >>> L * D * L.T == A
        True

         sympy.core.numbers nan oo N/A N/A N/A N/A self is_symmetric N/A N/A N/A ValueError LDL decomposition applies only to symmetric matrices. N/A N/A L D N/A N/A N/A N/A self as_mutable _LDL_sparse N/A N/A N/A N/A L has nan N/A N/A L has oo N/A N/A D has nan N/A N/A D has oo N/A N/A N/A ValueError LDL decomposition applies only to positive-definite matrices N/A N/A N/A N/A self _new L N/A N/A self _new D N/A solve_least_squares N/A N/A self rhs method N/A LDL N/A N/A Return the least-square fit to the data.

        By default the cholesky_solve routine is used (method='CH'); other
        methods of matrix inversion can be used. To find out which are
        available, see the docstring of the .inv() method.

        Examples
        ========

        >>> from sympy.matrices import SparseMatrix, Matrix, ones
        >>> A = Matrix([1, 2, 3])
        >>> B = Matrix([2, 3, 4])
        >>> S = SparseMatrix(A.row_join(B))
        >>> S
        Matrix([
        [1, 2],
        [2, 3],
        [3, 4]])

        If each line of S represent coefficients of Ax + By
        and x and y are [2, 3] then S*xy is:

        >>> r = S*Matrix([2, 3]); r
        Matrix([
        [ 8],
        [13],
        [18]])

        But let's add 1 to the middle value and then solve for the
        least-squares value of xy:

        >>> xy = S.solve_least_squares(Matrix([8, 14, 18])); xy
        Matrix([
        [ 5/3],
        [10/3]])

        The error is given by S*xy - r:

        >>> S*xy - r
        Matrix([
        [1/3],
        [1/3],
        [1/3]])
        >>> _.norm().n(2)
        0.58

        If a different xy is used, the norm will be higher:

        >>> xy += ones(2, 1)/10
        >>> (S*xy - r).norm().n(2)
        1.5

         N/A t N/A self T N/A N/A N/A N/A N/A N/A t self inv method method t rhs N/A solve N/A N/A self rhs method N/A LDL N/A N/A Return solution to self*soln = rhs using given inversion method.

        For a list of possible inversion methods, see the .inv() docstring.
         N/A N/A N/A self is_square N/A N/A N/A N/A self rows N/A self cols N/A N/A N/A ValueError Under-determined system. N/A N/A N/A N/A self rows N/A self cols N/A N/A N/A ValueError For over-determined system, M, having more rows than columns, try M.solve_least_squares(rhs). N/A N/A N/A N/A N/A self inv method method rhs N/A _eval_inverse N/A N/A self N/A kwargs N/A N/A Return the matrix inverse using Cholesky or LDL (default)
        decomposition as selected with the ``method`` keyword: 'CH' or 'LDL',
        respectively.

        Examples
        ========

        >>> from sympy import SparseMatrix, Matrix
        >>> A = SparseMatrix([
        ... [ 2, -1,  0],
        ... [-1,  2, -1],
        ... [ 0,  0,  2]])
        >>> A.inv('CH')
        Matrix([
        [2/3, 1/3, 1/6],
        [1/3, 2/3, 1/3],
        [  0,   0, 1/2]])
        >>> A.inv(method='LDL') # use of 'method=' is optional
        Matrix([
        [2/3, 1/3, 1/6],
        [1/3, 2/3, 1/3],
        [  0,   0, 1/2]])
        >>> A * _
        Matrix([
        [1, 0, 0],
        [0, 1, 0],
        [0, 0, 1]])

         N/A sym N/A N/A self is_symmetric N/A M N/A N/A self as_mutable N/A I N/A N/A M eye N/A M rows N/A N/A sym N/A N/A t N/A M T N/A r1 N/A M N/A N/A 0 N/A N/A M N/A t M N/A I N/A t I N/A method N/A N/A kwargs get method LDL N/A N/A method LDL N/A N/A solve N/A M _LDL_solve N/A N/A N/A method CH N/A N/A solve N/A M _cholesky_solve N/A N/A N/A NotImplementedError N/A Method may be "CH" or "LDL", not %s. method N/A rv N/A N/A M hstack N/A N/A solve N/A I N/A N/A N/A i N/A i N/A range N/A I cols N/A N/A sym N/A N/A scale N/A N/A r1 N/A rv N/A N/A N/A 0 N/A N/A 0 0 N/A rv scale N/A N/A N/A self _new rv N/A __eq__ N/A N/A self other N/A N/A N/A N/A N/A N/A N/A self shape N/A other shape N/A N/A False N/A N/A isinstance other SparseMatrix N/A N/A N/A N/A self _smat N/A other _smat N/A N/A N/A isinstance other MatrixBase N/A N/A N/A N/A self _smat N/A N/A MutableSparseMatrix other _smat N/A N/A N/A AttributeError N/A N/A False N/A __ne__ N/A N/A self other N/A N/A N/A N/A N/A self other N/A as_mutable N/A N/A self N/A N/A N/A Returns a mutable version of this matrix.

        Examples
        ========

        >>> from sympy import ImmutableMatrix
        >>> X = ImmutableMatrix([[1, 2], [3, 4]])
        >>> Y = X.as_mutable()
        >>> Y[1, 1] = 5 # Can set values in Y
        >>> Y
        Matrix([
        [1, 2],
        [3, 5]])
         N/A N/A MutableSparseMatrix self N/A as_immutable N/A N/A self N/A N/A N/A Returns an Immutable version of this Matrix. immutable ImmutableSparseMatrix N/A N/A ImmutableSparseMatrix self N/A nnz N/A N/A self N/A N/A N/A Returns the number of non-zero elements in Matrix. N/A N/A len N/A self _smat N/A zeros N/A N/A cls r c N/A None N/A N/A Return an r x c matrix of zeros, square if c is omitted. N/A c N/A N/A c None r c N/A r N/A as_int r N/A c N/A as_int c N/A N/A cls r c N/A N/A classmethod eye N/A N/A cls n N/A N/A N/A Return an n x n identity matrix. N/A n N/A as_int n N/A N/A cls n n N/A N/A i i N/A S One N/A i N/A range n N/A classmethod N/A MutableSparseMatrix N/A SparseMatrix MatrixBase N/A _new N/A N/A cls N/A args kwargs N/A N/A N/A cls args N/A classmethod as_mutable N/A N/A self N/A N/A N/A N/A N/A self copy N/A __setitem__ N/A N/A self key value N/A N/A N/A Assign value to position designated by key.

        Examples
        ========

        >>> from sympy.matrices import SparseMatrix, ones
        >>> M = SparseMatrix(2, 2, {})
        >>> M[1] = 1; M
        Matrix([
        [0, 1],
        [0, 0]])
        >>> M[1, 1] = 2; M
        Matrix([
        [0, 1],
        [0, 2]])
        >>> M = SparseMatrix(2, 2, {})
        >>> M[:, 1] = [1, 1]; M
        Matrix([
        [0, 1],
        [0, 1]])
        >>> M = SparseMatrix(2, 2, {})
        >>> M[1, :] = [[1, 1]]; M
        Matrix([
        [0, 0],
        [1, 1]])


        To replace row r you assign to position r*m where m
        is the number of columns:

        >>> M = SparseMatrix(4, 4, {})
        >>> m = M.cols
        >>> M[3*m] = ones(1, m)*2; M
        Matrix([
        [0, 0, 0, 0],
        [0, 0, 0, 0],
        [0, 0, 0, 0],
        [2, 2, 2, 2]])

        And to replace column c you can assign to position c:

        >>> M[2] = ones(m, 1)*4; M
        Matrix([
        [0, 0, 4, 0],
        [0, 0, 4, 0],
        [0, 0, 4, 0],
        [2, 2, 4, 2]])
         N/A rv N/A N/A self _setitem key value N/A N/A rv None N/A N/A N/A i j value rv N/A value N/A N/A N/A N/A self _smat N/A N/A i j value N/A N/A N/A N/A i j N/A self _smat N/A N/A N/A N/A self _smat N/A N/A i j N/A N/A __hash__ None row_del N/A N/A self k N/A N/A N/A Delete the given row of the matrix.

        Examples
        ========

        >>> from sympy.matrices import SparseMatrix
        >>> M = SparseMatrix([[0, 0], [0, 1]])
        >>> M
        Matrix([
        [0, 0],
        [0, 1]])
        >>> M.row_del(0)
        >>> M
        Matrix([[0, 1]])

        See Also
        ========

        col_del
         N/A newD N/A N/A k N/A a2idx k N/A self rows N/A N/A i j N/A self _smat N/A N/A N/A i k N/A N/A N/A N/A N/A i k N/A N/A N/A newD N/A N/A N/A i 1 j N/A N/A self _smat N/A N/A i j N/A N/A N/A newD N/A N/A i j N/A N/A self _smat N/A N/A i j N/A N/A self _smat newD N/A N/A self rows 1 N/A col_del N/A N/A self k N/A N/A N/A Delete the given column of the matrix.

        Examples
        ========

        >>> from sympy.matrices import SparseMatrix
        >>> M = SparseMatrix([[0, 0], [0, 1]])
        >>> M
        Matrix([
        [0, 0],
        [0, 1]])
        >>> M.col_del(0)
        >>> M
        Matrix([
        [0],
        [1]])

        See Also
        ========

        row_del
         N/A newD N/A N/A k N/A a2idx k N/A self cols N/A N/A i j N/A self _smat N/A N/A N/A j k N/A N/A N/A N/A N/A j k N/A N/A N/A newD N/A N/A i N/A j 1 N/A N/A self _smat N/A N/A i j N/A N/A N/A newD N/A N/A i j N/A N/A self _smat N/A N/A i j N/A N/A self _smat newD N/A N/A self cols 1 N/A row_swap N/A N/A self i j N/A N/A N/A Swap, in place, columns i and j.

        Examples
        ========

        >>> from sympy.matrices import SparseMatrix
        >>> S = SparseMatrix.eye(3); S[2, 1] = 2
        >>> S.row_swap(1, 0); S
        Matrix([
        [0, 1, 0],
        [1, 0, 0],
        [0, 2, 1]])
         N/A N/A i j N/A N/A N/A i j N/A j i N/A rows N/A N/A self row_list N/A temp N/A N/A N/A ii jj v rows N/A N/A N/A ii i N/A N/A N/A N/A N/A self _smat pop N/A ii jj N/A N/A N/A temp append N/A jj v N/A N/A N/A ii j N/A N/A N/A N/A N/A self _smat pop N/A ii jj N/A N/A N/A self _smat N/A N/A i jj v N/A N/A N/A ii j N/A N/A N/A N/A k v temp N/A N/A N/A N/A self _smat N/A N/A j k v N/A col_swap N/A N/A self i j N/A N/A N/A Swap, in place, columns i and j.

        Examples
        ========

        >>> from sympy.matrices import SparseMatrix
        >>> S = SparseMatrix.eye(3); S[2, 1] = 2
        >>> S.col_swap(1, 0); S
        Matrix([
        [0, 1, 0],
        [1, 0, 0],
        [2, 0, 1]])
         N/A N/A i j N/A N/A N/A i j N/A j i N/A rows N/A N/A self col_list N/A temp N/A N/A N/A ii jj v rows N/A N/A N/A jj i N/A N/A N/A N/A N/A self _smat pop N/A ii jj N/A N/A N/A temp append N/A ii v N/A N/A N/A jj j N/A N/A N/A N/A N/A self _smat pop N/A ii jj N/A N/A N/A self _smat N/A N/A ii i v N/A N/A N/A jj j N/A N/A N/A N/A k v temp N/A N/A N/A N/A self _smat N/A N/A k j v N/A row_join N/A N/A self other N/A N/A N/A Returns B appended after A (column-wise augmenting)::

            [A B]

        Examples
        ========

        >>> from sympy import SparseMatrix, Matrix
        >>> A = SparseMatrix(((1, 0, 1), (0, 1, 0), (1, 1, 0)))
        >>> A
        Matrix([
        [1, 0, 1],
        [0, 1, 0],
        [1, 1, 0]])
        >>> B = SparseMatrix(((1, 0, 0), (0, 1, 0), (0, 0, 1)))
        >>> B
        Matrix([
        [1, 0, 0],
        [0, 1, 0],
        [0, 0, 1]])
        >>> C = A.row_join(B); C
        Matrix([
        [1, 0, 1, 1, 0, 0],
        [0, 1, 0, 0, 1, 0],
        [1, 1, 0, 0, 0, 1]])
        >>> C == A.row_join(Matrix(B))
        True

        Joining at row ends is the same as appending columns at the end
        of the matrix:

        >>> C == A.col_insert(A.cols, B)
        True
         N/A N/A self N/A N/A N/A N/A type self other N/A N/A A B N/A self other N/A N/A N/A N/A A rows N/A B rows N/A N/A N/A ShapeError N/A A N/A N/A A copy N/A N/A N/A isinstance B SparseMatrix N/A N/A k 0 N/A b N/A B _mat N/A i N/A range N/A B rows N/A N/A j N/A range N/A B cols N/A N/A v N/A b N/A k N/A v N/A N/A N/A N/A A _smat N/A N/A i N/A j N/A A cols v N/A k 1 N/A N/A N/A N/A i j v N/A N/A N/A B _smat items N/A N/A N/A N/A A _smat N/A N/A i N/A j N/A A cols v N/A N/A A cols N/A B cols N/A A N/A col_join N/A N/A self other N/A N/A N/A Returns B augmented beneath A (row-wise joining)::

            [A]
            [B]

        Examples
        ========

        >>> from sympy import SparseMatrix, Matrix, ones
        >>> A = SparseMatrix(ones(3))
        >>> A
        Matrix([
        [1, 1, 1],
        [1, 1, 1],
        [1, 1, 1]])
        >>> B = SparseMatrix.eye(3)
        >>> B
        Matrix([
        [1, 0, 0],
        [0, 1, 0],
        [0, 0, 1]])
        >>> C = A.col_join(B); C
        Matrix([
        [1, 1, 1],
        [1, 1, 1],
        [1, 1, 1],
        [1, 0, 0],
        [0, 1, 0],
        [0, 0, 1]])
        >>> C == A.col_join(Matrix(B))
        True

        Joining along columns is the same as appending rows at the end
        of the matrix:

        >>> C == A.row_insert(A.rows, Matrix(B))
        True
         N/A N/A self N/A N/A N/A N/A type self other N/A N/A A B N/A self other N/A N/A N/A N/A A cols N/A B cols N/A N/A N/A ShapeError N/A A N/A N/A A copy N/A N/A N/A isinstance B SparseMatrix N/A N/A k 0 N/A b N/A B _mat N/A i N/A range N/A B rows N/A N/A j N/A range N/A B cols N/A N/A v N/A b N/A k N/A v N/A N/A N/A N/A A _smat N/A N/A N/A i N/A A rows j v N/A k 1 N/A N/A N/A N/A i j v N/A N/A N/A B _smat items N/A N/A N/A N/A A _smat N/A N/A N/A i N/A A rows j v N/A N/A A rows N/A B rows N/A A N/A copyin_list N/A N/A self key value N/A N/A N/A N/A N/A is_sequence value N/A N/A N/A TypeError `value` must be of type list or tuple. N/A N/A N/A self copyin_matrix key N/A Matrix value N/A copyin_matrix N/A N/A self key value N/A N/A N/A N/A rlo rhi clo chi N/A N/A self key2bounds key N/A shape N/A value shape N/A N/A dr dc N/A N/A rhi rlo N/A chi clo N/A N/A shape N/A dr dc N/A N/A N/A ShapeError The Matrix `value` doesn't have the same dimensions as the in sub-Matrix given by `key`. N/A N/A N/A isinstance value SparseMatrix N/A N/A i N/A range N/A value rows N/A N/A j N/A range N/A value cols N/A N/A N/A self N/A N/A N/A i rlo N/A j clo N/A value N/A N/A i j N/A N/A N/A N/A N/A rhi rlo N/A chi clo N/A len self N/A N/A i N/A range rlo rhi N/A N/A j N/A range clo chi N/A N/A N/A N/A N/A self _smat pop N/A i j None N/A N/A N/A i j v N/A N/A self row_list N/A N/A N/A N/A rlo i rhi N/A clo j chi N/A N/A N/A N/A N/A self _smat pop N/A i j None N/A N/A k v N/A N/A N/A value _smat items N/A N/A N/A i j k N/A N/A self N/A N/A N/A i rlo N/A j clo N/A value N/A N/A i j N/A zip_row_op N/A N/A self i k f N/A N/A N/A In-place operation on row ``i`` using two-arg functor whose args are
        interpreted as ``(self[i, j], self[k, j])``.

        Examples
        ========

        >>> from sympy.matrices import SparseMatrix
        >>> M = SparseMatrix.eye(3)*2
        >>> M[0, 1] = -1
        >>> M.zip_row_op(1, 0, lambda v, u: v + 2*u); M
        Matrix([
        [2, -1, 0],
        [4,  0, 0],
        [0,  0, 2]])

        See Also
        ========
        row
        row_op
        col_op

         N/A N/A N/A self row_op i N/A N/A N/A v j N/A N/A f v N/A self N/A N/A k j N/A row_op N/A N/A self i f N/A N/A N/A In-place operation on row ``i`` using two-arg functor whose args are
        interpreted as ``(self[i, j], j)``.

        Examples
        ========

        >>> from sympy.matrices import SparseMatrix
        >>> M = SparseMatrix.eye(3)*2
        >>> M[0, 1] = -1
        >>> M.row_op(1, lambda v, j: v + 2*M[0, j]); M
        Matrix([
        [2, -1, 0],
        [4,  0, 0],
        [0,  0, 2]])

        See Also
        ========
        row
        zip_row_op
        col_op

         N/A j N/A range N/A self cols N/A N/A v N/A N/A N/A self _smat get N/A i j N/A S Zero N/A fv N/A f v j N/A fv N/A N/A N/A N/A self _smat N/A N/A i j fv N/A N/A v N/A N/A N/A N/A N/A self _smat pop N/A i j N/A col_op N/A N/A self j f N/A N/A N/A In-place operation on col j using two-arg functor whose args are
        interpreted as (self[i, j], i) for i in range(self.rows).

        Examples
        ========

        >>> from sympy.matrices import SparseMatrix
        >>> M = SparseMatrix.eye(3)*2
        >>> M[1, 0] = -1
        >>> M.col_op(1, lambda v, i: v + 2*M[i, 0]); M
        Matrix([
        [ 2, 4, 0],
        [-1, 0, 0],
        [ 0, 0, 2]])
         N/A i N/A range N/A self rows N/A N/A v N/A N/A N/A self _smat get N/A i j N/A S Zero N/A fv N/A f v i N/A fv N/A N/A N/A N/A self _smat N/A N/A i j fv N/A N/A v N/A N/A N/A N/A N/A self _smat pop N/A i j N/A fill N/A N/A self value N/A N/A N/A Fill self with the given value.

        Notes
        =====

        Unless many values are going to be deleted (i.e. set to zero)
        this will create a matrix that is slower than a dense matrix in
        operations.

        Examples
        ========

        >>> from sympy.matrices import SparseMatrix
        >>> M = SparseMatrix.zeros(3); M
        Matrix([
        [0, 0, 0],
        [0, 0, 0],
        [0, 0, 0]])
        >>> M.fill(1); M
        Matrix([
        [1, 1, 1],
        [1, 1, 1],
        [1, 1, 1]])
         N/A N/A value N/A N/A N/A self _smat N/A N/A N/A v N/A N/A self _sympify value N/A N/A self _smat N/A dict N/A N/A N/A i j v N/A i N/A range N/A self rows N/A j N/A range N/A self cols N/A N/A