Module Expr Str ImportFrom alias alias alias Assign NameStore ListLoad Str Str Str Str Str Str Str Str Str Str Str Import alias Import alias identifier ImportFrom alias ImportFrom alias alias alias alias alias alias alias alias alias alias alias ImportFrom alias FunctionDef arguments args NameParam NameParam defaults NameLoad body Expr Str If CompareGt NameLoad AttributeLoad Call NameLoad NameLoad attr body If CompareIs NameLoad NameLoad body Assign NameStore BinOpMod Str NameLoad Raise Call NameLoad NameLoad Return Call NameLoad NameLoad decorator_list Assign NameStore Dict Num Num Num Num Num Num Num Str ListLoad Str NameLoad ListLoad Str NameLoad ListLoad Str NameLoad ListLoad Str NameLoad ListLoad Str NameLoad ListLoad Str NameLoad ListLoad Str NameLoad ListLoad Str NameLoad Assign NameStore Dict Num Num Num Num Num Num Num Num Num Num Num Str ListLoad Str NameLoad ListLoad Str NameLoad ListLoad Str NameLoad ListLoad Str NameLoad ListLoad Str NameLoad ListLoad Str NameLoad ListLoad Str NameLoad ListLoad Str NameLoad ListLoad Str NameLoad ListLoad Str NameLoad ListLoad Str NameLoad ListLoad Str NameLoad Assign NameStore Dict Str Str Str Str Str Str Call NameLoad ListLoad NameLoad Call NameLoad ListLoad NameLoad Call NameLoad ListLoad NameLoad Call NameLoad ListLoad NameLoad Num Num FunctionDef arguments args NameParam NameParam NameParam NameParam NameParam NameParam NameParam NameParam NameParam NameParam NameParam NameParam NameParam defaults NameLoad NameLoad NameLoad NameLoad Num Num NameLoad NameLoad Num NameLoad Num Num body Expr Str If CompareLtE NameLoad Num body Assign NameStore Dict Str Str Str Str Str Str Call NameLoad ListLoad NameLoad Call NameLoad ListLoad NameLoad Call NameLoad ListLoad NameLoad Call NameLoad ListLoad NameLoad Num Num Assign NameStore Call NameLoad NameLoad Assign TupleStore NameStore NameStore AttributeLoad NameLoad attr If NameLoad body For NameStore Call NameLoad NameLoad body If CompareNotEq SubscriptLoad SubscriptLoad NameLoad Index NameLoad Index Num SubscriptLoad SubscriptLoad NameLoad Index NameLoad Index Num body If CompareLt NameLoad Num body Expr Call AttributeLoad NameLoad attr Call NameLoad BinOpMod Str TupleLoad NameLoad NameLoad NameLoad Assign SubscriptStore SubscriptLoad NameLoad Index NameLoad Index Num SubscriptLoad SubscriptLoad NameLoad Index NameLoad Index Num If UnaryOpNot CompareLtLt Num NameLoad Num body Raise Call NameLoad Str If CompareIs NameLoad NameLoad body Assign NameStore Call NameLoad NameLoad NameLoad orelse Assign NameStore Call NameLoad NameLoad Assign NameStore CompareIsNot NameLoad NameLoad If NameLoad body Assign SubscriptStore NameLoad Index Str NameLoad If CompareIs NameLoad NameLoad body Assign SubscriptStore NameLoad Index Str SubscriptLoad NameLoad Index Num orelse Assign SubscriptStore NameLoad Index Str NameLoad If CompareIs NameLoad NameLoad body Assign SubscriptStore NameLoad Index Str SubscriptLoad NameLoad Index Num orelse Assign SubscriptStore NameLoad Index Str NameLoad orelse Assign SubscriptStore NameLoad Index Str Call NameLoad NameLoad NameLoad If UnaryOpNot CompareLtELtE Num NameLoad Num body Raise Call NameLoad BinOpMod Str NameLoad If UnaryOpNot CompareLtELtE Num NameLoad Num body Raise Call NameLoad Str If BoolOpOr UnaryOpNot CompareEq Call NameLoad NameLoad NameLoad BoolOpAnd CompareEq NameLoad Num UnaryOpNot CompareEq Call NameLoad NameLoad NameLoad body Raise Call NameLoad Str If CompareIs NameLoad NameLoad body Assign NameStore BinOpSub NameLoad Call NameLoad BinOpMult Num NameLoad If BoolOpAnd CompareIs NameLoad NameLoad CompareEq NameLoad Num body Raise Call NameLoad Str If CompareIsNot NameLoad NameLoad body Assign SubscriptStore NameLoad Index Str Call NameLoad NameLoad Assign NameStore Call NameLoad SubscriptLoad NameLoad Index Str If BoolOpAnd CompareEq NameLoad Num CompareLt NameLoad BinOpAdd BinOpMult Num NameLoad Num body Raise Call NameLoad Str If CompareLtE NameLoad NameLoad body Raise Call NameLoad Str If CompareIs NameLoad NameLoad body Assign NameStore BinOpAdd NameLoad BinOpMult Num NameLoad If BoolOpOr BoolOpAnd CompareGtE NameLoad Num CompareEq NameLoad Num CompareLt NameLoad Num body If NameLoad body Assign NameStore BinOpAdd NameLoad BinOpMult Num NameLoad orelse Assign NameStore BinOpAdd BinOpAdd NameLoad NameLoad Num Assign NameStore Call NameLoad NameLoad BinOpAdd BinOpMult Num NameLoad Num Assign NameStore SubscriptLoad NameLoad Index Str Assign NameStore SubscriptLoad NameLoad Index Str Assign NameStore SubscriptLoad NameLoad Index Str Assign NameStore SubscriptLoad NameLoad Index Str Assign NameStore SubscriptLoad NameLoad Index Str Assign NameStore SubscriptLoad NameLoad Index Str Assign TupleStore NameStore NameStore NameStore Call AttributeLoad NameLoad attr Call NameLoad Call NameLoad NameLoad NameLoad NameLoad NameLoad NameLoad NameLoad NameLoad NameLoad NameLoad NameLoad NameLoad NameLoad NameLoad NameLoad Assign SubscriptStore NameLoad Index Str SubscriptLoad NameLoad Index Str Assign SubscriptStore NameLoad Index Str SubscriptLoad NameLoad Index Str Assign SubscriptStore NameLoad Index Str SubscriptLoad NameLoad Index Str Assign SubscriptStore NameLoad Index Str NameLoad Assign SubscriptStore NameLoad Index Str SubscriptLoad NameLoad Index Str Assign SubscriptStore NameLoad Index Str SubscriptLoad NameLoad Index Str Assign NameStore SubscriptLoad NameLoad Index Str Assign NameStore SubscriptLoad NameLoad Index Str Assign NameStore Call NameLoad NameLoad Assign NameStore SubscriptLoad NameLoad Index Str Assign AttributeStore NameLoad attr TupleLoad NameLoad BinOpSub BinOpSub NameLoad NameLoad Num Assign NameStore TupleLoad ListLoad NameLoad Call NameLoad NameLoad NameLoad NameLoad If BoolOpAnd CompareLtE NameLoad Num UnaryOpNot NameLoad body Expr Call AttributeLoad NameLoad attr Call NameLoad BinOpAdd SubscriptLoad SubscriptLoad NameLoad Index NameLoad Index Num BinOpMod Str TupleLoad NameLoad Call NameLoad NameLoad NameLoad NameLoad NameLoad If BoolOpAnd CompareGt NameLoad Num UnaryOpNot NameLoad body If CompareIn NameLoad ListLoad Num Num Num body Expr Call AttributeLoad NameLoad attr Call NameLoad SubscriptLoad SubscriptLoad NameLoad Index NameLoad Index Num orelse TryExcept body Raise Call SubscriptLoad SubscriptLoad NameLoad Index NameLoad Index Num SubscriptLoad SubscriptLoad NameLoad Index NameLoad Index Num handlers ExceptHandler type NameLoad body Raise Call SubscriptLoad SubscriptLoad NameLoad Index Str Index Num SubscriptLoad SubscriptLoad NameLoad Index Str Index Num If NameLoad body TryExcept body Return TupleLoad NameLoad NameLoad NameLoad SubscriptLoad SubscriptLoad NameLoad Index NameLoad Index Num handlers ExceptHandler type NameLoad body Return TupleLoad NameLoad NameLoad NameLoad SubscriptLoad SubscriptLoad NameLoad Index Str Index Num orelse Return NameLoad decorator_list Assign NameStore Dict Str Str Str Call NameLoad ListLoad NameLoad Call NameLoad ListLoad NameLoad Call NameLoad ListLoad NameLoad FunctionDef arguments args NameParam NameParam NameParam NameParam NameParam NameParam NameParam NameParam NameParam NameParam NameParam NameParam defaults NameLoad NameLoad NameLoad Num Num NameLoad NameLoad Num Num Num body Expr Str If CompareLtE NameLoad Num body Assign NameStore Dict Assign TupleStore NameStore NameStore Call NameLoad NameLoad ListLoad NameLoad NameLoad Assign NameStore Call NameLoad NameLoad If CompareIs NameLoad NameLoad body Assign NameStore Call NameLoad NameLoad NameLoad If CompareIs NameLoad NameLoad body Assign NameStore Num orelse Assign NameStore Call NameLoad NameLoad If CompareIs NameLoad NameLoad body Assign NameStore BinOpSub NameLoad Call NameLoad BinOpMult Num NameLoad If UnaryOpNot CompareEq Call NameLoad NameLoad NameLoad body Raise Call NameLoad BinOpMod Str TupleLoad Call NameLoad NameLoad NameLoad If BoolOpOr CompareNotEq NameLoad Call NameLoad NameLoad CompareNotEq NameLoad Call NameLoad NameLoad body Raise Call NameLoad Str If UnaryOpNot CompareLtELtE Num NameLoad Num body Raise Call NameLoad BinOpMod Str NameLoad If CompareLtE NameLoad NameLoad body Raise Call NameLoad Str If CompareIs NameLoad NameLoad body Assign NameStore SubscriptLoad NameLoad Index Num If CompareIs NameLoad NameLoad body Assign NameStore SubscriptLoad NameLoad Index Num If UnaryOpNot CompareLtELtE Num NameLoad Num body Raise Call NameLoad Str If CompareIsNot NameLoad NameLoad body Assign NameStore Num If CompareEq NameLoad Num body If CompareIs NameLoad NameLoad body Raise Call NameLoad Str Assign NameStore Call NameLoad NameLoad Assign SubscriptStore NameLoad Index Str Call NameLoad TupleLoad BinOpAdd BinOpAdd NameLoad BinOpMult Num NameLoad Num NameLoad Assign SubscriptStore SubscriptLoad NameLoad Index Str Slice BinOpAdd NameLoad Num BinOpSub UnaryOpUSub NameLoad Num NameLoad Assign NameStore Call NameLoad SubscriptLoad NameLoad Index Str orelse If CompareEq NameLoad Num body If NameLoad body Assign NameStore Call NameLoad BinOpAdd NameLoad BinOpMult Num NameLoad BinOpAdd BinOpMult Num NameLoad Num orelse Assign NameStore Call NameLoad BinOpAdd BinOpAdd NameLoad NameLoad Num BinOpAdd BinOpMult Num NameLoad Num Assign NameStore Call NameLoad TupleLoad NameLoad NameLoad Assign SubscriptStore NameLoad Index Str NameLoad If CompareLtE NameLoad Num body If NameLoad body Assign SubscriptStore NameLoad Index Str Call NameLoad TupleLoad BinOpAdd BinOpMult NameLoad BinOpAdd NameLoad Num BinOpMult NameLoad BinOpAdd Num BinOpMult Num NameLoad NameLoad orelse Assign SubscriptStore NameLoad Index Str Call NameLoad TupleLoad BinOpAdd BinOpMult NameLoad BinOpAdd NameLoad Num BinOpMult NameLoad BinOpAdd Num BinOpMult Num NameLoad NameLoad Assign SubscriptStore NameLoad Index Str Call NameLoad TupleLoad NameLoad NameLoad TryExcept body Assign NameStore SubscriptLoad NameLoad Index Str Assign NameStore SubscriptLoad NameLoad Index Str Assign NameStore SubscriptLoad NameLoad Index Str handlers ExceptHandler type NameLoad body Raise Call NameLoad Str If UnaryOpNot NameLoad body Assign TupleStore NameStore NameStore NameStore NameStore Call AttributeLoad NameLoad attr NameLoad NameLoad NameLoad NameLoad NameLoad NameLoad NameLoad NameLoad NameLoad NameLoad NameLoad orelse Assign TupleStore NameStore NameStore NameStore NameStore Call AttributeLoad NameLoad attr NameLoad NameLoad NameLoad NameLoad NameLoad NameLoad NameLoad NameLoad NameLoad Assign NameStore TupleLoad SubscriptLoad NameLoad Slice NameLoad SubscriptLoad NameLoad Slice NameLoad NameLoad If BoolOpAnd CompareLtE NameLoad Num UnaryOpNot NameLoad body Assign NameStore BinOpAdd SubscriptLoad SubscriptLoad NameLoad Index NameLoad Index Num BinOpMod Str TupleLoad NameLoad Call NameLoad NameLoad NameLoad NameLoad NameLoad Expr Call AttributeLoad NameLoad attr Call NameLoad NameLoad If BoolOpAnd CompareGt NameLoad Num UnaryOpNot NameLoad body If CompareIn NameLoad ListLoad Num Num Num body Expr Call AttributeLoad NameLoad attr Call NameLoad SubscriptLoad SubscriptLoad NameLoad Index NameLoad Index Num orelse TryExcept body Raise Call SubscriptLoad SubscriptLoad NameLoad Index NameLoad Index Num SubscriptLoad SubscriptLoad NameLoad Index NameLoad Index Num handlers ExceptHandler type NameLoad body Raise Call SubscriptLoad SubscriptLoad NameLoad Index Str Index Num SubscriptLoad SubscriptLoad NameLoad Index Str Index Num If NameLoad body TryExcept body Return TupleLoad NameLoad NameLoad NameLoad SubscriptLoad SubscriptLoad NameLoad Index NameLoad Index Num handlers ExceptHandler type NameLoad body Return TupleLoad NameLoad NameLoad NameLoad SubscriptLoad SubscriptLoad NameLoad Index Str Index Num orelse Return NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam NameParam defaults Num Num body Expr Str Assign TupleStore NameStore NameStore NameStore NameLoad TryExcept body Expr SubscriptLoad SubscriptLoad NameLoad Index Num Index Num Assign NameStore NameLoad handlers ExceptHandler body Assign NameStore NameLoad If NameLoad body Return Call NameLoad Call NameLoad Lambda arguments args NameParam NameParam NameParam NameParam NameParam defaults NameLoad NameLoad NameLoad NameLoad Call NameLoad NameLoad ListLoad NameLoad NameLoad NameLoad NameLoad NameLoad NameLoad orelse If UnaryOpNot CompareLtELtE Num NameLoad NameLoad body Raise Call NameLoad BinOpMod Str TupleLoad NameLoad NameLoad If CompareNotIn NameLoad TupleLoad Num Num Num Num body Raise Call NameLoad BinOpMod Str NameLoad Assign NameStore Call NameLoad NameLoad Assign NameStore AttributeLoad NameLoad attr Assign NameStore Call AttributeLoad Call NameLoad NameLoad attr Assign TupleStore NameStore NameStore Call AttributeLoad NameLoad attr NameLoad NameLoad NameLoad NameLoad NameLoad NameLoad If CompareEq NameLoad Num body Raise Call NameLoad Str If CompareEq NameLoad Num body Raise Call NameLoad Str If NameLoad body Raise Call NameLoad Str Return Call AttributeLoad NameLoad attr NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam NameParam defaults Num body Expr Str Assign TupleStore NameStore NameStore NameStore NameLoad TryExcept body Expr SubscriptLoad SubscriptLoad NameLoad Index Num Index Num Assign NameStore NameLoad handlers ExceptHandler body Assign NameStore NameLoad If NameLoad body Return Call NameLoad Call NameLoad Lambda arguments args NameParam NameParam NameParam NameParam NameParam defaults NameLoad NameLoad NameLoad NameLoad Call NameLoad NameLoad NameLoad ListLoad NameLoad NameLoad NameLoad NameLoad orelse Assign TupleStore NameStore NameStore Call AttributeLoad NameLoad attr NameLoad NameLoad NameLoad NameLoad NameLoad If NameLoad body Return TupleLoad NameLoad NameLoad orelse Return NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults Num body Expr Str Assign TupleStore NameStore NameStore NameStore NameLoad If CompareNotEq NameLoad Num body Raise Call NameLoad Str TryExcept body Expr SubscriptLoad SubscriptLoad NameLoad Index Num Index Num Assign NameStore NameLoad handlers ExceptHandler body Assign NameStore NameLoad If NameLoad body Return Call NameLoad Call NameLoad Lambda arguments args NameParam NameParam NameParam NameParam defaults NameLoad NameLoad NameLoad Call NameLoad ListLoad NameLoad NameLoad NameLoad NameLoad NameLoad orelse If CompareLt Call NameLoad NameLoad Num body Raise Call NameLoad BinOpMod Str Call NameLoad NameLoad Assign TupleStore NameStore NameStore Call AttributeLoad NameLoad attr NameLoad NameLoad NameLoad NameLoad If CompareEq NameLoad Num body Raise Call NameLoad Str If CompareEq NameLoad Num body Return NameLoad If CompareEq NameLoad Num body Expr Call AttributeLoad NameLoad attr Call NameLoad Str Return NameLoad Raise Call NameLoad Str decorator_list FunctionDef arguments args NameParam NameParam defaults body Expr Str Assign TupleStore NameStore NameStore NameStore NameLoad TryExcept body Expr SubscriptLoad SubscriptLoad NameLoad Index Num Index Num Assign NameStore NameLoad handlers ExceptHandler body Assign NameStore NameLoad If NameLoad body Return Call NameLoad Call NameLoad Lambda arguments args NameParam NameParam NameParam NameParam defaults NameLoad NameLoad NameLoad Call NameLoad NameLoad ListLoad NameLoad NameLoad NameLoad NameLoad orelse Assign NameStore Call NameLoad NameLoad If CompareGt Call NameLoad NameLoad Num body Return Call NameLoad Call NameLoad Lambda arguments args NameParam NameParam defaults NameLoad Call NameLoad NameLoad NameLoad NameLoad Assign TupleStore NameStore NameStore Call AttributeLoad NameLoad attr NameLoad NameLoad NameLoad SubscriptLoad NameLoad Index Num If CompareEq NameLoad Num body Return NameLoad If CompareEq NameLoad Num body Raise Call NameLoad Str Raise Call NameLoad Str decorator_list Assign NameStore Dict Str Str Str Str Call NameLoad ListLoad NameLoad Call NameLoad ListLoad NameLoad Call NameLoad ListLoad NameLoad Call NameLoad ListLoad NameLoad FunctionDef arguments args NameParam NameParam NameParam NameParam NameParam NameParam NameParam NameParam NameParam NameParam NameParam NameParam NameParam NameParam NameParam NameParam NameParam NameParam NameParam defaults NameLoad NameLoad NameLoad NameLoad NameLoad Num Num Num NameLoad Num NameLoad NameLoad Num NameLoad NameLoad Num body Expr Str Assign TupleStore NameStore NameStore NameStore Call NameLoad NameLoad ListLoad NameLoad NameLoad NameLoad Assign NameStore Call NameLoad NameLoad If UnaryOpNot CompareEqEq NameLoad Call NameLoad NameLoad Call NameLoad NameLoad body Raise Call NameLoad Str If CompareIs NameLoad NameLoad body Assign NameStore Call NameLoad NameLoad NameLoad orelse Assign NameStore Call NameLoad NameLoad If UnaryOpNot CompareEq Call NameLoad NameLoad NameLoad body Raise Call NameLoad BinOpMod Str TupleLoad Call NameLoad NameLoad NameLoad If CompareIs NameLoad NameLoad body Assign NameStore Call AttributeLoad NameLoad attr If CompareIs NameLoad NameLoad body Assign NameStore Call AttributeLoad NameLoad attr If CompareIs NameLoad NameLoad body Assign NameStore Call AttributeLoad NameLoad attr If CompareIs NameLoad NameLoad body Assign NameStore Call AttributeLoad NameLoad attr If UnaryOpNot CompareLtELtE Num NameLoad Num body Raise Call NameLoad Str If CompareIs NameLoad NameLoad body Assign NameStore BinOpSub NameLoad Call NameLoad BinOpMult Num NameLoad If BoolOpAnd CompareIs NameLoad NameLoad CompareEq NameLoad Num body Raise Call NameLoad Str If CompareIsNot NameLoad NameLoad body Assign SubscriptStore NameLoad Index Str Call NameLoad NameLoad Assign NameStore Call NameLoad SubscriptLoad NameLoad Index Str If BoolOpAnd CompareIs NameLoad NameLoad CompareEq NameLoad Num body Raise Call NameLoad Str If CompareIsNot NameLoad NameLoad body Assign SubscriptStore NameLoad Index Str Call NameLoad NameLoad Assign NameStore Call NameLoad SubscriptLoad NameLoad Index Str If BoolOpAnd CompareEq NameLoad Num CompareLt NameLoad BinOpAdd BinOpMult Num NameLoad Num body Raise Call NameLoad Str If BoolOpAnd CompareEq NameLoad Num CompareLt NameLoad BinOpAdd BinOpMult Num NameLoad Num body Raise Call NameLoad Str If UnaryOpNot BoolOpAnd CompareLtELtE Num NameLoad Num CompareLtELtE Num NameLoad Num body Raise Call NameLoad BinOpMod Str TupleLoad NameLoad NameLoad If CompareLt NameLoad BinOpMult BinOpAdd NameLoad Num BinOpAdd NameLoad Num body Raise Call NameLoad Str If CompareIs NameLoad NameLoad body Assign NameStore Call NameLoad BinOpAdd NameLoad Call NameLoad BinOpDiv NameLoad Num If CompareIs NameLoad NameLoad body Assign NameStore Call NameLoad BinOpAdd NameLoad Call NameLoad BinOpDiv NameLoad Num Assign TupleStore NameStore NameStore TupleLoad Call NameLoad NameLoad BinOpAdd BinOpMult Num NameLoad Num Call NameLoad NameLoad BinOpAdd BinOpMult Num NameLoad Num If BoolOpAnd CompareGtE NameLoad Num CompareEq NameLoad Num body Assign NameStore Call NameLoad BinOpAdd NameLoad Call NameLoad BinOpMult Num NameLoad Assign NameStore Call NameLoad BinOpAdd NameLoad Call NameLoad BinOpMult Num NameLoad If CompareEq NameLoad Num body Assign SubscriptStore NameLoad Index Str Call NameLoad NameLoad Assign SubscriptStore NameLoad Index Str Call NameLoad NameLoad Assign TupleStore NameStore NameStore TupleLoad SubscriptLoad NameLoad Index Str SubscriptLoad NameLoad Index Str Assign NameStore SubscriptLoad NameLoad Index Str Assign NameStore BinOpSub BinOpSub NameLoad NameLoad Num Assign NameStore BinOpSub BinOpSub NameLoad NameLoad Num Assign NameStore BinOpAdd Call NameLoad NameLoad NameLoad Num Assign NameStore Call NameLoad NameLoad NameLoad Assign TupleStore NameStore NameStore TupleLoad BinOpAdd BinOpAdd BinOpMult NameLoad NameLoad NameLoad Num BinOpAdd BinOpAdd BinOpMult NameLoad NameLoad NameLoad Num Assign TupleStore NameStore NameStore TupleLoad NameLoad BinOpSub BinOpAdd NameLoad NameLoad NameLoad If CompareGt NameLoad NameLoad body Assign TupleStore NameStore NameStore TupleLoad NameLoad BinOpSub BinOpAdd NameLoad NameLoad NameLoad Assign NameStore Str Assign NameStore Call NameLoad BinOpAdd BinOpAdd BinOpAdd BinOpMult BinOpMult NameLoad NameLoad BinOpAdd BinOpAdd Num NameLoad NameLoad BinOpMult Num BinOpSub BinOpSub BinOpAdd BinOpAdd BinOpAdd NameLoad NameLoad BinOpMult NameLoad BinOpAdd NameLoad NameLoad NameLoad NameLoad NameLoad NameLoad Num keyword NameLoad Assign NameStore Call NameLoad BinOpAdd BinOpMult BinOpMult NameLoad NameLoad BinOpAdd NameLoad Num NameLoad keyword NameLoad Assign TupleStore NameStore NameStore NameStore NameStore Call AttributeLoad NameLoad attr NameLoad NameLoad NameLoad NameLoad NameLoad NameLoad NameLoad NameLoad NameLoad NameLoad NameLoad NameLoad NameLoad NameLoad NameLoad NameLoad NameLoad NameLoad NameLoad NameLoad Assign SubscriptStore NameLoad Index Str NameLoad Assign SubscriptStore NameLoad Index Str NameLoad Assign SubscriptStore NameLoad Index Str SubscriptLoad NameLoad Index Str Assign TupleStore NameStore NameStore TupleLoad SubscriptLoad NameLoad Index Str SubscriptLoad NameLoad Index Str Assign NameStore ListLoad NameLoad NameLoad NameLoad NameLoad NameLoad Assign NameStore Call NameLoad Num Call NameLoad Num NameLoad If BoolOpAnd CompareLtE NameLoad Num UnaryOpNot NameLoad body Assign NameStore BinOpAdd SubscriptLoad SubscriptLoad NameLoad Index NameLoad Index Num BinOpMod Str TupleLoad NameLoad NameLoad Call NameLoad NameLoad Call NameLoad NameLoad NameLoad NameLoad NameLoad Expr Call AttributeLoad NameLoad attr Call NameLoad NameLoad If BoolOpAnd CompareGt NameLoad Num UnaryOpNot NameLoad body If CompareIn NameLoad ListLoad Num Num Num Num Num body Assign NameStore BinOpMod Str TupleLoad NameLoad NameLoad Call NameLoad NameLoad Call NameLoad NameLoad NameLoad NameLoad NameLoad Expr Call AttributeLoad NameLoad attr Call NameLoad BinOpAdd SubscriptLoad SubscriptLoad NameLoad Index NameLoad Index Num NameLoad orelse TryExcept body Raise Call SubscriptLoad SubscriptLoad NameLoad Index NameLoad Index Num SubscriptLoad SubscriptLoad NameLoad Index NameLoad Index Num handlers ExceptHandler type NameLoad body Raise Call SubscriptLoad SubscriptLoad NameLoad Index Str Index Num SubscriptLoad SubscriptLoad NameLoad Index Str Index Num If NameLoad body TryExcept body Return TupleLoad NameLoad NameLoad NameLoad SubscriptLoad SubscriptLoad NameLoad Index NameLoad Index Num handlers ExceptHandler type NameLoad body Return TupleLoad NameLoad NameLoad NameLoad SubscriptLoad SubscriptLoad NameLoad Index Str Index Num orelse Return NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam NameParam NameParam defaults Num Num body Expr Str Assign TupleStore NameStore NameStore NameStore NameStore NameStore NameLoad If UnaryOpNot CompareLtELt Num NameLoad NameLoad body Raise Call NameLoad BinOpMod Str TupleLoad NameLoad NameLoad If UnaryOpNot CompareLtELt Num NameLoad NameLoad body Raise Call NameLoad BinOpMod Str TupleLoad NameLoad NameLoad Assign TupleStore NameStore NameStore Call NameLoad NameLoad ListLoad NameLoad NameLoad If BoolOpOr CompareNotEq Call NameLoad AttributeLoad NameLoad attr Num CompareNotEq Call NameLoad AttributeLoad NameLoad attr Num body Raise Call NameLoad Str Assign TupleStore NameStore NameStore Call AttributeLoad NameLoad attr NameLoad NameLoad NameLoad NameLoad NameLoad NameLoad NameLoad NameLoad NameLoad If CompareEq NameLoad Num body Raise Call NameLoad Str If NameLoad body Raise Call NameLoad Str Assign AttributeStore NameLoad attr TupleLoad Call NameLoad NameLoad Call NameLoad NameLoad If CompareGt Call NameLoad NameLoad Num body Return NameLoad If CompareGt Call NameLoad SubscriptLoad NameLoad Index Num Num body Return SubscriptLoad NameLoad Index Num Return SubscriptLoad SubscriptLoad NameLoad Index Num Index Num decorator_list FunctionDef arguments args NameParam NameParam NameParam NameParam NameParam defaults body Expr Str Assign TupleStore NameStore NameStore NameStore NameStore NameStore NameLoad Return Call AttributeLoad NameLoad attr NameLoad NameLoad NameLoad NameLoad NameLoad NameLoad NameLoad NameLoad NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam NameParam defaults Num Num body Expr Str Assign TupleStore NameStore NameStore NameStore NameLoad TryExcept body Expr SubscriptLoad SubscriptLoad NameLoad Index Num Index Num Assign NameStore NameLoad handlers ExceptHandler body Assign NameStore NameLoad If NameLoad body Assign NameStore ListLoad For NameStore NameLoad body Assign TupleStore NameStore NameStore NameStore Call NameLoad NameLoad ListLoad NameLoad NameLoad NameLoad NameLoad Expr Call AttributeLoad NameLoad attr NameLoad Return TupleLoad NameLoad NameLoad NameLoad orelse Assign TupleStore NameStore NameStore NameStore Call AttributeLoad NameLoad attr NameLoad NameLoad NameLoad NameLoad NameLoad NameLoad If CompareEq NameLoad Num body Raise Call NameLoad Str If NameLoad body Raise Call NameLoad Str Return TupleLoad NameLoad NameLoad NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults Num body Expr Str If CompareLt NameLoad Num body Return Call NameLoad NameLoad UnaryOpUSub NameLoad Assign TupleStore NameStore NameStore NameStore NameLoad If CompareGt NameLoad NameLoad body Raise Call NameLoad BinOpMod Str TupleLoad NameLoad SubscriptLoad NameLoad Index Num With Call AttributeLoad NameLoad attr keyword Str keyword Str body TryExcept body For NameStore Call NameLoad NameLoad body Assign NameStore BinOpSub SubscriptLoad NameLoad Slice BinOpAdd NameLoad Num Num SubscriptLoad NameLoad Slice Num BinOpSub UnaryOpUSub NameLoad Num Assign NameStore BinOpDiv BinOpMult BinOpSub SubscriptLoad NameLoad Slice Num BinOpSub Num NameLoad SubscriptLoad NameLoad Slice BinOpSub Num NameLoad NameLoad NameLoad Assign NameStore SubscriptLoad AttributeLoad NameLoad attr Index TupleLoad NameLoad BinOpMult ListLoad Num NameLoad Assign NameStore SubscriptLoad NameLoad Slice Num Num AugAssignSub NameStore Num handlers ExceptHandler type NameLoad body Raise Call NameLoad BinOpMod Str NameLoad Return TupleLoad NameLoad NameLoad NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults Num body Expr Str If CompareLt NameLoad Num body Return Call NameLoad NameLoad UnaryOpUSub NameLoad Assign TupleStore NameStore NameStore NameStore NameLoad For NameStore Call NameLoad NameLoad body Assign NameStore BinOpSub SubscriptLoad NameLoad Slice BinOpAdd NameLoad Num SubscriptLoad NameLoad Slice BinOpSub UnaryOpUSub NameLoad Num Assign NameStore BinOpDiv Call AttributeLoad NameLoad attr BinOpMult SubscriptLoad NameLoad Slice BinOpSub UnaryOpUSub NameLoad Num NameLoad BinOpAdd NameLoad Num Assign NameStore SubscriptLoad AttributeLoad NameLoad attr Index TupleLoad Num NameLoad BinOpMult ListLoad SubscriptLoad NameLoad Index Num BinOpAdd NameLoad Num Assign NameStore SubscriptLoad AttributeLoad NameLoad attr Index TupleLoad SubscriptLoad NameLoad Index Num NameLoad SubscriptLoad NameLoad Index Num AugAssignAdd NameStore Num Return TupleLoad NameLoad NameLoad NameLoad decorator_list
N/A N/A 
fitpack (dierckx in netlib) --- A Python-C wrapper to FITPACK (by P. Dierckx).
        FITPACK is a collection of FORTRAN programs for curve and surface
        fitting with splines and tensor product splines.

See
 http://www.cs.kuleuven.ac.be/cwis/research/nalag/research/topics/fitpack.html
or
 http://www.netlib.org/dierckx/index.html

Copyright 2002 Pearu Peterson all rights reserved,
Pearu Peterson <pearu@cens.ioc.ee>
Permission to use, modify, and distribute this software is given under the
terms of the SciPy (BSD style) license.  See LICENSE.txt that came with
this distribution for specifics.

NO WARRANTY IS EXPRESSED OR IMPLIED.  USE AT YOUR OWN RISK.

TODO: Make interfaces to the following fitpack functions:
    For univariate splines: cocosp, concon, fourco, insert
    For bivariate splines: profil, regrid, parsur, surev
 __future__ division print_function absolute_import N/A __all__ N/A splrep splprep splev splint sproot spalde bisplrep bisplev insert splder splantider N/A warnings N/A numpy np N/A _fitpack numpy atleast_1d array ones zeros sqrt ravel transpose empty iinfo intc asarray N/A dfitpack _intc_overflow N/A N/A x msg N/A None N/A N/A Cast the value to an intc and raise an OverflowError if the value
    cannot fit.
     N/A N/A x N/A N/A iinfo intc max N/A N/A N/A msg None N/A N/A msg N/A %r cannot fit into an intc x N/A N/A OverflowError msg N/A N/A intc x N/A N/A _iermess N/A 0 -1 -2 1 2 3 10 unknown N/A The spline has a residual sum of squares fp such that abs(fp-s)/s<=0.001 None N/A The spline is an interpolating spline (fp=0) None N/A The spline is weighted least-squares polynomial of degree k.
fp gives the upper bound fp0 for the smoothing factor s None N/A The required storage space exceeds the available storage space.
Probable causes: data (x,y) size is too small or smoothing parameter
s is too small (fp>s). ValueError N/A A theoretically impossible result when finding a smoothing spline
with fp = s. Probable cause: s too small. (abs(fp-s)/s>0.001) ValueError N/A The maximal number of iterations (20) allowed for finding smoothing
spline with fp=s has been reached. Probable cause: s too small.
(abs(fp-s)/s>0.001) ValueError N/A Error on input data ValueError N/A An error occurred TypeError N/A _iermess2 N/A 0 -1 -2 -3 1 2 3 4 5 10 11 unknown N/A The spline has a residual sum of squares fp such that abs(fp-s)/s<=0.001 None N/A The spline is an interpolating spline (fp=0) None N/A The spline is weighted least-squares polynomial of degree kx and ky.
fp gives the upper bound fp0 for the smoothing factor s None N/A Warning. The coefficients of the spline have been computed as the
minimal norm least-squares solution of a rank deficient system. None N/A The required storage space exceeds the available storage space.
Probable causes: nxest or nyest too small or s is too small. (fp>s) ValueError N/A A theoretically impossible result when finding a smoothing spline
with fp = s. Probable causes: s too small or badly chosen eps.
(abs(fp-s)/s>0.001) ValueError N/A The maximal number of iterations (20) allowed for finding smoothing
spline with fp=s has been reached. Probable cause: s too small.
(abs(fp-s)/s>0.001) ValueError N/A No more knots can be added because the number of B-spline
coefficients already exceeds the number of data points m.
Probable causes: either s or m too small. (fp>s) ValueError N/A No more knots can be added because the additional knot would
coincide with an old one. Probable cause: s too small or too large
a weight to an inaccurate data point. (fp>s) ValueError N/A Error on input data ValueError N/A rwrk2 too small, i.e. there is not enough workspace for computing
the minimal least-squares solution of a rank deficient system of
linear equations. ValueError N/A An error occurred TypeError N/A _parcur_cache N/A t wrk iwrk u ub ue N/A array N/A float N/A array N/A float N/A array N/A intc N/A array N/A float 0 1 splprep N/A N/A x w u ub ue k task s t full_output nest per quiet N/A None None None None 3 0 None None 0 None 0 1 N/A N/A 
    Find the B-spline representation of an N-dimensional curve.

    Given a list of N rank-1 arrays, `x`, which represent a curve in
    N-dimensional space parametrized by `u`, find a smooth approximating
    spline curve g(`u`). Uses the FORTRAN routine parcur from FITPACK.

    Parameters
    ----------
    x : array_like
        A list of sample vector arrays representing the curve.
    w : array_like, optional
        Strictly positive rank-1 array of weights the same length as `x[0]`.
        The weights are used in computing the weighted least-squares spline
        fit. If the errors in the `x` values have standard-deviation given by
        the vector d, then `w` should be 1/d. Default is ``ones(len(x[0]))``.
    u : array_like, optional
        An array of parameter values. If not given, these values are
        calculated automatically as ``M = len(x[0])``, where

            v[0] = 0

            v[i] = v[i-1] + distance(`x[i]`, `x[i-1]`)

            u[i] = v[i] / v[M-1]

    ub, ue : int, optional
        The end-points of the parameters interval.  Defaults to
        u[0] and u[-1].
    k : int, optional
        Degree of the spline. Cubic splines are recommended.
        Even values of `k` should be avoided especially with a small s-value.
        ``1 <= k <= 5``, default is 3.
    task : int, optional
        If task==0 (default), find t and c for a given smoothing factor, s.
        If task==1, find t and c for another value of the smoothing factor, s.
        There must have been a previous call with task=0 or task=1
        for the same set of data.
        If task=-1 find the weighted least square spline for a given set of
        knots, t.
    s : float, optional
        A smoothing condition.  The amount of smoothness is determined by
        satisfying the conditions: ``sum((w * (y - g))**2,axis=0) <= s``,
        where g(x) is the smoothed interpolation of (x,y).  The user can
        use `s` to control the trade-off between closeness and smoothness
        of fit.  Larger `s` means more smoothing while smaller values of `s`
        indicate less smoothing. Recommended values of `s` depend on the
        weights, w.  If the weights represent the inverse of the
        standard-deviation of y, then a good `s` value should be found in
        the range ``(m-sqrt(2*m),m+sqrt(2*m))``, where m is the number of
        data points in x, y, and w.
    t : int, optional
        The knots needed for task=-1.
    full_output : int, optional
        If non-zero, then return optional outputs.
    nest : int, optional
        An over-estimate of the total number of knots of the spline to
        help in determining the storage space.  By default nest=m/2.
        Always large enough is nest=m+k+1.
    per : int, optional
       If non-zero, data points are considered periodic with period
       ``x[m-1] - x[0]`` and a smooth periodic spline approximation is
       returned.  Values of ``y[m-1]`` and ``w[m-1]`` are not used.
    quiet : int, optional
         Non-zero to suppress messages.
         This parameter is deprecated; use standard Python warning filters
         instead.

    Returns
    -------
    tck : tuple
        A tuple (t,c,k) containing the vector of knots, the B-spline
        coefficients, and the degree of the spline.
    u : array
        An array of the values of the parameter.
    fp : float
        The weighted sum of squared residuals of the spline approximation.
    ier : int
        An integer flag about splrep success.  Success is indicated
        if ier<=0. If ier in [1,2,3] an error occurred but was not raised.
        Otherwise an error is raised.
    msg : str
        A message corresponding to the integer flag, ier.

    See Also
    --------
    splrep, splev, sproot, spalde, splint,
    bisplrep, bisplev
    UnivariateSpline, BivariateSpline

    Notes
    -----
    See `splev` for evaluation of the spline and its derivatives.
    The number of dimensions N must be smaller than 11.

    References
    ----------
    .. [1] P. Dierckx, "Algorithms for smoothing data with periodic and
        parametric splines, Computer Graphics and Image Processing",
        20 (1982) 171-184.
    .. [2] P. Dierckx, "Algorithms for smoothing data with periodic and
        parametric splines", report tw55, Dept. Computer Science,
        K.U.Leuven, 1981.
    .. [3] P. Dierckx, "Curve and surface fitting with splines", Monographs on
        Numerical Analysis, Oxford University Press, 1993.

     N/A N/A task 0 N/A N/A _parcur_cache N/A t wrk iwrk u ub ue N/A array N/A float N/A array N/A float N/A array N/A intc N/A array N/A float 0 1 N/A x N/A atleast_1d x N/A N/A idim m N/A x shape N/A per N/A N/A i N/A range idim N/A N/A N/A N/A N/A x N/A i N/A 0 N/A N/A x N/A i N/A -1 N/A N/A N/A quiet 2 N/A N/A N/A N/A warnings warn N/A RuntimeWarning N/A Setting x[%d][%d]=x[%d][0] N/A i m i N/A N/A N/A x N/A i N/A -1 N/A N/A x N/A i N/A 0 N/A N/A N/A 0 idim 11 N/A N/A N/A TypeError 0 < idim < 11 must hold N/A N/A w None N/A N/A w N/A ones m float N/A N/A w N/A atleast_1d w N/A ipar N/A u None N/A ipar N/A N/A N/A _parcur_cache N/A u u N/A N/A ub None N/A N/A N/A _parcur_cache N/A ub N/A u N/A 0 N/A N/A N/A _parcur_cache N/A ub ub N/A N/A ue None N/A N/A N/A _parcur_cache N/A ue N/A u N/A -1 N/A N/A N/A _parcur_cache N/A ue ue N/A N/A N/A _parcur_cache N/A u N/A zeros m float N/A N/A N/A 1 k 5 N/A N/A N/A TypeError N/A 1 <= k= %d <=5 must hold k N/A N/A N/A -1 task 1 N/A N/A N/A TypeError task must be -1, 0 or 1 N/A N/A N/A N/A N/A len w m N/A N/A ipar 1 N/A N/A N/A len u m N/A N/A N/A TypeError Mismatch of input dimensions N/A N/A s None N/A N/A s N/A m N/A sqrt N/A 2 m N/A N/A N/A t None N/A task -1 N/A N/A N/A TypeError Knots must be given for task=-1 N/A N/A t None N/A N/A N/A _parcur_cache N/A t N/A atleast_1d t N/A n N/A len N/A _parcur_cache N/A t N/A N/A N/A task -1 N/A n N/A N/A 2 k 2 N/A N/A N/A TypeError There must be at least 2*k+2 knots for task=-1 N/A N/A m k N/A N/A N/A TypeError m > k must hold N/A N/A nest None N/A N/A nest N/A m N/A 2 k N/A N/A N/A N/A task 0 N/A s 0 N/A nest 0 N/A N/A per N/A N/A nest N/A m N/A 2 k N/A N/A nest N/A N/A m k 1 N/A nest N/A max nest N/A N/A 2 k 3 N/A u N/A _parcur_cache N/A u N/A ub N/A _parcur_cache N/A ub N/A ue N/A _parcur_cache N/A ue N/A t N/A _parcur_cache N/A t N/A wrk N/A _parcur_cache N/A wrk N/A iwrk N/A _parcur_cache N/A iwrk N/A N/A t c o N/A N/A _fitpack _parcur N/A ravel N/A transpose x w u ub ue k task ipar s t nest wrk iwrk per N/A N/A _parcur_cache N/A u N/A o N/A u N/A N/A _parcur_cache N/A ub N/A o N/A ub N/A N/A _parcur_cache N/A ue N/A o N/A ue N/A N/A _parcur_cache N/A t t N/A N/A _parcur_cache N/A wrk N/A o N/A wrk N/A N/A _parcur_cache N/A iwrk N/A o N/A iwrk N/A ier N/A o N/A ier N/A fp N/A o N/A fp N/A n N/A len t N/A u N/A o N/A u N/A N/A c shape N/A idim N/A N/A n k 1 N/A tcku N/A N/A t N/A list c k u N/A N/A N/A ier 0 N/A quiet N/A N/A N/A N/A warnings warn N/A RuntimeWarning N/A N/A N/A _iermess N/A ier N/A 0 N/A 	k=%d n=%d m=%d fp=%f s=%f N/A k N/A len t m fp s N/A N/A N/A ier 0 N/A full_output N/A N/A N/A ier N/A 1 2 3 N/A N/A N/A N/A warnings warn N/A RuntimeWarning N/A N/A _iermess N/A ier N/A 0 N/A N/A N/A N/A N/A N/A N/A _iermess N/A ier N/A 1 N/A N/A _iermess N/A ier N/A 0 N/A N/A N/A KeyError N/A N/A N/A N/A N/A _iermess N/A unknown N/A 1 N/A N/A _iermess N/A unknown N/A 0 N/A full_output N/A N/A N/A N/A N/A tcku fp ier N/A N/A _iermess N/A ier N/A 0 N/A N/A N/A KeyError N/A N/A N/A tcku fp ier N/A N/A _iermess N/A unknown N/A 0 N/A N/A tcku N/A N/A _curfit_cache N/A t wrk iwrk N/A array N/A float N/A array N/A float N/A array N/A intc splrep N/A N/A x y w xb xe k task s t full_output per quiet N/A None None None 3 0 None None 0 0 1 N/A N/A 
    Find the B-spline representation of 1-D curve.

    Given the set of data points ``(x[i], y[i])`` determine a smooth spline
    approximation of degree k on the interval ``xb <= x <= xe``.

    Parameters
    ----------
    x, y : array_like
        The data points defining a curve y = f(x).
    w : array_like, optional
        Strictly positive rank-1 array of weights the same length as x and y.
        The weights are used in computing the weighted least-squares spline
        fit. If the errors in the y values have standard-deviation given by the
        vector d, then w should be 1/d. Default is ones(len(x)).
    xb, xe : float, optional
        The interval to fit.  If None, these default to x[0] and x[-1]
        respectively.
    k : int, optional
        The degree of the spline fit. It is recommended to use cubic splines.
        Even values of k should be avoided especially with small s values.
        1 <= k <= 5
    task : {1, 0, -1}, optional
        If task==0 find t and c for a given smoothing factor, s.

        If task==1 find t and c for another value of the smoothing factor, s.
        There must have been a previous call with task=0 or task=1 for the same
        set of data (t will be stored an used internally)

        If task=-1 find the weighted least square spline for a given set of
        knots, t. These should be interior knots as knots on the ends will be
        added automatically.
    s : float, optional
        A smoothing condition. The amount of smoothness is determined by
        satisfying the conditions: sum((w * (y - g))**2,axis=0) <= s where g(x)
        is the smoothed interpolation of (x,y). The user can use s to control
        the tradeoff between closeness and smoothness of fit. Larger s means
        more smoothing while smaller values of s indicate less smoothing.
        Recommended values of s depend on the weights, w. If the weights
        represent the inverse of the standard-deviation of y, then a good s
        value should be found in the range (m-sqrt(2*m),m+sqrt(2*m)) where m is
        the number of datapoints in x, y, and w. default : s=m-sqrt(2*m) if
        weights are supplied. s = 0.0 (interpolating) if no weights are
        supplied.
    t : array_like, optional
        The knots needed for task=-1. If given then task is automatically set
        to -1.
    full_output : bool, optional
        If non-zero, then return optional outputs.
    per : bool, optional
        If non-zero, data points are considered periodic with period x[m-1] -
        x[0] and a smooth periodic spline approximation is returned. Values of
        y[m-1] and w[m-1] are not used.
    quiet : bool, optional
        Non-zero to suppress messages.
        This parameter is deprecated; use standard Python warning filters
        instead.

    Returns
    -------
    tck : tuple
        (t,c,k) a tuple containing the vector of knots, the B-spline
        coefficients, and the degree of the spline.
    fp : array, optional
        The weighted sum of squared residuals of the spline approximation.
    ier : int, optional
        An integer flag about splrep success. Success is indicated if ier<=0.
        If ier in [1,2,3] an error occurred but was not raised. Otherwise an
        error is raised.
    msg : str, optional
        A message corresponding to the integer flag, ier.

    Notes
    -----
    See splev for evaluation of the spline and its derivatives.

    The user is responsible for assuring that the values of *x* are unique.
    Otherwise, *splrep* will not return sensible results.

    See Also
    --------
    UnivariateSpline, BivariateSpline
    splprep, splev, sproot, spalde, splint
    bisplrep, bisplev

    Notes
    -----
    See splev for evaluation of the spline and its derivatives. Uses the
    FORTRAN routine curfit from FITPACK.

    If provided, knots `t` must satisfy the Schoenberg-Whitney conditions,
    i.e., there must be a subset of data points ``x[j]`` such that
    ``t[j] < x[j] < t[j+k+1]``, for ``j=0, 1,...,n-k-2``.

    References
    ----------
    Based on algorithms described in [1]_, [2]_, [3]_, and [4]_:

    .. [1] P. Dierckx, "An algorithm for smoothing, differentiation and
       integration of experimental data using spline functions",
       J.Comp.Appl.Maths 1 (1975) 165-184.
    .. [2] P. Dierckx, "A fast algorithm for smoothing data on a rectangular
       grid while using spline functions", SIAM J.Numer.Anal. 19 (1982)
       1286-1304.
    .. [3] P. Dierckx, "An improved algorithm for curve fitting with spline
       functions", report tw54, Dept. Computer Science,K.U. Leuven, 1981.
    .. [4] P. Dierckx, "Curve and surface fitting with splines", Monographs on
       Numerical Analysis, Oxford University Press, 1993.

    Examples
    --------

    >>> import matplotlib.pyplot as plt
    >>> from scipy.interpolate import splev, splrep
    >>> x = np.linspace(0, 10, 10)
    >>> y = np.sin(x)
    >>> tck = splrep(x, y)
    >>> x2 = np.linspace(0, 10, 200)
    >>> y2 = splev(x2, tck)
    >>> plt.plot(x, y, 'o', x2, y2)
    >>> plt.show()

     N/A N/A task 0 N/A N/A _curfit_cache N/A N/A N/A x y N/A map atleast_1d N/A x y N/A m N/A len x N/A N/A w None N/A N/A w N/A ones m float N/A N/A s None N/A N/A s 0.0 N/A N/A w N/A atleast_1d w N/A N/A s None N/A N/A s N/A m N/A sqrt N/A 2 m N/A N/A N/A N/A len w m N/A N/A N/A TypeError N/A len(w)=%d is not equal to m=%d N/A N/A len w m N/A N/A N/A m N/A len y N/A m N/A len w N/A N/A N/A TypeError Lengths of the first three arguments (x,y,w) must be equal N/A N/A N/A 1 k 5 N/A N/A N/A TypeError N/A Given degree of the spline (k=%d) is not supported. (1<=k<=5) k N/A N/A m k N/A N/A N/A TypeError m > k must hold N/A N/A xb None N/A N/A xb N/A x N/A 0 N/A N/A xe None N/A N/A xe N/A x N/A -1 N/A N/A N/A -1 task 1 N/A N/A N/A TypeError task must be -1, 0 or 1 N/A N/A t None N/A N/A task -1 N/A N/A task -1 N/A N/A N/A t None N/A N/A N/A TypeError Knots must be given for task=-1 N/A numknots N/A len t N/A N/A _curfit_cache N/A t N/A empty N/A N/A N/A numknots N/A 2 k 2 float N/A N/A N/A _curfit_cache N/A t N/A N/A k 1 N/A N/A k 1 t N/A nest N/A len N/A _curfit_cache N/A t N/A N/A N/A task 0 N/A N/A per N/A N/A nest N/A max N/A m N/A 2 k N/A N/A 2 k 3 N/A N/A nest N/A max N/A N/A m k 1 N/A N/A 2 k 3 N/A t N/A empty N/A nest float N/A N/A _curfit_cache N/A t t N/A N/A task 0 N/A N/A per N/A N/A N/A _curfit_cache N/A wrk N/A empty N/A N/A N/A m N/A k 1 N/A nest N/A 8 N/A 5 k float N/A N/A N/A _curfit_cache N/A wrk N/A empty N/A N/A N/A m N/A k 1 N/A nest N/A 7 N/A 3 k float N/A N/A _curfit_cache N/A iwrk N/A empty N/A nest intc N/A N/A N/A t N/A _curfit_cache N/A t N/A wrk N/A _curfit_cache N/A wrk N/A iwrk N/A _curfit_cache N/A iwrk N/A N/A N/A KeyError N/A N/A N/A TypeError must call with task=1 only after call with task=0,-1 N/A N/A per N/A N/A N/A n c fp ier N/A N/A dfitpack curfit task x y w t wrk iwrk xb xe k s N/A N/A N/A n c fp ier N/A N/A dfitpack percur task x y w t wrk iwrk k s N/A tck N/A N/A t N/A n N/A c N/A n k N/A N/A N/A ier 0 N/A quiet N/A N/A _mess N/A N/A N/A _iermess N/A ier N/A 0 N/A 	k=%d n=%d m=%d fp=%f s=%f N/A k N/A len t m fp s N/A N/A N/A warnings warn N/A RuntimeWarning _mess N/A N/A N/A ier 0 N/A full_output N/A N/A N/A ier N/A 1 2 3 N/A N/A N/A N/A warnings warn N/A RuntimeWarning N/A N/A _iermess N/A ier N/A 0 N/A N/A N/A N/A N/A N/A N/A _iermess N/A ier N/A 1 N/A N/A _iermess N/A ier N/A 0 N/A N/A N/A KeyError N/A N/A N/A N/A N/A _iermess N/A unknown N/A 1 N/A N/A _iermess N/A unknown N/A 0 N/A full_output N/A N/A N/A N/A N/A tck fp ier N/A N/A _iermess N/A ier N/A 0 N/A N/A N/A KeyError N/A N/A N/A tck fp ier N/A N/A _iermess N/A unknown N/A 0 N/A N/A tck N/A splev N/A N/A x tck der ext N/A 0 0 N/A N/A 
    Evaluate a B-spline or its derivatives.

    Given the knots and coefficients of a B-spline representation, evaluate
    the value of the smoothing polynomial and its derivatives.  This is a
    wrapper around the FORTRAN routines splev and splder of FITPACK.

    Parameters
    ----------
    x : array_like
        An array of points at which to return the value of the smoothed
        spline or its derivatives.  If `tck` was returned from `splprep`,
        then the parameter values, u should be given.
    tck : tuple
        A sequence of length 3 returned by `splrep` or `splprep` containing
        the knots, coefficients, and degree of the spline.
    der : int, optional
        The order of derivative of the spline to compute (must be less than
        or equal to k).
    ext : int, optional
        Controls the value returned for elements of ``x`` not in the
        interval defined by the knot sequence.

        * if ext=0, return the extrapolated value.
        * if ext=1, return 0
        * if ext=2, raise a ValueError
        * if ext=3, return the boundary value.

        The default value is 0.

    Returns
    -------
    y : ndarray or list of ndarrays
        An array of values representing the spline function evaluated at
        the points in ``x``.  If `tck` was returned from `splprep`, then this
        is a list of arrays representing the curve in N-dimensional space.

    See Also
    --------
    splprep, splrep, sproot, spalde, splint
    bisplrep, bisplev

    References
    ----------
    .. [1] C. de Boor, "On calculating with b-splines", J. Approximation
        Theory, 6, p.50-62, 1972.
    .. [2] M.G. Cox, "The numerical evaluation of b-splines", J. Inst. Maths
        Applics, 10, p.134-149, 1972.
    .. [3] P. Dierckx, "Curve and surface fitting with splines", Monographs
        on Numerical Analysis, Oxford University Press, 1993.

     N/A N/A t c k tck N/A N/A N/A N/A N/A c N/A 0 N/A 0 N/A parametric True N/A N/A N/A N/A parametric False N/A parametric N/A N/A N/A list N/A map N/A N/A N/A c x t k der N/A x t k der N/A splev x N/A t c k der ext c N/A N/A N/A N/A 0 der k N/A N/A N/A ValueError N/A 0<=der=%d<=k=%d must hold N/A der k N/A N/A ext N/A 0 1 2 3 N/A N/A N/A ValueError N/A ext = %s not in (0, 1, 2, 3)  ext N/A x N/A asarray x N/A shape N/A x shape N/A x N/A N/A N/A atleast_1d x ravel N/A N/A y ier N/A N/A _fitpack _spl_ x der t c k ext N/A N/A ier 10 N/A N/A N/A ValueError Invalid input data N/A N/A ier 1 N/A N/A N/A ValueError Found x value not in the domain N/A ier N/A N/A N/A TypeError An error occurred N/A N/A N/A y reshape shape N/A splint N/A N/A a b tck full_output N/A 0 N/A N/A 
    Evaluate the definite integral of a B-spline.

    Given the knots and coefficients of a B-spline, evaluate the definite
    integral of the smoothing polynomial between two given points.

    Parameters
    ----------
    a, b : float
        The end-points of the integration interval.
    tck : tuple
        A tuple (t,c,k) containing the vector of knots, the B-spline
        coefficients, and the degree of the spline (see `splev`).
    full_output : int, optional
        Non-zero to return optional output.

    Returns
    -------
    integral : float
        The resulting integral.
    wrk : ndarray
        An array containing the integrals of the normalized B-splines
        defined on the set of knots.

    Notes
    -----
    splint silently assumes that the spline function is zero outside the data
    interval (a, b).

    See Also
    --------
    splprep, splrep, sproot, spalde, splev
    bisplrep, bisplev
    UnivariateSpline, BivariateSpline

    References
    ----------
    .. [1] P.W. Gaffney, The calculation of indefinite integrals of b-splines",
        J. Inst. Maths Applics, 17, p.37-41, 1976.
    .. [2] P. Dierckx, "Curve and surface fitting with splines", Monographs
        on Numerical Analysis, Oxford University Press, 1993.

     N/A N/A t c k tck N/A N/A N/A N/A N/A c N/A 0 N/A 0 N/A parametric True N/A N/A N/A N/A parametric False N/A parametric N/A N/A N/A list N/A map N/A N/A N/A c a b t k N/A a b t k N/A splint a b N/A t c k c N/A N/A N/A aint wrk N/A N/A _fitpack _splint t c k a b N/A full_output N/A N/A N/A aint wrk N/A N/A aint N/A sproot N/A N/A tck mest N/A 10 N/A N/A 
    Find the roots of a cubic B-spline.

    Given the knots (>=8) and coefficients of a cubic B-spline return the
    roots of the spline.

    Parameters
    ----------
    tck : tuple
        A tuple (t,c,k) containing the vector of knots,
        the B-spline coefficients, and the degree of the spline.
        The number of knots must be >= 8, and the degree must be 3.
        The knots must be a montonically increasing sequence.
    mest : int, optional
        An estimate of the number of zeros (Default is 10).

    Returns
    -------
    zeros : ndarray
        An array giving the roots of the spline.

    See also
    --------
    splprep, splrep, splint, spalde, splev
    bisplrep, bisplev
    UnivariateSpline, BivariateSpline


    References
    ----------
    .. [1] C. de Boor, "On calculating with b-splines", J. Approximation
        Theory, 6, p.50-62, 1972.
    .. [2] M.G. Cox, "The numerical evaluation of b-splines", J. Inst. Maths
        Applics, 10, p.134-149, 1972.
    .. [3] P. Dierckx, "Curve and surface fitting with splines", Monographs
        on Numerical Analysis, Oxford University Press, 1993.

     N/A N/A t c k tck N/A N/A k 3 N/A N/A N/A ValueError sproot works only for cubic (k=3) splines N/A N/A N/A N/A N/A c N/A 0 N/A 0 N/A parametric True N/A N/A N/A N/A parametric False N/A parametric N/A N/A N/A list N/A map N/A N/A N/A c t k mest N/A t k mest N/A sproot N/A t c k mest c N/A N/A N/A N/A len t 8 N/A N/A N/A TypeError N/A The number of knots %d>=8 N/A len t N/A N/A z ier N/A N/A _fitpack _sproot t c k mest N/A N/A ier 10 N/A N/A N/A TypeError Invalid input data. t1<=..<=t4<t5<..<tn-3<=..<=tn must hold. N/A N/A ier 0 N/A N/A z N/A N/A ier 1 N/A N/A N/A N/A warnings warn N/A RuntimeWarning The number of zeros exceeds mest N/A z N/A N/A TypeError Unknown error N/A spalde N/A N/A x tck N/A N/A N/A 
    Evaluate all derivatives of a B-spline.

    Given the knots and coefficients of a cubic B-spline compute all
    derivatives up to order k at a point (or set of points).

    Parameters
    ----------
    x : array_like
        A point or a set of points at which to evaluate the derivatives.
        Note that ``t(k) <= x <= t(n-k+1)`` must hold for each `x`.
    tck : tuple
        A tuple (t,c,k) containing the vector of knots,
        the B-spline coefficients, and the degree of the spline.

    Returns
    -------
    results : {ndarray, list of ndarrays}
        An array (or a list of arrays) containing all derivatives
        up to order k inclusive for each point `x`.

    See Also
    --------
    splprep, splrep, splint, sproot, splev, bisplrep, bisplev,
    UnivariateSpline, BivariateSpline

    References
    ----------
    .. [1] de Boor C : On calculating with b-splines, J. Approximation Theory
       6 (1972) 50-62.
    .. [2] Cox M.G. : The numerical evaluation of b-splines, J. Inst. Maths
       applics 10 (1972) 134-149.
    .. [3] Dierckx P. : Curve and surface fitting with splines, Monographs on
       Numerical Analysis, Oxford University Press, 1993.

     N/A N/A t c k tck N/A N/A N/A N/A N/A c N/A 0 N/A 0 N/A parametric True N/A N/A N/A N/A parametric False N/A parametric N/A N/A N/A list N/A map N/A N/A N/A c x t k N/A x t k N/A spalde x N/A t c k c N/A N/A x N/A atleast_1d x N/A N/A N/A len x 1 N/A N/A N/A list N/A map N/A N/A N/A x tck N/A tck N/A spalde x tck x N/A N/A d ier N/A N/A _fitpack _spalde t c k N/A x N/A 0 N/A N/A ier 0 N/A N/A d N/A N/A ier 10 N/A N/A N/A TypeError Invalid input data. t(k)<=x<=t(n-k+1) must hold. N/A N/A TypeError Unknown error N/A N/A _surfit_cache N/A tx ty wrk iwrk N/A array N/A float N/A array N/A float N/A array N/A float N/A array N/A intc bisplrep N/A N/A x y z w xb xe yb ye kx ky task s eps tx ty full_output nxest nyest quiet N/A None None None None None 3 3 0 None 1e-16 None None 0 None None 1 N/A N/A 
    Find a bivariate B-spline representation of a surface.

    Given a set of data points (x[i], y[i], z[i]) representing a surface
    z=f(x,y), compute a B-spline representation of the surface. Based on
    the routine SURFIT from FITPACK.

    Parameters
    ----------
    x, y, z : ndarray
        Rank-1 arrays of data points.
    w : ndarray, optional
        Rank-1 array of weights. By default ``w=np.ones(len(x))``.
    xb, xe : float, optional
        End points of approximation interval in `x`.
        By default ``xb = x.min(), xe=x.max()``.
    yb, ye : float, optional
        End points of approximation interval in `y`.
        By default ``yb=y.min(), ye = y.max()``.
    kx, ky : int, optional
        The degrees of the spline (1 <= kx, ky <= 5).
        Third order (kx=ky=3) is recommended.
    task : int, optional
        If task=0, find knots in x and y and coefficients for a given
        smoothing factor, s.
        If task=1, find knots and coefficients for another value of the
        smoothing factor, s.  bisplrep must have been previously called
        with task=0 or task=1.
        If task=-1, find coefficients for a given set of knots tx, ty.
    s : float, optional
        A non-negative smoothing factor.  If weights correspond
        to the inverse of the standard-deviation of the errors in z,
        then a good s-value should be found in the range
        ``(m-sqrt(2*m),m+sqrt(2*m))`` where m=len(x).
    eps : float, optional
        A threshold for determining the effective rank of an
        over-determined linear system of equations (0 < eps < 1).
        `eps` is not likely to need changing.
    tx, ty : ndarray, optional
        Rank-1 arrays of the knots of the spline for task=-1
    full_output : int, optional
        Non-zero to return optional outputs.
    nxest, nyest : int, optional
        Over-estimates of the total number of knots. If None then
        ``nxest = max(kx+sqrt(m/2),2*kx+3)``,
        ``nyest = max(ky+sqrt(m/2),2*ky+3)``.
    quiet : int, optional
        Non-zero to suppress printing of messages.
        This parameter is deprecated; use standard Python warning filters
        instead.

    Returns
    -------
    tck : array_like
        A list [tx, ty, c, kx, ky] containing the knots (tx, ty) and
        coefficients (c) of the bivariate B-spline representation of the
        surface along with the degree of the spline.
    fp : ndarray
        The weighted sum of squared residuals of the spline approximation.
    ier : int
        An integer flag about splrep success.  Success is indicated if
        ier<=0. If ier in [1,2,3] an error occurred but was not raised.
        Otherwise an error is raised.
    msg : str
        A message corresponding to the integer flag, ier.

    See Also
    --------
    splprep, splrep, splint, sproot, splev
    UnivariateSpline, BivariateSpline

    Notes
    -----
    See `bisplev` to evaluate the value of the B-spline given its tck
    representation.

    References
    ----------
    .. [1] Dierckx P.:An algorithm for surface fitting with spline functions
       Ima J. Numer. Anal. 1 (1981) 267-283.
    .. [2] Dierckx P.:An algorithm for surface fitting with spline functions
       report tw50, Dept. Computer Science,K.U.Leuven, 1980.
    .. [3] Dierckx P.:Curve and surface fitting with splines, Monographs on
       Numerical Analysis, Oxford University Press, 1993.

     N/A N/A x y z N/A map ravel N/A x y z N/A m N/A len x N/A N/A N/A m N/A len y N/A len z N/A N/A N/A TypeError len(x)==len(y)==len(z) must hold. N/A N/A w None N/A N/A w N/A ones m float N/A N/A w N/A atleast_1d w N/A N/A N/A N/A len w m N/A N/A N/A TypeError N/A len(w)=%d is not equal to m=%d N/A N/A len w m N/A N/A xb None N/A N/A xb N/A N/A x min N/A N/A xe None N/A N/A xe N/A N/A x max N/A N/A yb None N/A N/A yb N/A N/A y min N/A N/A ye None N/A N/A ye N/A N/A y max N/A N/A N/A -1 task 1 N/A N/A N/A TypeError task must be -1, 0 or 1 N/A N/A s None N/A N/A s N/A m N/A sqrt N/A 2 m N/A N/A N/A tx None N/A task -1 N/A N/A N/A TypeError Knots_x must be given for task=-1 N/A N/A tx None N/A N/A N/A _surfit_cache N/A tx N/A atleast_1d tx N/A nx N/A len N/A _surfit_cache N/A tx N/A N/A N/A ty None N/A task -1 N/A N/A N/A TypeError K nots_y must be given for task=-1 N/A N/A ty None N/A N/A N/A _surfit_cache N/A ty N/A atleast_1d ty N/A ny N/A len N/A _surfit_cache N/A ty N/A N/A N/A task -1 N/A nx N/A N/A 2 kx 2 N/A N/A N/A TypeError There must be at least 2*kx+2 knots_x for task=-1 N/A N/A N/A task -1 N/A ny N/A N/A 2 ky 2 N/A N/A N/A TypeError There must be at least 2*ky+2 knots_x for task=-1 N/A N/A N/A N/A 1 kx 5 N/A 1 ky 5 N/A N/A N/A TypeError N/A Given degree of the spline (kx,ky=%d,%d) is not supported. (1<=k<=5) N/A kx ky N/A N/A m N/A N/A kx 1 N/A ky 1 N/A N/A N/A TypeError m >= (kx+1)(ky+1) must hold N/A N/A nxest None N/A N/A nxest N/A int N/A kx N/A sqrt N/A m 2 N/A N/A nyest None N/A N/A nyest N/A int N/A ky N/A sqrt N/A m 2 N/A N/A nxest nyest N/A N/A max nxest N/A N/A 2 kx 3 N/A max nyest N/A N/A 2 ky 3 N/A N/A N/A task 0 N/A s 0 N/A N/A nxest N/A int N/A kx N/A sqrt N/A 3 m N/A nyest N/A int N/A ky N/A sqrt N/A 3 m N/A N/A task -1 N/A N/A N/A _surfit_cache N/A tx N/A atleast_1d tx N/A N/A _surfit_cache N/A ty N/A atleast_1d ty N/A N/A tx ty N/A N/A _surfit_cache N/A tx N/A _surfit_cache N/A ty N/A wrk N/A _surfit_cache N/A wrk N/A u N/A N/A nxest kx 1 N/A v N/A N/A nyest ky 1 N/A km N/A N/A max kx ky 1 N/A ne N/A max nxest nyest N/A N/A bx by N/A N/A N/A N/A kx v ky 1 N/A N/A N/A ky u kx 1 N/A N/A b1 b2 N/A bx N/A N/A bx v ky N/A N/A bx by N/A N/A N/A b1 b2 N/A by N/A N/A by u kx N/A msg Too many data points to interpolate N/A lwrk1 N/A _intc_overflow N/A N/A N/A N/A N/A u v N/A N/A 2 b1 b2 N/A 2 N/A N/A N/A N/A N/A u v N/A km N/A m ne ne kx ky b2 1 msg msg N/A lwrk2 N/A _intc_overflow N/A N/A N/A u v N/A b2 1 b2 msg msg N/A N/A tx ty c o N/A N/A _fitpack _surfit x y z w xb xe yb ye kx ky task s eps tx ty nxest nyest wrk lwrk1 lwrk2 N/A N/A _curfit_cache N/A tx tx N/A N/A _curfit_cache N/A ty ty N/A N/A _curfit_cache N/A wrk N/A o N/A wrk N/A N/A ier fp N/A N/A o N/A ier N/A o N/A fp N/A tck N/A tx ty c kx ky N/A ierm N/A min 11 N/A max -3 ier N/A N/A N/A ierm 0 N/A quiet N/A N/A _mess N/A N/A N/A _iermess2 N/A ierm N/A 0 N/A 	kx,ky=%d,%d nx,ny=%d,%d m=%d fp=%f s=%f N/A kx ky N/A len tx N/A len ty m fp s N/A N/A N/A warnings warn N/A RuntimeWarning _mess N/A N/A N/A ierm 0 N/A full_output N/A N/A N/A ier N/A 1 2 3 4 5 N/A N/A _mess N/A 
	kx,ky=%d,%d nx,ny=%d,%d m=%d fp=%f s=%f N/A kx ky N/A len tx N/A len ty m fp s N/A N/A N/A warnings warn N/A RuntimeWarning N/A N/A N/A _iermess2 N/A ierm N/A 0 _mess N/A N/A N/A N/A N/A N/A N/A _iermess2 N/A ierm N/A 1 N/A N/A _iermess2 N/A ierm N/A 0 N/A N/A N/A KeyError N/A N/A N/A N/A N/A _iermess2 N/A unknown N/A 1 N/A N/A _iermess2 N/A unknown N/A 0 N/A full_output N/A N/A N/A N/A N/A tck fp ier N/A N/A _iermess2 N/A ierm N/A 0 N/A N/A N/A KeyError N/A N/A N/A tck fp ier N/A N/A _iermess2 N/A unknown N/A 0 N/A N/A tck N/A bisplev N/A N/A x y tck dx dy N/A 0 0 N/A N/A 
    Evaluate a bivariate B-spline and its derivatives.

    Return a rank-2 array of spline function values (or spline derivative
    values) at points given by the cross-product of the rank-1 arrays `x` and
    `y`.  In special cases, return an array or just a float if either `x` or
    `y` or both are floats.  Based on BISPEV from FITPACK.

    Parameters
    ----------
    x, y : ndarray
        Rank-1 arrays specifying the domain over which to evaluate the
        spline or its derivative.
    tck : tuple
        A sequence of length 5 returned by `bisplrep` containing the knot
        locations, the coefficients, and the degree of the spline:
        [tx, ty, c, kx, ky].
    dx, dy : int, optional
        The orders of the partial derivatives in `x` and `y` respectively.

    Returns
    -------
    vals : ndarray
        The B-spline or its derivative evaluated over the set formed by
        the cross-product of `x` and `y`.

    See Also
    --------
    splprep, splrep, splint, sproot, splev
    UnivariateSpline, BivariateSpline

    Notes
    -----
        See `bisplrep` to generate the `tck` representation.

    References
    ----------
    .. [1] Dierckx P. : An algorithm for surface fitting
       with spline functions
       Ima J. Numer. Anal. 1 (1981) 267-283.
    .. [2] Dierckx P. : An algorithm for surface fitting
       with spline functions
       report tw50, Dept. Computer Science,K.U.Leuven, 1980.
    .. [3] Dierckx P. : Curve and surface fitting with splines,
       Monographs on Numerical Analysis, Oxford University Press, 1993.

     N/A N/A tx ty c kx ky tck N/A N/A N/A 0 dx kx N/A N/A N/A ValueError N/A 0 <= dx = %d < kx = %d must hold N/A dx kx N/A N/A N/A 0 dy ky N/A N/A N/A ValueError N/A 0 <= dy = %d < ky = %d must hold N/A dy ky N/A N/A x y N/A map atleast_1d N/A x y N/A N/A N/A N/A len N/A x shape 1 N/A N/A len N/A y shape 1 N/A N/A N/A ValueError First two entries should be rank-1 arrays. N/A N/A z ier N/A N/A _fitpack _bispev tx ty c kx ky x y dx dy N/A N/A ier 10 N/A N/A N/A ValueError Invalid input data N/A ier N/A N/A N/A TypeError An error occurred N/A N/A z shape N/A N/A len x N/A len y N/A N/A N/A len z 1 N/A N/A z N/A N/A N/A len N/A z N/A 0 1 N/A N/A N/A z N/A 0 N/A N/A N/A z N/A 0 N/A 0 N/A dblint N/A N/A xa xb ya yb tck N/A N/A N/A Evaluate the integral of a spline over area [xa,xb] x [ya,yb].

    Parameters
    ----------
    xa, xb : float
        The end-points of the x integration interval.
    ya, yb : float
        The end-points of the y integration interval.
    tck : list [tx, ty, c, kx, ky]
        A sequence of length 5 returned by bisplrep containing the knot
        locations tx, ty, the coefficients c, and the degrees kx, ky
        of the spline.

    Returns
    -------
    integ : float
        The value of the resulting integral.
     N/A N/A tx ty c kx ky tck N/A N/A N/A dfitpack dblint tx ty c kx ky xa xb ya yb N/A insert N/A N/A x tck m per N/A 1 0 N/A N/A 
    Insert knots into a B-spline.

    Given the knots and coefficients of a B-spline representation, create a
    new B-spline with a knot inserted `m` times at point `x`.
    This is a wrapper around the FORTRAN routine insert of FITPACK.

    Parameters
    ----------
    x (u) : array_like
        A 1-D point at which to insert a new knot(s).  If `tck` was returned
        from ``splprep``, then the parameter values, u should be given.
    tck : tuple
        A tuple (t,c,k) returned by ``splrep`` or ``splprep`` containing
        the vector of knots, the B-spline coefficients,
        and the degree of the spline.
    m : int, optional
        The number of times to insert the given knot (its multiplicity).
        Default is 1.
    per : int, optional
        If non-zero, the input spline is considered periodic.

    Returns
    -------
    tck : tuple
        A tuple (t,c,k) containing the vector of knots, the B-spline
        coefficients, and the degree of the new spline.
        ``t(k+1) <= x <= t(n-k)``, where k is the degree of the spline.
        In case of a periodic spline (``per != 0``) there must be
        either at least k interior knots t(j) satisfying ``t(k+1)<t(j)<=x``
        or at least k interior knots t(j) satisfying ``x<=t(j)<t(n-k)``.

    Notes
    -----
    Based on algorithms from [1]_ and [2]_.

    References
    ----------
    .. [1] W. Boehm, "Inserting new knots into b-spline curves.",
        Computer Aided Design, 12, p.199-201, 1980.
    .. [2] P. Dierckx, "Curve and surface fitting with splines, Monographs on
        Numerical Analysis", Oxford University Press, 1993.

     N/A N/A t c k tck N/A N/A N/A N/A N/A c N/A 0 N/A 0 N/A parametric True N/A N/A N/A N/A parametric False N/A parametric N/A N/A cc N/A N/A c_vals c N/A N/A N/A tt cc_val kk N/A insert x N/A t c_vals k m N/A N/A N/A cc append cc_val N/A N/A tt cc kk N/A N/A N/A tt cc ier N/A N/A _fitpack _insert per t c k x m N/A N/A ier 10 N/A N/A N/A ValueError Invalid input data N/A ier N/A N/A N/A TypeError An error occurred N/A N/A tt cc k N/A splder N/A N/A tck n N/A 1 N/A N/A 
    Compute the spline representation of the derivative of a given spline

    Parameters
    ----------
    tck : tuple of (t, c, k)
        Spline whose derivative to compute
    n : int, optional
        Order of derivative to evaluate. Default: 1

    Returns
    -------
    tck_der : tuple of (t2, c2, k2)
        Spline of order k2=k-n representing the derivative
        of the input spline.

    Notes
    -----

    .. versionadded:: 0.13.0

    See Also
    --------
    splantider, splev, spalde

    Examples
    --------
    This can be used for finding maxima of a curve:

    >>> from scipy.interpolate import splrep, splder, sproot
    >>> x = np.linspace(0, 10, 70)
    >>> y = np.sin(x)
    >>> spl = splrep(x, y, k=4)

    Now, differentiate the spline and find the zeros of the
    derivative. (NB: `sproot` only works for order 3 splines, so we
    fit an order 4 spline):

    >>> dspl = splder(spl)
    >>> sproot(dspl) / np.pi
    array([ 0.50000001,  1.5       ,  2.49999998])

    This agrees well with roots :math:`\pi/2 + n\pi` of
    :math:`\cos(x) = \sin'(x)`.

     N/A N/A n 0 N/A N/A N/A splantider tck N/A n N/A N/A t c k tck N/A N/A n k N/A N/A N/A ValueError N/A Order of derivative (n = %r) must be <= order of spline (k = %r) N/A n N/A tck N/A 2 N/A N/A N/A np errstate invalid raise divide raise N/A N/A N/A N/A j N/A range n N/A N/A dt N/A N/A t N/A N/A k 1 -1 N/A t N/A 1 N/A N/A k 1 N/A c N/A N/A N/A N/A c N/A 1 N/A -1 k N/A c N/A N/A -2 k k dt N/A c N/A N/A np r_ N/A N/A c N/A N/A 0 k N/A t N/A t N/A 1 -1 N/A k 1 N/A N/A N/A FloatingPointError N/A N/A N/A ValueError N/A The spline has internal repeated knots and is not differentiable %d times n N/A N/A t c k N/A splantider N/A N/A tck n N/A 1 N/A N/A 
    Compute the spline for the antiderivative (integral) of a given spline.

    Parameters
    ----------
    tck : tuple of (t, c, k)
        Spline whose antiderivative to compute
    n : int, optional
        Order of antiderivative to evaluate. Default: 1

    Returns
    -------
    tck_ader : tuple of (t2, c2, k2)
        Spline of order k2=k+n representing the antiderivative of the input
        spline.

    See Also
    --------
    splder, splev, spalde

    Notes
    -----
    The `splder` function is the inverse operation of this function.
    Namely, ``splder(splantider(tck))`` is identical to `tck`, modulo
    rounding error.

    .. versionadded:: 0.13.0

    Examples
    --------
    >>> from scipy.interpolate import splrep, splder, splantider, splev
    >>> x = np.linspace(0, np.pi/2, 70)
    >>> y = 1 / np.sqrt(1 - 0.8*np.sin(x)**2)
    >>> spl = splrep(x, y)

    The derivative is the inverse operation of the antiderivative,
    although some floating point error accumulates:

    >>> splev(1.7, spl), splev(1.7, splder(splantider(spl)))
    (array(2.1565429877197317), array(2.1565429877201865))

    Antiderivative can be used to evaluate definite integrals:

    >>> ispl = splantider(spl)
    >>> splev(np.pi/2, ispl) - splev(0, ispl)
    2.2572053588768486

    This is indeed an approximation to the complete elliptic integral
    :math:`K(m) = \int_0^{\pi/2} [1 - m\sin^2 x]^{-1/2} dx`:

    >>> from scipy.special import ellipk
    >>> ellipk(0.8)
    2.2572053268208538

     N/A N/A n 0 N/A N/A N/A splder tck N/A n N/A N/A t c k tck N/A j N/A range n N/A N/A dt N/A N/A t N/A N/A k 1 N/A t N/A N/A N/A k 1 N/A c N/A N/A N/A np cumsum N/A N/A c N/A N/A N/A k 1 dt N/A k 1 N/A c N/A N/A np r_ N/A N/A 0 c N/A N/A N/A c N/A -1 N/A k 2 N/A t N/A N/A np r_ N/A N/A N/A t N/A 0 t N/A t N/A -1 N/A k 1 N/A N/A t c k N/A