Sacado::Tay Namespace Reference

Namespace for Taylor polynomial AD classes. More...

Classes
class	CacheTaylorImplementation
	Taylor polynomial class using caching expression templates. More...
class	Expr< CacheTaylorImplementation< T > >
	CacheTaylor expression template specialization. More...
class	CacheTaylor
	Forward-mode AD class using dynamic memory allocation. More...
class	Expr
	Wrapper for a generic expression template. More...
class	ConstExpr
	Constant expression template. More...
class	UnaryExpr
	Unary expression template. More...
class	BinaryExpr
	Binary expression template. More...
class	BinaryExpr< ConstExpr< typename ExprT2::value_type >, ExprT2, Op >
	Binary expression template with first argument constant. More...
class	BinaryExpr< ExprT1, ConstExpr< typename ExprT1::value_type >, Op >
	Binary expression template with second argument constant. More...
class	UnaryPlusOp
class	UnaryMinusOp
class	ExpOp
class	LogOp
class	SqrtOp
class	CosOp
class	SinOp
class	CoshOp
class	SinhOp
class	FAbsOp
class	AdditionOp
class	AdditionOp< ExprT1, ConstExpr< typename ExprT1::value_type > >
class	AdditionOp< ConstExpr< typename ExprT2::value_type >, ExprT2 >
class	SubtractionOp
class	SubtractionOp< ExprT1, ConstExpr< typename ExprT1::value_type > >
class	SubtractionOp< ConstExpr< typename ExprT2::value_type >, ExprT2 >
class	MultiplicationOp
class	MultiplicationOp< ExprT1, ConstExpr< typename ExprT1::value_type > >
class	MultiplicationOp< ConstExpr< typename ExprT2::value_type >, ExprT2 >
class	DivisionOp
class	DivisionOp< ExprT1, ConstExpr< typename ExprT1::value_type > >
class	DivisionOp< ConstExpr< typename ExprT2::value_type >, ExprT2 >
class	MaxOp
class	MaxOp< ExprT1, ConstExpr< typename ExprT1::value_type > >
class	MaxOp< ConstExpr< typename ExprT2::value_type >, ExprT2 >
class	MinOp
class	MinOp< ExprT1, ConstExpr< typename ExprT1::value_type > >
class	MinOp< ConstExpr< typename ExprT2::value_type >, ExprT2 >
class	ASinQuadOp
class	ACosQuadOp
class	ATanQuadOp
struct	PowExprType
struct	PowExprType< typename ExprT2::value_type, ExprT2 >
struct	PowExprType< ExprT1, typename ExprT1::value_type >
struct	Log10ExprType
struct	TanExprType
struct	ASinExprType
struct	ACosExprType
struct	ATanExprType
struct	TanhExprType
class	Taylor
	Taylor polynomial class. More...
Functions
template<typename T >
Taylor< T >	exp (const Taylor< T > &)
template<typename T >
Taylor< T >	log (const Taylor< T > &)
template<typename T >
Taylor< T >	log10 (const Taylor< T > &)
template<typename T >
Taylor< T >	sqrt (const Taylor< T > &)
template<typename T >
Taylor< T >	cos (const Taylor< T > &)
template<typename T >
Taylor< T >	sin (const Taylor< T > &)
template<typename T >
Taylor< T >	tan (const Taylor< T > &)
template<typename T >
Taylor< T >	acos (const Taylor< T > &)
template<typename T >
Taylor< T >	asin (const Taylor< T > &)
template<typename T >
Taylor< T >	atan (const Taylor< T > &)
template<typename T >
Taylor< T >	cosh (const Taylor< T > &)
template<typename T >
Taylor< T >	sinh (const Taylor< T > &)
template<typename T >
Taylor< T >	tanh (const Taylor< T > &)
template<typename T >
Taylor< T >	acosh (const Taylor< T > &)
template<typename T >
Taylor< T >	asinh (const Taylor< T > &)
template<typename T >
Taylor< T >	atanh (const Taylor< T > &)
template<typename T >
Taylor< T >	abs (const Taylor< T > &)
template<typename T >
Taylor< T >	fabs (const Taylor< T > &)
template<typename T >
Taylor< T >	atan2 (const Taylor< T > &, const Taylor< T > &)
template<typename T >
Taylor< T >	atan2 (const typename Taylor< T >::value_type &, const Taylor< T > &)
template<typename T >
Taylor< T >	atan2 (const Taylor< T > &, const typename Taylor< T >::value_type &)
template<typename T >
Taylor< T >	pow (const Taylor< T > &, const Taylor< T > &)
template<typename T >
Taylor< T >	pow (const typename Taylor< T >::value_type &, const Taylor< T > &)
template<typename T >
Taylor< T >	pow (const Taylor< T > &, const typename Taylor< T >::value_type &)
template<typename T >
Taylor< T >	max (const Taylor< T > &, const Taylor< T > &)
template<typename T >
Taylor< T >	max (const typename Taylor< T >::value_type &, const Taylor< T > &)
template<typename T >
Taylor< T >	max (const Taylor< T > &, const typename Taylor< T >::value_type &)
template<typename T >
Taylor< T >	min (const Taylor< T > &, const Taylor< T > &)
template<typename T >
Taylor< T >	min (const typename Taylor< T >::value_type &, const Taylor< T > &)
template<typename T >
Taylor< T >	min (const Taylor< T > &, const typename Taylor< T >::value_type &)
template<typename T >
Expr< UnaryExpr< Expr< T > , UnaryPlusOp > >	operator+ (const Expr< T > &expr)
template<typename T >
Expr< UnaryExpr< Expr< T > , UnaryMinusOp > >	operator- (const Expr< T > &expr)
template<typename T >
Expr< UnaryExpr< Expr< T > , ExpOp > >	exp (const Expr< T > &expr)
template<typename T >
Expr< UnaryExpr< Expr< T > , LogOp > >	log (const Expr< T > &expr)
template<typename T >
Expr< UnaryExpr< Expr< T > , SqrtOp > >	sqrt (const Expr< T > &expr)
template<typename T >
Expr< UnaryExpr< Expr< T > , CosOp > >	cos (const Expr< T > &expr)
template<typename T >
Expr< UnaryExpr< Expr< T > , SinOp > >	sin (const Expr< T > &expr)
template<typename T >
Expr< UnaryExpr< Expr< T > , CoshOp > >	cosh (const Expr< T > &expr)
template<typename T >
Expr< UnaryExpr< Expr< T > , SinhOp > >	sinh (const Expr< T > &expr)
template<typename T >
Expr< UnaryExpr< Expr< T > , FAbsOp > >	abs (const Expr< T > &expr)
template<typename T >
Expr< UnaryExpr< Expr< T > , FAbsOp > >	fabs (const Expr< T > &expr)
template<typename T1 , typename T2 >
Expr< BinaryExpr< Expr< T1 > , Expr< T2 >, AdditionOp > >	operator+ (const Expr< T1 > &expr1, const Expr< T2 > &expr2)
template<typename T >
Expr< BinaryExpr< ConstExpr < typename Expr< T > ::value_type >, Expr< T > , AdditionOp > >	operator+ (const typename Expr< T >::value_type &c, const Expr< T > &expr)
template<typename T >
Expr< BinaryExpr< Expr< T > , ConstExpr< typename Expr< T > ::value_type >, AdditionOp > >	operator+ (const Expr< T > &expr, const typename Expr< T >::value_type &c)
template<typename T1 , typename T2 >
Expr< BinaryExpr< Expr< T1 > , Expr< T2 >, SubtractionOp > >	operator- (const Expr< T1 > &expr1, const Expr< T2 > &expr2)
template<typename T >
Expr< BinaryExpr< ConstExpr < typename Expr< T > ::value_type >, Expr< T > , SubtractionOp > >	operator- (const typename Expr< T >::value_type &c, const Expr< T > &expr)
template<typename T >
Expr< BinaryExpr< Expr< T > , ConstExpr< typename Expr< T > ::value_type >, SubtractionOp > >	operator- (const Expr< T > &expr, const typename Expr< T >::value_type &c)
template<typename T1 , typename T2 >
Expr< BinaryExpr< Expr< T1 > , Expr< T2 >, MultiplicationOp > >	operator* (const Expr< T1 > &expr1, const Expr< T2 > &expr2)
template<typename T >
Expr< BinaryExpr< ConstExpr < typename Expr< T > ::value_type >, Expr< T > , MultiplicationOp > >	operator* (const typename Expr< T >::value_type &c, const Expr< T > &expr)
template<typename T >
Expr< BinaryExpr< Expr< T > , ConstExpr< typename Expr< T > ::value_type > , MultiplicationOp > >	operator* (const Expr< T > &expr, const typename Expr< T >::value_type &c)
template<typename T1 , typename T2 >
Expr< BinaryExpr< Expr< T1 > , Expr< T2 >, DivisionOp > >	operator/ (const Expr< T1 > &expr1, const Expr< T2 > &expr2)
template<typename T >
Expr< BinaryExpr< ConstExpr < typename Expr< T > ::value_type >, Expr< T > , DivisionOp > >	operator/ (const typename Expr< T >::value_type &c, const Expr< T > &expr)
template<typename T >
Expr< BinaryExpr< Expr< T > , ConstExpr< typename Expr< T > ::value_type >, DivisionOp > >	operator/ (const Expr< T > &expr, const typename Expr< T >::value_type &c)
template<typename T1 , typename T2 >
mpl::disable_if< mpl::is_same < T1, T2 >, Expr< BinaryExpr < Expr< T1 >, Expr< T2 > , MaxOp > > >::type	max (const Expr< T1 > &expr1, const Expr< T2 > &expr2)
template<typename T >
Expr< BinaryExpr< ConstExpr < typename Expr< T > ::value_type >, Expr< T > , MaxOp > >	max (const typename Expr< T >::value_type &c, const Expr< T > &expr)
template<typename T >
Expr< BinaryExpr< Expr< T > , ConstExpr< typename Expr< T > ::value_type >, MaxOp > >	max (const Expr< T > &expr, const typename Expr< T >::value_type &c)
template<typename T1 , typename T2 >
mpl::disable_if< mpl::is_same < T1, T2 >, Expr< BinaryExpr < Expr< T1 >, Expr< T2 > , MinOp > > >::type	min (const Expr< T1 > &expr1, const Expr< T2 > &expr2)
template<typename T >
Expr< BinaryExpr< ConstExpr < typename Expr< T > ::value_type >, Expr< T > , MinOp > >	min (const typename Expr< T >::value_type &c, const Expr< T > &expr)
template<typename T >
Expr< BinaryExpr< Expr< T > , ConstExpr< typename Expr< T > ::value_type >, MinOp > >	min (const Expr< T > &expr, const typename Expr< T >::value_type &c)
template<typename T1 , typename T2 >
Expr< BinaryExpr< Expr< T1 > , Expr< T2 >, ASinQuadOp > >	asin_quad (const Expr< T1 > &expr1, const Expr< T2 > &expr2)
template<typename T1 , typename T2 >
Expr< BinaryExpr< Expr< T1 > , Expr< T2 >, ACosQuadOp > >	acos_quad (const Expr< T1 > &expr1, const Expr< T2 > &expr2)
template<typename T1 , typename T2 >
Expr< BinaryExpr< Expr< T1 > , Expr< T2 >, ATanQuadOp > >	atan_quad (const Expr< T1 > &expr1, const Expr< T2 > &expr2)
template<typename T1 , typename T2 >
PowExprType< Expr< T1 >, Expr < T2 > >::expr_type	pow (const Expr< T1 > &expr1, const Expr< T2 > &expr2)
template<typename T >
PowExprType< typename Expr< T > ::value_type, Expr< T > >::expr_type	pow (const typename Expr< T >::value_type &c, const Expr< T > &expr)
template<typename T >
PowExprType< Expr< T > , typename Expr< T > ::value_type >::expr_type	pow (const Expr< T > &expr, const typename Expr< T >::value_type &c)
template<typename T >
Log10ExprType< T >::expr_type	log10 (const Expr< T > &expr)
template<typename T >
TanExprType< T >::expr_type	tan (const Expr< T > &expr)
template<typename T >
ASinExprType< T >::expr_type	asin (const Expr< T > &expr)
template<typename T >
ACosExprType< T >::expr_type	acos (const Expr< T > &expr)
template<typename T >
ATanExprType< T >::expr_type	atan (const Expr< T > &expr)
template<typename T >
TanhExprType< T >::expr_type	tanh (const Expr< T > &expr)
template<typename ExprT1 , typename ExprT2 >
bool	operator== (const Expr< ExprT1 > &expr1, const Expr< ExprT2 > &expr2)
template<typename ExprT2 >
bool	operator== (const typename Expr< ExprT2 >::value_type &a, const Expr< ExprT2 > &expr2)
template<typename ExprT1 >
bool	operator== (const Expr< ExprT1 > &expr1, const typename Expr< ExprT1 >::value_type &b)
template<typename ExprT1 , typename ExprT2 >
bool	operator!= (const Expr< ExprT1 > &expr1, const Expr< ExprT2 > &expr2)
template<typename ExprT2 >
bool	operator!= (const typename Expr< ExprT2 >::value_type &a, const Expr< ExprT2 > &expr2)
template<typename ExprT1 >
bool	operator!= (const Expr< ExprT1 > &expr1, const typename Expr< ExprT1 >::value_type &b)
template<typename ExprT1 , typename ExprT2 >
bool	operator< (const Expr< ExprT1 > &expr1, const Expr< ExprT2 > &expr2)
template<typename ExprT2 >
bool	operator< (const typename Expr< ExprT2 >::value_type &a, const Expr< ExprT2 > &expr2)
template<typename ExprT1 >
bool	operator< (const Expr< ExprT1 > &expr1, const typename Expr< ExprT1 >::value_type &b)
template<typename ExprT1 , typename ExprT2 >
bool	operator> (const Expr< ExprT1 > &expr1, const Expr< ExprT2 > &expr2)
template<typename ExprT2 >
bool	operator> (const typename Expr< ExprT2 >::value_type &a, const Expr< ExprT2 > &expr2)
template<typename ExprT1 >
bool	operator> (const Expr< ExprT1 > &expr1, const typename Expr< ExprT1 >::value_type &b)
template<typename ExprT1 , typename ExprT2 >
bool	operator<= (const Expr< ExprT1 > &expr1, const Expr< ExprT2 > &expr2)
template<typename ExprT2 >
bool	operator<= (const typename Expr< ExprT2 >::value_type &a, const Expr< ExprT2 > &expr2)
template<typename ExprT1 >
bool	operator<= (const Expr< ExprT1 > &expr1, const typename Expr< ExprT1 >::value_type &b)
template<typename ExprT1 , typename ExprT2 >
bool	operator>= (const Expr< ExprT1 > &expr1, const Expr< ExprT2 > &expr2)
template<typename ExprT2 >
bool	operator>= (const typename Expr< ExprT2 >::value_type &a, const Expr< ExprT2 > &expr2)
template<typename ExprT1 >
bool	operator>= (const Expr< ExprT1 > &expr1, const typename Expr< ExprT1 >::value_type &b)
template<typename ExprT1 , typename ExprT2 >
bool	operator<<= (const Expr< ExprT1 > &expr1, const Expr< ExprT2 > &expr2)
template<typename ExprT2 >
bool	operator<<= (const typename Expr< ExprT2 >::value_type &a, const Expr< ExprT2 > &expr2)
template<typename ExprT1 >
bool	operator<<= (const Expr< ExprT1 > &expr1, const typename Expr< ExprT1 >::value_type &b)
template<typename ExprT1 , typename ExprT2 >
bool	operator>>= (const Expr< ExprT1 > &expr1, const Expr< ExprT2 > &expr2)
template<typename ExprT2 >
bool	operator>>= (const typename Expr< ExprT2 >::value_type &a, const Expr< ExprT2 > &expr2)
template<typename ExprT1 >
bool	operator>>= (const Expr< ExprT1 > &expr1, const typename Expr< ExprT1 >::value_type &b)
template<typename ExprT1 , typename ExprT2 >
bool	operator& (const Expr< ExprT1 > &expr1, const Expr< ExprT2 > &expr2)
template<typename ExprT2 >
bool	operator& (const typename Expr< ExprT2 >::value_type &a, const Expr< ExprT2 > &expr2)
template<typename ExprT1 >
bool	operator& (const Expr< ExprT1 > &expr1, const typename Expr< ExprT1 >::value_type &b)
template<typename ExprT1 , typename ExprT2 >
bool	operator| (const Expr< ExprT1 > &expr1, const Expr< ExprT2 > &expr2)
template<typename ExprT2 >
bool	operator| (const typename Expr< ExprT2 >::value_type &a, const Expr< ExprT2 > &expr2)
template<typename ExprT1 >
bool	operator| (const Expr< ExprT1 > &expr1, const typename Expr< ExprT1 >::value_type &b)
template<typename ExprT >
bool	operator! (const Expr< ExprT > &expr)
template<typename ExprT >
bool	toBool2 (const Expr< ExprT > &x)
template<typename ExprT1 , typename ExprT2 >
bool	operator&& (const Expr< ExprT1 > &expr1, const Expr< ExprT2 > &expr2)
template<typename ExprT2 >
bool	operator&& (const typename Expr< ExprT2 >::value_type &a, const Expr< ExprT2 > &expr2)
template<typename ExprT1 >
bool	operator&& (const Expr< ExprT1 > &expr1, const typename Expr< ExprT1 >::value_type &b)
template<typename ExprT1 , typename ExprT2 >
bool	operator|| (const Expr< ExprT1 > &expr1, const Expr< ExprT2 > &expr2)
template<typename ExprT2 >
bool	operator|| (const typename Expr< ExprT2 >::value_type &a, const Expr< ExprT2 > &expr2)
template<typename ExprT1 >
bool	operator|| (const Expr< ExprT1 > &expr1, const typename Expr< ExprT1 >::value_type &b)
template<typename ExprT >
std::ostream &	operator<< (std::ostream &os, const Expr< ExprT > &x)
template<typename T >
CacheTaylor< T >	diff (const CacheTaylor< T > &x, int n=1)
	Compute Taylor series of n-th derivative of x.
template<typename T >
Taylor< T >	diff (const Taylor< T > &x, int n=1)
	Compute Taylor series of n-th derivative of x.
template<typename T >
Taylor< T >	operator+ (const Taylor< T > &a, const Taylor< T > &b)
template<typename T >
Taylor< T >	operator+ (const typename Taylor< T >::value_type &a, const Taylor< T > &b)
template<typename T >
Taylor< T >	operator+ (const Taylor< T > &a, const typename Taylor< T >::value_type &b)
template<typename T >
Taylor< T >	operator- (const Taylor< T > &a, const Taylor< T > &b)
template<typename T >
Taylor< T >	operator- (const typename Taylor< T >::value_type &a, const Taylor< T > &b)
template<typename T >
Taylor< T >	operator- (const Taylor< T > &a, const typename Taylor< T >::value_type &b)
template<typename T >
Taylor< T >	operator* (const Taylor< T > &a, const Taylor< T > &b)
template<typename T >
Taylor< T >	operator* (const typename Taylor< T >::value_type &a, const Taylor< T > &b)
template<typename T >
Taylor< T >	operator* (const Taylor< T > &a, const typename Taylor< T >::value_type &b)
template<typename T >
Taylor< T >	operator/ (const Taylor< T > &a, const Taylor< T > &b)
template<typename T >
Taylor< T >	operator/ (const typename Taylor< T >::value_type &a, const Taylor< T > &b)
template<typename T >
Taylor< T >	operator/ (const Taylor< T > &a, const typename Taylor< T >::value_type &b)
template<typename T >
void	sincos (const Taylor< T > &a, Taylor< T > &s, Taylor< T > &c)
template<typename T >
void	sinhcosh (const Taylor< T > &a, Taylor< T > &s, Taylor< T > &c)
template<typename T >
Taylor< T >	quad (const typename Taylor< T >::value_type &c0, const Taylor< T > &a, const Taylor< T > &b)
template<typename T >
bool	operator== (const Taylor< T > &a, const Taylor< T > &b)
template<typename T >
bool	operator== (const typename Taylor< T >::value_type &a, const Taylor< T > &b)
template<typename T >
bool	operator== (const Taylor< T > &a, const typename Taylor< T >::value_type &b)
template<typename T >
bool	operator!= (const Taylor< T > &a, const Taylor< T > &b)
template<typename T >
bool	operator!= (const typename Taylor< T >::value_type &a, const Taylor< T > &b)
template<typename T >
bool	operator!= (const Taylor< T > &a, const typename Taylor< T >::value_type &b)
template<typename T >
bool	operator<= (const Taylor< T > &a, const Taylor< T > &b)
template<typename T >
bool	operator<= (const typename Taylor< T >::value_type &a, const Taylor< T > &b)
template<typename T >
bool	operator<= (const Taylor< T > &a, const typename Taylor< T >::value_type &b)
template<typename T >
bool	operator>= (const Taylor< T > &a, const Taylor< T > &b)
template<typename T >
bool	operator>= (const typename Taylor< T >::value_type &a, const Taylor< T > &b)
template<typename T >
bool	operator>= (const Taylor< T > &a, const typename Taylor< T >::value_type &b)
template<typename T >
bool	operator< (const Taylor< T > &a, const Taylor< T > &b)
template<typename T >
bool	operator< (const typename Taylor< T >::value_type &a, const Taylor< T > &b)
template<typename T >
bool	operator< (const Taylor< T > &a, const typename Taylor< T >::value_type &b)
template<typename T >
bool	operator> (const Taylor< T > &a, const Taylor< T > &b)
template<typename T >
bool	operator> (const typename Taylor< T >::value_type &a, const Taylor< T > &b)
template<typename T >
bool	operator> (const Taylor< T > &a, const typename Taylor< T >::value_type &b)
template<typename T >
std::ostream &	operator<< (std::ostream &os, const Taylor< T > &a)
template<typename T >
bool	toBool (const Taylor< T > &x)
template<typename T >
bool	operator&& (const Taylor< T > &x1, const Taylor< T > &x2)
template<typename T >
bool	operator&& (const typename Taylor< T >::value_type &a, const Taylor< T > &x2)
template<typename T >
bool	operator&& (const Taylor< T > &x1, const typename Taylor< T >::value_type &b)
template<typename T >
bool	operator|| (const Taylor< T > &x1, const Taylor< T > &x2)
template<typename T >
bool	operator|| (const typename Taylor< T >::value_type &a, const Taylor< T > &x2)
template<typename T >
bool	operator|| (const Taylor< T > &x1, const typename Taylor< T >::value_type &b)

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Detailed Description

Namespace for Taylor polynomial AD classes.