Sacado::Tay Namespace Reference

Namespace for Taylor polynomial AD classes. More...

Classes
class	Taylor
	Taylor polynomial class. More...
class	UnaryPlusOp
class	UnaryMinusOp
class	CacheTaylor
	Forward-mode AD class using dynamic memory allocation. More...
class	CacheTaylorImplementation
	Taylor polynomial class using caching expression templates. More...
class	Expr< CacheTaylorImplementation< T > >
	CacheTaylor expression template specialization. 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	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

Functions
template<typename T >
Taylor< T >	exp (const Base< Taylor< T > > &)
template<typename T >
Taylor< T >	log (const Base< Taylor< T > > &)
template<typename T >
Taylor< T >	log10 (const Base< Taylor< T > > &)
template<typename T >
Taylor< T >	sqrt (const Base< Taylor< T > > &)
template<typename T >
Taylor< T >	cos (const Base< Taylor< T > > &)
template<typename T >
Taylor< T >	sin (const Base< Taylor< T > > &)
template<typename T >
Taylor< T >	tan (const Base< Taylor< T > > &)
template<typename T >
Taylor< T >	acos (const Base< Taylor< T > > &)
template<typename T >
Taylor< T >	asin (const Base< Taylor< T > > &)
template<typename T >
Taylor< T >	atan (const Base< Taylor< T > > &)
template<typename T >
Taylor< T >	cosh (const Base< Taylor< T > > &)
template<typename T >
Taylor< T >	sinh (const Base< Taylor< T > > &)
template<typename T >
Taylor< T >	tanh (const Base< Taylor< T > > &)
template<typename T >
Taylor< T >	acosh (const Base< Taylor< T > > &)
template<typename T >
Taylor< T >	asinh (const Base< Taylor< T > > &)
template<typename T >
Taylor< T >	atanh (const Base< Taylor< T > > &)
template<typename T >
Taylor< T >	abs (const Base< Taylor< T > > &)
template<typename T >
Taylor< T >	fabs (const Base< Taylor< T > > &)
template<typename T >
Taylor< T >	cbrt (const Base< Taylor< T > > &)
template<typename T >
Taylor< T >	atan2 (const Base< Taylor< T > > &, const Base< Taylor< T > > &)
template<typename T >
Taylor< T >	atan2 (const typename Taylor< T >::value_type &, const Base< Taylor< T > > &)
template<typename T >
Taylor< T >	atan2 (const Base< Taylor< T > > &, const typename Taylor< T >::value_type &)
template<typename T >
Taylor< T >	pow (const Base< Taylor< T > > &, const Base< Taylor< T > > &)
template<typename T >
Taylor< T >	pow (const typename Taylor< T >::value_type &, const Base< Taylor< T > > &)
template<typename T >
Taylor< T >	pow (const Base< Taylor< T > > &, const typename Taylor< T >::value_type &)
template<typename T >
Taylor< T >	max (const Base< Taylor< T > > &, const Base< Taylor< T > > &)
template<typename T >
Taylor< T >	max (const typename Taylor< T >::value_type &, const Base< Taylor< T > > &)
template<typename T >
Taylor< T >	max (const Base< Taylor< T > > &, const typename Taylor< T >::value_type &)
template<typename T >
Taylor< T >	min (const Base< Taylor< T > > &, const Base< Taylor< T > > &)
template<typename T >
Taylor< T >	min (const typename Taylor< T >::value_type &, const Base< Taylor< T > > &)
template<typename T >
Taylor< T >	min (const Base< 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< std::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< std::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 Base< Taylor< T > > &a, const Base< Taylor< T > > &b)
template<typename T >
Taylor< T >	operator+ (const typename Taylor< T >::value_type &a, const Base< Taylor< T > > &b)
template<typename T >
Taylor< T >	operator+ (const Base< Taylor< T > > &a, const typename Taylor< T >::value_type &b)
template<typename T >
Taylor< T >	operator- (const Base< Taylor< T > > &a, const Base< Taylor< T > > &b)
template<typename T >
Taylor< T >	operator- (const typename Taylor< T >::value_type &a, const Base< Taylor< T > > &b)
template<typename T >
Taylor< T >	operator- (const Base< Taylor< T > > &a, const typename Taylor< T >::value_type &b)
template<typename T >
Taylor< T >	operator* (const Base< Taylor< T > > &a, const Base< Taylor< T > > &b)
template<typename T >
Taylor< T >	operator* (const typename Taylor< T >::value_type &a, const Base< Taylor< T > > &b)
template<typename T >
Taylor< T >	operator* (const Base< Taylor< T > > &a, const typename Taylor< T >::value_type &b)
template<typename T >
Taylor< T >	operator/ (const Base< Taylor< T > > &a, const Base< Taylor< T > > &b)
template<typename T >
Taylor< T >	operator/ (const typename Taylor< T >::value_type &a, const Base< Taylor< T > > &b)
template<typename T >
Taylor< T >	operator/ (const Base< Taylor< T > > &a, const typename Taylor< T >::value_type &b)
template<typename T >
void	sincos (const Base< Taylor< T > > &a, Taylor< T > &s, Taylor< T > &c)
template<typename T >
void	sinhcosh (const Base< Taylor< T > > &a, Taylor< T > &s, Taylor< T > &c)
template<typename T >
Taylor< T >	quad (const typename Taylor< T >::value_type &c0, const Base< Taylor< T > > &a, const Base< Taylor< T > > &b)
template<typename T >
bool	operator== (const Base< Taylor< T > > &a, const Base< Taylor< T > > &b)
template<typename T >
bool	operator== (const typename Taylor< T >::value_type &a, const Base< Taylor< T > > &b)
template<typename T >
bool	operator== (const Base< Taylor< T > > &a, const typename Taylor< T >::value_type &b)
template<typename T >
bool	operator!= (const Base< Taylor< T > > &a, const Base< Taylor< T > > &b)
template<typename T >
bool	operator!= (const typename Taylor< T >::value_type &a, const Base< Taylor< T > > &b)
template<typename T >
bool	operator!= (const Base< Taylor< T > > &a, const typename Taylor< T >::value_type &b)
template<typename T >
bool	operator<= (const Base< Taylor< T > > &a, const Base< Taylor< T > > &b)
template<typename T >
bool	operator<= (const typename Taylor< T >::value_type &a, const Base< Taylor< T > > &b)
template<typename T >
bool	operator<= (const Base< Taylor< T > > &a, const typename Taylor< T >::value_type &b)
template<typename T >
bool	operator>= (const Base< Taylor< T > > &a, const Base< Taylor< T > > &b)
template<typename T >
bool	operator>= (const typename Taylor< T >::value_type &a, const Base< Taylor< T > > &b)
template<typename T >
bool	operator>= (const Base< Taylor< T > > &a, const typename Taylor< T >::value_type &b)
template<typename T >
bool	operator< (const Base< Taylor< T > > &a, const Base< Taylor< T > > &b)
template<typename T >
bool	operator< (const typename Taylor< T >::value_type &a, const Base< Taylor< T > > &b)
template<typename T >
bool	operator< (const Base< Taylor< T > > &a, const typename Taylor< T >::value_type &b)
template<typename T >
bool	operator> (const Base< Taylor< T > > &a, const Base< Taylor< T > > &b)
template<typename T >
bool	operator> (const typename Taylor< T >::value_type &a, const Base< Taylor< T > > &b)
template<typename T >
bool	operator> (const Base< Taylor< T > > &a, const typename Taylor< T >::value_type &b)
template<typename T >
std::ostream &	operator<< (std::ostream &os, const Base< Taylor< T > > &a)
template<typename T >
bool	toBool (const Taylor< T > &x)
template<typename T >
bool	operator&& (const Base< Taylor< T > > &xx1, const Base< Taylor< T > > &xx2)
template<typename T >
bool	operator&& (const typename Taylor< T >::value_type &a, const Base< Taylor< T > > &xx2)
template<typename T >
bool	operator&& (const Base< Taylor< T > > &xx1, const typename Taylor< T >::value_type &b)
template<typename T >
bool	operator|| (const Base< Taylor< T > > &xx1, const Base< Taylor< T > > &xx2)
template<typename T >
bool	operator|| (const typename Taylor< T >::value_type &a, const Base< Taylor< T > > &xx2)
template<typename T >
bool	operator|| (const Base< Taylor< T > > &xx1, const typename Taylor< T >::value_type &b)

Detailed Description

Namespace for Taylor polynomial AD classes.