DACE Namespace Reference

Data Structures
class	AlgebraicMatrix
class	AlgebraicVector
class	compiledDA
class	DA
class	DACEException
class	DAFormatter
struct	DASimpleFormat
class	DASimpleFormatter
class	Interval
class	Monomial
class	PromotionTrait
class	PromotionTrait< T, T >
class	storedDA

Typedefs
typedef AlgebraicMatrix< DA >	matrixDA
	Short for AlgebraicMatrix<DA> More...
typedef AlgebraicMatrix< double >	matrixdb
	Short for AlgebraicMatrix<double> More...
typedef AlgebraicVector< DA >	vectorDA
	Shorthand notation for AlgebraicVector<DA>. More...
typedef AlgebraicVector< double >	vectordb
	Shorthand notation for AlgebraicVector<double>. More...

Functions
template<>
std::ostream &	operator<< (std::ostream &out, const AlgebraicMatrix< DA > &obj)
	DA specialization of output stream operator. More...
template<>
std::istream &	operator>> (std::istream &in, AlgebraicMatrix< DA > &obj)
	DA specialization of input stream operator. More...
template<>
std::vector< std::vector< double > >	linear (const AlgebraicVector< DA > &obj)
template<>
AlgebraicVector< DA >	trim (const AlgebraicVector< DA > &obj, unsigned int min, unsigned int max)
template<>
AlgebraicVector< DA >	deriv (const AlgebraicVector< DA > &obj, const unsigned int p)
template<>
AlgebraicVector< DA >	integ (const AlgebraicVector< DA > &obj, const unsigned int p)
template<>
compiledDA	compile (const AlgebraicVector< DA > &obj)
template<>
AlgebraicVector< DA >	plug (const AlgebraicVector< DA > &obj, const unsigned int var, const double val)
DA	operator+ (const DA &da1, const DA &da2)
DA	operator+ (const DA &da, const double c)
DA	operator+ (const double c, const DA &da)
DA	operator- (const DA &da1, const DA &da2)
DA	operator- (const DA &da, const double c)
DA	operator- (const double c, const DA &da)
DA	operator* (const DA &da1, const DA &da2)
DA	operator* (const DA &da, const double c)
DA	operator* (const double c, const DA &da)
DA	operator/ (const DA &da1, const DA &da2)
DA	operator/ (const DA &da, const double c)
DA	operator/ (const double c, const DA &da)
std::ostream &	operator<< (std::ostream &out, const DA &da)
std::istream &	operator>> (std::istream &in, DA &da)
int	isnan (const DA &da)
int	isinf (const DA &da)
double	cons (const DA &da)
AlgebraicVector< double >	linear (const DA &da)
AlgebraicVector< DA >	gradient (const DA &da)
DA	divide (const DA &da, const unsigned int var, const unsigned int p)
DA	deriv (const DA &da, const unsigned int i)
DA	deriv (const DA &da, const std::vector< unsigned int > ind)
DA	integ (const DA &da, const unsigned int i)
DA	integ (const DA &da, const std::vector< unsigned int > ind)
DA	trim (const DA &da, const unsigned int min, const unsigned int max)
DA	trunc (const DA &da)
DA	round (const DA &da)
DA	mod (const DA &da, double p)
DA	pow (const DA &da, int p)
DA	pow (const DA &da, double p)
DA	root (const DA &da, int p)
DA	minv (const DA &da)
DA	sqr (const DA &da)
DA	sqrt (const DA &da)
DA	isrt (const DA &da)
DA	cbrt (const DA &da)
DA	icrt (const DA &da)
DA	hypot (const DA &da1, const DA &da2)
DA	exp (const DA &da)
DA	log (const DA &da)
DA	logb (const DA &da, const double b)
DA	log10 (const DA &da)
DA	log2 (const DA &da)
DA	sin (const DA &da)
DA	cos (const DA &da)
DA	tan (const DA &da)
DA	asin (const DA &da)
DA	acos (const DA &da)
DA	atan (const DA &da)
DA	atan2 (const DA &da1, const DA &da2)
DA	sinh (const DA &da)
DA	cosh (const DA &da)
DA	tanh (const DA &da)
DA	asinh (const DA &da)
DA	acosh (const DA &da)
DA	atanh (const DA &da)
DA	erf (const DA &da)
DA	erfc (const DA &da)
DA	jn (const int n, const DA &da)
DA	yn (const int n, const DA &da)
DA	BesselJFunction (const int n, const DA &da)
DA	BesselYFunction (const int n, const DA &da)
DA	BesselIFunction (const int n, const DA &da, const bool scaled)
DA	BesselKFunction (const int n, const DA &da, const bool scaled)
DA	tgamma (const DA &da)
DA	lgamma (const DA &da)
DA	GammaFunction (const DA &da)
DA	LogGammaFunction (const DA &da)
DA	PsiFunction (const unsigned int n, const DA &da)
unsigned int	size (const DA &da)
double	abs (const DA &da)
double	norm (const DA &da, unsigned int type)
std::vector< double >	orderNorm (const DA &da, const unsigned int var, const unsigned int type)
std::vector< double >	estimNorm (const DA &da, const unsigned int var, const unsigned int type, const unsigned int nc)
std::vector< double >	estimNorm (const DA &da, std::vector< double > &err, const unsigned int var, const unsigned int type, const unsigned int nc)
Interval	bound (const DA &da)
double	convRadius (const DA &da, const double eps, const unsigned int type)
DA	plug (const DA &da, const unsigned int var, const double val)
DA	replaceVariable (const DA &da, const unsigned int from, const unsigned int to, const double val)
DA	scaleVariable (const DA &da, const unsigned int var, const double val)
DA	translateVariable (const DA &da, const unsigned int var, const double a, const double c)
compiledDA	compile (const DA &da)
std::string	toString (const DA &da)
void	write (const DA &da, std::ostream &os)
std::ostream &	operator<< (std::ostream &out, const storedDA &sda)
std::ostream &	operator<< (std::ostream &out, const DACEException &ex)
template<typename U >
std::ostream &	operator<< (std::ostream &out, const AlgebraicMatrix< U > &obj)
	Overload output stream operator. More...
template<>
DACE_API std::ostream &	operator<< (std::ostream &out, const AlgebraicMatrix< DA > &obj)
	DA specialization of output stream operator. More...
template<typename U >
std::istream &	operator>> (std::istream &in, AlgebraicMatrix< U > &obj)
	Overload input stream operator. More...
template<>
DACE_API std::istream &	operator>> (std::istream &in, AlgebraicMatrix< DA > &obj)
	DA specialization of input stream operator. More...
template<typename U , typename V >
AlgebraicMatrix< typename PromotionTrait< U, V >::returnType >	operator+ (const AlgebraicMatrix< U > &obj1, const AlgebraicMatrix< V > &obj2)
template<typename U , typename V >
AlgebraicMatrix< typename PromotionTrait< U, V >::returnType >	operator+ (const AlgebraicMatrix< U > &obj1, const V &obj2)
template<typename U , typename V >
AlgebraicMatrix< typename PromotionTrait< U, V >::returnType >	operator+ (const U &obj1, const AlgebraicMatrix< V > &obj2)
template<typename U , typename V >
AlgebraicMatrix< typename PromotionTrait< U, V >::returnType >	operator- (const AlgebraicMatrix< U > &obj1, const AlgebraicMatrix< V > &obj2)
template<typename U , typename V >
AlgebraicMatrix< typename PromotionTrait< U, V >::returnType >	operator- (const AlgebraicMatrix< U > &obj1, const V &obj2)
template<typename U , typename V >
AlgebraicMatrix< typename PromotionTrait< U, V >::returnType >	operator- (const U &obj1, const AlgebraicMatrix< V > &obj2)
template<typename U , typename V >
AlgebraicMatrix< typename PromotionTrait< U, V >::returnType >	operator* (const AlgebraicMatrix< U > &obj1, const AlgebraicMatrix< V > &obj2)
template<typename U , typename V >
AlgebraicMatrix< typename PromotionTrait< U, V >::returnType >	operator* (const AlgebraicMatrix< U > &obj1, const V &obj2)
template<typename U , typename V >
AlgebraicMatrix< typename PromotionTrait< U, V >::returnType >	operator* (const U &obj1, const AlgebraicMatrix< V > &obj2)
template<typename U , typename V >
AlgebraicVector< typename PromotionTrait< U, V >::returnType >	operator* (const AlgebraicVector< U > &obj1, const AlgebraicMatrix< V > &obj2)
template<typename U , typename V >
AlgebraicVector< typename PromotionTrait< U, V >::returnType >	operator* (const AlgebraicMatrix< U > &obj1, const AlgebraicVector< V > &obj2)
template<class T >
AlgebraicMatrix< T >	transpose (const AlgebraicMatrix< T > &obj)
template<class T >
T	det (const AlgebraicMatrix< T > &obj)
template<class T >
AlgebraicMatrix< T >	inv (const AlgebraicMatrix< T > &obj)
template<class T >
AlgebraicMatrix< double >	cons (const AlgebraicMatrix< T > &obj)
template<typename U , typename V >
AlgebraicVector< typename PromotionTrait< U, V >::returnType >	operator+ (const AlgebraicVector< U > &obj1, const AlgebraicVector< V > &obj2)
template<typename U , typename V >
AlgebraicVector< typename PromotionTrait< U, V >::returnType >	operator+ (const AlgebraicVector< U > &obj1, const V &obj2)
template<typename U , typename V >
AlgebraicVector< typename PromotionTrait< U, V >::returnType >	operator+ (const U &obj1, const AlgebraicVector< V > &obj2)
template<typename U , typename V >
AlgebraicVector< typename PromotionTrait< U, V >::returnType >	operator- (const AlgebraicVector< U > &obj1, const AlgebraicVector< V > &obj2)
template<typename U , typename V >
AlgebraicVector< typename PromotionTrait< U, V >::returnType >	operator- (const AlgebraicVector< U > &obj1, const V &obj2)
template<typename U , typename V >
AlgebraicVector< typename PromotionTrait< U, V >::returnType >	operator- (const U &obj1, const AlgebraicVector< V > &obj2)
template<typename U , typename V >
AlgebraicVector< typename PromotionTrait< U, V >::returnType >	operator* (const AlgebraicVector< U > &obj1, const AlgebraicVector< V > &obj2)
template<typename U , typename V >
AlgebraicVector< typename PromotionTrait< U, V >::returnType >	operator* (const AlgebraicVector< U > &obj1, const V &obj2)
template<typename U , typename V >
AlgebraicVector< typename PromotionTrait< U, V >::returnType >	operator* (const U &obj1, const AlgebraicVector< V > &obj2)
template<typename U , typename V >
AlgebraicVector< typename PromotionTrait< U, V >::returnType >	operator/ (const AlgebraicVector< U > &obj1, const AlgebraicVector< V > &obj2)
template<typename U , typename V >
AlgebraicVector< typename PromotionTrait< U, V >::returnType >	operator/ (const AlgebraicVector< U > &obj1, const V &obj2)
template<typename U , typename V >
AlgebraicVector< typename PromotionTrait< U, V >::returnType >	operator/ (const U &obj1, const AlgebraicVector< V > &obj2)
template<typename U >
std::ostream &	operator<< (std::ostream &out, const AlgebraicVector< U > &obj)
	Overload output stream operator. More...
template<typename U >
std::istream &	operator>> (std::istream &in, AlgebraicVector< U > &obj)
	Overload input stream operator. More...
template<typename T >
AlgebraicVector< double >	cons (const AlgebraicVector< T > &obj)
template<typename T >
std::vector< std::vector< double > >	linear (const AlgebraicVector< T > &obj)
template<typename T >
AlgebraicVector< T >	deriv (const AlgebraicVector< T > &obj, const unsigned int p)
template<typename T >
AlgebraicVector< T >	integ (const AlgebraicVector< T > &obj, const unsigned int p)
template<typename T >
AlgebraicVector< T >	pow (const AlgebraicVector< T > &obj, const int p)
template<typename T >
AlgebraicVector< T >	root (const AlgebraicVector< T > &obj, const int p=2)
template<typename T >
AlgebraicVector< T >	minv (const AlgebraicVector< T > &obj)
template<typename T >
AlgebraicVector< T >	sqr (const AlgebraicVector< T > &obj)
template<typename T >
AlgebraicVector< T >	sqrt (const AlgebraicVector< T > &obj)
template<typename T >
AlgebraicVector< T >	isrt (const AlgebraicVector< T > &obj)
template<typename T >
AlgebraicVector< T >	exp (const AlgebraicVector< T > &obj)
template<typename T >
AlgebraicVector< T >	log (const AlgebraicVector< T > &obj)
template<typename T >
AlgebraicVector< T >	logb (const AlgebraicVector< T > &obj, const double b=10.0)
template<typename T >
AlgebraicVector< T >	sin (const AlgebraicVector< T > &obj)
template<typename T >
AlgebraicVector< T >	cos (const AlgebraicVector< T > &obj)
template<typename T >
AlgebraicVector< T >	tan (const AlgebraicVector< T > &obj)
template<typename T >
AlgebraicVector< T >	asin (const AlgebraicVector< T > &obj)
template<typename T >
AlgebraicVector< T >	acos (const AlgebraicVector< T > &obj)
template<typename T >
AlgebraicVector< T >	atan (const AlgebraicVector< T > &obj)
template<typename T >
AlgebraicVector< T >	atan2 (const AlgebraicVector< T > &obj1, const AlgebraicVector< T > &obj2)
template<typename T >
AlgebraicVector< T >	sinh (const AlgebraicVector< T > &obj)
template<typename T >
AlgebraicVector< T >	cosh (const AlgebraicVector< T > &obj)
template<typename T >
AlgebraicVector< T >	tanh (const AlgebraicVector< T > &obj)
template<typename T >
AlgebraicVector< T >	asinh (const AlgebraicVector< T > &obj)
template<typename T >
AlgebraicVector< T >	acosh (const AlgebraicVector< T > &obj)
template<typename T >
AlgebraicVector< T >	atanh (const AlgebraicVector< T > &obj)
template<typename U , typename V >
PromotionTrait< U, V >::returnType	dot (const AlgebraicVector< U > &obj1, const AlgebraicVector< V > &obj2)
template<typename U , typename V >
AlgebraicVector< typename PromotionTrait< U, V >::returnType >	cross (const AlgebraicVector< U > &obj1, const AlgebraicVector< V > &obj2)
template<typename T >
T	vnorm (const AlgebraicVector< T > &obj)
template<typename T >
AlgebraicVector< T >	normalize (const AlgebraicVector< T > &obj)
template<typename T >
AlgebraicVector< T >	trim (const AlgebraicVector< T > &obj, unsigned int min, unsigned int max=DA::getMaxOrder())
template<typename T , typename V >
V	eval (const AlgebraicVector< T > &obj, const V &args)
template<typename T , typename U >
AlgebraicVector< U >	eval (const AlgebraicVector< T > &obj, const std::initializer_list< U > l)
template<typename T , typename U >
AlgebraicVector< U >	evalScalar (const AlgebraicVector< T > &obj, const U &arg)
template<typename T >
compiledDA	compile (const AlgebraicVector< T > &obj)
template<typename T >
AlgebraicVector< T >	plug (const AlgebraicVector< T > &obj, const unsigned int var, const double val=0.0)
template<>
DACE_API std::vector< std::vector< double > >	linear (const AlgebraicVector< DA > &obj)
template<>
DACE_API AlgebraicVector< DA >	trim (const AlgebraicVector< DA > &obj, unsigned int min, unsigned int max)
template<>
DACE_API AlgebraicVector< DA >	deriv (const AlgebraicVector< DA > &obj, const unsigned int p)
template<>
DACE_API AlgebraicVector< DA >	integ (const AlgebraicVector< DA > &obj, const unsigned int p)
template<>
DACE_API compiledDA	compile (const AlgebraicVector< DA > &obj)
template<>
DACE_API AlgebraicVector< DA >	plug (const AlgebraicVector< DA > &obj, const unsigned int var, const double val)
template<typename V >
V	eval (const AlgebraicVector< DA > &obj, const V &args)
template<typename T >
AlgebraicVector< T >	eval (const AlgebraicVector< DA > &obj, const std::initializer_list< T > l)
template<typename U >
AlgebraicVector< U >	evalScalar (const AlgebraicVector< DA > &obj, const U &arg)
template<class T >
T	eval (const DA &da, const std::vector< T > &args)
template<class T >
T	eval (const DA &da, const T args[], const unsigned int length)
template<class T >
T	evalScalar (const DA &da, const T &arg)
DACE_API double	cons (const double x)
	Constant part (i.e. the value x) More...
DACE_API double	logb (const double x, const double b=10.0)
	Logarithm relative to base b. More...
DACE_API double	isrt (const double x)
	Inverse square root. More...
DACE_API double	sqr (const double x)
	Square. More...
DACE_API double	minv (const double x)
	Multiplicative inverse. More...
DACE_API double	root (const double x, const int p=2)
	p-th root More...
DACE_API std::ostream &	operator<< (std::ostream &out, const Monomial &m)

Typedef Documentation

matrixDA

typedef AlgebraicMatrix<DA> DACE::matrixDA

Short for AlgebraicMatrix<DA>

matrixdb

typedef AlgebraicMatrix<double> DACE::matrixdb

Short for AlgebraicMatrix<double>

vectorDA

typedef AlgebraicVector<DA> DACE::vectorDA

Shorthand notation for AlgebraicVector<DA>.

vectordb

typedef AlgebraicVector<double> DACE::vectordb

Shorthand notation for AlgebraicVector<double>.

Function Documentation

abs()

DACE_API double DACE::abs

(

const DA &

da

)

Compute the max norm of a DA object.

Parameters

[in]

da

a given DA object.

Returns

A double corresponding to the result of the operation.

Exceptions

DACE::DACEException

See also

DA::abs

acos() [1/2]

template<typename T >

AlgebraicVector< T > DACE::acos

(

const AlgebraicVector< T > &

obj

)

Compute the arccosine of a AlgebraicVector<T>. The result is copied in a new AlgebraicVector<T>.

Parameters

[in]

obj

AlgebraicVector<T>.

Returns

A new AlgebraicVector<T> containing the result of the operation.

See also

AlgebraicVector<T>::acos

Compute the arccosine of a AlgebraicVector<T>. The result is copied in a new AlgebraicVector<T>.

Parameters

[in]

obj

AlgebraicVector<T>.

Returns

A new AlgebraicVector<T> containing the result of the operation.

See also

AlgebraicVector<T>::acos

acos() [2/2]

DACE_API DA DACE::acos

(

const DA &

da

)

Compute the arccosine of a DA object. The result is copied in a new DA object.

Parameters

[in]

da

a given DA object.

Returns

A new DA object containing the result of the operation.

Exceptions

DACE::DACEException

See also

DA::acos

acosh() [1/2]

template<typename T >

AlgebraicVector< T > DACE::acosh

(

const AlgebraicVector< T > &

obj

)

Compute the hyperbolic arccosine of a AlgebraicVector<T>. The result is copied in a new AlgebraicVector<T>.

Parameters

[in]

obj

AlgebraicVector<T>.

Returns

A new AlgebraicVector<T> containing the result of the operation.

See also

AlgebraicVector<T>::acosh

Compute the hyperbolic arccosine of a AlgebraicVector<T>. The result is copied in a new AlgebraicVector<T>.

Parameters

[in]

obj

AlgebraicVector<T>.

Returns

A new AlgebraicVector<T> containing the result of the operation.

See also

AlgebraicVector<T>::acosh

acosh() [2/2]

DACE_API DA DACE::acosh

(

const DA &

da

)

Compute the hyperbolic arccosine of a DA object. The result is copied in a new DA object.

Parameters

[in]

da

a given DA object.

Returns

A new DA object containing the result of the operation.

Exceptions

DACE::DACEException

See also

DA::acosh

asin() [1/2]

template<typename T >

AlgebraicVector< T > DACE::asin

(

const AlgebraicVector< T > &

obj

)

Compute the arcsine of a AlgebraicVector<T>. The result is copied in a new AlgebraicVector<T>.

Parameters

[in]

obj

AlgebraicVector<T>.

Returns

A new AlgebraicVector<T> containing the result of the operation.

See also

AlgebraicVector<T>::asin

Compute the arcsine of a AlgebraicVector<T>. The result is copied in a new AlgebraicVector<T>.

Parameters

[in]

obj

AlgebraicVector<T>.

Returns

A new AlgebraicVector<T> containing the result of the operation.

See also

AlgebraicVector<T>::asin

asin() [2/2]

DACE_API DA DACE::asin

(

const DA &

da

)

Compute the arcsine of a DA object. The result is copied in a new DA object.

Parameters

[in]

da

a given DA object.

Returns

A new DA object containing the result of the operation.

Exceptions

DACE::DACEException

See also

DA::asin

asinh() [1/2]

template<typename T >

AlgebraicVector< T > DACE::asinh

(

const AlgebraicVector< T > &

obj

)

Compute the hyperbolic arcsine of a AlgebraicVector<T>. The result is copied in a new AlgebraicVector<T>.

Parameters

[in]

obj

AlgebraicVector<T>.

Returns

A new AlgebraicVector<T> containing the result of the operation.

See also

AlgebraicVector<T>::asinh

Compute the hyperbolic arcsine of a AlgebraicVector<T>. The result is copied in a new AlgebraicVector<T>.

Parameters

[in]

obj

AlgebraicVector<T>.

Returns

A new AlgebraicVector<T> containing the result of the operation.

See also

AlgebraicVector<T>::asinh

asinh() [2/2]

DACE_API DA DACE::asinh

(

const DA &

da

)

Compute the hyperbolic arcsine of a DA object. The result is copied in a new DA object.

Parameters

[in]

da

a given DA object.

Returns

A new DA object containing the result of the operation.

Exceptions

DACE::DACEException

See also

DA::asinh

atan() [1/2]

template<typename T >

AlgebraicVector< T > DACE::atan

(

const AlgebraicVector< T > &

obj

)

Compute the arctangent of a AlgebraicVector<T>. The result is copied in a new AlgebraicVector<T>.

Parameters

[in]

obj

AlgebraicVector<T>.

Returns

A new AlgebraicVector<T> containing the result of the operation.

See also

AlgebraicVector<T>::atan

Compute the arctangent of a AlgebraicVector<T>. The result is copied in a new AlgebraicVector<T>.

Parameters

[in]

obj

AlgebraicVector<T>.

Returns

A new AlgebraicVector<T> containing the result of the operation.

See also

AlgebraicVector<T>::atan

atan() [2/2]

DACE_API DA DACE::atan

(

const DA &

da

)

Compute the arctangent of a DA object. The result is copied in a new DA object.

Parameters

[in]

da

a given DA object.

Returns

A new DA object containing the result of the operation.

Exceptions

DACE::DACEException

See also

DA::atan

atan2() [1/2]

template<typename T >

AlgebraicVector< T > DACE::atan2	(	const AlgebraicVector< T > &	obj1,
		const AlgebraicVector< T > &	obj2
	)

Compute the four-quadrant tangent of obj1/obj2. The result is copied in a new AlgebraicVector<T>.

Parameters

[in]	obj1	AlgebraicVector<T>.
[in]	obj2	AlgebraicVector<T>.

Returns

A new AlgebraicVector<T> containing the result of the operation in [-pi, pi].

See also

AlgebraicVector<T>::atan2

Compute the four-quadrant tangent of obj1/obj2. The result is copied in a new AlgebraicVector<T>.

Parameters

[in]	obj1	AlgebraicVector<T>.
[in]	obj2	AlgebraicVector<T>.

Returns

A new AlgebraicVector<T> containing the result of the operation in [-pi, pi].

See also

AlgebraicVector<T>::atan2

atan2() [2/2]

DACE_API DA DACE::atan2	(	const DA &	da1,
		const DA &	da2
	)

Compute the four-quadrant arctangent of da1/da2. The result is copied in a new DA object.

Parameters

[in]	da1	DA object
[in]	da2	DA object

Returns

A new DA object containing the result of the operation in [-pi, pi].

Exceptions

DACE::DACEException

See also

DA::atan2

atanh() [1/2]

template<typename T >

AlgebraicVector< T > DACE::atanh

(

const AlgebraicVector< T > &

obj

)

Compute the hyperbolic arctangent of a AlgebraicVector<T>. The result is copied in a new AlgebraicVector<T>.

Parameters

[in]

obj

AlgebraicVector<T>.

Returns

A new AlgebraicVector<T> containing the result of the operation.

See also

AlgebraicVector<T>::atanh

Compute the hyperbolic arctangent of a AlgebraicVector<T>. The result is copied in a new AlgebraicVector<T>.

Parameters

[in]

obj

AlgebraicVector<T>.

Returns

A new AlgebraicVector<T> containing the result of the operation.

See also

AlgebraicVector<T>::atanh

atanh() [2/2]

DACE_API DA DACE::atanh

(

const DA &

da

)

Compute the hyperbolic arctangent of a DA object. The result is copied in a new DA object.

Parameters

[in]

da

a given DA object.

Returns

A new DA object containing the result of the operation.

Exceptions

DACE::DACEException

See also

DA::atanh

BesselIFunction()

DACE_API DA DACE::BesselIFunction	(	const int	n,
		const DA &	da,
		const bool	scaled
	)

Compute the n-th modified Bessel function of first type I_n of a DA object. The result is copied in a new DA object.

Parameters

[in]	n	order of the Bessel function
[in]	da	a given DA object.
[in]	scaled	if true, the modified Bessel function is scaled by a factor exp(-x), i.e. exp(-x)I_n(x) is returned.

Returns

A new DA object containing the result of the operation.

Exceptions

DACE::DACEException

Note

The DA must have non-negative constant part while the order is allowed to be negative.

See also

DA::BesselIFunction

BesselJFunction()

DACE_API DA DACE::BesselJFunction	(	const int	n,
		const DA &	da
	)

Compute the n-th Bessel function of first type J_n of a DA object. The result is copied in a new DA object.

Parameters

[in]	n	order of the Bessel function
[in]	da	a given DA object.

Returns

A new DA object containing the result of the operation.

Exceptions

DACE::DACEException

Note

The DA must have non-negative constant part while the order is allowed to be negative.

See also

DA::BesselJFunction

BesselKFunction()

DACE_API DA DACE::BesselKFunction	(	const int	n,
		const DA &	da,
		const bool	scaled
	)

Compute the n-th modified Bessel function of second type K_n of a DA object. The result is copied in a new DA object.

Parameters

[in]	n	order of the Bessel function
[in]	da	a given DA object.
[in]	scaled	if true, the modified Bessel function is scaled by a factor exp(-x), i.e. exp(-x)K_n(x) is returned.

Returns

A new DA object containing the result of the operation.

Exceptions

DACE::DACEException

Note

The DA must have non-negative constant part while the order is allowed to be negative.

See also

DA::BesselKFunction

BesselYFunction()

DACE_API DA DACE::BesselYFunction	(	const int	n,
		const DA &	da
	)

Compute the n-th Bessel function of second type Y_n of a DA object. The result is copied in a new DA object.

Parameters

[in]	n	order of the Bessel function
[in]	da	a given DA object.

Returns

A new DA object containing the result of the operation.

Exceptions

DACE::DACEException

Note

The DA must have non-negative constant part while the order is allowed to be negative.

See also

DA::BesselYFunction

bound()

DACE_API Interval DACE::bound

(

const DA &

da

)

Compute lower and upper bounds of a DA object.

Parameters

[in]

da

a given DA object.

Returns

An Interval object containing both the lower and the upper bound of the DA object.

Exceptions

DACE::DACEException

See also

DA::bound

cbrt()

DACE_API DA DACE::cbrt

(

const DA &

da

)

Compute the cubic root of a DA object. The result is copied in a new DA object.

Parameters

[in]

da

a given DA object.

Returns

A new DA object containing the result of the operation.

Exceptions

DACE::DACEException

See also

DA::cbrt

compile() [1/4]

template<typename T >

compiledDA DACE::compile

(

const AlgebraicVector< T > &

obj

)

compile() [2/4]

template<>

DACE_API compiledDA DACE::compile

(

const AlgebraicVector< DA > &

obj

)

Compile vector of polynomials and create a compiledDA object.

Parameters

[in]

obj

The AlgebraicVector to compile.

Returns

The compiled DA object.

Note

This DA specific function is only available in AlgebraicVector<DA>. When called on AlgebraicVectors of other types (e.g. double), a compiler error will be the result.

compile() [3/4]

template<>

compiledDA DACE::compile

(

const AlgebraicVector< DA > &

obj

)

Compile vector of polynomials and create a compiledDA object.

Parameters

[in]

obj

The AlgebraicVector to compile.

Returns

The compiled DA object.

Note

This DA specific function is only available in AlgebraicVector<DA>. When called on AlgebraicVectors of other types (e.g. double), a compiler error will be the result.

compile() [4/4]

DACE_API compiledDA DACE::compile

(

const DA &

da

)

Compile a given DA object and create a compiledDA object.

Returns

A compiled DA object.

Exceptions

DACE::DACEException

See also

DA::compile

cons() [1/4]

double DACE::cons

(

const double

x

)

Constant part (i.e. the value x)

Constant part. For double type this is just x.

Parameters

[in]

x

Function argument.

Constant part. For double type this is just x.

Parameters

[in]

x

Function argument.

cons() [2/4]

template<class T >

AlgebraicMatrix< double > DACE::cons

(

const AlgebraicMatrix< T > &

obj

)

Extract the constant part of a AlgebraicMatrix The result is copied in a new AlgebraicMatrix.

Parameters

[in]

obj

An AlgebraicMatrix

Returns

A new AlgebraicMatrix that contains the constant part of the original.

See also

AlgebraicMatrix<T>::cons

Extract the constant part of a AlgebraicMatrix The result is copied in a new AlgebraicMatrix.

Parameters

[in]

obj

An AlgebraicMatrix

Returns

A new AlgebraicMatrix that contains the constant part of the original.

See also

AlgebraicMatrix<T>::cons

cons() [3/4]

template<typename T >

AlgebraicVector< double > DACE::cons

(

const AlgebraicVector< T > &

obj

)

Return the constant part of a AlgebraicVector<T>.

Returns

An AlgebraicVector<double>.

See also

AlgebraicVector<T>::cons

Return the constant part of a AlgebraicVector<T>.

Returns

An AlgebraicVector<double>.

See also

AlgebraicVector<T>::cons

cons() [4/4]

DACE_API double DACE::cons

(

const DA &

da

)

Return the constant part of a DA object.

Parameters

[in]

da

a given DA object.

Returns

A double corresponding to the constant part of the DA object.

Exceptions

DACE::DACEException

convRadius()

DACE_API double DACE::convRadius	(	const DA &	da,
		const double	eps,
		const unsigned int	type
	)

Estimate the convergence radius of the given DA.

Parameters

[in]	da	the given DA object.
[in]	eps	requested tolerance.
[in]	type	type of norm (sum norm is used as default)

Returns

A double corresponding to the estimated convergence radius.

Exceptions

DACE::DACEException

See also

DA::conv_radius

cos() [1/2]

template<typename T >

AlgebraicVector< T > DACE::cos

(

const AlgebraicVector< T > &

obj

)

Compute the cosine of a AlgebraicVector<T>. The result is copied in a new AlgebraicVector<T>.

Parameters

[in]

obj

AlgebraicVector<T>.

Returns

A new AlgebraicVector<T> containing the result of the operation.

See also

AlgebraicVector<T>::cos

Compute the cosine of a AlgebraicVector<T>. The result is copied in a new AlgebraicVector<T>.

Parameters

[in]

obj

AlgebraicVector<T>.

Returns

A new AlgebraicVector<T> containing the result of the operation.

See also

AlgebraicVector<T>::cos

cos() [2/2]

DACE_API DA DACE::cos

(

const DA &

da

)

Compute the cosine of a DA object. The result is copied in a new DA object.

Parameters

[in]

da

a given DA object.

Returns

A new DA object containing the result of the operation.

Exceptions

DACE::DACEException

See also

DA::cos

cosh() [1/2]

template<typename T >

AlgebraicVector< T > DACE::cosh

(

const AlgebraicVector< T > &

obj

)

Compute the hyperbolic cosine of a AlgebraicVector<T>. The result is copied in a new AlgebraicVector<T>.

Parameters

[in]

obj

AlgebraicVector<T>.

Returns

A new AlgebraicVector<T> containing the result of the operation.

See also

AlgebraicVector<T>::cosh

Compute the hyperbolic cosine of a AlgebraicVector<T>. The result is copied in a new AlgebraicVector<T>.

Parameters

[in]

obj

AlgebraicVector<T>.

Returns

A new AlgebraicVector<T> containing the result of the operation.

See also

AlgebraicVector<T>::cosh

cosh() [2/2]

DACE_API DA DACE::cosh

(

const DA &

da

)

Compute the hyperbolic cosine of a DA object. The result is copied in a new DA object.

Parameters

[in]

da

a given DA object.

Returns

A new DA object containing the result of the operation.

Exceptions

DACE::DACEException

See also

DA::cosh

cross()

template<typename U , typename V >

AlgebraicVector< typename PromotionTrait< U, V >::returnType > DACE::cross	(	const AlgebraicVector< U > &	obj1,
		const AlgebraicVector< V > &	obj2
	)

Compute the cross product between two 3D AlgebraicVectors.

Parameters

[in]	obj1	a AlgebraicVector.
[in]	obj2	a AlgebraicVector.

Returns

A new AlgebraicVector, containing the result of the operation.

Compute the cross product between two 3D AlgebraicVectors.

Parameters

[in]	obj1	a AlgebraicVector.
[in]	obj2	a AlgebraicVector.

Returns

A new AlgebraicVector, containing the result of the operation.

deriv() [1/5]

template<typename T >

AlgebraicVector<T> DACE::deriv	(	const AlgebraicVector< T > &	obj,
		const unsigned int	p
	)

deriv() [2/5]

template<>

DACE_API AlgebraicVector<DA> DACE::deriv	(	const AlgebraicVector< DA > &	obj,
		const unsigned int	p
	)

Compute the derivative of a AlgebraicVector<T> with respect to variable p. The result is copied in a new AlgebraicVector<T>.

Parameters

[in]	obj	AlgebraicVector<T>.
[in]	p	variable with respect to which the derivative is calculated.

Returns

A new AlgebraicVector<T> containing the result of the derivation.

Note

This DA specific function is only available in AlgebraicVector<DA>. When called on AlgebraicVectors of other types (e.g. double), a compiler error will be the result.

See also

AlgebraicVector<T>::deriv

deriv() [3/5]

template<>

AlgebraicVector<DA> DACE::deriv	(	const AlgebraicVector< DA > &	obj,
		const unsigned int	p
	)

Compute the derivative of a AlgebraicVector<T> with respect to variable p. The result is copied in a new AlgebraicVector<T>.

Parameters

[in]	obj	AlgebraicVector<T>.
[in]	p	variable with respect to which the derivative is calculated.

Returns

A new AlgebraicVector<T> containing the result of the derivation.

Note

This DA specific function is only available in AlgebraicVector<DA>. When called on AlgebraicVectors of other types (e.g. double), a compiler error will be the result.

See also

AlgebraicVector<T>::deriv

deriv() [4/5]

DACE_API DA DACE::deriv	(	const DA &	da,
		const unsigned int	i
	)

Compute the derivative of a DA object with respect to variable i. The result is copied in a new DA object.

Parameters

[in]	da	DA object.
[in]	i	variable with respect to which the derivative is calculated.

Returns

A new DA object containing the result of the derivation.

Exceptions

DACE::DACEException

See also

DA::deriv

deriv() [5/5]

DACE_API DA DACE::deriv	(	const DA &	da,
		const std::vector< unsigned int >	ind
	)

Compute the derivative of a DA object with respect to variables ind. The result is copied in a new DA object.

Parameters

[in]	da	DA object.
[in]	ind	vector containing the number of derivatives to take for each independent variable. If ind has fewer entries than there are independent variables, the missing entries are assumed to be zero. If ind has more entries than there are independent variables, extra values are ignored.

Returns

A new DA object containing the result of the derivation.

Exceptions

DACE::DACEException

See also

DA::deriv

det()

template<class T >

T DACE::det

(

const AlgebraicMatrix< T > &

obj

)

Compute the determinant of an AlgebraicMatrix.

Parameters

[in]

obj

An AlgebraicMatrix

Returns

A variable that is the determinant of the AlgebraiMatrix.

See also

AlgebraicMatrix<T>::det

Compute the determinant of an AlgebraicMatrix.

Parameters

[in]

obj

An AlgebraicMatrix

Returns

A variable that is the determinant of the AlgebraiMatrix.

See also

AlgebraicMatrix<T>::det

divide()

DACE_API DA DACE::divide	(	const DA &	da,
		const unsigned int	var,
		const unsigned int	p
	)

Divide by independent variable var raised to power p. The result is copied in a new DA object.

Parameters

[in]	da	DA object.
[in]	var	variable number to divide by.
[in]	p	power of variable var to divide by.

Returns

A new DA object containing the result of the division.

Exceptions

DACE::DACEException

See also

DA::divide

dot()

template<typename U , typename V >

PromotionTrait< U, V >::returnType DACE::dot	(	const AlgebraicVector< U > &	obj1,
		const AlgebraicVector< V > &	obj2
	)

Compute the dot product between two AlgebraicVectors.

Parameters

[in]	obj1	a AlgebraicVector.
[in]	obj2	a AlgebraicVector.

Returns

A scalar value, containing the result of the operation.

Compute the dot product between two AlgebraicVectors.

Parameters

[in]	obj1	a AlgebraicVector.
[in]	obj2	a AlgebraicVector.

Returns

A scalar value, containing the result of the operation.

erf()

DACE_API DA DACE::erf

(

const DA &

da

)

Compute the error function of a DA object. The result is copied in a new DA object.

Parameters

[in]

da

a given DA object.

Returns

A new DA object containing the result of the operation.

Exceptions

DACE::DACEException

See also

DA::erf

erfc()

DACE_API DA DACE::erfc

(

const DA &

da

)

Compute the complementary error function of a DA object. The result is copied in a new DA object.

Parameters

[in]

da

a given DA object.

Returns

A new DA object containing the result of the operation.

Exceptions

DACE::DACEException

See also

DA::erfc

estimNorm() [1/2]

DACE_API std::vector< double > DACE::estimNorm	(	const DA &	da,
		const unsigned int	var,
		const unsigned int	type,
		const unsigned int	nc
	)

Estimate different types of order sorted norms for terms of a DA object up to a specified order.

Parameters

[in]	da	a given DA object.
[in]	var	order 0: Terms are sorted by their order (Default) >0: Terms are sorted by the exponent of variable var
[in]	type	type of norm to be computed. Possible norms are: 0: Max norm (Default) 1: Sum norm >1: Vector norm of given type
[in]	nc	maximum order (Default order = Max order)

Returns

A double corresponding to the result of the operation.

Exceptions

DACE::DACEException

Note

If estimation is not possible, zero is returned for all requested orders.

See also

DA::estim

estimNorm() [2/2]

DACE_API std::vector< double > DACE::estimNorm	(	const DA &	da,
		std::vector< double > &	err,
		const unsigned int	var,
		const unsigned int	type,
		const unsigned int	nc
	)

Estimate different types of order sorted norms for terms of a DA object up to a specified order with error estimates.

Parameters

[in]	da	a given DA object.
[out]	err	returns the amount by which the estimate underestimates the actual ordered norm of the terms in the polynomial up to the minimum of nc or the maximum computation order.
[in]	var	order 0: Terms are sorted by their order (Default) >0: Terms are sorted by the exponent of variable var
[in]	type	type of norm to be computed. Possible norms are: 0: Max norm (Default) 1: Sum norm >1: Vector norm of given type
[in]	nc	maximum order (Default order = Max order)

Returns

A double corresponding to the result of the operation.

Exceptions

DACE::DACEException

Note

If estimation is not possible, zero is returned for all requested orders.

See also

DA::estim

eval() [1/6]

template<typename T , typename V >

V DACE::eval	(	const AlgebraicVector< T > &	obj,
		const V &	args
	)

eval() [2/6]

template<typename T , typename U >

AlgebraicVector<U> DACE::eval	(	const AlgebraicVector< T > &	obj,
		const std::initializer_list< U >	l
	)

eval() [3/6]

template<class T >

T DACE::eval	(	const DA &	da,
		const std::vector< T > &	args
	)

Generic evaluation of the DA with a vector of arithmetic type T arguments.

Parameters

[in]	da	a given DA object.
[in]	args	std::vector<T> of arithmetic type T with which the DA vector is evaluated.

Returns

The result of the evaluation.

Exceptions

DACE::DACEException

Note

To be used only for single polynomial evaluation. For multiple evaluations of the same polynomial use the corresponding method in class compiledDA.

This function can be called with a braced initializer list. However, C++ is not able to derive the type of elements of an initializer list automatically. That means eval() must be called explicitly as e.g. eval<double>(x, {1.0, 2.0, 3.0}) when used with initializer lists.

See also

compiledDA

Generic evaluation of the DA with a vector of arithmetic type T arguments.

Parameters

[in]	da	a given DA object.
[in]	args	std::vector<T> of arithmetic type T with which the DA vector is evaluated.

Returns

The result of the evaluation.

Exceptions

DACE::DACEException

Note

To be used only for single polynomial evaluation. For multiple evaluations of the same polynomial use the corresponding method in class compiledDA.

This function can be called with a braced initializer list. However, C++ is not able to derive the type of elements of an initializer list automatically. That means eval() must be called explicitly as e.g. eval<double>(x, {1.0, 2.0, 3.0}) when used with initializer lists.

See also

compiledDA

eval() [4/6]

template<class T >

T DACE::eval	(	const DA &	da,
		const T	args[],
		const unsigned int	length
	)

Generic evaluation of the DA with an array of arithmetic type T arguments.

Parameters

[in]	da	a given DA object.
[in]	args	array of arithmetic type T with which the DA vector is evaluated.
[in]	length	number of elements in the array args.

Returns

The result of the evaluation.

Exceptions

DACE::DACEException

Note

To be used only for single polynomial evaluation. For multiple evaluations of the same polynomial use the corresponding method in class compiledDA.

See also

compiledDA::eval

Generic evaluation of the DA with an array of arithmetic type T arguments.

Parameters

[in]	da	a given DA object.
[in]	args	array of arithmetic type T with which the DA vector is evaluated.
[in]	length	number of elements in the array args.

Returns

The result of the evaluation.

Exceptions

DACE::DACEException

Note

To be used only for single polynomial evaluation. For multiple evaluations of the same polynomial use the corresponding method in class compiledDA.

See also

compiledDA::eval

eval() [5/6]

template<typename V >

V DACE::eval	(	const AlgebraicVector< DA > &	obj,
		const V &	args
	)

Evaluate an AlgebraicVector<DA> with a vector type V of arguments and return a vector of type V with the results.

Parameters

[in]	obj	An AlgebraicVector<DA>.
[in]	args	Vector type V containing the arguments.

Returns

A new vector of type V containing the results of the evaluation process.

See also

AlgebraicVector<T>::eval()

eval() [6/6]

template<typename T >

AlgebraicVector<T> DACE::eval	(	const AlgebraicVector< DA > &	obj,
		const std::initializer_list< T >	l
	)

Evaluate an AlgebraicVector<DA> with an braced initializer list of type T and return an AlgebraicVector of type T with the results.

Parameters

[in]	obj	An AlgebraicVector<DA>.
[in]	l	Braced initializer list containing the arguments.

Returns

A new AlgebraicVector of type T containing the results of the evaluation.

Note

C++ is not able to derive the type of elements of an initializer list automatically. That means eval() must be called explicitly as e.g. eval<double>(x, {1.0, 2.0, 3.0}) when used with initializer lists.

See also

AlgebraicVector<T>::eval()

evalScalar() [1/3]

template<typename T , typename U >

AlgebraicVector<U> DACE::evalScalar	(	const AlgebraicVector< T > &	obj,
		const U &	arg
	)

evalScalar() [2/3]

template<class T >

T DACE::evalScalar	(	const DA &	da,
		const T &	arg
	)

Generic evaluation of the DA with a single arithmetic type T arguments.

Parameters

[in]	da	a given DA object.
[in]	arg	single variable of arithmetic type T of the first independent DA variable.

Returns

The result of the evaluation.

Exceptions

DACE::DACEException

Note

To be used only for single polynomial evaluation. For multiple evaluations of the same polynomial use the corresponding method in class compiledDA.

See also

compiledDA::evalScalar

Generic evaluation of the DA with a single arithmetic type T arguments.

Parameters

[in]	da	a given DA object.
[in]	arg	single variable of arithmetic type T of the first independent DA variable.

Returns

The result of the evaluation.

Exceptions

DACE::DACEException

Note

To be used only for single polynomial evaluation. For multiple evaluations of the same polynomial use the corresponding method in class compiledDA.

See also

compiledDA::evalScalar

evalScalar() [3/3]

template<typename U >

AlgebraicVector<U> DACE::evalScalar	(	const AlgebraicVector< DA > &	obj,
		const U &	arg
	)

Evaluate an AlgebraicVector<DA> with a single scalar argument of type U and return an AlgebraicVector<U> containing the results.

Parameters

[in]	obj	The AlgebraicVector<T> to evaluate.
[in]	arg	The argument of type U.

Returns

A new AlgebraicVector<U> containing the results of the evaluation process.

See also

AlgebraicVector<T>::evalScalar()

exp() [1/2]

template<typename T >

AlgebraicVector< T > DACE::exp

(

const AlgebraicVector< T > &

obj

)

Compute the exponential of a AlgebraicVector<T>. The result is copied in a new AlgebraicVector<T>.

Parameters

[in]

obj

AlgebraicVector<T>.

Returns

A new AlgebraicVector<T> containing the result of the operation.

See also

AlgebraicVector<T>::exp

Compute the exponential of a AlgebraicVector<T>. The result is copied in a new AlgebraicVector<T>.

Parameters

[in]

obj

AlgebraicVector<T>.

Returns

A new AlgebraicVector<T> containing the result of the operation.

See also

AlgebraicVector<T>::exp

exp() [2/2]

DACE_API DA DACE::exp

(

const DA &

da

)

Compute the exponential of a DA object. The result is copied in a new DA object.

Parameters

[in]

da

a given DA object.

Returns

A new DA object containing the result of the operation.

Exceptions

DACE::DACEException

See also

DA::exp

GammaFunction()

DACE_API DA DACE::GammaFunction

(

const DA &

da

)

Compute the Gamma function of a DA object. The result is copied in a new DA object.

Parameters

[in]

da

a given DA object.

Returns

A new DA object containing the result of the operation.

Exceptions

DACE::DACEException

See also

DA::GammaFunction

gradient()

DACE_API AlgebraicVector< DA > DACE::gradient

(

const DA &

da

)

Compute the gradient of a DA object.

Parameters

[in]

da

the given DA object.

Returns

A AlgebraicVector<DA> containing the derivatives of the DA object with respect to all independent DA variables.

Exceptions

DACE::DACEException

hypot()

DACE_API DA DACE::hypot	(	const DA &	da1,
		const DA &	da2
	)

Compute the hypotenuse (sqrt(da1*da1 + da2*da2)) of two DA objects. The result is copied in a new DA object.

Parameters

[in]	da1	first DA object.
[in]	da2	second DA object.

Returns

A new DA object containing the result of the operation.

Exceptions

DACE::DACEException

See also

DA::hypot

icrt()

DACE_API DA DACE::icrt

(

const DA &

da

)

Compute the inverse cubic root of a DA object. The result is copied in a new DA object.

Parameters

[in]

da

a given DA object.

Returns

A new DA object containing the result of the operation.

Exceptions

DACE::DACEException

See also

DA::icrt

integ() [1/5]

template<typename T >

AlgebraicVector<T> DACE::integ	(	const AlgebraicVector< T > &	obj,
		const unsigned int	p
	)

integ() [2/5]

template<>

DACE_API AlgebraicVector<DA> DACE::integ	(	const AlgebraicVector< DA > &	obj,
		const unsigned int	p
	)

Compute the integral of a AlgebraicVector<T> with respect to variable p. The result is copied in a new AlgebraicVector<T>.

Parameters

[in]	obj	AlgebraicVector<T>.
[in]	p	variable with respect to which the integral is calculated.

Returns

A new AlgebraicVector<T> containing the result of the integration.

Note

This DA specific function is only available in AlgebraicVector<DA>. When called on AlgebraicVectors of other types (e.g. double), a compiler error will be the result.

See also

AlgebraicVector<T>::integ

integ() [3/5]

template<>

AlgebraicVector<DA> DACE::integ	(	const AlgebraicVector< DA > &	obj,
		const unsigned int	p
	)

Compute the integral of a AlgebraicVector<T> with respect to variable p. The result is copied in a new AlgebraicVector<T>.

Parameters

[in]	obj	AlgebraicVector<T>.
[in]	p	variable with respect to which the integral is calculated.

Returns

A new AlgebraicVector<T> containing the result of the integration.

Note

This DA specific function is only available in AlgebraicVector<DA>. When called on AlgebraicVectors of other types (e.g. double), a compiler error will be the result.

See also

AlgebraicVector<T>::integ

integ() [4/5]

DACE_API DA DACE::integ	(	const DA &	da,
		const unsigned int	i
	)

Compute the integral of a DA object with respect to variable i. The result is copied in a new DA object.

Parameters

[in]	da	DA object.
[in]	i	variable with respect to which the integral is calculated.

Returns

A new DA object containing the result of the integration.

Exceptions

DACE::DACEException

See also

DA::integ

integ() [5/5]

DACE_API DA DACE::integ	(	const DA &	da,
		const std::vector< unsigned int >	ind
	)

Compute the integral of a DA object with respect to variable i. The result is copied in a new DA object.

Parameters

[in]	da	DA object.
[in]	ind	vector containing the number of derivatives to take for each independent variable. If ind has fewer entries than there are independent variables, the missing entries are assumed to be zero. If ind has more entries than there are independent variables, extra values are ignored.

Returns

A new DA object containing the result of the integration.

Exceptions

DACE::DACEException

See also

DA::integ

inv()

template<class T >

AlgebraicMatrix< T > DACE::inv

(

const AlgebraicMatrix< T > &

obj

)

Compute the inverse of an AlgebraicMatrix.

Parameters

[in]

obj

An AlgebraicMatrix

Returns

An AlgebraicMatrix that is the inverse of the original AlgebraicMatrix.

See also

AlgebraicMatrix<T>::inverse

Compute the inverse of an AlgebraicMatrix.

Parameters

[in]

obj

An AlgebraicMatrix

Returns

An AlgebraicMatrix that is the inverse of the original AlgebraicMatrix.

See also

AlgebraicMatrix<T>::inverse

isinf()

DACE_API int DACE::isinf

(

const DA &

da

)

Check if a DA object has any INF coefficients.

Parameters

[in]

da

a given DA object.

Returns

True if any coefficients of the DA object are INF.

Exceptions

DACE::DACEException

isnan()

DACE_API int DACE::isnan

(

const DA &

da

)

Check if a DA object has any NAN coefficients.

Parameters

[in]

da

a given DA object.

Returns

True if any coefficients of the DA object are NAN.

Exceptions

DACE::DACEException

isrt() [1/3]

double DACE::isrt

(

const double

x

)

Inverse square root.

Inverse square root 1/sqrt(x).

Parameters

[in]

x

Function argument.

Inverse square root 1/sqrt(x).

Parameters

[in]

x

Function argument.

isrt() [2/3]

template<typename T >

AlgebraicVector< T > DACE::isrt

(

const AlgebraicVector< T > &

obj

)

Compute the inverse square root of a AlgebraicVector<T>. The result is copied in a new AlgebraicVector<T>.

Parameters

[in]

obj

AlgebraicVector<T>.

Returns

A new AlgebraicVector<T> containing the result of the operation.

See also

AlgebraicVector<T>::isrt

Compute the inverse square root of a AlgebraicVector<T>. The result is copied in a new AlgebraicVector<T>.

Parameters

[in]

obj

AlgebraicVector<T>.

Returns

A new AlgebraicVector<T> containing the result of the operation.

See also

AlgebraicVector<T>::isrt

isrt() [3/3]

DACE_API DA DACE::isrt

(

const DA &

da

)

Compute the inverse square root of a DA object. The result is copied in a new DA object.

Parameters

[in]

da

a given DA object.

Returns

A new DA object containing the result of the operation.

Exceptions

DACE::DACEException

See also

DA::isrt

jn()

DACE_API DA DACE::jn	(	const int	n,
		const DA &	da
	)

Compute the n-th Bessel function of first type J_n of a DA object. The result is copied in a new DA object.

Parameters

[in]	n	order of the Bessel function.
[in]	da	a given DA object.

Returns

A new DA object containing the result of the operation.

Exceptions

DACE::DACEException

Note

The DA must have non-negative constant part while the order is allowed to be negative.

Alias of BesselJFunction for C compatible naming.

See also

DA::BesselJFunction

lgamma()

DACE_API DA DACE::lgamma

(

const DA &

da

)

Compute the Log Gamma function of a DA object. The result is copied in a new DA object.

Parameters

[in]

da

a given DA object.

Returns

A new DA object containing the result of the operation.

Exceptions

DACE::DACEException

See also

DA::LogGammaFunction

Note

Alias of LogGammaFunction() for C99 compatible naming.

linear() [1/4]

template<typename T >

std::vector< std::vector<double> > DACE::linear

(

const AlgebraicVector< T > &

obj

)

linear() [2/4]

template<>

DACE_API std::vector< std::vector<double> > DACE::linear

(

const AlgebraicVector< DA > &

obj

)

Return the linear part of a AlgebraicVector<T>. Only defined for AlgebraicVector<DA>.

Parameters

[in]

obj

AlgebraicVector<T> to extract linear part from

Returns

A std::vector< std::vector<double> > containing the linear parts of each component of the AlgebraicVector<DA> obj.

Note

This DA specific function is only available in AlgebraicVector<DA>. When called on AlgebraicVectors of other types (e.g. double), a compiler error will be the result.

See also

AlgebraicVector<T>::linear

linear() [3/4]

template<>

std::vector< std::vector<double> > DACE::linear

(

const AlgebraicVector< DA > &

obj

)

Return the linear part of a AlgebraicVector<T>. Only defined for AlgebraicVector<DA>.

Parameters

[in]

obj

AlgebraicVector<T> to extract linear part from

Returns

A std::vector< std::vector<double> > containing the linear parts of each component of the AlgebraicVector<DA> obj.

Note

This DA specific function is only available in AlgebraicVector<DA>. When called on AlgebraicVectors of other types (e.g. double), a compiler error will be the result.

See also

AlgebraicVector<T>::linear

linear() [4/4]

DACE_API AlgebraicVector< double > DACE::linear

(

const DA &

da

)

Return the linear part of a DA object.

Parameters

[in]

da

a given DA object.

Returns

An AlgebraicVector<dobule> containing the linear coefficients of each independent DA variable in the given DA object.

Exceptions

DACE::DACEException

log() [1/2]

template<typename T >

AlgebraicVector< T > DACE::log

(

const AlgebraicVector< T > &

obj

)

Compute the natural logarithm of a AlgebraicVector<T>. The result is copied in a new AlgebraicVector<T>.

Parameters

[in]

obj

AlgebraicVector<T>.

Returns

A new AlgebraicVector<T> containing the result of the operation.

See also

AlgebraicVector<T>::log

Compute the natural logarithm of a AlgebraicVector<T>. The result is copied in a new AlgebraicVector<T>.

Parameters

[in]

obj

AlgebraicVector<T>.

Returns

A new AlgebraicVector<T> containing the result of the operation.

See also

AlgebraicVector<T>::log

log() [2/2]

DACE_API DA DACE::log

(

const DA &

da

)

Compute the natural logarithm of a DA object. The result is copied in a new DA object.

Parameters

[in]

da

a given DA object.

Returns

A new DA object containing the result of the operation.

Exceptions

DACE::DACEException

See also

DA::log

log10()

DACE_API DA DACE::log10

(

const DA &

da

)

Compute the 10 based logarithm of a DA object. The result is copied in a new DA object.

Parameters

[in]

da

a given DA object.

Returns

A new DA object containing the result of the operation.

Exceptions

DACE::DACEException

See also

DA::log10

log2()

DACE_API DA DACE::log2

(

const DA &

da

)

Compute the 2 based logarithm of a DA object. The result is copied in a new DA object.

Parameters

[in]

da

a given DA object.

Returns

A new DA object containing the result of the operation.

Exceptions

DACE::DACEException

See also

DA::log2

logb() [1/3]

double DACE::logb	(	const double	x,
		const double	b = 10.0
	)

Logarithm relative to base b.

Logarithm relative to base b.

Parameters

[in]	x	Function argument.
[in]	b	Base of the logarithm (must be positive).

Logarithm relative to base b.

Parameters

[in]	x	Function argument.
[in]	b	Base of the logarithm (must be positive).

logb() [2/3]

template<typename T >

AlgebraicVector< T > DACE::logb	(	const AlgebraicVector< T > &	obj,
		const double	b = 10.0
	)

Compute the logarithm of a AlgebraicVector<T> with respect to a given base. The result is copied in a new AlgebraicVector<T>.

Parameters

[in]	obj	AlgebraicVector<T>.
[in]	b	base with respect to which the logarithm is computed (default = 10).

Returns

A new AlgebraicVector<T> containing the result of the operation.

See also

AlgebraicVector<T>::logb

Compute the logarithm of a AlgebraicVector<T> with respect to a given base. The result is copied in a new AlgebraicVector<T>.

Parameters

[in]	obj	AlgebraicVector<T>.
[in]	b	base with respect to which the logarithm is computed (default = 10).

Returns

A new AlgebraicVector<T> containing the result of the operation.

See also

AlgebraicVector<T>::logb

logb() [3/3]

DACE_API DA DACE::logb	(	const DA &	da,
		const double	b
	)

Compute the logarithm of a DA object with respect to a given base. The result is copied in a new DA object.

Parameters

[in]	da	a given DA object.
[in]	b	base with respect to which the logarithm is computed (base 10 set as default base).

Returns

A new DA object containing the result of the operation.

Exceptions

DACE::DACEException

See also

DA::logb

LogGammaFunction()

DACE_API DA DACE::LogGammaFunction

(

const DA &

da

)

Compute the Log Gamma function of a DA object. The result is copied in a new DA object.

Parameters

[in]

da

a given DA object.

Returns

A new DA object containing the result of the operation.

Exceptions

DACE::DACEException

See also

DA::LogGammaFunction

minv() [1/3]

double DACE::minv

(

const double

x

)

Multiplicative inverse.

Multiplicative inverse 1/x.

Parameters

[in]

x

Function argument.

Multiplicative inverse 1/x.

Parameters

[in]

x

Function argument.

minv() [2/3]

template<typename T >

AlgebraicVector< T > DACE::minv

(

const AlgebraicVector< T > &

obj

)

Compute the multiplicative inverse of a AlgebraicVector<T>. The result is copied in a new AlgebraicVector<T>.

Parameters

[in]

obj

AlgebraicVector<T>.

Returns

A new AlgebraicVector<T> containing the result of the operation.

See also

AlgebraicVector<T>::minv

Compute the multiplicative inverse of a AlgebraicVector<T>. The result is copied in a new AlgebraicVector<T>.

Parameters

[in]

obj

AlgebraicVector<T>.

Returns

A new AlgebraicVector<T> containing the result of the operation.

See also

AlgebraicVector<T>::minv

minv() [3/3]

DACE_API DA DACE::minv

(

const DA &

da

)

Compute the multiplicative inverse of a DA object. The result is copied in a new DA object.

Parameters

[in]

da

a given DA object.

Returns

A new DA object containing the result of the operation.

Exceptions

DACE::DACEException

See also

DA::minv

mod()

DACE_API DA DACE::mod	(	const DA &	da,
		double	p
	)

Compute the floating-point remainder of c/p (c modulo p), where c is the constant part of the given DA object. The result is copied in a new DA object.

Parameters

[in]	da	a given DA object.
[in]	p	costant with respect to which the modulo function is computed.

Returns

A new DA object containing the result of the operation.

Exceptions

DACE::DACEException

See also

DA::mod

norm()

DACE_API double DACE::norm	(	const DA &	da,
		unsigned int	type
	)

Compute different types of norms for a DA object.

Parameters

[in]	da	a given DA object.
[in]	type	type of norm to be computed. Possible norms are: 0: Max norm (Default) 1: Sum norm >1: Vector norm of given type

Returns

A double corresponding to the result of the operation.

Exceptions

DACE::DACEException

See also

DA::norm

normalize()

template<typename T >

AlgebraicVector< T > DACE::normalize

(

const AlgebraicVector< T > &

obj

)

Normalize an AlgebraicVector<T>.

Parameters

[in]

obj

An AlgebraicVector<T> to normalize.

Returns

An AlgebraicVector<T> of unit length.

See also

AlgebraicVector<T>::normalize

Normalize an AlgebraicVector<T>.

Parameters

[in]

obj

An AlgebraicVector<T> to normalize.

Returns

An AlgebraicVector<T> of unit length.

See also

AlgebraicVector<T>::normalize

operator*() [1/11]

template<typename U , typename V >

AlgebraicMatrix< typename PromotionTrait< U, V >::returnType > DACE::operator*	(	const AlgebraicMatrix< U > &	obj1,
		const AlgebraicMatrix< V > &	obj2
	)

Compute the multiplication between two AlgebraicMatrices.

Parameters

[in]	obj1	first AlgebraicMatrix \( (n \times m) \)
[in]	obj2	second AlgebraicMatrix \( (m \times p) \).

Returns

A new AlgebraicMatrix, of size \( (n \times p) \) containing the result of the operation (obj1*obj2).

See also

AlgebraicMatrix<T>::operator*

Compute the multiplication between two AlgebraicMatrices.

Parameters

[in]	obj1	first AlgebraicMatrix \( (n \times m) \)
[in]	obj2	second AlgebraicMatrix \( (m \times p) \).

Returns

A new AlgebraicMatrix, of size \( (n \times p) \) containing the result of the operation (obj1*obj2).

See also

AlgebraicMatrix<T>::operator*

operator*() [2/11]

template<typename U , typename V >

AlgebraicMatrix< typename PromotionTrait< U, V >::returnType > DACE::operator*	(	const AlgebraicMatrix< U > &	obj1,
		const V &	obj2
	)

Compute the multiplication between a AlgebraicMatrix and a scalar value.

Parameters

[in]	obj1	a AlgebraicMatrix.
[in]	obj2	a scalar value.

Returns

A new AlgebraicMatrix, containing the result of the operation (obj1*obj2).

See also

AlgebraicMatrix<T>::operator*

Compute the multiplication between a AlgebraicMatrix and a scalar value.

Parameters

[in]	obj1	a AlgebraicMatrix.
[in]	obj2	a scalar value.

Returns

A new AlgebraicMatrix, containing the result of the operation (obj1*obj2).

See also

AlgebraicMatrix<T>::operator*

operator*() [3/11]

template<typename U , typename V >

AlgebraicMatrix< typename PromotionTrait< U, V >::returnType > DACE::operator*	(	const U &	obj1,
		const AlgebraicMatrix< V > &	obj2
	)

Compute the multiplication between a scalar value and a AlgebraicMatrix.

Parameters

[in]	obj1	a scalar value.
[in]	obj2	a AlgebraicMatrix.

Returns

A new DAvector, containing the result of the operation (obj1*obj2).

See also

AlgebraicMatrix<T>::operator*

Compute the multiplication between a scalar value and a AlgebraicMatrix.

Parameters

[in]	obj1	a scalar value.
[in]	obj2	a AlgebraicMatrix.

Returns

A new DAvector, containing the result of the operation (obj1*obj2).

See also

AlgebraicMatrix<T>::operator*

operator*() [4/11]

template<typename U , typename V >

AlgebraicVector< typename PromotionTrait< U, V >::returnType > DACE::operator*	(	const AlgebraicVector< U > &	obj1,
		const AlgebraicMatrix< V > &	obj2
	)

Compute the multiplication between a AlgebraicVector (row) and a AlgebraicMatrix.

Parameters

[in]	obj1	a AlgebraicVector
[in]	obj2	a AlgebraicMatrix

Returns

A new AlgebraicVector, containing the result of the operation (obj1*obj2)

See also

AlgebraicMatrix<T>::operator*

Compute the multiplication between a AlgebraicVector (row) and a AlgebraicMatrix.

Parameters

[in]	obj1	a AlgebraicVector
[in]	obj2	a AlgebraicMatrix

Returns

A new AlgebraicVector, containing the result of the operation (obj1*obj2)

See also

AlgebraicMatrix<T>::operator*

operator*() [5/11]

template<typename U , typename V >

AlgebraicVector< typename PromotionTrait< U, V >::returnType > DACE::operator*	(	const AlgebraicMatrix< U > &	obj1,
		const AlgebraicVector< V > &	obj2
	)

Compute the multiplication between a AlgebraicMatrix and a AlgebraicVector (column) .

Parameters

[in]	obj1	a AlgebraicMatrix.
[in]	obj2	a AlgebraicVector.

Returns

A new AlgebraicVector, containing the result of the operation (obj1*obj2).

See also

AlgebraicMatrix<T>::operator*

Compute the multiplication between a AlgebraicMatrix and a AlgebraicVector (column) .

Parameters

[in]	obj1	a AlgebraicMatrix.
[in]	obj2	a AlgebraicVector.

Returns

A new AlgebraicVector, containing the result of the operation (obj1*obj2).

See also

AlgebraicMatrix<T>::operator*

operator*() [6/11]

template<typename U , typename V >

AlgebraicVector< typename PromotionTrait< U, V >::returnType > DACE::operator*	(	const AlgebraicVector< U > &	obj1,
		const AlgebraicVector< V > &	obj2
	)

Compute the element-wise multiplication between two AlgebraicVectors.

Parameters

[in]	obj1	first AlgebraicVector.
[in]	obj2	second AlgebraicVector.

Returns

A new AlgebraicVector, containing the result of the operation (obj1*obj2).

Exceptions

std::runtime_error

Compute the element-wise multiplication between two AlgebraicVectors.

Parameters

[in]	obj1	first AlgebraicVector.
[in]	obj2	second AlgebraicVector.

Returns

A new AlgebraicVector, containing the result of the operation (obj1*obj2).

Exceptions

std::runtime_error

operator*() [7/11]

template<typename U , typename V >

AlgebraicVector< typename PromotionTrait< U, V >::returnType > DACE::operator*	(	const AlgebraicVector< U > &	obj1,
		const V &	obj2
	)

Compute the multiplication between a AlgebraicVector and a scalar value.

Parameters

[in]	obj1	a AlgebraicVector.
[in]	obj2	a scalar value.

Returns

A new AlgebraicVector, containing the result of the operation (obj1*obj2).

Compute the multiplication between a AlgebraicVector and a scalar value.

Parameters

[in]	obj1	a AlgebraicVector.
[in]	obj2	a scalar value.

Returns

A new AlgebraicVector, containing the result of the operation (obj1*obj2).

operator*() [8/11]

template<typename U , typename V >

AlgebraicVector< typename PromotionTrait< U, V >::returnType > DACE::operator*	(	const U &	obj1,
		const AlgebraicVector< V > &	obj2
	)

Compute the multiplication between a scalar value and a AlgebraicVector.

Parameters

[in]	obj1	a scalar value.
[in]	obj2	a AlgebraicVector.

Returns

A new AlgebraicVector, containing the result of the operation (obj1*obj2).

Compute the multiplication between a scalar value and a AlgebraicVector.

Parameters

[in]	obj1	a scalar value.
[in]	obj2	a AlgebraicVector.

Returns

A new AlgebraicVector, containing the result of the operation (obj1*obj2).

operator*() [9/11]

DA DACE::operator*	(	const DA &	da1,
		const DA &	da2
	)

Compute the multiplication between two DA objects. The result is copied in a new DA object.

Parameters

[in]	da1	first DA object.
[in]	da2	second DA object.

Returns

A new DA object containing the result of the operation (da1*da2).

Exceptions

DACE::DACEException

operator*() [10/11]

DA DACE::operator*	(	const DA &	da,
		const double	c
	)

Compute the multiplication between a DA object and a given constant. The result is copied in a new DA object.

Parameters

[in]	da	DA object.
[in]	c	given constant.

Returns

A new DA object containing the result of the operation (da*c).

Exceptions

DACE::DACEException

operator*() [11/11]

DA DACE::operator*	(	const double	c,
		const DA &	da
	)

Compute the multiplication between a given constant and a DA object. The result is copied in a new DA object.

Parameters

[in]	c	given constant.
[in]	da	DA object.

Returns

A new DA object containing the result of the operation (c*da).

Exceptions

DACE::DACEException

operator+() [1/9]

template<typename U , typename V >

AlgebraicMatrix< typename PromotionTrait< U, V >::returnType > DACE::operator+	(	const AlgebraicMatrix< U > &	obj1,
		const AlgebraicMatrix< V > &	obj2
	)

Compute the addition between two AlgebraicMatrices.

Parameters

[in]	obj1	the first AlgebraicMatrix.
[in]	obj2	the second AlgebraicMatrix.

Returns

A new AlgebraicMatrix, containing the result of the operation (obj1+obj2).

See also

AlgebraicMatrix<T>::operator+

Compute the addition between two AlgebraicMatrices.

Parameters

[in]	obj1	the first AlgebraicMatrix.
[in]	obj2	the second AlgebraicMatrix.

Returns

A new AlgebraicMatrix, containing the result of the operation (obj1+obj2).

See also

AlgebraicMatrix<T>::operator+

operator+() [2/9]

template<typename U , typename V >

AlgebraicMatrix< typename PromotionTrait< U, V >::returnType > DACE::operator+	(	const AlgebraicMatrix< U > &	obj1,
		const V &	obj2
	)

Compute the addition between a AlgebraicMatrix and a scalar value.

Parameters

[in]	obj1	a AlgebraicMatrix.
[in]	obj2	a scalar value.

Returns

A new AlgebraicMatrix, containing the result of the operation (obj1+obj2).

See also

AlgebraicMatrix<T>::operator+

Compute the addition between a AlgebraicMatrix and a scalar value.

Parameters

[in]	obj1	a AlgebraicMatrix.
[in]	obj2	a scalar value.

Returns

A new AlgebraicMatrix, containing the result of the operation (obj1+obj2).

See also

AlgebraicMatrix<T>::operator+

operator+() [3/9]

template<typename U , typename V >

AlgebraicMatrix< typename PromotionTrait< U, V >::returnType > DACE::operator+	(	const U &	obj1,
		const AlgebraicMatrix< V > &	obj2
	)

Compute the addition between a scalar value and a AlgebraicMatrix.

Parameters

[in]	obj1	a scalar value.
[in]	obj2	a AlgebraicMatrix.

Returns

A new AlgebraicMatrix, containing the result of the operation (obj1+obj2).

See also

AlgebraicMatrix<T>::operator+

Compute the addition between a scalar value and a AlgebraicMatrix.

Parameters

[in]	obj1	a scalar value.
[in]	obj2	a AlgebraicMatrix.

Returns

A new AlgebraicMatrix, containing the result of the operation (obj1+obj2).

See also

AlgebraicMatrix<T>::operator+

operator+() [4/9]

template<typename U , typename V >

AlgebraicVector< typename PromotionTrait< U, V >::returnType > DACE::operator+	(	const AlgebraicVector< U > &	obj1,
		const AlgebraicVector< V > &	obj2
	)

Compute the addition between two AlgebraicVectors.

Parameters

[in]	obj1	first AlgebraicVector.
[in]	obj2	second AlgebraicVector.

Returns

A new AlgebraicVector, containing the result of the operation (obj1+obj2).

Exceptions

std::runtime_error

Compute the addition between two AlgebraicVectors.

Parameters

[in]	obj1	first AlgebraicVector.
[in]	obj2	second AlgebraicVector.

Returns

A new AlgebraicVector, containing the result of the operation (obj1+obj2).

Exceptions

std::runtime_error

operator+() [5/9]

template<typename U , typename V >

AlgebraicVector< typename PromotionTrait< U, V >::returnType > DACE::operator+	(	const AlgebraicVector< U > &	obj1,
		const V &	obj2
	)

Compute the addition between a AlgebraicVector and a scalar value.

Parameters

[in]	obj1	a AlgebraicVector.
[in]	obj2	a scalar value.

Returns

A new AlgebraicVector, containing the result of the operation (obj1+obj2).

Compute the addition between a AlgebraicVector and a scalar value.

Parameters

[in]	obj1	a AlgebraicVector.
[in]	obj2	a scalar value.

Returns

A new AlgebraicVector, containing the result of the operation (obj1+obj2).

operator+() [6/9]

template<typename U , typename V >

AlgebraicVector< typename PromotionTrait< U, V >::returnType > DACE::operator+	(	const U &	obj1,
		const AlgebraicVector< V > &	obj2
	)

Compute the addition between a scalar value and a AlgebraicVector.

Parameters

[in]	obj1	a scalar value.
[in]	obj2	a AlgebraicVector.

Returns

A new AlgebraicVector, containing the result of the operation (obj1+obj2).

Compute the addition between a scalar value and a AlgebraicVector.

Parameters

[in]	obj1	a scalar value.
[in]	obj2	a AlgebraicVector.

Returns

A new AlgebraicVector, containing the result of the operation (obj1+obj2).

operator+() [7/9]

DA DACE::operator+	(	const DA &	da1,
		const DA &	da2
	)

Compute the addition between two DA objects. The result is copied in a new DA object.

Parameters

[in]	da1	first DA object.
[in]	da2	second DA object.

Returns

A new DA object containing the result of the operation (da1+da2).

Exceptions

DACE::DACEException

operator+() [8/9]

DA DACE::operator+	(	const DA &	da,
		const double	c
	)

Compute the addition between a DA object and a given constant. The result is copied in a new DA object.

Parameters

[in]	da	DA object.
[in]	c	given constant.

Returns

A new DA object containing the result of the operation (da+c).

Exceptions

DACE::DACEException

operator+() [9/9]

DA DACE::operator+	(	const double	c,
		const DA &	da
	)

Compute the addition between a given constant and a DA object. The result is copied in a new DA object.

Parameters

[in]	c	given constant.
[in]	da	DA object.

Returns

A new DA object containing the result of the operation (c+da).

Exceptions

DACE::DACEException

operator-() [1/9]

template<typename U , typename V >

AlgebraicMatrix< typename PromotionTrait< U, V >::returnType > DACE::operator-	(	const AlgebraicMatrix< U > &	obj1,
		const AlgebraicMatrix< V > &	obj2
	)

Compute the subtraction between two AlgebraicMatrices.

Parameters

[in]	obj1	first AlgebraicMatrx.
[in]	obj2	second AlgebraicMatrix.

Returns

A new AlgebraicMatrix, containing the result of the operation (obj1-obj2).

See also

AlgebraicMatrix<T>::operator-

Compute the subtraction between two AlgebraicMatrices.

Parameters

[in]	obj1	first AlgebraicMatrx.
[in]	obj2	second AlgebraicMatrix.

Returns

A new AlgebraicMatrix, containing the result of the operation (obj1-obj2).

See also

AlgebraicMatrix<T>::operator-

operator-() [2/9]

template<typename U , typename V >

AlgebraicMatrix< typename PromotionTrait< U, V >::returnType > DACE::operator-	(	const AlgebraicMatrix< U > &	obj1,
		const V &	obj2
	)

Compute the subtraction between a AlgebraicMatrix and a scalar value.

Parameters

[in]	obj1	a AlgebraicMatrix.
[in]	obj2	a scalar value.

Returns

A new AlgebraicMatrix, containing the result of the operation (obj1-obj2).

See also

AlgebraicMatrix<T>::operator-

Compute the subtraction between a AlgebraicMatrix and a scalar value.

Parameters

[in]	obj1	a AlgebraicMatrix.
[in]	obj2	a scalar value.

Returns

A new AlgebraicMatrix, containing the result of the operation (obj1-obj2).

See also

AlgebraicMatrix<T>::operator-

operator-() [3/9]

template<typename U , typename V >

AlgebraicMatrix< typename PromotionTrait< U, V >::returnType > DACE::operator-	(	const U &	obj1,
		const AlgebraicMatrix< V > &	obj2
	)

Compute the subtraction between a scalar value and a AlgebraicMatrix.

Parameters

[in]	obj1	a scalar value.
[in]	obj2	a AlgebraicMatrix.

Returns

A new AlgebraicMatrix, containing the result of the operation (obj1-obj2).

See also

AlgebraicMatrix<T>::operator-

Compute the subtraction between a scalar value and a AlgebraicMatrix.

Parameters

[in]	obj1	a scalar value.
[in]	obj2	a AlgebraicMatrix.

Returns

A new AlgebraicMatrix, containing the result of the operation (obj1-obj2).

See also

AlgebraicMatrix<T>::operator-

operator-() [4/9]

template<typename U , typename V >

AlgebraicVector< typename PromotionTrait< U, V >::returnType > DACE::operator-	(	const AlgebraicVector< U > &	obj1,
		const AlgebraicVector< V > &	obj2
	)

Compute the subtraction between two AlgebraicVectors.

Parameters

[in]	obj1	first AlgebraicVector.
[in]	obj2	second AlgebraicVector.

Returns

A new AlgebraicVector, containing the result of the operation (obj1-obj2).

Exceptions

std::runtime_error

Compute the subtraction between two AlgebraicVectors.

Parameters

[in]	obj1	first AlgebraicVector.
[in]	obj2	second AlgebraicVector.

Returns

A new AlgebraicVector, containing the result of the operation (obj1-obj2).

Exceptions

std::runtime_error

operator-() [5/9]

template<typename U , typename V >

AlgebraicVector< typename PromotionTrait< U, V >::returnType > DACE::operator-	(	const AlgebraicVector< U > &	obj1,
		const V &	obj2
	)

Compute the subtraction between a AlgebraicVector and a scalar value.

Parameters

[in]	obj1	a AlgebraicVector.
[in]	obj2	a scalar value.

Returns

A new AlgebraicVector, containing the result of the operation (obj1-obj2).

Compute the subtraction between a AlgebraicVector and a scalar value.

Parameters

[in]	obj1	a AlgebraicVector.
[in]	obj2	a scalar value.

Returns

A new AlgebraicVector, containing the result of the operation (obj1-obj2).

operator-() [6/9]

template<typename U , typename V >

AlgebraicVector< typename PromotionTrait< U, V >::returnType > DACE::operator-	(	const U &	obj1,
		const AlgebraicVector< V > &	obj2
	)

Compute the subtraction between a scalar value and a AlgebraicVector.

Parameters

[in]	obj1	a scalar value.
[in]	obj2	a AlgebraicVector.

Returns

A new AlgebraicVector, containing the result of the operation (obj1-obj2).

Compute the subtraction between a scalar value and a AlgebraicVector.

Parameters

[in]	obj1	a scalar value.
[in]	obj2	a AlgebraicVector.

Returns

A new AlgebraicVector, containing the result of the operation (obj1-obj2).

operator-() [7/9]

DA DACE::operator-	(	const DA &	da1,
		const DA &	da2
	)

Compute the subtraction between two DA objects. The result is copied in a new DA object.

Parameters

[in]	da1	first DA object.
[in]	da2	second DA object.

Returns

A new DA object containing the result of the operation (da1-da2).

Exceptions

DACE::DACEException

operator-() [8/9]

DA DACE::operator-	(	const DA &	da,
		const double	c
	)

Compute the subtraction between a DA object and a given constant. The result is copied in a new DA object.

Parameters

[in]	da	DA object.
[in]	c	given constant.

Returns

A new DA object containing the result of the operation (da-c).

Exceptions

DACE::DACEException

operator-() [9/9]

DA DACE::operator-	(	const double	c,
		const DA &	da
	)

Compute the subtraction between a given constant and a DA object. The result is copied in a new DA object.

Parameters

[in]	c	given constant.
[in]	da	DA object.

Returns

A new DA object containing the result of the operation (c-da).

Exceptions

DACE::DACEException

operator/() [1/6]

template<typename U , typename V >

AlgebraicVector< typename PromotionTrait< U, V >::returnType > DACE::operator/	(	const AlgebraicVector< U > &	obj1,
		const AlgebraicVector< V > &	obj2
	)

Compute the element-wise division between two AlgebraicVectors.

Parameters

[in]	obj1	first AlgebraicVector.
[in]	obj2	second AlgebraicVector.

Returns

A new AlgebraicVector, containing the result of the operation (obj1/obj2).

Exceptions

std::runtime_error

Compute the element-wise division between two AlgebraicVectors.

Parameters

[in]	obj1	first AlgebraicVector.
[in]	obj2	second AlgebraicVector.

Returns

A new AlgebraicVector, containing the result of the operation (obj1/obj2).

Exceptions

std::runtime_error

operator/() [2/6]

template<typename U , typename V >

AlgebraicVector< typename PromotionTrait< U, V >::returnType > DACE::operator/	(	const AlgebraicVector< U > &	obj1,
		const V &	obj2
	)

Compute the division between a AlgebraicVector and a scalar value.

Parameters

[in]	obj1	a AlgebraicVector.
[in]	obj2	a scalar value.

Returns

A new AlgebraicVector, containing the result of the operation (obj1/obj2).

Compute the division between a AlgebraicVector and a scalar value.

Parameters

[in]	obj1	a AlgebraicVector.
[in]	obj2	a scalar value.

Returns

A new AlgebraicVector, containing the result of the operation (obj1/obj2).

operator/() [3/6]

template<typename U , typename V >

AlgebraicVector< typename PromotionTrait< U, V >::returnType > DACE::operator/	(	const U &	obj1,
		const AlgebraicVector< V > &	obj2
	)

Compute the division between a scalar value and a AlgebraicVector.

Parameters

[in]	obj1	a scalar value.
[in]	obj2	a AlgebraicVector.

Returns

A new AlgebraicVector, containing the result of the operation (obj1/obj2).

Compute the division between a scalar value and a AlgebraicVector.

Parameters

[in]	obj1	a scalar value.
[in]	obj2	a AlgebraicVector.

Returns

A new AlgebraicVector, containing the result of the operation (obj1/obj2).

operator/() [4/6]

DA DACE::operator/	(	const DA &	da1,
		const DA &	da2
	)

Compute the division between two DA objects. The result is copied in a new DA object.

Parameters

[in]	da1	first DA object.
[in]	da2	second DA object.

Returns

A new DA object containing the result of the operation (da1/da2).

Exceptions

DACE::DACEException

operator/() [5/6]

DA DACE::operator/	(	const DA &	da,
		const double	c
	)

Compute the division between a DA object and a given constant. The result is copied in a new DA object.

Parameters

[in]	da	DA object.
[in]	c	given constant.

Returns

A new DA object containing the result of the operation (da/c).

Exceptions

DACE::DACEException

operator/() [6/6]

DA DACE::operator/	(	const double	c,
		const DA &	da
	)

Compute the division between a given constant and a DA object. The result is copied in a new DA object.

Parameters

[in]	c	given constant.
[in]	da	DA object.

Returns

A new DA object containing the result of the operation (c/da).

Exceptions

DACE::DACEException

operator<<() [1/8]

template<>

std::ostream& DACE::operator<<	(	std::ostream &	out,
		const AlgebraicMatrix< DA > &	obj
	)

DA specialization of output stream operator.

Specialized stream output operator for DA matrices.

Parameters

[in]	out	Standard output stream.
[in]	obj	AlgebraicMatrix<DA> to be printed in the stream

Returns

Reference to the standard output stream.

operator<<() [2/8]

std::ostream & DACE::operator<<	(	std::ostream &	out,
		const Monomial &	m
	)

Overload output stream operator.

Overload of std::operator<< in iostream.

Parameters

[in]	out	standard output stream.
[in]	m	Monomial vector to be printed in the stream

Returns

The output stream out.

Overload of std::operator<< in iostream.

Parameters

[in]	out	standard output stream.
[in]	m	Monomial vector to be printed in the stream

Returns

The output stream out.

operator<<() [3/8]

template<typename U >

std::ostream & DACE::operator<<	(	std::ostream &	out,
		const AlgebraicMatrix< U > &	obj
	)

Overload output stream operator.

Overload of std::operator<< in iostream.

Parameters

[in]	out	standard output stream.
[in]	obj	AlgebraicMatrix<U> to be printed in the stream

Returns

Standard output stream.

Overload of std::operator<< in iostream.

Parameters

[in]	out	standard output stream.
[in]	obj	AlgebraicMatrix<U> to be printed in the stream

Returns

Standard output stream.

operator<<() [4/8]

template<>

DACE_API std::ostream& DACE::operator<<	(	std::ostream &	out,
		const AlgebraicMatrix< DA > &	obj
	)

DA specialization of output stream operator.

Specialized stream output operator for DA matrices.

Parameters

[in]	out	Standard output stream.
[in]	obj	AlgebraicMatrix<DA> to be printed in the stream

Returns

Reference to the standard output stream.

operator<<() [5/8]

template<typename U >

std::ostream & DACE::operator<<	(	std::ostream &	out,
		const AlgebraicVector< U > &	obj
	)

Overload output stream operator.

Output a vector to a C++ output stream.

Parameters

[in]	out	standard output stream.
[in]	obj	AlgebraicVector<U> to be written to the stream

Returns

Reference to output stream out.

Output a vector to a C++ output stream.

Parameters

[in]	out	standard output stream.
[in]	obj	AlgebraicVector<U> to be written to the stream

Returns

Reference to output stream out.

operator<<() [6/8]

std::ostream& DACE::operator<<	(	std::ostream &	out,
		const DACEException &	ex
	)

Overload of std::operator<< in iostream.

Parameters

[in]	out	standard output stream.
[in]	ex	Exception to be printed in the stream

Returns

Output stream out.

operator<<() [7/8]

std::ostream& DACE::operator<<	(	std::ostream &	out,
		const DA &	da
	)

Overload of std::operator<< in iostream.

Parameters

[in]	out	standard output stream.
[in]	da	DA object to be printed in the stream

Returns

Standard output stream.

Exceptions

DACE::DACEException

See also

DA::toString

operator<<() [8/8]

std::ostream& DACE::operator<<	(	std::ostream &	out,
		const storedDA &	sda
	)

operator>>() [1/5]

template<>

std::istream& DACE::operator>>	(	std::istream &	in,
		AlgebraicMatrix< DA > &	obj
	)

DA specialization of input stream operator.

Specialized stream input operator for DA matrices.

Parameters

[in]	in	Standard input stream.
[out]	obj	AlgebraicMatrix<DA> to be read from the stream

Returns

Reference to the standard input stream.

operator>>() [2/5]

template<typename U >

std::istream & DACE::operator>>	(	std::istream &	in,
		AlgebraicMatrix< U > &	obj
	)

Overload input stream operator.

Overload of std::operator>> in iostream.

Parameters

[in]	in	standard input stream.
[in]	obj	AlgebraicMatrix<U> to be created from the stream

Returns

Standard input stream.

Overload of std::operator>> in iostream.

Parameters

[in]	in	standard input stream.
[in]	obj	AlgebraicMatrix<U> to be created from the stream

Returns

Standard input stream.

operator>>() [3/5]

template<>

DACE_API std::istream& DACE::operator>>	(	std::istream &	in,
		AlgebraicMatrix< DA > &	obj
	)

DA specialization of input stream operator.

Specialized stream input operator for DA matrices.

Parameters

[in]	in	Standard input stream.
[out]	obj	AlgebraicMatrix<DA> to be read from the stream

Returns

Reference to the standard input stream.

operator>>() [4/5]

template<typename U >

std::istream & DACE::operator>>	(	std::istream &	in,
		AlgebraicVector< U > &	obj
	)

Overload input stream operator.

Input a vector from a C++ input stream.

Parameters

[in]	in	standard input stream.
[in]	obj	AlgebraicVector<U> to be read from the stream

Returns

Reference to input stream in.

Input a vector from a C++ input stream.

Parameters

[in]	in	standard input stream.
[in]	obj	AlgebraicVector<U> to be read from the stream

Returns

Reference to input stream in.

operator>>() [5/5]

std::istream& DACE::operator>>	(	std::istream &	in,
		DA &	da
	)

Overload of std::operator>> in iostream. Reads both string and binary DA representations from a file.

Parameters

[in]	in	standard input stream.
[in]	da	DA object to be created from the stream

Returns

Standard input stream.

Exceptions

DACE::DACEException

Note

When using binary IO operations, make sure the stream is opened in ios_base::binary mode! Some C++ libraries are known to mangle the input otherwise which will break the ability to read binary DA objects. Setting the binary flag for all IO (also text based) does not affect the output and is recommended.

See also

DA::fromString

orderNorm()

DACE_API std::vector< double > DACE::orderNorm	(	const DA &	da,
		const unsigned int	var,
		const unsigned int	type
	)

Compute different types of order sorted norms for terms of a DA object.

Parameters

[in]	da	a given DA object.
[in]	var	order 0: Terms are sorted by their order (Default) >0: Terms are sorted by the exponent of variable var
[in]	type	type of norm to be computed. Possible norms are: 0: Max norm (Default) 1: Sum norm >1: Vector norm of given type

Returns

A double corresponding to the result of the operation.

Exceptions

DACE::DACEException

See also

DA::onorm

plug() [1/4]

template<typename T >

AlgebraicVector<T> DACE::plug	(	const AlgebraicVector< T > &	obj,
		const unsigned int	var,
		const double	val = 0.0
	)

plug() [2/4]

template<>

DACE_API AlgebraicVector<DA> DACE::plug	(	const AlgebraicVector< DA > &	obj,
		const unsigned int	var,
		const double	val
	)

Partial evaluation of vector of polynomials. In each element of the vector, variable var is replaced by the value val. The resulting vector of DAs is returned.

Parameters

[in]	obj	The vector to partially evaluate.
[in]	var	Variable number to be replaced.
[in]	val	Value by which to replace the variable.

Returns

A new DA object containing the resulting DA object.

Note

This DA specific function is only available in AlgebraicVector<DA>. When called on AlgebraicVectors of other types (e.g. double), a compiler error will be the result.

plug() [3/4]

template<>

AlgebraicVector<DA> DACE::plug	(	const AlgebraicVector< DA > &	obj,
		const unsigned int	var,
		const double	val
	)

Partial evaluation of vector of polynomials. In each element of the vector, variable var is replaced by the value val. The resulting vector of DAs is returned.

Parameters

[in]	obj	The vector to partially evaluate.
[in]	var	Variable number to be replaced.
[in]	val	Value by which to replace the variable.

Returns

A new DA object containing the resulting DA object.

Note

This DA specific function is only available in AlgebraicVector<DA>. When called on AlgebraicVectors of other types (e.g. double), a compiler error will be the result.

plug() [4/4]

DACE_API DA DACE::plug	(	const DA &	da,
		const unsigned int	var,
		const double	val
	)

Partial evaluation of a DA object. In the DA object, variable var is replaced by the value val. The resulting DA object is returned.

Parameters

[in]	da	a given DA object.
[in]	var	variable number to be replaced
[in]	val	value by which to replace the variable

Returns

A new DA object containing the resulting DA object.

Exceptions

DACE::DACEException

See also

DA::plug

pow() [1/3]

template<typename T >

AlgebraicVector< T > DACE::pow	(	const AlgebraicVector< T > &	obj,
		const int	p
	)

Elevate a AlgebraicVector<T> to a given integer power. The result is copied in a new AlgebraicVector<T>.

Parameters

[in]	obj	AlgebraicVector<T>.
[in]	p	power at which the AlgebraicVector is elevated.

Returns

A new AlgebraicVector<T> containing the result of the operation.

See also

AlgebraicVector<T>::pow

Elevate a AlgebraicVector<T> to a given integer power. The result is copied in a new AlgebraicVector<T>.

Parameters

[in]	obj	AlgebraicVector<T>.
[in]	p	power at which the AlgebraicVector is elevated.

Returns

A new AlgebraicVector<T> containing the result of the operation.

See also

AlgebraicVector<T>::pow

pow() [2/3]

DACE_API DA DACE::pow	(	const DA &	da,
		int	p
	)

Raise a DA object to a given integer power. The result is copied in a new DA object.

Parameters

[in]	da	a given DA object.
[in]	p	power at which the DA object is elevated.

Returns

A new DA object containing the result of the operation.

Exceptions

DACE::DACEException

See also

DA::pow

pow() [3/3]

DACE_API DA DACE::pow	(	const DA &	da,
		double	p
	)

Raise a DA object to a given integer power. The constant part must be positive. The result is copied in a new DA object.

Parameters

[in]	da	a given DA object.
[in]	p	power at which the DA object is elevated.

Returns

A new DA object containing the result of the operation.

Exceptions

DACE::DACEException

See also

DA::pow

PsiFunction()

DACE_API DA DACE::PsiFunction	(	const unsigned int	n,
		const DA &	da
	)

Compute the n-th Psi function of a DA object. The result is copied in a new DA object.

Parameters

[in]	n	order of the Psi function to compute.
[in]	da	a given DA object.

Returns

A new DA object containing the result of the operation.

Exceptions

DACE::DACEException

See also

DA::PsiFunction

replaceVariable()

DACE_API DA DACE::replaceVariable	(	const DA &	da,
		const unsigned int	from,
		const unsigned int	to,
		const double	val
	)

Partial evaluation of a DA object. In the DA object, variable from is replaced by the value val times variable to. The resulting DA object is returned.

Parameters

[in]	da	a given DA object.
[in]	from	variable number to be replaced
[in]	to	variable number to be inserted instead
[in]	val	value by which to scale the inserted variable

Returns

A new DA object containing the resulting DA object.

Exceptions

DACE::DACEException

See also

DA::replaceVariable

root() [1/3]

double DACE::root	(	const double	x,
		const int	p = 2
	)

p-th root

p-th root of x.

Parameters

[in]	x	Function argument.
[in]	p	Root to take.

p-th root of x.

Parameters

[in]	x	Function argument.
[in]	p	Root to take.

root() [2/3]

template<typename T >

AlgebraicVector< T > DACE::root	(	const AlgebraicVector< T > &	obj,
		const int	p = 2
	)

Compute the p-th root of a AlgebraicVector<T>. The result is copied in a new AlgebraicVector<T>.

Parameters

[in]	obj	AlgebraicVector<T>.
[in]	p	root to be computed (default = 2).

Returns

A new AlgebraicVector<T> containing the result of the operation.

See also

AlgebraicVector<T>::root

Compute the p-th root of a AlgebraicVector<T>. The result is copied in a new AlgebraicVector<T>.

Parameters

[in]	obj	AlgebraicVector<T>.
[in]	p	root to be computed (default = 2).

Returns

A new AlgebraicVector<T> containing the result of the operation.

See also

AlgebraicVector<T>::root

root() [3/3]

DACE_API DA DACE::root	(	const DA &	da,
		int	p
	)

Compute the p-th root of a DA object. The result is copied in a new DA object.

Parameters

[in]	da	a given DA object.
[in]	p	root to be computed.

Returns

A new DA object containing the result of the operation.

Exceptions

DACE::DACEException

See also

DA::root

round()

DACE_API DA DACE::round

(

const DA &

da

)

Round the constant part of a DA object to an integer. The result is copied in a new DA object.

Parameters

[in]

da

a given DA object.

Returns

A new DA object with a rounded constant part.

Exceptions

DACE::DACEException

See also

DA::round

scaleVariable()

DACE_API DA DACE::scaleVariable	(	const DA &	da,
		const unsigned int	var,
		const double	val
	)

Scaling of an independent variable. In the DA object, variable var is replaced by the value val times var. The resulting DA object is returned.

Parameters

[in]	da	a given DA object.
[in]	var	variable number to be scaled
[in]	val	value by which to scale the variable

Returns

A new DA object containing the resulting DA object.

Exceptions

DACE::DACEException

See also

DA::scaleVariable

sin() [1/2]

template<typename T >

AlgebraicVector< T > DACE::sin

(

const AlgebraicVector< T > &

obj

)

Compute the sine of a AlgebraicVector<T>. The result is copied in a new AlgebraicVector<T>.

Parameters

[in]

obj

AlgebraicVector<T>.

Returns

A new AlgebraicVector<T> containing the result of the operation.

See also

AlgebraicVector<T>::sin

Compute the sine of a AlgebraicVector<T>. The result is copied in a new AlgebraicVector<T>.

Parameters

[in]

obj

AlgebraicVector<T>.

Returns

A new AlgebraicVector<T> containing the result of the operation.

See also

AlgebraicVector<T>::sin

sin() [2/2]

DACE_API DA DACE::sin

(

const DA &

da

)

Compute the sine of a DA object. The result is copied in a new DA object.

Parameters

[in]

da

a given DA object.

Returns

A new DA object containing the result of the operation.

Exceptions

DACE::DACEException

See also

DA::sin

sinh() [1/2]

template<typename T >

AlgebraicVector< T > DACE::sinh

(

const AlgebraicVector< T > &

obj

)

Compute the hyperbolic sine of a AlgebraicVector<T>. The result is copied in a new AlgebraicVector<T>.

Parameters

[in]

obj

AlgebraicVector<T>.

Returns

A new AlgebraicVector<T> containing the result of the operation.

See also

AlgebraicVector<T>::sinh

Compute the hyperbolic sine of a AlgebraicVector<T>. The result is copied in a new AlgebraicVector<T>.

Parameters

[in]

obj

AlgebraicVector<T>.

Returns

A new AlgebraicVector<T> containing the result of the operation.

See also

AlgebraicVector<T>::sinh

sinh() [2/2]

DACE_API DA DACE::sinh

(

const DA &

da

)

Compute the hyperbolic sine of a DA object. The result is copied in a new DA object.

Parameters

[in]

da

a given DA object.

Returns

A new DA object containing the result of the operation.

Exceptions

DACE::DACEException

See also

DA::sinh

size()

DACE_API unsigned int DACE::size

(

const DA &

da

)

Return the number of non-zero coefficients of a DA object.

Parameters

[in]

da

a given DA object.

Returns

The number of non-zero coefficients of the DA object.

Exceptions

DACE::DACEException

See also

DA::size

sqr() [1/3]

double DACE::sqr

(

const double

x

)

Square.

Square of x.

Parameters

[in]

x

Function argument.

Square of x.

Parameters

[in]

x

Function argument.

sqr() [2/3]

template<typename T >

AlgebraicVector< T > DACE::sqr

(

const AlgebraicVector< T > &

obj

)

Compute the square of a AlgebraicVector<T>. The result is copied in a new AlgebraicVector<T>.

Parameters

[in]

obj

AlgebraicVector<T>.

Returns

A new AlgebraicVector<T> containing the result of the operation.

See also

AlgebraicVector<T>::sqr

Compute the square of a AlgebraicVector<T>. The result is copied in a new AlgebraicVector<T>.

Parameters

[in]

obj

AlgebraicVector<T>.

Returns

A new AlgebraicVector<T> containing the result of the operation.

See also

AlgebraicVector<T>::sqr

sqr() [3/3]

DACE_API DA DACE::sqr

(

const DA &

da

)

Compute the square of a DA object. The result is copied in a new DA object.

Parameters

[in]

da

a given DA object.

Returns

A new DA object containing the result of the operation.

Exceptions

DACE::DACEException

See also

DA::sqr

sqrt() [1/2]

template<typename T >

AlgebraicVector< T > DACE::sqrt

(

const AlgebraicVector< T > &

obj

)

Compute the square root of a AlgebraicVector<T>. The result is copied in a new AlgebraicVector<T>.

Parameters

[in]

obj

AlgebraicVector<T>.

Returns

A new AlgebraicVector<T> containing the result of the operation.

See also

AlgebraicVector<T>::sqrt

Compute the square root of a AlgebraicVector<T>. The result is copied in a new AlgebraicVector<T>.

Parameters

[in]

obj

AlgebraicVector<T>.

Returns

A new AlgebraicVector<T> containing the result of the operation.

See also

AlgebraicVector<T>::sqrt

sqrt() [2/2]

DACE_API DA DACE::sqrt

(

const DA &

da

)

Compute the square root of a DA object. The result is copied in a new DA object.

Parameters

[in]

da

a given DA object.

Returns

A new DA object containing the result of the operation.

Exceptions

DACE::DACEException

See also

DA::sqrt

tan() [1/2]

template<typename T >

AlgebraicVector< T > DACE::tan

(

const AlgebraicVector< T > &

obj

)

Compute the tangent of a AlgebraicVector<T>. The result is copied in a new AlgebraicVector<T>.

Parameters

[in]

obj

AlgebraicVector<T>.

Returns

A new AlgebraicVector<T> containing the result of the operation.

See also

AlgebraicVector<T>::tan

Compute the tangent of a AlgebraicVector<T>. The result is copied in a new AlgebraicVector<T>.

Parameters

[in]

obj

AlgebraicVector<T>.

Returns

A new AlgebraicVector<T> containing the result of the operation.

See also

AlgebraicVector<T>::tan

tan() [2/2]

DACE_API DA DACE::tan

(

const DA &

da

)

Compute the tangent of a DA object. The result is copied in a new DA object.

Parameters

[in]

da

a given DA object.

Returns

A new DA object containing the result of the operation.

Exceptions

DACE::DACEException

See also

DA::tan

tanh() [1/2]

template<typename T >

AlgebraicVector< T > DACE::tanh

(

const AlgebraicVector< T > &

obj

)

Compute the hyperbolic tangent of a AlgebraicVector<T>. The result is copied in a new AlgebraicVector<T>.

Parameters

[in]

obj

AlgebraicVector<T>.

Returns

A new AlgebraicVector<T> containing the result of the operation.

See also

AlgebraicVector<T>::tanh

Compute the hyperbolic tangent of a AlgebraicVector<T>. The result is copied in a new AlgebraicVector<T>.

Parameters

[in]

obj

AlgebraicVector<T>.

Returns

A new AlgebraicVector<T> containing the result of the operation.

See also

AlgebraicVector<T>::tanh

tanh() [2/2]

DACE_API DA DACE::tanh

(

const DA &

da

)

Compute the hyperbolic tangent of a DA object. The result is copied in a new DA object.

Parameters

[in]

da

a given DA object.

Returns

A new DA object containing the result of the operation.

Exceptions

DACE::DACEException

See also

DA::tanh

tgamma()

DACE_API DA DACE::tgamma

(

const DA &

da

)

Compute the Gamma function of a DA object. The result is copied in a new DA object.

Parameters

[in]

da

a given DA object.

Returns

A new DA object containing the result of the operation.

Exceptions

DACE::DACEException

See also

DA::GammaFunction

Note

Alias of GammaFunction() for C99 compatible naming.

toString()

DACE_API std::string DACE::toString

(

const DA &

da

)

Convert DA object to a string.

Parameters

[in]

da

a given DA object.

Returns

A string.

Exceptions

DACE::DACEException

See also

DA::toString

translateVariable()

DACE_API DA DACE::translateVariable	(	const DA &	da,
		const unsigned int	var,
		const double	a,
		const double	c
	)

Affine translation of an independent variable. In the DA object, variable var is replaced by a*var + c. The resulting DA object is returned.

Parameters

[in]	da	a given DA object.
[in]	var	variable number to be translated
[in]	a	value by which to scale the variable
[in]	c	value by which to shift the variable

Returns

A new DA object containing the resulting DA object.

Exceptions

DACE::DACEException

See also

DA::translateVariable

transpose()

template<class T >

AlgebraicMatrix< T > DACE::transpose

(

const AlgebraicMatrix< T > &

obj

)

Compute the transpose of an AlgebraicMatrix.

Parameters

[in]

obj

An AlgebraicMatrix

Returns

An AlgebraicMatrix that is the transpose of the original AlgebraicMatrix.

See also

AlgebraicMatrix<T>::transpose

Compute the transpose of an AlgebraicMatrix.

Parameters

[in]

obj

An AlgebraicMatrix

Returns

An AlgebraicMatrix that is the transpose of the original AlgebraicMatrix.

See also

AlgebraicMatrix<T>::transpose

trim() [1/4]

template<typename T >

AlgebraicVector<T> DACE::trim	(	const AlgebraicVector< T > &	obj,
		unsigned int	min,
		unsigned int	max = DA::getMaxOrder()
	)

trim() [2/4]

template<>

DACE_API AlgebraicVector<DA> DACE::trim	(	const AlgebraicVector< DA > &	obj,
		unsigned int	min,
		unsigned int	max
	)

Returns an AlgebraicVector<DA> with all monomials of order less than min and greater than max removed (trimmed). The result is copied in a new AlgebraicVector<DA>.

Parameters

[in]	obj	the AlgebraicVector<DA> to be trimmed.
[in]	min	minimum order to be preserved.
[in]	max	maximum order to be preserved.

Returns

A new AlgebraicVector<DA> containing the result of the trimming.

Note

This DA specific function is only available in AlgebraicVector<DA>. When called on AlgebraicVectors of other types (e.g. double), a compiler error will be the result.

See also

AlgebraicVector<T>::trim

trim() [3/4]

template<>

AlgebraicVector<DA> DACE::trim	(	const AlgebraicVector< DA > &	obj,
		unsigned int	min,
		unsigned int	max
	)

Returns an AlgebraicVector<DA> with all monomials of order less than min and greater than max removed (trimmed). The result is copied in a new AlgebraicVector<DA>.

Parameters

[in]	obj	the AlgebraicVector<DA> to be trimmed.
[in]	min	minimum order to be preserved.
[in]	max	maximum order to be preserved.

Returns

A new AlgebraicVector<DA> containing the result of the trimming.

Note

This DA specific function is only available in AlgebraicVector<DA>. When called on AlgebraicVectors of other types (e.g. double), a compiler error will be the result.

See also

AlgebraicVector<T>::trim

trim() [4/4]

DACE_API DA DACE::trim	(	const DA &	da,
		const unsigned int	min,
		const unsigned int	max
	)

Returns a DA object with all monomials of order less than min and greater than max removed (trimmed). The result is copied in a new DA object.

Parameters

[in]	da	DA object.
[in]	min	The minimum order to keep in the DA object.
[in]	max	The maximum order to keep in the DA object.

Returns

A new DA object containing the result of the trimming.

Exceptions

DACE::DACEException

See also

DA::trim

trunc()

DACE_API DA DACE::trunc

(

const DA &

da

)

Truncate the constant part of a DA object to an integer. The result is copied in a new DA object.

Parameters

[in]

da

a given DA object.

Returns

A new DA object with a truncated constant part.

Exceptions

DACE::DACEException

See also

DA::trunc

vnorm()

template<typename T >

T DACE::vnorm

(

const AlgebraicVector< T > &

obj

)

Compute the Euclidean vector norm (length) of an AlgebraicVector<T>.

Parameters

[in]

obj

AlgebraicVector<T>.

Returns

A scalar value containing the result of the operation.

See also

AlgebraicVector<T>::norm

Compute the Euclidean vector norm (length) of an AlgebraicVector<T>.

Parameters

[in]

obj

AlgebraicVector<T>.

Returns

A scalar value containing the result of the operation.

See also

AlgebraicVector<T>::norm

write()

DACE_API void DACE::write	(	const DA &	da,
		std::ostream &	os
	)

Write binary representation of DA object to given stream os.

Parameters

[in]	da	a given DA object.
[in]	os	the output stream to write to.

Exceptions

DACE::DACEException

See also

DA::write

yn()

DACE_API DA DACE::yn	(	const int	n,
		const DA &	da
	)

Compute the n-th Bessel function of second type Y_n of a DA object. The result is copied in a new DA object.

Parameters

[in]	n	order of the Bessel function.
[in]	da	a given DA object.

Returns

A new DA object containing the result of the operation.

Exceptions

DACE::DACEException

Note

The DA must have non-negative constant part while the order is allowed to be negative.

Alias of BesselYFunction for C compatible naming.

See also

DA::BesselYFunction