#include <dace/DA.h>

Public Member Functions
	DA ()
	Default constructor. More...

	DA (const DA &da)
	Copy constructor. More...

	DA (DA &&da)
	Move constructor. More...

	DA (const int i, const double c=1.0)
	Constructor for DA identities. More...

	DA (const unsigned int i, const double c=1.0)
	Constructor for DA identities. More...

	DA (const double c)
	Constructor for DA constants. More...

	~DA () throw ()
	Destructor. More...

int	isnan () const

int	isinf () const

double	cons () const
	Get constant part of a DA. More...

AlgebraicVector< double >	linear () const
	Get linear part of a DA. More...

AlgebraicVector< DA >	gradient () const
	Gradient vector with respect to all independent DA variables. More...

double	getCoefficient (const std::vector< unsigned int > &jj) const
	Get specific coefficient. More...

void	setCoefficient (const std::vector< unsigned int > &jj, const double coeff)
	Set specific coefficient. More...

Monomial	getMonomial (const unsigned int npos) const
	Get the Monomial at given position. More...

void	getMonomial (const unsigned int npos, Monomial &m) const
	Extract the Monomial at given position. More...

std::vector< Monomial >	getMonomials () const
	Get std::vector of all non-zero Monomials. More...

DA &	operator= (DA &&da)
	Move assignment from existing DA. More...

DA &	operator= (const DA &da)
	Assignment from existing DA. More...

DA &	operator= (const double c)
	Assignment from existing double. More...

DA &	operator+= (const DA &da)
	Add another DA to this DA. More...

DA &	operator+= (const double c)
	Add another double to this DA. More...

DA &	operator-= (const DA &da)
	Subtract another DA from this DA. More...

DA &	operator-= (const double c)
	Subtract another double from this DA. More...

DA &	operator*= (const DA &da)
	Multiply this DA by another DA. More...

DA &	operator*= (const double c)
	Multiply this DA by another double. More...

DA &	operator/= (const DA &da)
	Divide this DA by another DA. More...

DA &	operator/= (const double c)
	Divide this DA by another double. More...

DA	operator- () const
	Negate this DA. More...

DA	multiplyMonomials (const DA &da) const
	Multiply the DA with the argument da monomial by monomial (i.e. coefficient-wise) More...

DA	divide (const unsigned int var, const unsigned int p=1) const
	Divide by an independent variable to some power. More...

DA	deriv (const unsigned int i) const
	Derivative with respect to given variable. More...

DA	deriv (const std::vector< unsigned int > ind) const
	Derivative with respect to given variables. More...

DA	integ (const unsigned int i) const
	Integral with respect to given variable. More...

DA	integ (const std::vector< unsigned int > ind) const
	Integral with respect to given variables. More...

DA	trim (const unsigned int min, const unsigned int max=DA::getMaxOrder()) const
	Trim the coefficients only include orders between min and max, inclusively. More...

DA	trunc () const
	Truncate the constant part to an integer. More...

DA	round () const
	Round the constant part to an integer. More...

DA	mod (const double p) const
	Modulo of the constant part. More...

DA	pow (const int p) const
	Exponentiation to given (integer) power. More...

DA	pow (const double p) const
	Exponentiation to given double power. More...

DA	root (const int p=2) const
	p-th root More...

DA	minv () const
	multiplicative inverse More...

DA	sqr () const
	square More...

DA	sqrt () const
	square root More...

DA	isrt () const
	inverse square root More...

DA	cbrt () const
	cubic root More...

DA	icrt () const
	inverse cubic root More...

DA	hypot (const DA &da) const
	hypotenuse More...

DA	exp () const
	exponential More...

DA	log () const
	natural logarithm More...

DA	logb (const double b=10.0) const
	logarithm with respect to given base More...

DA	log10 () const
	10 based logarithm More...

DA	log2 () const
	2 based logarithm More...

DA	sin () const
	sine More...

DA	cos () const
	cosine More...

DA	tan () const
	tangent More...

DA	asin () const
	arcsine More...

DA	acos () const
	arccosine More...

DA	atan () const
	arctangent More...

DA	atan2 (const DA &da) const
	arctangent in [-pi, pi] More...

DA	sinh () const
	hyperbolic sine More...

DA	cosh () const
	hyperbolic cosine More...

DA	tanh () const
	hyperbolic tangent More...

DA	asinh () const
	hyperbolic arcsine More...

DA	acosh () const
	hyperbolic arccosine More...

DA	atanh () const
	hyperbolic arctangent More...

DA	erf () const
	error function More...

DA	erfc () const
	complementary error function More...

DA	BesselJFunction (const int n) const
	Bessel function J_n. More...

DA	BesselYFunction (const int n) const
	Bessel function Y_n. More...

DA	BesselIFunction (const int n, const bool scaled=false) const
	Bessel function I_n. More...

DA	BesselKFunction (const int n, const bool scaled=false) const
	Bessel function K_n. More...

DA	GammaFunction () const
	Gamma function. More...

DA	LogGammaFunction () const
	Logartihmic Gamma function. More...

DA	PsiFunction (const unsigned int n) const
	Psi function. More...

unsigned int	size () const
	Number of non-zero coefficients. More...

double	abs () const
	Maximum absolute value of all coefficients. More...

double	norm (const unsigned int type=0) const
	Different types of norms over all coefficients. More...

std::vector< double >	orderNorm (const unsigned int var=0, const unsigned int type=0) const
	Different types of norms over coefficients of each order separately. More...

std::vector< double >	estimNorm (const unsigned int var=0, const unsigned int type=0, const unsigned int nc=DA::getMaxOrder()) const
	Estimate of different types of order sorted norms. More...

std::vector< double >	estimNorm (std::vector< double > &err, const unsigned int var=0, const unsigned int type=0, const unsigned int nc=DA::getMaxOrder()) const
	Estimate of different types of order sorted norms with error of the estimate. More...

Interval	bound () const
	Estimate range bound over [-1,1] for each independent variable. More...

double	convRadius (const double eps, const unsigned int type=1) const
	Estimate the convergence radius of the current DA. More...

template<class T >
T	eval (const std::vector< T > &args) const
	Evaluation with a vector of arguments (not efficient for repeated evaluation!) More...

template<class T >
T	eval (const T args[], const unsigned int length) const
	Evaluation with an array of arguments (not efficient for repeated evaluation!) More...

template<class T >
T	evalScalar (const T &arg) const
	Evaluation with a single arithmetic type T argument (not efficient for repeated evaluation!) More...

compiledDA	compile () const
	Compile current DA for efficient repeated evaluation. More...

DA	plug (const unsigned int var, const double val=0.0) const
	Partial evaluation to replace given independent DA variable by value val. More...

double	evalMonomials (const DA &values) const
	evaluate the DA providing the value of every monomial in da More...

DA	replaceVariable (const unsigned int from=0, const unsigned int to=0, const double val=1.0) const
	Replace variable number from by val times variable number to. More...

DA	scaleVariable (const unsigned int var=0, const double val=1.0) const
	Scale variable number var by val. More...

DA	translateVariable (const unsigned int var=0, const double a=1.0, const double c=0.0) const
	Translate variable number var to a*var + c. More...

std::string	toString () const
	Convert to string representation. More...

void	write (std::ostream &os) const
	Write binary representation of DA to stream. More...

Static Public Member Functions
static void	init (const unsigned int ord, const unsigned int nvar)
	DACE initialization. More...

static bool	isInitialized ()
	Get DACE initialization status. More...

static void	version (int &maj, int &min, int &patch)
	DACE core routines version. More...

static void	checkVersion ()
	Check DACE C++ interface and core routines version for compatibility. More...

static double	setEps (const double eps)
	Set truncation epsilon. More...

static double	getEps ()
	Get truncation epsilon. More...

static double	getEpsMac ()
	Get the machine epsilon. More...

static unsigned int	getMaxOrder ()
	Get the maximum order. More...

static unsigned int	getMaxVariables ()
	Get the maximum number of variables. More...

static unsigned int	getMaxMonomials ()
	Get the maximum monomials. More...

static unsigned int	getTO ()
	Get truncation order. More...

static unsigned int	setTO (const unsigned int ot=DA::getMaxOrder())
	Set truncation order. More...

static void	pushTO (const unsigned int ot=DA::getMaxOrder())
	Set truncation order and save previous value. More...

static void	popTO ()
	Restore truncation order to value before last DA::pushTO() More...

static DA	random (const double cm)
	Create new DA filled with random coefficients. More...

static DA	identity (const unsigned int var)
	Create the DA identity for independent DA variable var. More...

static DA	fromString (const std::string &str)
	Create new DA from string. More...

static DA	fromString (const std::vector< std::string > &str)
	Create new DA from vector of strings. More...

static DA	read (std::istream &is)
	Create new DA from blob read from binary file. More...

static void	memdump ()
	Dump memory status to screen (for debugging purposes only) More...

Friends
class	compiledDA

class	storedDA

DA DACE_API	operator+ (const DA &da1, const DA &da2)
	Addition between two DAs. More...

DA DACE_API	operator+ (const DA &da, const double c)
	Addition between a DA and a constant. More...

DA DACE_API	operator+ (const double c, const DA &da)
	Addition between a constant and a DA. More...

DA DACE_API	operator- (const DA &da1, const DA &da2)
	Subtraction between two DAs. More...

DA DACE_API	operator- (const DA &da, const double c)
	Subtraction between a DA and a constant. More...

DA DACE_API	operator- (const double c, const DA &da)
	Subtraction between a constant and a DA. More...

DA DACE_API	operator* (const DA &da1, const DA &da2)
	Multiplication between two DAs. More...

DA DACE_API	operator* (const DA &da, const double c)
	Multiplication between a DA and a constant. More...

DA DACE_API	operator* (const double c, const DA &da)
	Multiplication between a constant and a DA. More...

DA DACE_API	operator/ (const DA &da1, const DA &da2)
	Division between two DAs. More...

DA DACE_API	operator/ (const DA &da, const double c)
	Division between a DA and a constant. More...

DA DACE_API	operator/ (const double c, const DA &da)
	Division between a constant and a DA. More...

DACE_API std::ostream &	operator<< (std::ostream &out, const DA &da)
	Output to C++ stream in text form. More...

DACE_API std::istream &	operator>> (std::istream &in, DA &da)
	Input from C++ stream in text form. More...

Detailed Description

Basic DA class representing a single polynomial.

Constructor & Destructor Documentation

◆ DA() [1/6]

DACE::DA::DA ( )

Default constructor.

Create an empty DA object representing the constant zero function.

Exceptions

DACE::DACEException

◆ DA() [2/6]

DACE::DA::DA ( const DA & da )

Copy constructor.

Create a copy of a DA object.

Parameters

[in] da object to be copied.

Exceptions

DACE::DACEException

◆ DA() [3/6]

DACE::DA::DA ( DA && da )

Move constructor.

Move all resources from a DA object to us without copying.

Parameters

[in] da object to be moved.

Exceptions

DACE::DACEException

◆ DA() [4/6]

DACE::DA::DA	(	const int	i,
		const double	c = `1.0`
	)

explicit

Constructor for DA identities.

Create a DA object as c times the independent variable number i.

Note: When used in its one argument form (with the default argument 1.0 for c), this routine MUST be called with an integer type as the first argument, e.g. DA(1). Expressions involving floating point data types such as DA(1.0) will be interpreted as the constant DA object of the given value instead of the first independent DA variable.

Parameters

[in]	i	independent variable number (i=0 means the constant part).
[in]	c	coefficient corresponding to the given independent variable. By default, this value is assumed to be 1.0.

Exceptions

DACE::DACEException

◆ DA() [5/6]

DACE::DA::DA	(	const unsigned int	i,
		const double	c = `1.0`
	)

explicit

Constructor for DA identities.

Create a DA object as c times the independent variable number i.

Note: When used in its one argument form (with the default argument 1.0 for c), this routine MUST be called with an integer type as the first argument, e.g. DA(1). Expressions involving floating point data types such as DA(1.0) will be interpreted as the constant DA of the given value instead of the first independent variable.

Parameters

[in]	i	independent variable number (i=0 means the constant part).
[in]	c	coefficient corresponding to the given independent variable. By default, this value is assumed to be 1.0.

Exceptions

DACE::DACEException

◆ DA() [6/6]

DACE::DA::DA ( const double c )

Constructor for DA constants.

Create a DA object with the constant part equal to c.

Note: This routine MUST be called with a floating point type as the first argument, e.g. DA(1.0). Expressions involving integer data types such as DA(1) will be interpreted as the first independent DA variable instead of the constant DA object of the given value.

Parameters

[in] c A double value set as constant part of the DA object.

Exceptions

DACE::DACEException

◆ ~DA()

DACE::DA::~DA	(	)
throw	(
	)

Destructor.

Destroy a DA object and free the associated object in the DACE core.

Member Function Documentation

◆ abs()

double DACE::DA::abs ( ) const

Maximum absolute value of all coefficients.

Compute the max norm of a DA object.

Returns: A double corresponding to the result of the operation.

Exceptions

DACE::DACEException

◆ acos()

DA DACE::DA::acos ( ) const

arccosine

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

Returns: A new DA object containing the result of the operation.

Exceptions

DACE::DACEException

◆ acosh()

DA DACE::DA::acosh ( ) const

hyperbolic arccosine

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

Returns: A new DA object containing the result of the operation.

Exceptions

DACE::DACEException

◆ asin()

DA DACE::DA::asin ( ) const

arcsine

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

Returns: A new DA object containing the result of the operation.

Exceptions

DACE::DACEException

◆ asinh()

DA DACE::DA::asinh ( ) const

hyperbolic arcsine

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

Returns: A new DA object containing the result of the operation.

Exceptions

DACE::DACEException

◆ atan()

DA DACE::DA::atan ( ) const

arctangent

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

Returns: A new DA object containing the result of the operation.

Exceptions

DACE::DACEException

◆ atan2()

DA DACE::DA::atan2 ( const DA & da ) const

arctangent in [-pi, pi]

Compute the four-quadrant arctangent of Y/X. Y is the current DA object, whereas X is the given da. The result is copied in a new DA object.

Parameters

[in] da DA object

Returns: A new DA object containing the result of the operation Y/X in [-pi, pi].

Exceptions

DACE::DACEException

◆ atanh()

DA DACE::DA::atanh ( ) const

hyperbolic arctangent

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

Returns: A new DA object containing the result of the operation.

Exceptions

DACE::DACEException

◆ BesselIFunction()

DA DACE::DA::BesselIFunction	(	const int	n,
		const bool	scaled = `false`
	)		const

Bessel function I_n.

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]	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.; This function fails if the result is too large to be represented in double precision.

◆ BesselJFunction()

DA DACE::DA::BesselJFunction ( const int n ) const

Bessel function J_n.

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

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.; This function fails if the result is too large to be represented in double precision.

◆ BesselKFunction()

DA DACE::DA::BesselKFunction	(	const int	n,
		const bool	scaled = `false`
	)		const

Bessel function K_n.

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]	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.; This function fails if the result is too large to be represented in double precision.

◆ BesselYFunction()

DA DACE::DA::BesselYFunction ( const int n ) const

Bessel function Y_n.

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

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.; This function fails if the result is too large to be represented in double precision.

◆ bound()

Interval DACE::DA::bound ( ) const

Estimate range bound over [-1,1] for each independent variable.

Compute lower and upper bounds of a DA object.

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

Exceptions

DACE::DACEException

See also: Interval

◆ cbrt()

DA DACE::DA::cbrt ( ) const

cubic root

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

Returns: A new DA object containing the result of the operation.

Exceptions

DACE::DACEException

◆ checkVersion()

void DACE::DA::checkVersion ( )

static

Check DACE C++ interface and core routines version for compatibility.

Check the DACE core library version linked to this C++ interface against the interface version and throw an exception if the versions don't match.

Exceptions

DACE::DACEException

Note: This routine is called automatically by DA::init to ensure compatibility with the current runtime environment.

◆ compile()

compiledDA DACE::DA::compile ( ) const

Compile current DA for efficient repeated evaluation.

Compile current DA object and create a compiledDA object.

Returns: The compiled DA object.

Exceptions

DACE::DACEException

◆ cons()

double DACE::DA::cons ( ) const

Get constant part of a DA.

Return the constant part of a DA object.

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

Exceptions

DACE::DACEException

◆ convRadius()

double DACE::DA::convRadius	(	const double	eps,
		const unsigned int	type = `1`
	)		const

Estimate the convergence radius of the current DA.

Estimate the convergence radius of the DA object.

Parameters

[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

◆ cos()

DA DACE::DA::cos ( ) const

cosine

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

Returns: A new DA object containing the result of the operation.

Exceptions

DACE::DACEException

◆ cosh()

DA DACE::DA::cosh ( ) const

hyperbolic cosine

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

Returns: A new DA object containing the result of the operation.

Exceptions

DACE::DACEException

◆ deriv() [1/2]

DA DACE::DA::deriv ( const unsigned int i ) const

Derivative with respect to given variable.

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

Parameters

[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

◆ deriv() [2/2]

DA DACE::DA::deriv ( const std::vector< unsigned int > ind ) const

Derivative with respect to given variables.

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

Parameters

[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

◆ divide()

DA DACE::DA::divide	(	const unsigned int	var,
		const unsigned int	p = `1`
	)		const

Divide by an independent variable to some power.

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

Parameters

[in]	var	independente variable number to divide by.
[in]	p	power of the independent variable.

Returns: A new DA object containing the result.

Exceptions

DACE::DACEException

◆ erf()

DA DACE::DA::erf ( ) const

error function

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

Returns: A new DA object containing the result of the operation.

Exceptions

DACE::DACEException

◆ erfc()

DA DACE::DA::erfc ( ) const

complementary error function

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

Returns: A new DA object containing the result of the operation.

Exceptions

DACE::DACEException

◆ estimNorm() [1/2]

std::vector< double > DACE::DA::estimNorm	(	const unsigned int	var = `0`,
		const unsigned int	type = `0`,
		const unsigned int	nc = `DA::getMaxOrder()`
	)		const

Estimate of different types of order sorted norms.

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

Parameters

[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 to be estimated (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.

◆ estimNorm() [2/2]

std::vector< double > DACE::DA::estimNorm	(	std::vector< double > &	err,
		const unsigned int	var = `0`,
		const unsigned int	type = `0`,
		const unsigned int	nc = `DA::getMaxOrder()`
	)		const

Estimate of different types of order sorted norms with error of the estimate.

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

Parameters

[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 to be estimated (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.

◆ eval() [1/2]

template<class T >

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

Evaluation with a vector of arguments (not efficient for repeated evaluation!)

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

Parameters

[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>({1.0, 2.0, 3.0}) when used with initializer lists.

See also: compiledDA::eval

◆ eval() [2/2]

template<class T >

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

Evaluation with an array of arguments (not efficient for repeated evaluation!)

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

Parameters

[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

◆ evalMonomials()

double DACE::DA::evalMonomials ( const DA & values ) const

evaluate the DA providing the value of every monomial in da

Evaluates the DA vector using the coefficients in argument values as the values for each monomial. This is equivalent to a monomial-wise dot product of two DA vectors.

Parameters

[in] values DA vector containing the values of each monomial

Returns: The result of the evaluation.

Exceptions

DACE::DACEException

See also: DA::multiplyMonomial

◆ evalScalar()

template<class T >

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

Evaluation with a single arithmetic type T argument (not efficient for repeated evaluation!)

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

Parameters

[in] arg single variable of arithmetic type T of the first independent DA variable.

Returns: The result of the evaluation.

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

◆ exp()

DA DACE::DA::exp ( ) const

exponential

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

Returns: A new DA object containing the result of the operation.

Exceptions

DACE::DACEException

◆ fromString() [1/2]

DA DACE::DA::fromString ( const std::string & str )

static

Create new DA from string.

Convert a string to DA object.

Parameters

[in] str string.

Returns: A DA object.

Exceptions

DACE::DACEException

◆ fromString() [2/2]

DA DACE::DA::fromString ( const std::vector< std::string > & str )

static

Create new DA from vector of strings.

Convert a vector of strings to DA object.

Parameters

[in] str vector of strings, each representing one line of the input.

Returns: A DA object.

Exceptions

DACE::DACEException

◆ GammaFunction()

DA DACE::DA::GammaFunction ( ) const

Gamma function.

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

Returns: A new DA object containing the result of the operation.

Exceptions

DACE::DACEException

◆ getCoefficient()

double DACE::DA::getCoefficient ( const std::vector< unsigned int > & jj ) const

Get specific coefficient.

Return a specific coefficient of a DA object.

Parameters

[in] jj vector of the exponents of the coefficient to retrieve.

Returns: The coefficient of DA object corresponding to the given vector of exponents.

Exceptions

DACE::DACEException

◆ getEps()

double DACE::DA::getEps ( )

static

Get truncation epsilon.

Return the cutoff value eps currently set for the computations.

Returns: The cutoff value of eps, or zero if undefined.

Exceptions

DACE::DACEException

◆ getEpsMac()

double DACE::DA::getEpsMac ( )

static

Get the machine epsilon.

Return the machine epsilon (pessimistic estimate).

Returns: The machine epsilon, or zero if undefined.

Exceptions

DACE::DACEException

◆ getMaxMonomials()

unsigned int DACE::DA::getMaxMonomials ( )

static

Get the maximum monomials.

Return the maximum number of monomials available with the order and number of variables specified.

Returns: The maximum number of monomials, or zero if undefined.

Exceptions

DACE::DACEException

◆ getMaxOrder()

unsigned int DACE::DA::getMaxOrder ( )

static

Get the maximum order.

Return the maximum order currently set for the computations.

Returns: The maximum order, or zero if undefined.

Exceptions

DACE::DACEException

◆ getMaxVariables()

unsigned int DACE::DA::getMaxVariables ( )

static

Get the maximum number of variables.

Return the maximum number of variables set for the computations.

Returns: The maximum number of variables, or zero if undefined.

Exceptions

DACE::DACEException

◆ getMonomial() [1/2]

Monomial DACE::DA::getMonomial ( const unsigned int npos ) const

Get the Monomial at given position.

Return the Monomial corresponding to the non-zero coefficient at the given position in the DA object (monomials use one based indexing!).

Parameters

[in] npos position within the DA object. The ordering of the Monomials within a DA object is implementation dependent and does not correspond to the order in which Monomials are listed in the ASCII output routines.

Returns: A Monomial object containing both the coefficient and the vector of exponents corresponding to the given position. If the requested monomial is not present in the DA object, a Monomial with coefficient set to 0.0 is returned.

Exceptions

DACE::DACEException

See also: Monomial; DA::getMonomial; DA::getMonomials

◆ getMonomial() [2/2]

void DACE::DA::getMonomial	(	const unsigned int	npos,
		Monomial &	m
	)		const

Extract the Monomial at given position.

Return the Monomial corresponding to the non-zero coefficient at the given position in the DA object (monomials use one based indexing!).

Parameters

[in]	npos	position within the DA object. The ordering of the Monomials within a DA object is implementation dependent and does not correspond to the order in which Monomials are listed in the ASCII output routines.
[out]	m	the monomial object in which to store the corresponding monomial.

Exceptions

DACE::DACEException

See also: Monomial; DA::getMonomial; DA::getMonomials

◆ getMonomials()

std::vector< Monomial > DACE::DA::getMonomials ( ) const

Get std::vector of all non-zero Monomials.

Return a vector of all Monomials in the DA object (differently from getMonomial() where only a single Monomial, corresponding to a specified position in the DA object, is returned).

Returns: A vector of Monomial objects containing both the coefficient and the exponents corresponding to each monomial in the DA object. The monomials are returned in the same order as in the DACE ASCII output (that is, they are sorted by order).

Exceptions

DACE::DACEException

See also: Monomial; DA::getMonomial

◆ getTO()

unsigned int DACE::DA::getTO ( )

static

Get truncation order.

Return the truncation order currently set for the computations. All terms larger than the truncation order are discarded in subsequent operations.

Returns: current truncation order, or zero if undefined.

Exceptions

DACE::DACEException

See also: DA::setTO; DA::pushTO; DA::popTO

◆ gradient()

AlgebraicVector< DA > DACE::DA::gradient ( ) const

Gradient vector with respect to all independent DA variables.

Compute the gradient of the DA object.

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

Exceptions

DACE::DACEException

◆ hypot()

DA DACE::DA::hypot ( const DA & da ) const

hypotenuse

Compute the hypotenuse (sqrt(a*a+b*b)) of a DA object and the given DA argument. The result is copied in a new DA object.

Returns: A new DA object containing the result of the operation.

Exceptions

DACE::DACEException

◆ icrt()

DA DACE::DA::icrt ( ) const

inverse cubic root

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

Returns: A new DA object containing the result of the operation.

Exceptions

DACE::DACEException

◆ identity()

DA DACE::DA::identity ( const unsigned int var )

static

Create the DA identity for independent DA variable var.

Create a DA object representing the identity function in independent DA variable number var. This is just an alias for DA::DA(var).

Parameters

[in] var The independent DA variable number

Exceptions

DACE::DACEException

See also: DA::DA

◆ init()

void DACE::DA::init	(	const unsigned int	ord,
		const unsigned int	nvar
	)

static

DACE initialization.

Initialize the DACE control arrays and set the maximum order and the maximum number of variables.

Note: MUST BE CALLED BEFORE ANY OTHER DA ROUTINE CAN BE USED.; This routine performs a mandatory version check to compare the version of the C++ interface used to compile the program to the version of the DACE library that is linked dynamically at runtime.

Parameters

[in]	ord	order of the Taylor polynomials;
[in]	nvar	number of variables considered.

See also: DA::checkVersion

◆ integ() [1/2]

DA DACE::DA::integ ( const unsigned int i ) const

Integral with respect to given variable.

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

Parameters

[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

◆ integ() [2/2]

DA DACE::DA::integ ( const std::vector< unsigned int > ind ) const

Integral with respect to given variables.

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

Parameters

[in] ind vector containing the number of integrals 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 than there are independent variables, extra values are ignored.

Returns: A new DA object containing the result of the integration.

Exceptions

DACE::DACEException

◆ isinf()

int DACE::DA::isinf ( ) const

Check if a DA object has any INF coefficients.

Returns: True is any coefficients of the DA object are INF.

Exceptions

DACE::DACEException

◆ isInitialized()

bool DACE::DA::isInitialized ( )

static

Get DACE initialization status.

Returns the inizialisation status of the DACE.

Returns: Returns true if the DACE has previously been initialized by a call to DA::init, or false otherwise.

See also: DA::init

◆ isnan()

int DACE::DA::isnan ( ) const

Check if a DA object has any NAN coefficients.

Returns: True is any coefficients of the DA object are NAN.

Exceptions

DACE::DACEException

◆ isrt()

DA DACE::DA::isrt ( ) const

inverse square root

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

Returns: A new DA object containing the result of the operation.

Exceptions

DACE::DACEException

◆ linear()

AlgebraicVector< double > DACE::DA::linear ( ) const

Get linear part of a DA.

Return the linear part of a DA object.

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

Exceptions

DACE::DACEException

◆ log()

DA DACE::DA::log ( ) const

natural logarithm

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

Returns: A new DA object containing the result of the operation.

Exceptions

DACE::DACEException

◆ log10()

DA DACE::DA::log10 ( ) const

10 based logarithm

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

Returns: A new DA object containing the result of the operation.

Exceptions

DACE::DACEException

◆ log2()

DA DACE::DA::log2 ( ) const

2 based logarithm

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

Returns: A new DA object containing the result of the operation.

Exceptions

DACE::DACEException

◆ logb()

DA DACE::DA::logb ( const double b = 10.0 ) const

logarithm with respect to given base

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

Parameters

[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

◆ LogGammaFunction()

DA DACE::DA::LogGammaFunction ( ) const

Logartihmic Gamma function.

Compute the Logarithmic Gamma function (i.e. the natural logarithm of Gamma) of a DA object. The result is copied in a new DA object.

Returns: A new DA object containing the result of the operation.

Exceptions

DACE::DACEException

◆ memdump()

void DACE::DA::memdump ( )

static

Dump memory status to screen (for debugging purposes only)

◆ minv()

DA DACE::DA::minv ( ) const

multiplicative inverse

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

Returns: A new DA object containing the result of the operation.

Exceptions

DACE::DACEException

◆ mod()

DA DACE::DA::mod ( const double p ) const

Modulo of the constant part.

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

Parameters

[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

◆ multiplyMonomials()

DA DACE::DA::multiplyMonomials ( const DA & da ) const

Multiply the DA with the argument da monomial by monomial (i.e. coefficient-wise)

Multiply the DA vector with another DA vector da monomial by monomial. This is the equivalent of coefficient-wise multiplication (like in DA addition).

Parameters

[in] da DA vector to multiply with coefficient-wise

Returns: A new DA object containing the result of the operation.

Exceptions

DACE::DACEException

See also: DA::evalMonomial

◆ norm()

double DACE::DA::norm ( const unsigned int type = 0 ) const

Different types of norms over all coefficients.

Compute different types of norms for a DA object.

Parameters

[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

◆ operator*=() [1/2]

DA & DACE::DA::operator*= ( const DA & da )

Multiply this DA by another DA.

Compute the product between the current DA object and the given one. The result is directly copied into the current DA object.

Parameters

[in] da DA object to be multiplied.

Returns: The current DA object with modified contents.

Exceptions

DACE::DACEException

◆ operator*=() [2/2]

DA & DACE::DA::operator*= ( const double c )

Multiply this DA by another double.

Compute the product between the current DA object and a given constant. The result is directly copied into the current DA object.

Parameters

[in] c constant value to be multiplied.

Returns: The current DA object with modified contents.

Exceptions

DACE::DACEException

◆ operator+=() [1/2]

DA & DACE::DA::operator+= ( const DA & da )

Add another DA to this DA.

Compute the sum between the DA object and the given one. The result is directly copied into the current DA object.

Parameters

[in] da DA object to be added.

Returns: The current DA object with modified contents.

Exceptions

DACE::DACEException

◆ operator+=() [2/2]

DA & DACE::DA::operator+= ( const double c )

Add another double to this DA.

Compute the sum between the current DA object and a given constant. The result is directly copied into the current DA object.

Parameters

[in] c constant value to be added.

Returns: The current DA object with modified contents.

Exceptions

DACE::DACEException

◆ operator-()

DA DACE::DA::operator- ( ) const

Negate this DA.

Compute the additive inverse of the given DA object. The result is copied in a new DA vector.

Returns: A new DA object with the opposite sign.

Exceptions

DACE::DACEException

◆ operator-=() [1/2]

DA & DACE::DA::operator-= ( const DA & da )

Subtract another DA from this DA.

Compute the difference between the current DA object and the given one. The result is directly copied into the current DA object.

Parameters

[in] da DA object to be subtracted.

Returns: The current DA object with modified contents.

Exceptions

DACE::DACEException

◆ operator-=() [2/2]

DA & DACE::DA::operator-= ( const double c )

Subtract another double from this DA.

Compute the difference between the current DA object and a given constant. The result is directly copied into the current DA object.

Parameters

[in] c constant value to be subtracted.

Returns: The current DA object with modified contents.

Exceptions

DACE::DACEException

◆ operator/=() [1/2]

DA & DACE::DA::operator/= ( const DA & da )

Divide this DA by another DA.

Compute the division between the current DA object and the given one. The result is directly copied into the current DA object.

Parameters

[in] da DA object through which the current DA is divided by.

Returns: The current DA object with modified contents.

Exceptions

DACE::DACEException

◆ operator/=() [2/2]

DA & DACE::DA::operator/= ( const double c )

Divide this DA by another double.

Compute the division between the current DA object and a given constant. The result is directly copied into the current DA object.

Parameters

[in] c constant value through which the current DA is divided by.

Returns: The current DA object with modified contents.

Exceptions

DACE::DACEException

◆ operator=() [1/3]

DA & DACE::DA::operator= ( DA && da )

Move assignment from existing DA.

Move all resources from a DA object to us without copying.

Parameters

[in] da object to be moved.

Exceptions

DACE::DACEException

◆ operator=() [2/3]

DA & DACE::DA::operator= ( const DA & da )

Assignment from existing DA.

Copy the content of a given DA object da into the DA object.

Parameters

[in] da DA object to be copied.

Returns: The DA object with the same content of the given DA object.

Exceptions

DACE::DACEException

◆ operator=() [3/3]

DA & DACE::DA::operator= ( const double c )

Assignment from existing double.

Copy a constant polynomial of value c into the DA.

Parameters

[in] c Constant value to be copied.

Returns: The DA object representing the constant function with value c.

Exceptions

DACE::DACEException

◆ orderNorm()

std::vector< double > DACE::DA::orderNorm	(	const unsigned int	var = `0`,
		const unsigned int	type = `0`
	)		const

Different types of norms over coefficients of each order separately.

Extract different types of order sorted norms from a DA object.

Parameters

[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

◆ plug()

DA DACE::DA::plug	(	const unsigned int	var,
		const double	val = `0.0`
	)		const

Partial evaluation to replace given independent DA variable by value 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]	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

◆ popTO()

void DACE::DA::popTO ( )

static

Restore truncation order to value before last DA::pushTO()

Restore the previous truncation order from the truncation order stack. All terms larger than the truncation order are discarded in subsequent operations.

Exceptions

DACE::DACEException

See also: DA::getTO; DA::setTO; DA::pushTO

◆ pow() [1/2]

DA DACE::DA::pow ( const int p ) const

Exponentiation to given (integer) power.

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

Parameters

[in] p power to which the DA object is raised.

Returns: A new DA object containing the result of the operation.

Exceptions

DACE::DACEException

◆ pow() [2/2]

DA DACE::DA::pow ( const double p ) const

Exponentiation to given double power.

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

Parameters

[in] p power to which the DA object is raised.

Returns: A new DA object containing the result of the operation.

Exceptions

DACE::DACEException

◆ PsiFunction()

DA DACE::DA::PsiFunction ( const unsigned int n ) const

Psi function.

Compute the n-th order Psi function, i.e. the (n+1)st derivative of the Logarithmic Gamma function, of a DA object. The result is copied in a new DA object.

Returns: A new DA object containing the result of the operation.

Exceptions

DACE::DACEException

◆ pushTO()

void DACE::DA::pushTO ( const unsigned int ot = DA::getMaxOrder() )

static

Set truncation order and save previous value.

Set a new truncation order, saving the previous one on the truncation order stack. All terms larger than the truncation order are discarded in subsequent operations.

Parameters

[in] ot new truncation order.

Exceptions

DACE::DACEException

See also: DA::getTO; DA::setTO; DA::popTO

◆ random()

DA DACE::DA::random ( const double cm )

static

Create new DA filled with random coefficients.

Create a DA object and fill with random entries.

Parameters

[in] cm filling factor (for cm < 0, the DA object is filled with random numbers; for cm > 0, the DA object is filled with weighted decaying numbers).

Exceptions

DACE::DACEException

◆ read()

DA DACE::DA::read ( std::istream & is )

static

Create new DA from blob read from binary file.

Read a binary representation of a DA from is.

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.

◆ replaceVariable()

DA DACE::DA::replaceVariable	(	const unsigned int	from = `0`,
		const unsigned int	to = `0`,
		const double	val = `1.0`
	)		const

Replace variable number from by val times variable number to.

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]	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()

DA DACE::DA::root ( const int p = 2 ) const

p-th root

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

Parameters

[in] p root to be computed.

Returns: A new DA object containing the result of the operation.

Exceptions

DACE::DACEException

◆ round()

DA DACE::DA::round ( ) const

Round the constant part to an integer.

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

Returns: A new DA object with a rounded constant part.

Exceptions

DACE::DACEException

◆ scaleVariable()

DA DACE::DA::scaleVariable	(	const unsigned int	var = `0`,
		const double	val = `1.0`
	)		const

Scale variable number var by 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]	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

◆ setCoefficient()

void DACE::DA::setCoefficient	(	const std::vector< unsigned int > &	jj,
		const double	coeff
	)

Set specific coefficient.

Set a specific coefficient into a DA object.

Parameters

[in]	jj	vector of the exponents of the coefficient to be set.
[in]	coeff	value to be set as coefficient.

Exceptions

DACE::DACEException

◆ setEps()

double DACE::DA::setEps ( const double eps )

static

Set truncation epsilon.

Set the cutoff value eps to a new value and return the previous value.

Parameters

[in] eps new cutoff value.

Returns: The previous cutoff value of eps, or zero if undefined.

Exceptions

DACE::DACEException

◆ setTO()

unsigned int DACE::DA::setTO ( const unsigned int ot = DA::getMaxOrder() )

static

Set truncation order.

Set the truncation order ot to a new value and return the previous value. All terms larger than the truncation order are discarded in subsequent operations.

Parameters

[in] ot new truncation order.

Returns: previous truncation order, or zero if undefined.

Exceptions

DACE::DACEException

See also: DA::getTO; DA::pushTO; DA::popTO

◆ sin()

DA DACE::DA::sin ( ) const

sine

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

Returns: A new DA object containing the result of the operation.

Exceptions

DACE::DACEException

◆ sinh()

DA DACE::DA::sinh ( ) const

hyperbolic sine

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

Returns: A new DA object containing the result of the operation.

Exceptions

DACE::DACEException

◆ size()

unsigned int DACE::DA::size ( ) const

Number of non-zero coefficients.

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

Returns: The number of non-zero coefficients stored in the DA object.

Exceptions

DACE::DACEException

◆ sqr()

DA DACE::DA::sqr ( ) const

square

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

Returns: A new DA object containing the result of the operation.

Exceptions

DACE::DACEException

◆ sqrt()

DA DACE::DA::sqrt ( ) const

square root

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

Returns: A new DA object containing the result of the operation.

Exceptions

DACE::DACEException

◆ tan()

DA DACE::DA::tan ( ) const

tangent

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

Returns: A new DA object containing the result of the operation.

Exceptions

DACE::DACEException

◆ tanh()

DA DACE::DA::tanh ( ) const

hyperbolic tangent

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

Returns: A new DA object containing the result of the operation.

Exceptions

DACE::DACEException

◆ toString()

std::string DACE::DA::toString ( ) const

Convert to string representation.

Convert DA object to string.

Returns: A string.

Exceptions

DACE::DACEException

◆ translateVariable()

DA DACE::DA::translateVariable	(	const unsigned int	var = `0`,
		const double	a = `1.0`,
		const double	c = `0.0`
	)		const

Translate variable number var to a*var + 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]	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

◆ trim()

DA DACE::DA::trim	(	const unsigned int	min,
		const unsigned int	max = `DA::getMaxOrder()`
	)		const

Trim the coefficients only include orders between min and max, inclusively.

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

Parameters

[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

◆ trunc()

DA DACE::DA::trunc ( ) const

Truncate the constant part to an integer.

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

Returns: A new DA object with a truncated constant part.

Exceptions

DACE::DACEException

◆ version()

void DACE::DA::version	(	int &	maj,
		int &	min,
		int &	patch
	)

static

DACE core routines version.

Return the major and minor version number of the DACE along with the patch level of the library.

Parameters

[out]	maj	major DACE version number;
[out]	min	minor DACE version number;
[out]	patch	patch level of DACE version.

See also: DA::checkVersion

◆ write()

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

Write binary representation of DA to stream.

Write a binary representation of the DA as a blob to os.

Exceptions

DACE::DACEException

Friends And Related Function Documentation

◆ compiledDA

friend class compiledDA

friend

◆ operator* [1/3]

DA DACE_API operator*	(	const DA &	da1,
		const DA &	da2
	)

friend

Multiplication between two DAs.

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* [2/3]

DA DACE_API operator*	(	const DA &	da,
		const double	c
	)

friend

Multiplication between a DA and a constant.

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* [3/3]

DA DACE_API operator*	(	const double	c,
		const DA &	da
	)

friend

Multiplication between a constant and a 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+ [1/3]

DA DACE_API operator+	(	const DA &	da1,
		const DA &	da2
	)

friend

Addition between two DAs.

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+ [2/3]

DA DACE_API operator+	(	const DA &	da,
		const double	c
	)

friend

Addition between a DA and a constant.

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+ [3/3]

DA DACE_API operator+	(	const double	c,
		const DA &	da
	)

friend

Addition between a constant and a 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- [1/3]

DA DACE_API operator-	(	const DA &	da1,
		const DA &	da2
	)

friend

Subtraction between two DAs.

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- [2/3]

DA DACE_API operator-	(	const DA &	da,
		const double	c
	)

friend

Subtraction between a DA and a constant.

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- [3/3]

DA DACE_API operator-	(	const double	c,
		const DA &	da
	)

friend

Subtraction between a constant and a 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/ [1/3]

DA DACE_API operator/	(	const DA &	da1,
		const DA &	da2
	)

friend

Division between two DAs.

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/ [2/3]

DA DACE_API operator/	(	const DA &	da,
		const double	c
	)

friend

Division between a DA and a constant.

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/ [3/3]

DA DACE_API operator/	(	const double	c,
		const DA &	da
	)

friend

Division between a constant and a 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<<

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

friend

Output to C++ stream in text form.

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>>

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

friend

Input from C++ stream in text form.

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

◆ storedDA

friend class storedDA

friend

The documentation for this class was generated from the following files:

include/dace/DA.h
DA.cpp
include/dace/DA_t.h

Public Member Functions

Static Public Member Functions

Friends

Detailed Description

Constructor & Destructor Documentation

◆ DA() [1/6]

◆ DA() [2/6]

◆ DA() [3/6]

◆ DA() [4/6]

◆ DA() [5/6]

◆ DA() [6/6]

◆ ~DA()

Member Function Documentation

◆ abs()

◆ acos()

◆ acosh()

◆ asin()

◆ asinh()

◆ atan()

◆ atan2()

◆ atanh()

◆ BesselIFunction()

◆ BesselJFunction()

◆ BesselKFunction()

◆ BesselYFunction()

◆ bound()

◆ cbrt()

◆ checkVersion()

◆ compile()

◆ cons()

◆ convRadius()

◆ cos()

◆ cosh()

◆ deriv() [1/2]

◆ deriv() [2/2]

◆ divide()

◆ erf()

◆ erfc()

◆ estimNorm() [1/2]

◆ estimNorm() [2/2]

◆ eval() [1/2]

◆ eval() [2/2]

◆ evalMonomials()

◆ evalScalar()

◆ exp()

◆ fromString() [1/2]

◆ fromString() [2/2]

◆ GammaFunction()

◆ getCoefficient()

◆ getEps()

◆ getEpsMac()

◆ getMaxMonomials()

◆ getMaxOrder()

◆ getMaxVariables()

◆ getMonomial() [1/2]

◆ getMonomial() [2/2]

◆ getMonomials()

◆ getTO()

◆ gradient()

◆ hypot()

◆ icrt()

◆ identity()

◆ init()

◆ integ() [1/2]

◆ integ() [2/2]

◆ isinf()

◆ isInitialized()

◆ isnan()

◆ isrt()

◆ linear()

◆ log()

◆ log10()

◆ log2()

◆ logb()

◆ LogGammaFunction()

◆ memdump()

◆ minv()

◆ mod()

◆ multiplyMonomials()

◆ norm()