#include <Sqrt.hpp>

Inheritance diagram for atl::Sqrt< REAL_T, EXPR >:

Public Types
typedef REAL_T	BASE_TYPE

typedef REAL_T	BASE_TYPE

Public Member Functions
	Sqrt (const ExpressionBase< REAL_T, EXPR > &a)

const REAL_T	GetValue () const

const REAL_T	GetValue (size_t i, size_t j=0) const

void	PushIds (typename atl::StackEntry< REAL_T >::vi_storage &ids) const

void	PushIds (typename atl::StackEntry< REAL_T >::vi_storage &ids, size_t i, size_t j=0) const

const REAL_T	EvaluateDerivative (uint32_t id) const

REAL_T	EvaluateDerivative (uint32_t a, uint32_t b) const

REAL_T	EvaluateDerivative (uint32_t x, uint32_t y, uint32_t z) const

const REAL_T	EvaluateDerivative (uint32_t id, size_t i, size_t j=0) const

REAL_T	EvaluateDerivative (uint32_t a, uint32_t b, size_t i, size_t j=0) const

REAL_T	EvaluateDerivative (uint32_t x, uint32_t y, uint32_t z, size_t i, size_t j=0) const

size_t	GetColumns () const

size_t	GetRows () const

bool	IsScalar () const

	Sqrt (const ExpressionBase< REAL_T, EXPR > &a)

const REAL_T	GetValue () const

const REAL_T	GetValue (size_t i, size_t j=0) const

bool	IsNonlinear () const

void	PushIds (typename atl::StackEntry< REAL_T >::vi_storage &ids) const

void	PushIds (typename atl::StackEntry< REAL_T >::vi_storage &ids, size_t i, size_t j=0) const

const REAL_T	EvaluateDerivative (uint32_t x) const

REAL_T	EvaluateDerivative (uint32_t x, uint32_t y) const

REAL_T	EvaluateDerivative (uint32_t x, uint32_t y, uint32_t z) const

const REAL_T	EvaluateDerivative (uint32_t x, size_t i, size_t j=0) const

REAL_T	EvaluateDerivative (uint32_t x, uint32_t y, size_t i, size_t j=0) const

REAL_T	EvaluateDerivative (uint32_t x, uint32_t y, uint32_t z, size_t i, size_t j=0) const

size_t	GetRows () const

bool	IsScalar () const

const std::string	ToExpressionTemplateString () const

Public Member Functions inherited from atl::ExpressionBase< REAL_T, Sqrt< REAL_T, EXPR > >
const Sqrt< REAL_T, EXPR > &	Cast () const

const Sqrt< REAL_T, EXPR > &	Cast () const

const REAL_T	GetValue () const

const REAL_T	GetValue (size_t i, size_t j=0) const

const REAL_T	GetValue () const

const REAL_T	GetValue (size_t i, size_t j=0) const

bool	IsNonlinear () const

bool	IsNonlinear () const

void	PushIds (typename atl::StackEntry< REAL_T >::vi_storage &ids) const

void	PushIds (typename atl::StackEntry< REAL_T >::vi_storage &ids, size_t i, size_t j=0) const

void	PushIds (typename atl::StackEntry< REAL_T >::vi_storage &ids) const

void	PushIds (typename atl::StackEntry< REAL_T >::vi_storage &ids, size_t i, size_t j=0) const

REAL_T	EvaluateDerivative (uint32_t a) const

REAL_T	EvaluateDerivative (uint32_t a, uint32_t b) const

REAL_T	EvaluateDerivative (uint32_t x, uint32_t y, uint32_t z) const

REAL_T	EvaluateDerivative (uint32_t a, size_t i, size_t j=0) const

REAL_T	EvaluateDerivative (uint32_t a, uint32_t b, size_t i, size_t j=0) const

REAL_T	EvaluateDerivative (uint32_t x, uint32_t y, uint32_t z, size_t i, size_t j=0) const

REAL_T	EvaluateDerivative (uint32_t x) const

REAL_T	EvaluateDerivative (uint32_t x, uint32_t y) const

REAL_T	EvaluateDerivative (uint32_t x, uint32_t y, uint32_t z) const

REAL_T	EvaluateDerivative (uint32_t x, size_t i, size_t j=0) const

REAL_T	EvaluateDerivative (uint32_t x, uint32_t y, size_t i, size_t j=0) const

REAL_T	EvaluateDerivative (uint32_t x, uint32_t y, uint32_t z, size_t i, size_t j=0) const

const ExpressionBase &	operator= (const ExpressionBase &exp) const

const ExpressionBase &	operator= (const ExpressionBase &exp) const

size_t	GetColumns () const

size_t	GetColumns () const

size_t	GetRows () const

size_t	GetRows () const

bool	IsScalar () const

bool	IsScalar () const

std::string	ToExpressionTemplateString () const

Public Attributes
const EXPR &	expr_m

Detailed Description

template<class REAL_T, class EXPR>
struct atl::Sqrt< REAL_T, EXPR >

Expression template to handle square root of a variable or container expressions.

\( \sqrt f(x) \)

or

\( \sqrt f_{i,j}(x) \)

Constructor & Destructor Documentation

template<class REAL_T , class EXPR >

atl::Sqrt< REAL_T, EXPR >::Sqrt ( const ExpressionBase< REAL_T, EXPR > & a )

inline

Constructor

Parameters

a

Member Function Documentation

template<class REAL_T , class EXPR >

const REAL_T atl::Sqrt< REAL_T, EXPR >::EvaluateDerivative ( uint32_t x ) const

inline

Evaluates the first-order derivative with respect to x.

\( {{{{d}\over{d\,x}}\,f(x)}\over{2\,\sqrt{f(x)}}} \)

Parameters

x

Returns

template<class REAL_T , class EXPR >

REAL_T atl::Sqrt< REAL_T, EXPR >::EvaluateDerivative	(	uint32_t	x,
		uint32_t	y
	)		const

inline

Evaluates the second-order derivative with respect to x and y.

\( {{{{d^2}\over{d\,x\,d\,y}}\,f(x,y)}\over{2\,\sqrt{f(x,y )}}}-{{{{d}\over{d\,x}}\,f(x,y)\,\left({{d}\over{d\,y}}\, f(x,y)\right)}\over{4\,f(x,y)^{{{3}\over{2}}}}} \)

Parameters

x
y

Returns

template<class REAL_T , class EXPR >

REAL_T atl::Sqrt< REAL_T, EXPR >::EvaluateDerivative	(	uint32_t	x,
		uint32_t	y,
		uint32_t	z
	)		const

inline

Evaluates the third-order derivative with respect to x, y, and z.

\( {{3\,\left({{d}\over{d\,x}}\,f(x,y,z)\right)\,\left({{d }\over{d\,y}}\,f(x,y,z)\right)\,\left({{d}\over{d\,z}}\,f_{i,j }(x,y,z)\right)}\over{8\,f(x,y,z)^{{{5}\over{2}}}}}-{{{{d^2 }\over{d\,x\,d\,y}}\,f(x,y,z)\,\left({{d}\over{d\,z}}\,f (x,y,z)\right)}\over{4\,f(x,y,z)^{{{3}\over{2}}}}}-{{{{d }\over{d\,x}}\,f(x,y,z)\,\left({{d^2}\over{d\,y\,d\,z}}\,f_{i, j}(x,y,z)\right)}\over{4\,f(x,y,z)^{{{3}\over{2}}}}}-{{{{d^2 }\over{d\,x\,d\,z}}\,f(x,y,z)\,\left({{d}\over{d\,y}}\,f (x,y,z)\right)}\over{4\,f(x,y,z)^{{{3}\over{2}}}}}+{{{{d^3 }\over{d\,x\,d\,y\,d\,z}}\,f(x,y,z)}\over{2\,\sqrt{f(x,y ,z)}}} \)

Parameters

x
y
z

Returns

template<class REAL_T , class EXPR >

const REAL_T atl::Sqrt< REAL_T, EXPR >::EvaluateDerivative	(	uint32_t	x,
		size_t	i,
		size_t	j = `0`
	)		const

inline

Evaluates the first-order derivative with respect to x at index {i,j}.

\( {{{{d}\over{d\,x}}\,f_{i,j}(x)}\over{2\,\sqrt{f_{i,j}(x)}}} \)

Parameters

x
i
j

Returns

template<class REAL_T , class EXPR >

REAL_T atl::Sqrt< REAL_T, EXPR >::EvaluateDerivative	(	uint32_t	x,
		uint32_t	y,
		size_t	i,
		size_t	j = `0`
	)		const

inline

Evaluates the second-order derivative with respect to x and y at index {i,j}.

\( {{{{d^2}\over{d\,x\,d\,y}}\,f_{i,j}(x,y)}\over{2\,\sqrt{f_{i,j}(x,y )}}}-{{{{d}\over{d\,x}}\,f_{i,j}(x,y)\,\left({{d}\over{d\,y}}\,f_{i, j}(x,y)\right)}\over{4\,f_{i,j}(x,y)^{{{3}\over{2}}}}} \)

Parameters

x
y
i
j

Returns

template<class REAL_T , class EXPR >

REAL_T atl::Sqrt< REAL_T, EXPR >::EvaluateDerivative	(	uint32_t	x,
		uint32_t	y,
		uint32_t	z,
		size_t	i,
		size_t	j = `0`
	)		const

inline

Evaluates the third-order derivative with respect to x, y, and z at index {i,j}.

\( {{3\,\left({{d}\over{d\,x}}\,f_{i,j}(x,y,z)\right)\,\left({{d }\over{d\,y}}\,f_{i,j}(x,y,z)\right)\,\left({{d}\over{d\,z}}\,f_{i,j }(x,y,z)\right)}\over{8\,f_{i,j}(x,y,z)^{{{5}\over{2}}}}}-{{{{d^2 }\over{d\,x\,d\,y}}\,f_{i,j}(x,y,z)\,\left({{d}\over{d\,z}}\,f_{i,j} (x,y,z)\right)}\over{4\,f_{i,j}(x,y,z)^{{{3}\over{2}}}}}-{{{{d }\over{d\,x}}\,f_{i,j}(x,y,z)\,\left({{d^2}\over{d\,y\,d\,z}}\,f_{i, j}(x,y,z)\right)}\over{4\,f_{i,j}(x,y,z)^{{{3}\over{2}}}}}-{{{{d^2 }\over{d\,x\,d\,z}}\,f_{i,j}(x,y,z)\,\left({{d}\over{d\,y}}\,f_{i,j} (x,y,z)\right)}\over{4\,f_{i,j}(x,y,z)^{{{3}\over{2}}}}}+{{{{d^3 }\over{d\,x\,d\,y\,d\,z}}\,f_{i,j}(x,y,z)}\over{2\,\sqrt{f_{i,j}(x,y ,z)}}} \)

Parameters

x
y
z
i
j

Returns

template<class REAL_T , class EXPR >

size_t atl::Sqrt< REAL_T, EXPR >::GetRows ( ) const

inline

Return the number of rows.

Returns

template<class REAL_T , class EXPR >

const REAL_T atl::Sqrt< REAL_T, EXPR >::GetValue ( ) const

inline

Compute the square root of the evaluated expression.

Returns

template<class REAL_T , class EXPR >

const REAL_T atl::Sqrt< REAL_T, EXPR >::GetValue	(	size_t	i,
		size_t	j = `0`
	)		const

inline

Compute the square root of the evaluated expression at index {i,j}.

Returns

template<class REAL_T , class EXPR >

bool atl::Sqrt< REAL_T, EXPR >::IsNonlinear ( ) const

inline

Returns true.

Returns

template<class REAL_T , class EXPR >

bool atl::Sqrt< REAL_T, EXPR >::IsScalar ( ) const

inline

True if this expression is a scalar.

Returns

template<class REAL_T , class EXPR >

void atl::Sqrt< REAL_T, EXPR >::PushIds ( typename atl::StackEntry< REAL_T >::vi_storage & ids ) const

inline

Push variable info into a set.

Parameters

ids

template<class REAL_T , class EXPR >

void atl::Sqrt< REAL_T, EXPR >::PushIds	(	typename atl::StackEntry< REAL_T >::vi_storage &	ids,
		size_t	i,
		size_t	j = `0`
	)		const

inline

Push variable info into a set at index {i,j}.

Parameters

ids
i
j

template<class REAL_T , class EXPR >

const std::string atl::Sqrt< REAL_T, EXPR >::ToExpressionTemplateString ( ) const

inline

Create a string representation of this expression template.

Returns

The documentation for this struct was generated from the following file:

ATL2/Sqrt.hpp

Public Types

Public Member Functions

Public Attributes

Detailed Description

template<class REAL_T, class EXPR> struct atl::Sqrt< REAL_T, EXPR >

Constructor & Destructor Documentation

Member Function Documentation

template<class REAL_T, class EXPR>
struct atl::Sqrt< REAL_T, EXPR >