A scalar multi-variate polynomial containing sines and cosines. More...

#include <drake/util/TrigPoly.h>

Classes
struct	Product

struct	SinCosVars

Public Types
typedef _CoefficientType	CoefficientType

typedef Polynomial< CoefficientType >	PolyType

typedef PolyType::VarType	VarType

typedef std::map< VarType, SinCosVars >	SinCosMap

Public Member Functions
	TrigPoly ()
	Constructs a vacuous TrigPoly. More...

	TrigPoly (const CoefficientType &scalar)
	Constructs a constant TrigPoly. More...

	TrigPoly (const PolyType &p, const SinCosMap &_sin_cos_map)
	Constructs a TrigPoly on the associated Polynomial p, but with the additional information about sin and cos relations in _sin_cos_map. More...

	TrigPoly (const PolyType &q, const PolyType &s, const PolyType &c)
	Constructs a TrigPoly version of q, but with the additional information that the variables s and c represent the sine and cosine of q. More...

const PolyType &	getPolynomial (void) const
	Returns the underlying Polynomial for this TrigPoly. More...

const SinCosMap &	getSinCosMap (void) const
	Returns the SinCosMap for this TrigPoly. More...

std::set< VarType >	getVariables () const
	Returns all of the base (non-sin/cos) variables in this TrigPoly. More...

template<typename T >
Product< CoefficientType, T >::type	evaluateMultivariate (const std::map< VarType, T > &var_values) const
	Given a value for every variable in this expression, evaluates it. More...

virtual TrigPoly< CoefficientType >	evaluatePartial (const std::map< VarType, CoefficientType > &var_values) const
	Partially evaluates this expression, returning the resulting expression. More...

bool	operator== (const TrigPoly &other) const
	Compares two TrigPolys for equality. More...

TrigPoly &	operator+= (const TrigPoly &other)

TrigPoly &	operator-= (const TrigPoly &other)

TrigPoly &	operator*= (const TrigPoly &other)

TrigPoly &	operator+= (const CoefficientType &scalar)

TrigPoly &	operator-= (const CoefficientType &scalar)

TrigPoly &	operator*= (const CoefficientType &scalar)

TrigPoly &	operator/= (const CoefficientType &scalar)

const TrigPoly	operator+ (const TrigPoly &other) const

const TrigPoly	operator- (const TrigPoly &other) const

const TrigPoly	operator- () const

const TrigPoly	operator* (const TrigPoly &other) const

const TrigPoly	operator/ (const CoefficientType &scalar) const

Friends
TrigPoly	sin (const TrigPoly &p)
	A version of sin that handles TrigPoly arguments through ADL. More...

TrigPoly	cos (const TrigPoly &p)
	A version of cos that handles TrigPoly arguments through ADL. More...

const TrigPoly	operator+ (const TrigPoly &p, const CoefficientType &scalar)

const TrigPoly	operator+ (const CoefficientType &scalar, const TrigPoly &p)

const TrigPoly	operator- (const TrigPoly &p, const CoefficientType &scalar)

const TrigPoly	operator- (const CoefficientType &scalar, const TrigPoly &p)

const TrigPoly	operator* (const TrigPoly &p, const CoefficientType &scalar)

const TrigPoly	operator* (const CoefficientType &scalar, const TrigPoly &p)

std::ostream &	operator<< (std::ostream &os, const TrigPoly< CoefficientType > &tp)

Detailed Description

template<typename _CoefficientType = double>
class TrigPoly< _CoefficientType >

A scalar multi-variate polynomial containing sines and cosines.

TrigPoly represents a Polynomial some of whose variables actually represent the sines or cosines of other variables. Sines and cosines of first-order polynomials (affine combinations of variables) are decomposed into polynomials of the sines and cosines of individual variables via the Prosthaphaeresis formulae.

Any variables which will appear in the arguments to trigonometric functions must be declared in the "SinCosMap" (created automatically by most TrigPoly constructors); attempting to, e.g., use sin(x) without first creating a SinCosMap mapping for 'x' will result in an exception.

The same variable may not appear more than once in the sin_cos_map, regardless of position.

For example:

Polynomial base_x("x"), s("s"), c("c");
TrigPoly x(base_x, s, c)  // This "x" knows that s = sin(x)
                          // and that c = cos(x)
cout << sin(x)                     // emits "s1"
cout << sin(x) * x                 // emits "x1*s1"
cout << sin(x + x) * x             // emits "x1*s1*c1 + x1*c1*s1"

NOTE: Certain analyses may not succeed when individual Monomials contain both x and sin(x) or cos(x) terms. This restriction is not currently enforced programmatically; TODO(ggould-tri) fix this in the future.

Member Typedef Documentation

typedef _CoefficientType CoefficientType

typedef Polynomial<CoefficientType> PolyType

typedef std::map<VarType, SinCosVars> SinCosMap

typedef PolyType::VarType VarType

Constructor & Destructor Documentation

TrigPoly ( )

inline

Constructs a vacuous TrigPoly.

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TrigPoly ( const CoefficientType & scalar )

inline

Constructs a constant TrigPoly.

TrigPoly	(	const PolyType &	p,
		const SinCosMap &	_sin_cos_map
	)

inline

Constructs a TrigPoly on the associated Polynomial p, but with the additional information about sin and cos relations in _sin_cos_map.

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TrigPoly	(	const PolyType &	q,
		const PolyType &	s,
		const PolyType &	c
	)

inline

Constructs a TrigPoly version of q, but with the additional information that the variables s and c represent the sine and cosine of q.

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Member Function Documentation

Product<CoefficientType, T>::type evaluateMultivariate ( const std::map< VarType, T > & var_values ) const

inline

Given a value for every variable in this expression, evaluates it.

By analogy with Polynomial::evaluateMultivariate(). Values must be supplied for all base variables; supplying values for sin/cos variables is an error.

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virtual TrigPoly<CoefficientType> evaluatePartial ( const std::map< VarType, CoefficientType > & var_values ) const

inlinevirtual

Partially evaluates this expression, returning the resulting expression.

By analogy with Polynomial::evaluatePartial. Values must be supplied for all base variables only; supplying values for sin/cos variables is an error.

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const PolyType& getPolynomial ( void ) const

inline

Returns the underlying Polynomial for this TrigPoly.

const SinCosMap& getSinCosMap ( void ) const

inline

Returns the SinCosMap for this TrigPoly.

std::set<VarType> getVariables ( ) const

inline

Returns all of the base (non-sin/cos) variables in this TrigPoly.

const TrigPoly operator* ( const TrigPoly< _CoefficientType > & other ) const

inline

TrigPoly& operator*= ( const TrigPoly< _CoefficientType > & other )

inline

TrigPoly& operator*= ( const CoefficientType & scalar )

inline

const TrigPoly operator+ ( const TrigPoly< _CoefficientType > & other ) const

inline

TrigPoly& operator+= ( const TrigPoly< _CoefficientType > & other )

inline

TrigPoly& operator+= ( const CoefficientType & scalar )

inline

const TrigPoly operator- ( const TrigPoly< _CoefficientType > & other ) const

inline

const TrigPoly operator- ( ) const

inline

TrigPoly& operator-= ( const TrigPoly< _CoefficientType > & other )

inline

TrigPoly& operator-= ( const CoefficientType & scalar )

inline

const TrigPoly operator/ ( const CoefficientType & scalar ) const

inline

TrigPoly& operator/= ( const CoefficientType & scalar )

inline

bool operator== ( const TrigPoly< _CoefficientType > & other ) const

inline

Compares two TrigPolys for equality.

Note that the question of equality of TrigPolys is a bit subtle. It is not immediately clear if two TrigPolys whose poly and sin_cos_map members differ equivalently (eg, a + b (b = cos(a)) and a + c (c = cos(a))) should be considered equal.

For simplicity we only consider exactly equality rather than semantic equivalence. However that decision could reasonably revisited in the future.

Friends And Related Function Documentation

TrigPoly cos ( const TrigPoly< _CoefficientType > & p )

friend

A version of cos that handles TrigPoly arguments through ADL.

Implements cos(x) for a TrigPoly x.

x must be of degree 0 or 1, and must contain only variables that have entries in its SinCosMap.

const TrigPoly operator*	(	const TrigPoly< _CoefficientType > &	p,
		const CoefficientType &	scalar
	)

friend

const TrigPoly operator*	(	const CoefficientType &	scalar,
		const TrigPoly< _CoefficientType > &	p
	)

friend

const TrigPoly operator+	(	const TrigPoly< _CoefficientType > &	p,
		const CoefficientType &	scalar
	)

friend

const TrigPoly operator+	(	const CoefficientType &	scalar,
		const TrigPoly< _CoefficientType > &	p
	)

friend

const TrigPoly operator-	(	const TrigPoly< _CoefficientType > &	p,
		const CoefficientType &	scalar
	)

friend

const TrigPoly operator-	(	const CoefficientType &	scalar,
		const TrigPoly< _CoefficientType > &	p
	)

friend

std::ostream& operator<<	(	std::ostream &	os,
		const TrigPoly< CoefficientType > &	tp
	)

friend

TrigPoly sin ( const TrigPoly< _CoefficientType > & p )

friend

A version of sin that handles TrigPoly arguments through ADL.

Implements sin(x) for a TrigPoly x.

x must be of degree 0 or 1, and must contain only variables that have entries in its SinCosMap.

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

drake/util/TrigPoly.h

Classes

Public Types

Public Member Functions

Friends

Detailed Description

template<typename _CoefficientType = double> class TrigPoly< _CoefficientType >

Member Typedef Documentation

Constructor & Destructor Documentation

Member Function Documentation

Friends And Related Function Documentation

template<typename _CoefficientType = double>
class TrigPoly< _CoefficientType >