Sundance::Deriv Class Reference

Inheritance diagram for Sundance::Deriv:

List of all members.

Public Member Functions

Deriv ()

Deriv (int coordDir)

Deriv (const SymbolicFuncElement *func, const SpatialDerivSpecifier &d)

Deriv (const SymbolicFunc *func, const SpatialDerivSpecifier &d)

bool operator< (const Deriv &other) const

bool operator== (const Deriv &other) const

std::string toString (bool verbose=false) const

bool isCoordDeriv () const

bool isFunctionalDeriv () const

bool isTestFunction () const

bool isUnknownFunction () const

bool isParameter () const

Deriv derivWrtMultiIndex (const MultiIndex &mi) const

bool canBeDifferentiated () const

int dofID () const

Return the DOF ID of my operative function, for example, if I am $\frac{\partial}{\partial D_y u_x}$ then return dofID $({\bf u})$ . If I'm not a functional derivative, throw an error.

const FunctionIdentifier & fid () const

const SpatialDerivSpecifier & opOnFunc () const

const AlgebraSpecifier & algSpec () const

const AlgebraSpecifier & funcAlgSpec () const

RCP< const CommonFuncDataStub > data () const

int coordDerivDir () const

const SymbolicFuncElement * symbFuncElem () const

const SymbolicFunc * symbFunc () const

Private Member Functions

const SymbolicFuncDescriptor * sfdPtr () const

void checkConsistencyOfOperations () const

Static Private Member Functions

static AlgebraSpecifier derivAlgSpec (const AlgebraSpecifier &a, const SpatialDerivSpecifier &sds)

Private Attributes

AlgebraSpecifier myAlgSpec_

FunctionIdentifier fid_

SpatialDerivSpecifier sds_

const SymbolicFuncElement * symbFuncElem_

const SymbolicFunc * symbFunc_

int coordDerivDir_

Related Functions

(Note that these are not member functions.)

Deriv coordDeriv (int d)

Deriv coordDeriv (const MultiIndex &mi)

Deriv funcDeriv (const SymbolicFuncElement *symbFunc)

Deriv funcDeriv (const SymbolicFuncElement *symbFunc, const MultiIndex &mi)

Deriv funcDeriv (const SymbolicFunc *symbFunc)

Deriv funcDeriv (const SymbolicFunc *symbFunc, const MultiIndex &mi)

Deriv normalDeriv (const SymbolicFuncElement *symbFunc)

Detailed Description

The purpose of this class is to represent first-order spatial or functional differential operators. This object should not be confused with the user-level Derivative object, which represents spatial differential operators as appearing in a user-level problem specification.

Functional vs spatial derivatives

The bridge theorem involves expressions of the form

$\frac{\partial \mathcal{F}}{\partial L(u)} L(\phi_u)$

and

$\frac{\partial^2 \mathcal{F}}{\partial L(u)\partial M(v)} L(\phi_u)M(\psi_v)$

where $L(u)$ is some spatial differential operator acting on the function $u$ , and $\phi_u$ is a basis function with which $u$ is represented. A derivative such as $\frac{\partial \mathcal{F}}{\partial L(u)}$ will be called a functional derivative to distinguish it from derivatives with respect to spatial coordinates, such as $\frac{\partial \mathcal{F}}{\partial x}$ . The following table shows the types of derivative currently supported.

Operation Geometry of derivative value Operating function geometry Operating spatial operator Operating function subtype

$\frac{\partial}{\partial x}$ Scalar Coordinate component N/A N/A

$\frac{\partial}{\partial p}$ Scalar Scalar ( $L^2$ ) Identity SymbolicFuncElement

$\frac{\partial}{\partial D_\alpha p}$ Coordinate component Scalar ( $H^1$ ) Partial derivative $D_\alpha$ SymbolicFuncElement

$\frac{\partial}{\partial D_n p}$ Normal component Scalar ( $H^1$ ) Normal derivative ${\bf n}\cdot \nabla$ SymbolicFuncElement

$\frac{\partial}{\partial \mathrm{div}({\bf u})}$ Scalar Vector ( ${\bf H}(div)$ ) Divergence SymbolicFunc

$\frac{\partial}{\partial {\bf u\cdot e_\alpha}}$ Coordinate component Vector ( ${\bf H}^1$ , ${\bf H}(div)$ , or ${\bf H}(curl)$ ) Inner product with coordinate unit vector SymbolicFuncElement

$\frac{\partial}{\partial {\bf u\cdot n}}$ Normal component Vector ( ${\bf H}^1$ or ${\bf H}(div)$ ) Inner product with normal unit vector SymbolicFunc

$\frac{\partial}{\partial D_\alpha ({\bf u\cdot e_\beta})}$ Coordinate component Vector ( ${\bf H}^1$ ) Inner product with normal unit vector SymbolicFuncElement

Definition at line 143 of file SundanceDeriv.hpp.

Constructor & Destructor Documentation

Deriv::Deriv ( )

An empty ctor is needed for use with std::vector. The empty ctor creates a null derivative, representing an identity operator.

Definition at line 49 of file SundanceDeriv.cpp.

Referenced by derivWrtMultiIndex().

Deriv::Deriv ( int coordDir )

Construct a deriv wrt a coordinate, e.g., $D_x$ .

Definition at line 54 of file SundanceDeriv.cpp.

Deriv::Deriv	(	const SymbolicFuncElement *	func,
		const SpatialDerivSpecifier &	d
	)

Construct a deriv wrt an object of length one, for example, a scalar function or a single component of a vector function, or possibly a spatial derivative of such an object. Examples:

is a scalar-valued function

Definition at line 62 of file SundanceDeriv.cpp.

References Sundance::FunctionIdentifier::algSpec(), checkConsistencyOfOperations(), derivAlgSpec(), Sundance::FunctionWithID::fid(), fid_, and myAlgSpec_.

Deriv::Deriv	(	const SymbolicFunc *	func,
		const SpatialDerivSpecifier &	d
	)

Construct a deriv wrt a function

Definition at line 79 of file SundanceDeriv.cpp.

References Sundance::FunctionIdentifier::algSpec(), checkConsistencyOfOperations(), derivAlgSpec(), Sundance::FunctionWithID::fid(), fid_, and myAlgSpec_.

Member Function Documentation

const AlgebraSpecifier& Sundance::Deriv::algSpec ( ) const [inline]

Indicate my algebra type

Definition at line 227 of file SundanceDeriv.hpp.

References myAlgSpec_.

bool Deriv::canBeDifferentiated ( ) const

Whether it's possible to take a spatial derivative of this object

Definition at line 222 of file SundanceDeriv.cpp.

References Sundance::EnumTypeField< DerivType >::assertType(), Sundance::FunctionalDT, Sundance::SpatialDerivSpecifier::isIdentity(), isParameter(), Sundance::SpatialDerivSpecifier::isPartial(), and opOnFunc().

void Deriv::checkConsistencyOfOperations ( ) const [private]

Definition at line 96 of file SundanceDeriv.cpp.

References fid_, Sundance::SpatialDerivSpecifier::isDivergence(), Sundance::SpatialDerivSpecifier::isNormal(), Sundance::SpatialDerivSpecifier::isPartial(), Sundance::FunctionIdentifier::isVector(), and sds_.

Referenced by Deriv().

int Deriv::coordDerivDir ( ) const

If I am a coordinate derivative, return my direction

Definition at line 229 of file SundanceDeriv.cpp.

References Sundance::EnumTypeField< DerivType >::assertType(), coordDerivDir_, and Sundance::CoordDT.

Referenced by Sundance::DiffOpEvaluator::DiffOpEvaluator(), operator<(), and toString().

RCP< const CommonFuncDataStub > Deriv::data ( ) const

Return a pointer to my function's data

Definition at line 235 of file SundanceDeriv.cpp.

References Sundance::EnumTypeField< DerivType >::assertType(), Sundance::SymbolicFunc::commonData(), Sundance::SymbolicFuncElement::commonData(), Sundance::FunctionalDT, symbFunc_, and symbFuncElem_.

AlgebraSpecifier Deriv::derivAlgSpec	(	const AlgebraSpecifier &	a,
		const SpatialDerivSpecifier &	sds
	)			`[static, private]`

Definition at line 284 of file SundanceDeriv.cpp.

References Sundance::SpatialDerivSpecifier::derivOrder(), Sundance::MultiIndex::firstOrderDirection(), Sundance::IdentitySDT, Sundance::SpatialDerivSpecifier::isDivergence(), Sundance::SpatialDerivSpecifier::isNormal(), Sundance::SpatialDerivSpecifier::isPartial(), Sundance::SpatialDerivSpecifier::mi(), Sundance::NormalAT, and Sundance::ScalarAT.

Referenced by Deriv().

Deriv Deriv::derivWrtMultiIndex ( const MultiIndex & mi ) const

Create a new functional derivative in which the function has been differentiated spatially by the given multi index, for example, derivWrtMultiIndex(MultiIndex(0,0,1)) transforms $\frac{\partial}{\partial p}$ to $\frac{\partial}{\partial D_z p}$

Definition at line 259 of file SundanceDeriv.cpp.

References Sundance::EnumTypeField< DerivType >::assertType(), Deriv(), Sundance::SpatialDerivSpecifier::derivWrtMultiIndex(), Sundance::FunctionalDT, Sundance::SpatialDerivSpecifier::isDivergence(), isParameter(), Sundance::MultiIndex::order(), sds_, symbFunc_, and symbFuncElem_.

Referenced by Sundance::applyTx().

int Deriv::dofID ( ) const

Return the DOF ID of my operative function, for example, if I am $\frac{\partial}{\partial D_y u_x}$ then return dofID $({\bf u})$ . If I'm not a functional derivative, throw an error.

Definition at line 210 of file SundanceDeriv.cpp.

References Sundance::EnumTypeField< DerivType >::assertType(), Sundance::FunctionIdentifier::dofID(), fid_, and Sundance::FunctionalDT.

const FunctionIdentifier & Deriv::fid ( ) const

Return the ID for my operative function

Definition at line 247 of file SundanceDeriv.cpp.

References Sundance::EnumTypeField< DerivType >::assertType(), fid_, and Sundance::FunctionalDT.

Referenced by Sundance::DiffOpEvaluator::backedDerivs(), Sundance::GrouperBase::extractWeakForm(), and operator<().

const AlgebraSpecifier & Deriv::funcAlgSpec ( ) const

Indicate the algebra type of my operative function

Definition at line 216 of file SundanceDeriv.cpp.

References Sundance::FunctionIdentifier::algSpec(), Sundance::EnumTypeField< DerivType >::assertType(), fid_, and Sundance::FunctionalDT.

bool Sundance::Deriv::isCoordDeriv ( ) const [inline]

True if this is a derivative wrt a spatial coordinate

Definition at line 186 of file SundanceDeriv.hpp.

References Sundance::CoordDT, and Sundance::EnumTypeField< DerivType >::type().

Referenced by Sundance::DiffOpEvaluator::backedDerivs(), and Sundance::DiffOpEvaluator::DiffOpEvaluator().

bool Sundance::Deriv::isFunctionalDeriv ( ) const [inline]

True if this is a derivative wrt a function or a spatial derivative of a function

Definition at line 190 of file SundanceDeriv.hpp.

References Sundance::FunctionalDT, and Sundance::EnumTypeField< DerivType >::type().

Referenced by Sundance::EquationSet::addToVarUnkPairs(), Sundance::applyTx(), Sundance::GrouperBase::extractWeakForm(), isParameter(), isTestFunction(), isUnknownFunction(), and Sundance::CoordDeriv::lessThan().

bool Deriv::isParameter ( ) const

True if my operative function is a parameter

Definition at line 201 of file SundanceDeriv.cpp.

References isFunctionalDeriv(), Sundance::SymbolicFuncDescriptor::isParameter(), and sfdPtr().

Referenced by canBeDifferentiated(), derivWrtMultiIndex(), and Sundance::GrouperBase::extractWeakForm().

bool Deriv::isTestFunction ( ) const

True if my operative function is a test function

Definition at line 182 of file SundanceDeriv.cpp.

References isFunctionalDeriv(), Sundance::SymbolicFuncDescriptor::isTestFunction(), and sfdPtr().

bool Deriv::isUnknownFunction ( ) const

True if my operative function is unknown

Definition at line 191 of file SundanceDeriv.cpp.

References isFunctionalDeriv(), Sundance::SymbolicFuncDescriptor::isUnknownFunction(), and sfdPtr().

bool Deriv::operator< ( const Deriv & other ) const

Comparison operator for use in sets and maps

Definition at line 104 of file SundanceDeriv.cpp.

References coordDerivDir(), Sundance::CoordDT, fid(), sds_, Sundance::EnumTypeField< T >::type(), and Sundance::EnumTypeField< DerivType >::type().

bool Deriv::operator== ( const Deriv & other ) const

Equality test operator

Definition at line 122 of file SundanceDeriv.cpp.

const SpatialDerivSpecifier & Deriv::opOnFunc ( ) const

Return the spatial derivative acting on my operative function

Definition at line 253 of file SundanceDeriv.cpp.

References Sundance::EnumTypeField< DerivType >::assertType(), Sundance::FunctionalDT, and sds_.

Referenced by Sundance::applyTx(), Sundance::DiffOpEvaluator::backedDerivs(), canBeDifferentiated(), Sundance::DiffOpEvaluator::DiffOpEvaluator(), Sundance::GrouperBase::extractWeakForm(), and toString().

const SymbolicFuncDescriptor * Deriv::sfdPtr ( ) const [private]

Definition at line 168 of file SundanceDeriv.cpp.

References Sundance::EnumTypeField< DerivType >::assertType(), Sundance::FunctionalDT, symbFunc_, and symbFuncElem_.

Referenced by isParameter(), isTestFunction(), and isUnknownFunction().

const SymbolicFunc* Sundance::Deriv::symbFunc ( ) const [inline]

Return a pointer to my operative function

Definition at line 242 of file SundanceDeriv.hpp.

References symbFunc_.

const SymbolicFuncElement* Sundance::Deriv::symbFuncElem ( ) const [inline]

Return a pointer to my operative function

Definition at line 239 of file SundanceDeriv.hpp.

References symbFuncElem_.

Referenced by Sundance::DiffOpEvaluator::DiffOpEvaluator(), and Sundance::GrouperBase::extractWeakForm().

std::string Deriv::toString ( bool verbose = false ) const

Write to a std::string

Parameters:

verbose

If true, write all details for the object. If false, write a simple description giving only the function name and the specification of a derivative.

Definition at line 127 of file SundanceDeriv.cpp.

References coordDerivDir(), Sundance::CoordDT, Sundance::MultiIndex::firstOrderDirection(), Sundance::FunctionalDT, Sundance::SpatialDerivSpecifier::mi(), Sundance::NullDT, opOnFunc(), symbFunc_, symbFuncElem_, Sundance::ExprBase::toString(), and Sundance::EnumTypeField< DerivType >::type().

Friends And Related Function Documentation

Deriv coordDeriv ( const MultiIndex & mi ) [related]

Definition at line 322 of file SundanceDeriv.cpp.

Deriv coordDeriv ( int d ) [related]

Definition at line 317 of file SundanceDeriv.cpp.

Referenced by Sundance::DiscreteFuncElement::internalDetermineR(), and Sundance::CoordDeriv::lessThan().

Deriv funcDeriv	(	const SymbolicFunc *	symbFunc,
		const MultiIndex &	mi
	)			`[related]`

Definition at line 345 of file SundanceDeriv.cpp.

Deriv funcDeriv ( const SymbolicFunc * symbFunc ) [related]

Definition at line 339 of file SundanceDeriv.cpp.

Deriv funcDeriv	(	const SymbolicFuncElement *	symbFunc,
		const MultiIndex &	mi
	)			`[related]`

Definition at line 333 of file SundanceDeriv.cpp.

Deriv funcDeriv ( const SymbolicFuncElement * symbFunc ) [related]

Definition at line 328 of file SundanceDeriv.cpp.

Deriv normalDeriv ( const SymbolicFuncElement * symbFunc ) [related]

Definition at line 352 of file SundanceDeriv.cpp.

Member Data Documentation

int Sundance::Deriv::coordDerivDir_ [private]

Definition at line 265 of file SundanceDeriv.hpp.

Referenced by coordDerivDir().

FunctionIdentifier Sundance::Deriv::fid_ [private]

Definition at line 257 of file SundanceDeriv.hpp.

Referenced by checkConsistencyOfOperations(), Deriv(), dofID(), fid(), and funcAlgSpec().

AlgebraSpecifier Sundance::Deriv::myAlgSpec_ [private]

Definition at line 255 of file SundanceDeriv.hpp.

Referenced by algSpec(), and Deriv().

SpatialDerivSpecifier Sundance::Deriv::sds_ [private]

Definition at line 259 of file SundanceDeriv.hpp.

Referenced by checkConsistencyOfOperations(), derivWrtMultiIndex(), operator<(), and opOnFunc().

const SymbolicFunc* Sundance::Deriv::symbFunc_ [private]

Definition at line 263 of file SundanceDeriv.hpp.

Referenced by data(), derivWrtMultiIndex(), sfdPtr(), symbFunc(), and toString().

const SymbolicFuncElement* Sundance::Deriv::symbFuncElem_ [private]

Definition at line 261 of file SundanceDeriv.hpp.

Referenced by data(), derivWrtMultiIndex(), sfdPtr(), symbFuncElem(), and toString().


Public Member Functions
	Deriv ()
	Deriv (int coordDir)
	Deriv (const SymbolicFuncElement *func, const SpatialDerivSpecifier &d)
	Deriv (const SymbolicFunc *func, const SpatialDerivSpecifier &d)
bool	operator< (const Deriv &other) const
bool	operator== (const Deriv &other) const
std::string	toString (bool verbose=false) const
bool	isCoordDeriv () const
bool	isFunctionalDeriv () const
bool	isTestFunction () const
bool	isUnknownFunction () const
bool	isParameter () const
Deriv	derivWrtMultiIndex (const MultiIndex &mi) const
bool	canBeDifferentiated () const
int	dofID () const
	Return the DOF ID of my operative function, for example, if I am $\frac{\partial}{\partial D_y u_x}$ then return `dofID` $({\bf u})$ . If I'm not a functional derivative, throw an error.
const FunctionIdentifier &	fid () const
const SpatialDerivSpecifier &	opOnFunc () const
const AlgebraSpecifier &	algSpec () const
const AlgebraSpecifier &	funcAlgSpec () const
RCP< const CommonFuncDataStub >	data () const
int	coordDerivDir () const
const SymbolicFuncElement *	symbFuncElem () const
const SymbolicFunc *	symbFunc () const
Private Member Functions
const SymbolicFuncDescriptor *	sfdPtr () const
void	checkConsistencyOfOperations () const
Static Private Member Functions
static AlgebraSpecifier	derivAlgSpec (const AlgebraSpecifier &a, const SpatialDerivSpecifier &sds)
Private Attributes
AlgebraSpecifier	myAlgSpec_
FunctionIdentifier	fid_
SpatialDerivSpecifier	sds_
const SymbolicFuncElement *	symbFuncElem_
const SymbolicFunc *	symbFunc_
int	coordDerivDir_
Related Functions
(Note that these are not member functions.)
Deriv	coordDeriv (int d)
Deriv	coordDeriv (const MultiIndex &mi)
Deriv	funcDeriv (const SymbolicFuncElement *symbFunc)
Deriv	funcDeriv (const SymbolicFuncElement *symbFunc, const MultiIndex &mi)
Deriv	funcDeriv (const SymbolicFunc *symbFunc)
Deriv	funcDeriv (const SymbolicFunc *symbFunc, const MultiIndex &mi)
Deriv	normalDeriv (const SymbolicFuncElement *symbFunc)

Operation	Geometry of derivative value	Operating function geometry	Operating spatial operator	Operating function subtype
$\frac{\partial}{\partial x}$	Scalar	Coordinate component	N/A	N/A
$\frac{\partial}{\partial p}$	Scalar	Scalar ()	Identity	SymbolicFuncElement
$\frac{\partial}{\partial D_\alpha p}$	Coordinate component	Scalar ()	Partial derivative $D_\alpha$	SymbolicFuncElement
$\frac{\partial}{\partial D_n p}$	Normal component	Scalar ()	Normal derivative ${\bf n}\cdot \nabla$	SymbolicFuncElement
$\frac{\partial}{\partial \mathrm{div}({\bf u})}$	Scalar	Vector ( ${\bf H}(div)$ )	Divergence	SymbolicFunc
$\frac{\partial}{\partial {\bf u\cdot e_\alpha}}$	Coordinate component	Vector ( ${\bf H}^1$ , ${\bf H}(div)$ , or ${\bf H}(curl)$ )	Inner product with coordinate unit vector	SymbolicFuncElement
$\frac{\partial}{\partial {\bf u\cdot n}}$	Normal component	Vector ( ${\bf H}^1$ or ${\bf H}(div)$ )	Inner product with normal unit vector	SymbolicFunc
$\frac{\partial}{\partial D_\alpha ({\bf u\cdot e_\beta})}$	Coordinate component	Vector ( ${\bf H}^1$ )	Inner product with normal unit vector	SymbolicFuncElement