Inheritance diagram for Sundance::Deriv:

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 ( )	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

Definition at line 154 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 60 of file SundanceDeriv.cpp.

Referenced by derivWrtMultiIndex().

Deriv::Deriv ( int coordDir )

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

Definition at line 65 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 73 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 90 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 238 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 233 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 107 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 240 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 246 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 295 of file SundanceDeriv.cpp.

References Sundance::SpatialDerivSpecifier::derivOrder(), Sundance::MultiIndex::firstOrderDirection(), funcAlgSpec(), 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 270 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 221 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 258 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 227 of file SundanceDeriv.cpp.

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

Referenced by derivAlgSpec().

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

True if this is a derivative wrt a spatial coordinate

Definition at line 197 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 201 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 212 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 193 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 202 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 115 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 133 of file SundanceDeriv.cpp.

const SpatialDerivSpecifier & Deriv::opOnFunc ( ) const

Return the spatial derivative acting on my operative function

Definition at line 264 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 179 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 253 of file SundanceDeriv.hpp.

References symbFunc_.

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

Return a pointer to my operative function

Definition at line 250 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 138 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().