Inheritance diagram for Sundance::Expr:

Public Member Functions
	Expr ()
	Expr (Handleable< ExprBase > *rawPtr)
	Expr (const RefCountPtr< ExprBase > &smartPtr)
	Expr (const double &c)
	Expr (const std::complex< double > &c)
Expr	operator+ (const Expr &other) const
Expr	operator- (const Expr &other) const
Expr	operator* (const Expr &other) const
Expr	operator/ (const Expr &other) const
Expr	operator/ (const double &other) const
Expr	operator/ (const std::complex< double > &other) const
Expr	operator- () const
Expr	real () const
Expr	imag () const
Expr	conj () const
const Expr &	operator[] (int i) const
int	size () const
int	totalSize () const
void	append (const Expr &expr)
Expr	flatten () const
Expr	flattenSpectral () const
std::string	toString () const
XMLObject	toXML () const
bool	isComplex () const
bool	isSpectral () const
bool	isTestElement () const
bool	isUnknownElement () const
void	setParameterValue (const double &value)
double	getParameterValue () const
bool	isIndependentOf (const Expr &u) const
bool	isLinearInTests () const
bool	everyTermHasTestFunctions () const
bool	hasTestFunctions () const
bool	isLinearForm (const Expr &u) const
bool	isQuadraticForm (const Expr &u) const
void	getUnknowns (Set< int > &unkID, Array< Expr > &unks) const
void	getTests (Set< int > &testID, Array< Expr > &tests) const
bool	lessThan (const Expr &other) const
bool	operator< (const Expr &other) const
bool	sameAs (const Expr &other) const
Sundance::Map< Expr, int >	getSumTree () const
const ScalarExpr *	scalarExpr () const
const FuncElementBase *	funcElement () const
Static Public Member Functions
static bool &	evaluationCachingOn ()
static bool &	showAllParens ()
static Expr	handle (const RCP< ExprBase > &ptr)
static Time &	opTimer ()
static Time &	outputTimer ()
Private Member Functions
Expr	sum (const Expr &other, int sign) const
Expr	multiply (const Expr &other) const
Expr	divide (const Expr &other) const
bool	tryAddComplex (const Expr &L, const Expr &R, int sign, Expr &rtn) const
bool	tryMultiplyComplex (const Expr &L, const Expr &R, Expr &rtn) const
Related Functions
(Note that these are not member functions.)
Expr	EssentialBC (const Handle< CellFilterStub > &domain, const Expr &integrand, const WatchFlag &watch=WatchFlag())
Expr	EssentialBC (const Handle< CellFilterStub > &domain, const Expr &integrand, const Handle< QuadratureFamilyStub > &quad, const WatchFlag &watch=WatchFlag())
Expr	EssentialBC (const Handle< CellFilterStub > &domain, const Expr &integrand, const Handle< QuadratureFamilyStub > &quad, const ParametrizedCurve &curve, const WatchFlag &watch=WatchFlag())
std::ostream &	operator<< (std::ostream &os, const Expr &e)
Expr	operator+ (const double &a, const Expr &x)
Expr	operator- (const double &a, const Expr &x)
Expr	operator* (const double &a, const Expr &x)
Expr	operator/ (const double &a, const Expr &x)
Expr	operator+ (const std::complex< double > &a, const Expr &x)
Expr	operator- (const std::complex< double > &a, const Expr &x)
Expr	operator* (const std::complex< double > &a, const Expr &x)
Expr	operator/ (const std::complex< double > &a, const Expr &x)
Expr	Re (const Expr &a)
Expr	Im (const Expr &a)
Expr	conj (const Expr &a)
Expr	Complex (const Expr &real, const Expr &imag)
Expr	List (const Expr &a)
Expr	List (const Expr &a, const Expr &b)
Expr	List (const Expr &a, const Expr &b, const Expr &c)
Expr	List (const Expr &a, const Expr &b, const Expr &c, const Expr &d)
Expr	List (const Expr &a, const Expr &b, const Expr &c, const Expr &d, const Expr &e)
Expr	List (const Expr &a, const Expr &b, const Expr &c, const Expr &d, const Expr &e, const Expr &f)
Expr	List (const Expr &a, const Expr &b, const Expr &c, const Expr &d, const Expr &e, const Expr &f, const Expr &g)
Expr	List (const Expr &a, const Expr &b, const Expr &c, const Expr &d, const Expr &e, const Expr &f, const Expr &g, const Expr &h)
Expr	List (const Expr &a, const Expr &b, const Expr &c, const Expr &d, const Expr &e, const Expr &f, const Expr &g, const Expr &h, const Expr &i)
Expr	List (const Expr &a, const Expr &b, const Expr &c, const Expr &d, const Expr &e, const Expr &f, const Expr &g, const Expr &h, const Expr &i, const Expr &j)
Expr	FunctionalDerivative (const Expr &F, const Expr &u)
Expr	gradient (int dim)
Expr	div (const Expr &f)
Expr	cross (const Expr &a, const Expr &b)
Expr	curl (const Expr &f)
Expr	colonProduct (const Expr &A, const Expr &B)
Expr	outerProduct (const Expr &a, const Expr &b)
bool	isSquareMatrix (const Expr &x, int &N)
bool	isVector (const Expr &x, int &N)
Elementary math functions
Expr	reciprocal (const Expr &arg)
Expr	fabs (const Expr &arg)
Expr	sign (const Expr &arg)
Expr	exp (const Expr &arg)
Expr	log (const Expr &arg)
Expr	sqrt (const Expr &arg)
Expr	sin (const Expr &arg)
Expr	cos (const Expr &arg)
Expr	tan (const Expr &arg)
Expr	asin (const Expr &arg)
Expr	acos (const Expr &arg)
Expr	atan (const Expr &arg)
Expr	sinh (const Expr &arg)
Expr	cosh (const Expr &arg)
Expr	tanh (const Expr &arg)
Expr	asinh (const Expr &arg)
Expr	acosh (const Expr &arg)
Expr	atanh (const Expr &arg)

Detailed Description

User-level expression class. Expr is a handle to a reference-counted pointer to a ExprBase subtype. As such, expression copies and assignments are shallow.

Lists

Expressions can be grouped into lists with an arbitrary structure. Important special cases are scalar, vector, and tensor expressions.

Creating Lists

Vector expressions
```
 Expr v = List(vx, vy, vz);
```

Heterogeneous lists

 // Form vector {vx, vy, vz} 
 Expr v = List(vx, vy, vz);
 Expr q = new TestFunction(new Lagrange(1));
 // Form heterogeneous list {{vx, vy, vz}, q}
 Expr state = List(v, q);

Probing Lists

Finding the size of the top level of a list

 // Form vector {vx, vy, vz} 
 Expr v = List(vx, vy, vz);
 Expr q = new TestFunction(new Lagrange(1));
 // Form heterogeneous list {{vx, vy, vz}, q}
 Expr state = List(v, q);
 // Check top-level size of state list {{vx, vy, vz}, q}
 int stateSize = state.size(); // returns 2

Finding the total size of a list

 // Check total size of state list 
 int totalSize = state.totalSize(); // returns 4

Manipulating Lists

Arithmetic Operations

Addition
```
 Expr sum = x + y;
```
The operands must have identical list structures.
Subtraction
```
 Expr diff = x - y;
```
The operands must have identical list structures.
Multiplication
```
 Expr product = x * y;
```
The operands must have list structures such that the product can be interpreted as a scalar-vector product or as an inner product between vectors or tensors. The multiplication operator is also used to represent the application of a differential operator.
Division
```
 Expr quotient = x / y;
```
The denominator must be scalar-valued.

Expression Subtypes

The user-level expression subtypes are listed below, along with examples of their use.

UnknownFunction - Represents an unknown function in a finite-element problem. Unknown functions can be scalar-valued or vector valued.

Example of creation of a scalar-valued unknown function:
```
 Expr u = new UnknownFunction(new Lagrange(1));
```
Example of creation of a vector-valued unknown function:
```
 Expr u = new UnknownFunction(List(new Lagrange(1), new Lagrange(1)));
```
TestFunction - Represents a test function in a finite-element problem. Test functions can be scalar-valued or vector valued.

Example of creation of a scalar-valued test function:
```
 Expr v = new TestFunction(new Lagrange(1));
```
Example of creation of a vector-valued test function:
```
 Expr u = new TestFunction(List(new Lagrange(1), new Lagrange(1)));
```
Derivative - Represents a spatial derivative operator. Spatial derivatives are applied using the multiplication operator.
```
 Expr dx = new Derivative(0);
 Expr convect = (u*dx)*u;
```
Derivative expressions are scalar valued. However, vector differential operators can be created using the List operator. For example,
```
 Expr dx = new Derivative(0);
 Expr dy = new Derivative(1);
 Expr grad = List(dx, dy);
```

CoordExpr - Represents a coordinate functions.

 Expr x = new CoordExpr(0);
 Expr y = new CoordExpr(1);
 Expr r = sqrt(x*x + y*y);

Coordinate expressions are scalar valued.

CellDiameterExpr - Represents the diameter of a cell. Cell diameters are often used in stabilized methods.
```
 Expr h = new CellDiameterExpr();
 Expr streamlineDiffusion = eps*h*h*((u*grad)*v)*((u*grad)*T);
```
Cell diameter expressions are scalar valued.

Definition at line 206 of file SundanceExpr.hpp.

Constructor & Destructor Documentation

Sundance::Expr::Expr ( ) [inline]

Empty ctor

Definition at line 210 of file SundanceExpr.hpp.

Referenced by handle().

Sundance::Expr::Expr ( Handleable< ExprBase > * rawPtr ) [inline]

Construct a Expr with a raw pointer to a ExprBase

Definition at line 210 of file SundanceExpr.hpp.

Sundance::Expr::Expr ( const RefCountPtr< ExprBase > & smartPtr ) [inline]

Construct a Expr with a smart pointer to a ExprBase

Definition at line 210 of file SundanceExpr.hpp.

Expr::Expr ( const double & c )

Construct with a constant. Creates a ConstantExpr.

Definition at line 113 of file SundanceExpr.cpp.

Expr::Expr ( const std::complex< double > & c )

Construct with a complex constant. Creates a ComplexExpr.

Definition at line 117 of file SundanceExpr.cpp.

Member Function Documentation

void Expr::append ( const Expr & expr )

Append a new element to this list

Definition at line 685 of file SundanceExpr.cpp.

References Sundance::ListExpr::append(), and Playa::Handle< ExprBase >::ptr().

Referenced by Sundance::ListExpr::flatten(), and Sundance::ListExpr::join().

Expr Expr::conj ( ) const

Return complex conjugate

Definition at line 827 of file SundanceExpr.cpp.

References imag(), isComplex(), real(), and size().

Referenced by conj(), and operator/().

Expr Expr::divide ( const Expr & other ) const [private]

Divide two scalar expressions

Definition at line 479 of file SundanceExpr.cpp.

References Playa::Handle< PointerType >::ptr().

Referenced by operator/().

static bool& Sundance::Expr::evaluationCachingOn ( ) [inline, static]

Turn evaluation caching on

Definition at line 338 of file SundanceExpr.hpp.

bool Expr::everyTermHasTestFunctions ( ) const

Indicate whether every term in the expression contains test functions

Definition at line 914 of file SundanceExpr.cpp.

References Sundance::ScalarExpr::everyTermHasTestFunctions(), Playa::Handle< ExprBase >::ptr(), and scalarExpr().

Referenced by Sundance::SumOfIntegrals::everyTermHasTestFunctions().

Expr Expr::flatten ( ) const

Flatten this list

Definition at line 712 of file SundanceExpr.cpp.

References Sundance::ListExpr::flatten(), and Playa::Handle< ExprBase >::ptr().

Referenced by Sundance::ListExpr::flatten(), Sundance::FunctionSupportResolver::flattenSpectral(), flattenSpectral(), Sundance::EquationSet::flattenSpectral(), Sundance::FunctionalEvaluator::FunctionalEvaluator(), Sundance::UserDefOp::getScalarArgs(), Sundance::EquationSet::init(), Sundance::SymbolicFuncElement::isIndependentOf(), Sundance::SymbolicFuncElement::isLinearForm(), Sundance::SymbPreprocessor::setupFwdProblem(), Sundance::SymbPreprocessor::setupSensitivities(), Sundance::SymbPreprocessor::setupVariations(), Sundance::LinearPDEConstrainedObj::solveStateAndAdjoint(), and Sundance::NonlinearPDEConstrainedObj::solveStateAndAdjoint().

Expr Expr::flattenSpectral ( ) const

Flatten list and spectral structure

Definition at line 723 of file SundanceExpr.cpp.

References flatten(), and size().

Referenced by Sundance::LinearProblem::LinearProblem(), and Sundance::NLOp::NLOp().

const FuncElementBase * Expr::funcElement ( ) const

Definition at line 992 of file SundanceExpr.cpp.

References Playa::Handle< ExprBase >::ptr().

double Expr::getParameterValue ( ) const

Definition at line 857 of file SundanceExpr.cpp.

References Playa::Handle< ExprBase >::ptr(), and Sundance::Parameter::value().

Sundance::Map< Expr, int > Expr::getSumTree ( ) const

Definition at line 206 of file SundanceExpr.cpp.

References Sundance::UnaryExpr::arg(), Playa::Handle< ExprBase >::ptr(), Sundance::Map< Key, Value, Compare >::put(), and toString().

Referenced by Sundance::ReorderSum::doTransform().

void Expr::getTests	(	Set< int > &	testID,
		Array< Expr > &	tests
	)		const

Find the test functions appearing in this expression

Definition at line 962 of file SundanceExpr.cpp.

References Sundance::Set< Key, Compare >::contains(), Sundance::FunctionIdentifier::dofID(), Sundance::FunctionWithID::fid(), Sundance::ScalarExpr::getTests(), Playa::Handle< ExprBase >::ptr(), Sundance::Set< Key, Compare >::put(), and scalarExpr().

void Expr::getUnknowns	(	Set< int > &	unkID,
		Array< Expr > &	unks
	)		const

Find the unknown functions appearing in this expression

Definition at line 938 of file SundanceExpr.cpp.

References Sundance::Set< Key, Compare >::contains(), Sundance::FunctionIdentifier::dofID(), Sundance::FunctionWithID::fid(), Sundance::ScalarExpr::getUnknowns(), Playa::Handle< ExprBase >::ptr(), Sundance::Set< Key, Compare >::put(), and scalarExpr().

static Expr Sundance::Expr::handle ( const RCP< ExprBase > & ptr ) [inline, static]

Create a new handle for an existing ptr.

Definition at line 346 of file SundanceExpr.hpp.

References Expr().

bool Expr::hasTestFunctions ( ) const

Indicate whether the expression contains test functions

Definition at line 905 of file SundanceExpr.cpp.

References Sundance::ScalarExpr::hasTestFunctions(), Playa::Handle< ExprBase >::ptr(), and scalarExpr().

Referenced by Sundance::SumOfIntegrals::hasTestFunctions(), and Sundance::SumOfIntegrals::integralHasTestFunctions().

Expr Expr::imag ( ) const

Return imaginary part of a complex expression

Definition at line 804 of file SundanceExpr.cpp.

References Sundance::ComplexExpr::imag(), isComplex(), Playa::Handle< ExprBase >::ptr(), and size().

Referenced by conj(), Im(), operator-(), operator/(), and tryAddComplex().

bool Expr::isComplex ( ) const

Definition at line 122 of file SundanceExpr.cpp.

References Playa::Handle< ExprBase >::ptr().

Referenced by Sundance::Complex(), conj(), imag(), operator-(), operator/(), real(), tryAddComplex(), and tryMultiplyComplex().

bool Expr::isIndependentOf ( const Expr & u ) const

Indicate whether the expression is independent of the given functions

Definition at line 867 of file SundanceExpr.cpp.

References Sundance::ScalarExpr::isIndependentOf(), Playa::Handle< ExprBase >::ptr(), and scalarExpr().

Referenced by Sundance::SumOfIntegrals::isIndependentOf().

bool Expr::isLinearForm ( const Expr & u ) const

Indicate whether the expression is linear in the given functions

Definition at line 876 of file SundanceExpr.cpp.

References Sundance::ScalarExpr::isLinearForm(), Playa::Handle< ExprBase >::ptr(), and scalarExpr().

Referenced by Sundance::SumOfIntegrals::isLinearForm().

bool Expr::isLinearInTests ( ) const

Indicate whether the expression is nonlinear with respect to test functions

Definition at line 896 of file SundanceExpr.cpp.

References Sundance::ScalarExpr::isLinearInTests(), Playa::Handle< ExprBase >::ptr(), and scalarExpr().

Referenced by Sundance::SumOfIntegrals::isLinearInTests().

bool Expr::isQuadraticForm ( const Expr & u ) const

Indicate whether the expression is quadratic in the given functions

Definition at line 886 of file SundanceExpr.cpp.

References Sundance::ScalarExpr::isQuadraticForm(), Playa::Handle< ExprBase >::ptr(), and scalarExpr().

Referenced by Sundance::SumOfIntegrals::isQuadraticForm().

bool Expr::isSpectral ( ) const

Definition at line 129 of file SundanceExpr.cpp.

References Playa::Handle< ExprBase >::ptr().

Referenced by operator/().

bool Expr::isTestElement ( ) const

Definition at line 922 of file SundanceExpr.cpp.

References Playa::Handle< ExprBase >::ptr().

bool Expr::isUnknownElement ( ) const

Definition at line 930 of file SundanceExpr.cpp.

References Playa::Handle< ExprBase >::ptr().

bool Expr::lessThan ( const Expr & other ) const

Comparison operator for ordering expr trees, DO NOT use for comparison of numerical values.

Definition at line 166 of file SundanceExpr.cpp.

References Sundance::ConstantExpr::lessThan(), Sundance::ScalarExpr::lessThan(), Playa::Handle< PointerType >::ptr(), Playa::Handle< ExprBase >::ptr(), and toString().

Referenced by Sundance::ReorderSum::doTransform(), Sundance::ExprWithChildren::lessThan(), operator<(), and sameAs().

Expr Expr::multiply ( const Expr & other ) const [private]

Multiply two scalar expressions

Definition at line 486 of file SundanceExpr.cpp.

References Sundance::ObjectWithClassVerbosity< SymbolicTransformation >::classVerbosity(), handle(), Playa::Out::println(), Playa::Handle< PointerType >::ptr(), Playa::Handle< ExprBase >::ptr(), and toString().

Referenced by operator*().

Expr Expr::operator* ( const Expr & other ) const

Multiply two expressions. The operands must have list structures such that the product can be interpreted as a scalar-vector product or as an inner product between vectors or tensors. The multiplication operator is also used to represent the application of a differential operator.

Definition at line 396 of file SundanceExpr.cpp.

References multiply(), opTimer(), prodTimer(), size(), toString(), totalSize(), and tryMultiplyComplex().

Referenced by operator/().

Expr Expr::operator+ ( const Expr & other ) const

Add two expressions. The operands must have identical list structures.

Definition at line 297 of file SundanceExpr.cpp.

References opTimer(), size(), sum(), sumTimer(), and tryAddComplex().

Expr Expr::operator- ( const Expr & other ) const

Subtract two expressions. The operands must have identical list structures.

Definition at line 327 of file SundanceExpr.cpp.

References opTimer(), size(), sum(), sumTimer(), and tryAddComplex().

Expr Expr::operator- ( ) const

Unary minus operator

Definition at line 519 of file SundanceExpr.cpp.

References Sundance::UnaryExpr::arg(), imag(), isComplex(), opTimer(), real(), size(), unaryMinusTimer(), and Sundance::ConstantExpr::value().

Expr Expr::operator/ ( const Expr & other ) const

Divide one expression by another. The right operand must be a scalar.

Definition at line 592 of file SundanceExpr.cpp.

References conj(), divide(), imag(), isComplex(), isSpectral(), opTimer(), real(), size(), and toString().

Expr Sundance::Expr::operator/ ( const double & other ) const [inline]

Divide an expression by a double.

Definition at line 237 of file SundanceExpr.hpp.

References operator*().

Expr Sundance::Expr::operator/ ( const std::complex< double > & other ) const [inline]

Divide an expression by a complex.

Definition at line 241 of file SundanceExpr.hpp.

References operator*().

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

Comparison operator for ordering expr trees, DO NOT use for comparison of numerical values.

Definition at line 161 of file SundanceExpr.cpp.

References lessThan().

const Expr & Expr::operator[] ( int i ) const

List element accessor

Definition at line 651 of file SundanceExpr.cpp.

References Sundance::ListExpr::element(), Playa::Handle< PointerType >::ptr(), Playa::Handle< ExprBase >::ptr(), size(), and toString().

static Time& Sundance::Expr::opTimer ( ) [inline, static]

Definition at line 350 of file SundanceExpr.hpp.

Referenced by operator*(), operator+(), operator-(), and operator/().

static Time& Sundance::Expr::outputTimer ( ) [inline, static]

Definition at line 357 of file SundanceExpr.hpp.

Referenced by toString(), and toXML().

Expr Expr::real ( ) const

Return real part of a complex expression

Definition at line 782 of file SundanceExpr.cpp.

References isComplex(), Playa::Handle< ExprBase >::ptr(), Sundance::ComplexExpr::real(), and size().

Referenced by conj(), operator-(), operator/(), Re(), and tryAddComplex().

bool Expr::sameAs ( const Expr & other ) const

Equality test operator for ordering expr trees, DO NOT use for comparison of numerical values.

Definition at line 154 of file SundanceExpr.cpp.

References lessThan().

Referenced by tryMultiplyComplex().

const ScalarExpr * Expr::scalarExpr ( ) const

Definition at line 985 of file SundanceExpr.cpp.

References Playa::Handle< ExprBase >::ptr().

Referenced by everyTermHasTestFunctions(), getTests(), getUnknowns(), hasTestFunctions(), isIndependentOf(), isLinearForm(), isLinearInTests(), and isQuadraticForm().

void Expr::setParameterValue ( const double & value )

Definition at line 848 of file SundanceExpr.cpp.

References Playa::Handle< ExprBase >::ptr(), and Sundance::Parameter::setValue().

Referenced by main(), and Sundance::TransientStepProblem::step().

static bool& Sundance::Expr::showAllParens ( ) [inline, static]

Show parentheses around every pair of operands

Definition at line 343 of file SundanceExpr.hpp.

Referenced by Sundance::BinaryExpr::toText().

int Expr::size ( ) const

Number of elements in top level of list

Definition at line 756 of file SundanceExpr.cpp.

References Playa::Handle< ExprBase >::ptr(), and Sundance::ListExpr::size().

Referenced by Sundance::DefaultIterCallback::call(), Sundance::Complex(), Sundance::L2NormCalculator::computeNorms(), Sundance::NLOp::computeSensitivities(), conj(), Sundance::copyDiscreteFunction(), Sundance::cross(), Sundance::curl(), Sundance::describeFunction(), Sundance::div(), Sundance::EquationSet::EquationSet(), Sundance::ExprFieldWrapper::ExprFieldWrapper(), Sundance::ListExpr::flatten(), Sundance::FunctionSupportResolver::flattenSpectral(), flattenSpectral(), Sundance::EquationSet::flattenSpectral(), Sundance::FunctionSupportResolver::FunctionSupportResolver(), Sundance::getDiscreteFunctionMesh(), Sundance::getDiscreteFunctionVector(), Sundance::getDiscreteSpace(), Sundance::EvaluatableExpr::getEvalExpr(), Sundance::UserDefOp::getScalarArgs(), imag(), Sundance::L2Projector::init(), Sundance::SymbolicFuncElement::isIndependentOf(), Sundance::SymbolicFuncElement::isLinearForm(), Sundance::isSquareMatrix(), Sundance::isVector(), Sundance::ListExpr::join(), Sundance::LinearProblem::LinearProblem(), Sundance::Functional::linearVariationalProb(), Sundance::makeZeros(), Sundance::NitscheStokesNoSlipBC(), Sundance::FunctionSupportResolver::numFixedParams(), Sundance::FunctionSupportResolver::numUnkParams(), operator*(), operator+(), operator-(), operator/(), operator[](), Sundance::SymbPreprocessor::processInputFuncs(), Sundance::SymbPreprocessor::processInputParams(), real(), Sundance::setDiscreteFunctionVector(), Sundance::SymbPreprocessor::setupFwdProblem(), Sundance::SymbPreprocessor::setupSensitivities(), Sundance::LinearPDEConstrainedObj::solveStateAndAdjoint(), Sundance::NonlinearPDEConstrainedObj::solveStateAndAdjoint(), tryAddComplex(), tryMultiplyComplex(), Sundance::CToAInterpolator::updateField(), Sundance::DoublingStepController::write(), and Sundance::LinearSolveDriver::writeIntoSolutionExpr().

Expr Expr::sum	(	const Expr &	other,
		int	sign
	)		const `[private]`

Add two scalar expressions

Definition at line 358 of file SundanceExpr.cpp.

References Sundance::ObjectWithClassVerbosity< SymbolicTransformation >::classVerbosity(), handle(), Playa::Out::println(), Playa::Handle< PointerType >::ptr(), Playa::Handle< ExprBase >::ptr(), and toString().

Referenced by operator+(), and operator-().

string Expr::toString ( ) const

Definition at line 144 of file SundanceExpr.cpp.

References outputTimer(), and Playa::Handle< ExprBase >::ptr().

Referenced by Sundance::SymbolicTransformation::chooseSign(), Sundance::NLOp::computeSensitivities(), Sundance::RearrangeRightSumWithConstant::doTransform(), Sundance::RearrangeLeftSumWithConstant::doTransform(), Sundance::RearrangeRightProductWithConstant::doTransform(), Sundance::RearrangeLeftProductWithConstant::doTransform(), getSumTree(), lessThan(), multiply(), operator*(), operator/(), operator[](), Sundance::SymbPreprocessor::processInputFuncs(), Sundance::SymbPreprocessor::processInputParams(), Sundance::SymbPreprocessor::setupVariations(), sum(), Sundance::UnaryMinus::toText(), Sundance::SumOfBCs::toText(), Sundance::NonlinearUnaryOp::toText(), Sundance::UserDefOpElement::toText(), Sundance::DiffOp::toText(), and Sundance::SumOfIntegrals::toText().

int Expr::totalSize ( ) const

Total number of elements in list.

Definition at line 769 of file SundanceExpr.cpp.

References Playa::Handle< ExprBase >::ptr(), and Sundance::ListExpr::totalSize().

Referenced by Sundance::Complex(), Sundance::isSquareMatrix(), Sundance::isVector(), and operator*().

XMLObject Expr::toXML ( ) const

Definition at line 137 of file SundanceExpr.cpp.

References outputTimer(), and Playa::Handle< ExprBase >::ptr().

Referenced by Sundance::SumOfBCs::toXML(), Sundance::FunctionalPolynomial::toXML(), and Sundance::SumOfIntegrals::toXML().

bool Expr::tryAddComplex	(	const Expr &	L,
		const Expr &	R,
		int	sign,
		Expr &	rtn
	)		const `[private]`

Try transformations of complex addition

Definition at line 235 of file SundanceExpr.cpp.

References imag(), isComplex(), real(), size(), and trySumComplexTimer().

Referenced by operator+(), and operator-().

bool Expr::tryMultiplyComplex	(	const Expr &	L,
		const Expr &	R,
		Expr &	rtn
	)		const `[private]`

Try transformations of complex multiplication

Definition at line 265 of file SundanceExpr.cpp.

References Im(), isComplex(), Re(), sameAs(), size(), and tryMultiplyComplexTimer().

Referenced by operator*().

Friends And Related Function Documentation

Expr acos ( const Expr & arg ) [related]

"inverse cosine"

Expr acosh ( const Expr & arg ) [related]

"inverse hyperbolic cosine"

Expr asin ( const Expr & arg ) [related]

"inverse sine"

Expr asinh ( const Expr & arg ) [related]

"inverse hyperbolic sine"

Expr atan ( const Expr & arg ) [related]

"inverse tangent"

Referenced by force(), and main().

Expr atanh ( const Expr & arg ) [related]

"inverse hyperbolic tangent"

Expr colonProduct	(	const Expr &	A,
		const Expr &	B
	)		`[related]`

Compute the colon (Frobenius) product of two matrices. The result is a scalar.

Definition at line 102 of file SundanceVectorCalculus.cpp.

Expr Complex	(	const Expr &	real,
		const Expr &	imag
	)		`[related]`

Definition at line 1006 of file SundanceExpr.cpp.

Expr conj ( const Expr & a ) [related]

Definition at line 460 of file SundanceExpr.hpp.

References conj().

Expr cos ( const Expr & arg ) [related]

"cosine function"

Referenced by force(), main(), and rhsF().

Expr cosh ( const Expr & arg ) [related]

"hyperbolic cosine"

Expr cross	(	const Expr &	a,
		const Expr &	b
	)		`[related]`

Definition at line 72 of file SundanceVectorCalculus.cpp.

Expr curl ( const Expr & f ) [related]

Definition at line 95 of file SundanceVectorCalculus.cpp.

Expr div ( const Expr & f ) [related]

Definition at line 60 of file SundanceVectorCalculus.cpp.

Expr EssentialBC	(	const Handle< CellFilterStub > &	domain,
		const Expr &	integrand,
		const WatchFlag &	watch = `WatchFlag()`
	)		`[related]`

Referenced by main().

Expr EssentialBC	(	const Handle< CellFilterStub > &	domain,
		const Expr &	integrand,
		const Handle< QuadratureFamilyStub > &	quad,
		const WatchFlag &	watch = `WatchFlag()`
	)		`[related]`

Expr EssentialBC	(	const Handle< CellFilterStub > &	domain,
		const Expr &	integrand,
		const Handle< QuadratureFamilyStub > &	quad,
		const ParametrizedCurve &	curve,
		const WatchFlag &	watch = `WatchFlag()`
	)		`[related]`

Expr exp ( const Expr & arg ) [related]

"exponential function"

Referenced by main().

Expr fabs ( const Expr & arg ) [related]

"absolute value"

Expr FunctionalDerivative	(	const Expr &	F,
		const Expr &	u
	)		`[related]`

Returns an expression that evaluates the functional derivative $\frac{\partial F}{\partial u}.$ The functional derivatives are evaluated internally using automatic differentiation.

Because functional derivatives required for linearization and optimization are already done internally, it is unusual for explicit functional derivatives to be needed at the user level. One case where they are needed is in SUPG stabilization of conservation laws.

Parameters:

F	any evaluatable expression, possibly list-valued
u	an unknown function or list of unknown functions

Expr gradient ( int dim ) [related]

Definition at line 50 of file SundanceVectorCalculus.cpp.

Referenced by main().

Expr Im ( const Expr & a ) [related]

Definition at line 457 of file SundanceExpr.hpp.

References imag().

Referenced by tryMultiplyComplex().

bool isSquareMatrix	(	const Expr &	x,
		int &	N
	)		`[related]`

Indicate whether the given expression is a square matrix. If so, return by reference argument the size of the matrix.

A scalar is a 1 by 1 matrix.

Definition at line 164 of file SundanceVectorCalculus.cpp.

bool isVector	(	const Expr &	x,
		int &	N
	)		`[related]`

Indicate whether the given expression is a vector. If so, return by reference argument the size of the vector.

A scalar is a vector of dimension 1.

Definition at line 149 of file SundanceVectorCalculus.cpp.

Expr List ( const Expr & a ) [related]

Definition at line 1054 of file SundanceExpr.cpp.

Referenced by main().

Expr List	(	const Expr &	a,
		const Expr &	b
	)		`[related]`

Definition at line 1059 of file SundanceExpr.cpp.

Expr List	(	const Expr &	a,
		const Expr &	b,
		const Expr &	c
	)		`[related]`

Definition at line 1064 of file SundanceExpr.cpp.

Expr List	(	const Expr &	a,
		const Expr &	b,
		const Expr &	c,
		const Expr &	d
	)		`[related]`

Definition at line 1069 of file SundanceExpr.cpp.

Expr List	(	const Expr &	a,
		const Expr &	b,
		const Expr &	c,
		const Expr &	d,
		const Expr &	e
	)		`[related]`

Definition at line 1075 of file SundanceExpr.cpp.

Expr List	(	const Expr &	a,
		const Expr &	b,
		const Expr &	c,
		const Expr &	d,
		const Expr &	e,
		const Expr &	f
	)		`[related]`

Definition at line 1081 of file SundanceExpr.cpp.

Expr List	(	const Expr &	a,
		const Expr &	b,
		const Expr &	c,
		const Expr &	d,
		const Expr &	e,
		const Expr &	f,
		const Expr &	g
	)		`[related]`

Definition at line 1087 of file SundanceExpr.cpp.

Expr List	(	const Expr &	a,
		const Expr &	b,
		const Expr &	c,
		const Expr &	d,
		const Expr &	e,
		const Expr &	f,
		const Expr &	g,
		const Expr &	h
	)		`[related]`

Definition at line 1094 of file SundanceExpr.cpp.

Expr List	(	const Expr &	a,
		const Expr &	b,
		const Expr &	c,
		const Expr &	d,
		const Expr &	e,
		const Expr &	f,
		const Expr &	g,
		const Expr &	h,
		const Expr &	i
	)		`[related]`

Expr List	(	const Expr &	a,
		const Expr &	b,
		const Expr &	c,
		const Expr &	d,
		const Expr &	e,
		const Expr &	f,
		const Expr &	g,
		const Expr &	h,
		const Expr &	i,
		const Expr &	j
	)		`[related]`

Expr log ( const Expr & arg ) [related]

"logarithm"

Expr operator*	(	const double &	a,
		const Expr &	x
	)		`[related]`

Definition at line 430 of file SundanceExpr.hpp.

Expr operator*	(	const std::complex< double > &	a,
		const Expr &	x
	)		`[related]`

Definition at line 446 of file SundanceExpr.hpp.

Expr operator+	(	const double &	a,
		const Expr &	x
	)		`[related]`

Definition at line 422 of file SundanceExpr.hpp.

Expr operator+	(	const std::complex< double > &	a,
		const Expr &	x
	)		`[related]`

Definition at line 438 of file SundanceExpr.hpp.

Expr operator-	(	const double &	a,
		const Expr &	x
	)		`[related]`

Definition at line 426 of file SundanceExpr.hpp.

Expr operator-	(	const std::complex< double > &	a,
		const Expr &	x
	)		`[related]`

Definition at line 442 of file SundanceExpr.hpp.

Expr operator/	(	const double &	a,
		const Expr &	x
	)		`[related]`

Definition at line 434 of file SundanceExpr.hpp.

Expr operator/	(	const std::complex< double > &	a,
		const Expr &	x
	)		`[related]`

Definition at line 450 of file SundanceExpr.hpp.

std::ostream & operator<<	(	std::ostream &	os,
		const Expr &	e
	)		`[related]`

Definition at line 415 of file SundanceExpr.hpp.

References Playa::Handle< PointerType >::ptr().

Expr outerProduct	(	const Expr &	a,
		const Expr &	b
	)		`[related]`

Compute the outer (Kronecker) product of two vectors. The result is a dim(a) by dim(b) rectangular matrix.

Definition at line 127 of file SundanceVectorCalculus.cpp.

Expr Re ( const Expr & a ) [related]

Definition at line 454 of file SundanceExpr.hpp.

References real().

Referenced by tryMultiplyComplex().

Expr reciprocal ( const Expr & arg ) [related]

"reciprocal function"

Expr sign ( const Expr & arg ) [related]

"sign function"

Expr sin ( const Expr & arg ) [related]

"sine function"

Referenced by force(), main(), and rhsF().

Expr sinh ( const Expr & arg ) [related]

"hyperbolic sine"

Referenced by main().

Expr sqrt ( const Expr & arg ) [related]

"square root"]

Referenced by main().

Expr tan ( const Expr & arg ) [related]

"tangent function"

Expr tanh ( const Expr & arg ) [related]

"hyperbolic tangent"

Public Member Functions

Static Public Member Functions

Private Member Functions

Related Functions

Detailed Description

Lists

Creating Lists

Probing Lists

Manipulating Lists

Arithmetic Operations

Expression Subtypes

Constructor & Destructor Documentation

Member Function Documentation

Friends And Related Function Documentation