Sundance::Expr Class Reference

User-level expression class. More...

Inheritance diagram for Sundance::Expr:

List of all members.

Public Member Functions
	Expr ()
	Empty ctor.
	Expr (Handleable< ExprBase > *rawPtr)
	Construct a Expr with a raw pointer to a ExprBase.
	Expr (const RefCountPtr< ExprBase > &smartPtr)
	Construct a Expr with a smart pointer to a ExprBase.
	Expr (const double &c)
	Construct with a constant.
	Expr (const std::complex< double > &c)
	Construct with a complex constant.
Expr	operator+ (const Expr &other) const
	Add two expressions.
Expr	operator- (const Expr &other) const
	Subtract two expressions.
Expr	operator* (const Expr &other) const
	Multiply two expressions.
Expr	operator/ (const Expr &other) const
	Divide one expression by another.
Expr	operator/ (const double &other) const
	Divide an expression by a double.
Expr	operator/ (const std::complex< double > &other) const
	Divide an expression by a complex.
Expr	operator- () const
	Unary minus operator.
Expr	real () const
	Return real part of a complex expression.
Expr	imag () const
	Return imaginary part of a complex expression.
Expr	conj () const
	Return complex conjugate.
const Expr &	operator[] (int i) const
	List element accessor.
int	size () const
	Number of elements in top level of list.
int	totalSize () const
	Total number of elements in list.
void	append (const Expr &expr)
	Append a new element to this list.
Expr	flatten () const
	Flatten this list.
Expr	flattenSpectral () const
	Flatten list and spectral structure.
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
	Indicate whether the expression is independent of the given functions.
bool	isLinearInTests () const
	Indicate whether the expression is nonlinear with respect to test functions.
bool	everyTermHasTestFunctions () const
	Indicate whether every term in the expression contains test functions.
bool	hasTestFunctions () const
	Indicate whether the expression contains test functions.
bool	isLinearForm (const Expr &u) const
	Indicate whether the expression is linear in the given functions.
bool	isQuadraticForm (const Expr &u) const
	Indicate whether the expression is quadratic in the given functions.
void	getUnknowns (Set< int > &unkID, Array< Expr > &unks) const
	Find the unknown functions appearing in this expression.
void	getTests (Set< int > &testID, Array< Expr > &tests) const
	Find the test functions appearing in this expression.
bool	lessThan (const Expr &other) const
	Comparison operator for ordering expr trees, DO NOT use for comparison of numerical values.
bool	operator< (const Expr &other) const
	Comparison operator for ordering expr trees, DO NOT use for comparison of numerical values.
bool	sameAs (const Expr &other) const
	Equality test operator for ordering expr trees, DO NOT use for comparison of numerical values.
Sundance::Map< Expr, int >	getSumTree () const
const ScalarExpr *	scalarExpr () const
const FuncElementBase *	funcElement () const
Static Public Member Functions
static bool &	evaluationCachingOn ()
	Turn evaluation caching on.
static bool &	showAllParens ()
	Show parentheses around every pair of operands.
static Expr	handle (const RCP< ExprBase > &ptr)
	Create a new handle for an existing ptr.
static Time &	opTimer ()
static Time &	outputTimer ()
Private Member Functions
Expr	sum (const Expr &other, int sign) const
	Add two scalar expressions.
Expr	multiply (const Expr &other) const
	Multiply two scalar expressions.
Expr	divide (const Expr &other) const
	Divide two scalar expressions.
bool	tryAddComplex (const Expr &L, const Expr &R, int sign, Expr &rtn) const
	Try transformations of complex addition.
bool	tryMultiplyComplex (const Expr &L, const Expr &R, Expr &rtn) const
	Try transformations of complex multiplication.
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 195 of file SundanceExpr.hpp.

---

Constructor & Destructor Documentation

Sundance::Expr::Expr

(

)

[inline]

Empty ctor.

Definition at line 199 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 199 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 199 of file SundanceExpr.hpp.

Expr::Expr

(

const double &

c

)

Construct with a constant.

Creates a ConstantExpr.

Definition at line 102 of file SundanceExpr.cpp.

Expr::Expr

(

const std::complex< double > &

c

)

Construct with a complex constant.

Creates a ComplexExpr.

Definition at line 106 of file SundanceExpr.cpp.

---

Member Function Documentation

void Expr::append

(

const Expr &

expr

)

Append a new element to this list.

Definition at line 674 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 816 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 468 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 327 of file SundanceExpr.hpp.

bool Expr::everyTermHasTestFunctions

(

)

const

Indicate whether every term in the expression contains test functions.

Definition at line 903 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 701 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(), and Sundance::SymbPreprocessor::setupVariations().

Expr Expr::flattenSpectral

(

)

const

Flatten list and spectral structure.

Definition at line 712 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 981 of file SundanceExpr.cpp.

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

double Expr::getParameterValue

(

)

const

Definition at line 846 of file SundanceExpr.cpp.

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

Sundance::Map< Expr, int > Expr::getSumTree

(

)

const

Definition at line 195 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 951 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 927 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 335 of file SundanceExpr.hpp.

References Expr().

Referenced by Sundance::FunctionalPolynomial::addPoly(), Sundance::ExprWithChildren::child(), Sundance::SymbolicTransformation::chooseSign(), Sundance::SumIntegrals::doTransform(), Sundance::RearrangeLeftSumWithConstant::doTransform(), Sundance::RearrangeRightSumWithConstant::doTransform(), Sundance::RemoveUnaryMinusFromSum::doTransform(), Sundance::MoveConstantsToLeftOfSum::doTransform(), Sundance::ReorderSum::doTransform(), Sundance::RearrangeLeftProductWithConstant::doTransform(), Sundance::RearrangeRightProductWithConstant::doTransform(), Sundance::DistributeSumOfDiffOps::doTransform(), Sundance::BringConstantOutsideDiffOp::doTransform(), Sundance::KillDiffOpOnConstant::doTransform(), Sundance::AssociateHungryDiffOpWithOperand::doTransform(), Sundance::MoveUnaryMinusOutsideProduct::doTransform(), Sundance::MoveConstantsToLeftOfProduct::doTransform(), Sundance::RemoveMinusOneFromProduct::doTransform(), Sundance::RemoveOneFromProduct::doTransform(), Sundance::ExprWithChildren::lessThan(), multiply(), Sundance::FunctionalPolynomial::multiplyPoly(), Sundance::FunctionalPolynomial::multiplyScalar(), sum(), and Sundance::FunctionalPolynomial::toXML().

bool Expr::hasTestFunctions

(

)

const

Indicate whether the expression contains test functions.

Definition at line 894 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 793 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 111 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 856 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 865 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 885 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 875 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 118 of file SundanceExpr.cpp.

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

Referenced by operator/().

bool Expr::isTestElement

(

)

const

Definition at line 911 of file SundanceExpr.cpp.

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

bool Expr::isUnknownElement

(

)

const

Definition at line 919 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 155 of file SundanceExpr.cpp.

References 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 475 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 385 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 286 of file SundanceExpr.cpp.

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

Expr Expr::operator-

(

)

const

Unary minus operator.

Definition at line 508 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

Subtract two expressions.

The operands must have identical list structures.

Definition at line 316 of file SundanceExpr.cpp.

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

Expr Sundance::Expr::operator/

(

const std::complex< double > &

other

)

const [inline]

Divide an expression by a complex.

Definition at line 230 of file SundanceExpr.hpp.

References operator*().

Expr Sundance::Expr::operator/

(

const double &

other

)

const [inline]

Divide an expression by a double.

Definition at line 226 of file SundanceExpr.hpp.

References operator*().

Expr Expr::operator/

(

const Expr &

other

)

const

Divide one expression by another.

The right operand must be a scalar.

Definition at line 581 of file SundanceExpr.cpp.

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

bool Expr::operator<

(

const Expr &

other

)

const

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

Definition at line 150 of file SundanceExpr.cpp.

References lessThan().

const Expr & Expr::operator[]

(

int

i

)

const

List element accessor.

Definition at line 640 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 339 of file SundanceExpr.hpp.

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

static Time& Sundance::Expr::outputTimer

(

)

[inline, static]

Definition at line 346 of file SundanceExpr.hpp.

Referenced by toString(), and toXML().

Expr Expr::real

(

)

const

Return real part of a complex expression.

Definition at line 771 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 143 of file SundanceExpr.cpp.

References lessThan().

Referenced by tryMultiplyComplex().

const ScalarExpr * Expr::scalarExpr

(

)

const

Definition at line 974 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 837 of file SundanceExpr.cpp.

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

Referenced by Sundance::TransientStepProblem::step().

static bool& Sundance::Expr::showAllParens

(

)

[inline, static]

Show parentheses around every pair of operands.

Definition at line 332 of file SundanceExpr.hpp.

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

int Expr::size

(

)

const

Number of elements in top level of list.

Definition at line 745 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::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::NonlinearPDEConstrainedObj::solveStateAndAdjoint(), Sundance::LinearPDEConstrainedObj::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 347 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 133 of file SundanceExpr.cpp.

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

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

int Expr::totalSize

(

)

const

Total number of elements in list.

Definition at line 758 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 126 of file SundanceExpr.cpp.

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

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

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

Try transformations of complex addition.

Definition at line 224 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 254 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"

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 91 of file SundanceVectorCalculus.cpp.

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

Definition at line 995 of file SundanceExpr.cpp.

Expr conj

(

const Expr &

a

)

[related]

Definition at line 449 of file SundanceExpr.hpp.

References conj().

Expr cos

(

const Expr &

arg

)

[related]

"cosine function"

Expr cosh

(

const Expr &

arg

)

[related]

"hyperbolic cosine"

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

Definition at line 61 of file SundanceVectorCalculus.cpp.

Expr curl

(

const Expr &

f

)

[related]

Definition at line 84 of file SundanceVectorCalculus.cpp.

Expr div

(

const Expr &

f

)

[related]

Definition at line 49 of file SundanceVectorCalculus.cpp.

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

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 WatchFlag &	watch = WatchFlag()
	)			[related]

Expr exp

(

const Expr &

arg

)

[related]

"exponential function"

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 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 39 of file SundanceVectorCalculus.cpp.

Expr Im

(

const Expr &

a

)

[related]

Definition at line 446 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 153 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 138 of file SundanceVectorCalculus.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,
		const Expr &	j
	)			[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
	)			[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
	)			[related]

Definition at line 1083 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 1076 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 1070 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 1064 of file SundanceExpr.cpp.

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

Definition at line 1058 of file SundanceExpr.cpp.

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

Definition at line 1053 of file SundanceExpr.cpp.

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

Definition at line 1048 of file SundanceExpr.cpp.

Expr List

(

const Expr &

a

)

[related]

Definition at line 1043 of file SundanceExpr.cpp.

Expr log

(

const Expr &

arg

)

[related]

"logarithm"

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

Definition at line 435 of file SundanceExpr.hpp.

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

Definition at line 419 of file SundanceExpr.hpp.

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

Definition at line 427 of file SundanceExpr.hpp.

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

Definition at line 411 of file SundanceExpr.hpp.

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

Definition at line 431 of file SundanceExpr.hpp.

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

Definition at line 415 of file SundanceExpr.hpp.

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

Definition at line 439 of file SundanceExpr.hpp.

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

Definition at line 423 of file SundanceExpr.hpp.

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

Definition at line 404 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 116 of file SundanceVectorCalculus.cpp.

Expr Re

(

const Expr &

a

)

[related]

Definition at line 443 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"

Expr sinh

(

const Expr &

arg

)

[related]

"hyperbolic sine"

Expr sqrt

(

const Expr &

arg

)

[related]

"square root"]

Expr tan

(

const Expr &

arg

)

[related]

"tangent function"

Expr tanh

(

const Expr &

arg

)

[related]

"hyperbolic tangent"