Inheritance diagram for Sundance::MultipleDeriv:

Public Member Functions
	MultipleDeriv ()
	MultipleDeriv (const Deriv &d)
	MultipleDeriv (const Deriv &d1, const Deriv &d2)
int	order () const
int	spatialOrder () const
MultiIndex	spatialDeriv () const
void	productRulePermutations (ProductRulePerms &perms) const
MultipleDeriv	product (const MultipleDeriv &other) const
MultipleDeriv	factorOutDeriv (const Deriv &x) const
MultipleDeriv	factorOutDeriv (const MultipleDeriv &x) const
bool	containsDeriv (const MultipleDeriv &x) const
bool	isInRequiredSet (const Set< MultiSet< int > > &funcCombinations, const Set< MultiIndex > &multiIndices) const
MultiSet< FunctionIdentifier >	funcIDs () const
MultiSet< int >	dofIDs () const
Static Public Member Functions
Utilities used in computing product rule permutations
static int	pow2 (int n)
static Array< int >	bitsOfAnInteger (int x, int n)

Detailed Description

Class MultipleDeriv is a multiple functional derivative operator represented as a multiset of first-order derivatives. The derivatives are each Deriv objects, so the multiple derivative can be an arbitrary mixture of spatial and functional derivatives.

Product rule application

Class MultipleDeriv contains a utility method for computing the derivatives that appear in the general product rule, as used in automatic differentiation of products and spatial derivatives. The arbitrary order, multivariable product rule gives the derivative of a product $L\cdot R$ with respect to a multiset of variables $\{u_1, u_2, \dots, u_N\}$ as the sum

$D_{u_1} D_{u_2} \cdots D_{u_N} (L \cdot R) =\sum_{i=1}^{2^N} \left[\prod_{j=1}^N D_{u_j}^{b_{i,j}}\right] L \times \left[\prod_{j=1}^N D_{u_j}^{1-b_{i,j}}\right] R$

where $b_{i,j}$ is the $j$ -th bit in the binary representation of $i$ . Method productRulePermutations() enumerates all the permutations that apply to the left and right operands in this sum, and returns the arrays of left operators and right operators through non-const reference arguments. The left and right arguments return

${\rm left = Array}_{i=1}^{2^N} \{\prod_{j=1}^N D_{u_j}^{b_{i,j}}\}$

${\rm right = Array}_{i=1}^{2^N} \{\prod_{j=1}^N D_{u_j}^{1-b_{i,j}}\}$

Each element in these arrays is a multiple derivative, and is naturally represented with a MultipleDeriv object.

Definition at line 99 of file SundanceMultipleDeriv.hpp.

Constructor & Destructor Documentation

MultipleDeriv::MultipleDeriv ( )

Construct an empty multiple derivative

Definition at line 49 of file SundanceMultipleDeriv.cpp.

Referenced by factorOutDeriv().

MultipleDeriv::MultipleDeriv ( const Deriv & d )

Construct a first-order multiple deriv

Definition at line 53 of file SundanceMultipleDeriv.cpp.

References Sundance::MultiSet< Deriv >::put().

MultipleDeriv::MultipleDeriv	(	const Deriv &	d1,
		const Deriv &	d2
	)

Construct a second-order multiple deriv

Definition at line 58 of file SundanceMultipleDeriv.cpp.

References Sundance::MultiSet< Deriv >::put().

Member Function Documentation

Array< int > MultipleDeriv::bitsOfAnInteger	(	int	x,
		int	n
	)		`[static]`

Compute the n bits of an integer x < 2^n. The bits are ordered least-to-most significant.

Definition at line 239 of file SundanceMultipleDeriv.cpp.

References pow2().

bool MultipleDeriv::containsDeriv ( const MultipleDeriv & x ) const

Return true is all single derivatives appearing in x also appear in this.

Definition at line 153 of file SundanceMultipleDeriv.cpp.

MultiSet< int > MultipleDeriv::dofIDs ( ) const

Definition at line 107 of file SundanceMultipleDeriv.cpp.

References Sundance::MultiSet< Key >::put().

MultipleDeriv MultipleDeriv::factorOutDeriv ( const Deriv & x ) const

Return a copy of this derivative, but with the specified single derivative removed. For example, if <t>this</t> is $\{u,v,w\}$ , calling <t>factorOutDeriv(v)</t> will return $\{u,w\}$ .

Definition at line 138 of file SundanceMultipleDeriv.cpp.

References MultipleDeriv().

Referenced by Sundance::DiffOpEvaluator::backedDerivs(), Sundance::DiffOpEvaluator::remainder(), and Sundance::EvaluatableExpr::setDivision().

MultipleDeriv MultipleDeriv::factorOutDeriv ( const MultipleDeriv & x ) const

Return a copy of this derivative, but with all single derivs in the the argument removed. For example, if <t>this</t> is $\{u,v,w\}$ , calling <t>factorOutDeriv(u,v)</t> will return $\{w\}$ .

Definition at line 162 of file SundanceMultipleDeriv.cpp.

References MultipleDeriv().

MultiSet< FunctionIdentifier > MultipleDeriv::funcIDs ( ) const

Definition at line 92 of file SundanceMultipleDeriv.cpp.

References Sundance::MultiSet< Key >::put().

bool MultipleDeriv::isInRequiredSet	(	const Set< MultiSet< int > > &	funcCombinations,
		const Set< MultiIndex > &	multiIndices
	)		const

Definition at line 179 of file SundanceMultipleDeriv.cpp.

References Sundance::Set< Key, Compare >::contains().

Referenced by Sundance::EvaluatableExpr::computeInputR().

int Sundance::MultipleDeriv::order ( ) const [inline]

Return the order of this derivative. Since a multiple derivative is a multiset of first-order derivatives, the order of the multiple derivative is the size of the set.

Definition at line 116 of file SundanceMultipleDeriv.hpp.

Referenced by Sundance::SparsitySuperset::addDeriv(), Sundance::EquationSet::addToVarUnkPairs(), Sundance::applyZx(), Sundance::DiffOpEvaluator::backedDerivs(), Sundance::CellDiameterExprEvaluator::CellDiameterExprEvaluator(), Sundance::CellVectorEvaluator::CellVectorEvaluator(), Sundance::chainRuleDerivsOfArgs(), Sundance::ConstantEvaluator::ConstantEvaluator(), Sundance::CoordExprEvaluator::CoordExprEvaluator(), Sundance::CurveNormEvaluator::CurveNormEvaluator(), Sundance::ChainRuleEvaluator::derivComboMultiplicity(), Sundance::DiffOpEvaluator::DiffOpEvaluator(), Sundance::TrivialGrouper::findGroups(), Sundance::DiffOpEvaluator::increasedDerivs(), Sundance::increasingOrder< MultipleDeriv >::operator()(), Sundance::ProductEvaluator::ProductEvaluator(), Sundance::DiffOpEvaluator::remainder(), Sundance::UserDefOpCommonEvaluator::UserDefOpCommonEvaluator(), and Sundance::UserDefOpEvaluator::UserDefOpEvaluator().