Defines the linear algebra or vector space interface. More...

#include <ROL_Vector.hpp>

Inheritance diagram for ROL::Vector< Real >:

Public Member Functions
virtual	~Vector ()

virtual void	plus (const Vector &x)=0
	Compute \(y \leftarrow y + x\), where \(y = \mathtt{*this}\). More...

virtual void	scale (const Real alpha)=0
	Compute \(y \leftarrow \alpha y\) where \(y = \mathtt{*this}\). More...

virtual Real	dot (const Vector &x) const =0
	Compute \( \langle y,x \rangle \) where \(y = \mathtt{*this}\). More...

virtual Real	norm () const =0
	Returns \( \\| y \\| \) where \(y = \mathtt{*this}\). More...

virtual ROL::Ptr< Vector >	clone () const =0
	Clone to make a new (uninitialized) vector. More...

virtual void	axpy (const Real alpha, const Vector &x)
	Compute \(y \leftarrow \alpha x + y\) where \(y = \mathtt{*this}\). More...

virtual void	zero ()
	Set to zero vector. More...

virtual ROL::Ptr< Vector >	basis (const int i) const
	Return i-th basis vector. More...

virtual int	dimension () const
	Return dimension of the vector space. More...

virtual void	set (const Vector &x)
	Set \(y \leftarrow x\) where \(y = \mathtt{*this}\). More...

virtual const Vector &	dual () const
	Return dual representation of \(\mathtt{*this}\), for example, the result of applying a Riesz map, or change of basis, or change of memory layout. More...

virtual void	applyUnary (const Elementwise::UnaryFunction< Real > &f)

virtual void	applyBinary (const Elementwise::BinaryFunction< Real > &f, const Vector &x)

virtual Real	reduce (const Elementwise::ReductionOp< Real > &r) const

virtual void	print (std::ostream &outStream) const

virtual void	setScalar (const Real C)
	Set \(y \leftarrow C\) where \(C\in\mathbb{R}\). More...

virtual void	randomize (const Real l=0.0, const Real u=1.0)
	Set vector to be uniform random between [l,u]. More...

virtual std::vector< Real >	checkVector (const Vector< Real > &x, const Vector< Real > &y, const bool printToStream=true, std::ostream &outStream=std::cout) const
	Verify vector-space methods. More...

Detailed Description

template<class Real>
class ROL::Vector< Real >

Defines the linear algebra or vector space interface.

The basic linear algebra interface, to be implemented by the user, includes:

plus – vector addition;
scale – scalar multiplication;
dot – dot (scalar) product of vectors;
norm – vector norm;
clone – cloning of existing vectors.

The dot product can represent an inner product (in Hilbert space) or a duality pairing (in general Banach space).

There are additional virtual member functions that can be overloaded for computational efficiency.

Definition at line 80 of file ROL_Vector.hpp.

Constructor & Destructor Documentation

template<class Real>

virtual ROL::Vector< Real >::~Vector ( )

inlinevirtual

Definition at line 87 of file ROL_Vector.hpp.

Member Function Documentation

template<class Real>

virtual void ROL::Vector< Real >::plus ( const Vector< Real > & x )

pure virtual

Compute \(y \leftarrow y + x\), where \(y = \mathtt{*this}\).

Parameters

[in] x is the vector to be added to \(\mathtt{*this}\).

On return \(\mathtt{*this} = \mathtt{*this} + x\).

template<class Real>

virtual void ROL::Vector< Real >::scale ( const Real alpha )

pure virtual

Compute \(y \leftarrow \alpha y\) where \(y = \mathtt{*this}\).

Parameters

[in] alpha is the scaling of \(\mathtt{*this}\).

On return \(\mathtt{*this} = \alpha (\mathtt{*this}) \).

template<class Real>

virtual Real ROL::Vector< Real >::dot ( const Vector< Real > & x ) const

pure virtual

Compute \( \langle y,x \rangle \) where \(y = \mathtt{*this}\).

Parameters

[in] x is the vector that forms the dot product with \(\mathtt{*this}\).

Returns: The number equal to \(\langle \mathtt{*this}, x \rangle\).

Referenced by ROL::CompositeStep< Real >::accept(), ROL::Sketch< Real >::advance(), ROL::DyadicOperator< Real >::apply(), ROL::NullSpaceOperator< Real >::apply(), ROL::lBFGS< Real >::applyB(), ROL::lBFGS< Real >::applyH(), ROL::ConstraintFromObjective< Real >::applyJacobian(), ROL::Constraint< Real >::checkAdjointConsistencyJacobian(), ROL::Constraint_SimOpt< Real >::checkAdjointConsistencyJacobian_1(), ROL::Constraint_SimOpt< Real >::checkAdjointConsistencyJacobian_2(), ROL::Objective< Real >::checkGradient(), ROL::Objective_SimOpt< Real >::checkGradient_1(), ROL::Objective_SimOpt< Real >::checkGradient_2(), ROL::Objective< Real >::checkHessSym(), ROL::BundleStep< Real >::compute(), ROL::RandVarFunctional< Real >::computeGradVec(), ROL::LinMore< Real >::dcauchy(), ROL::ZOO::Objective_Zakharov< Real >::dirDeriv(), ROL::Bundle< Real >::dotGi(), ROL::LinMore< Real >::dprsrch(), ROL::LinMore< Real >::dtrpcg(), ROL::LineSearchStep< Real >::GradDotStep(), ROL::ZOO::Objective_Zakharov< Real >::gradient(), ROL::Objective< Real >::gradient(), ROL::Objective_SimOpt< Real >::gradient_1(), ROL::Objective_SimOpt< Real >::gradient_2(), ROL::PH_ErrorObjective< Real >::hessVec(), ROL::PH_RegretObjective< Real >::hessVec(), ROL::PH_ProbObjective< Real >::hessVec(), ROL::ZOO::Objective_Zakharov< Real >::invHessVec(), ROL::DoubleDogLeg< Real >::run(), ROL::LinMore< Real >::run(), ROL::Constraint< Real >::solveAugmentedSystem(), ROL::CompositeStep< Real >::solveTangentialSubproblem(), ROL::LineSearch< Real >::status(), ROL::TrustRegion< Real >::update(), ROL::lSR1< Real >::updateStorage(), ROL::Secant< Real >::updateStorage(), ROL::Objective_FSsolver< Real >::value(), ROL::ZOO::Objective_SumOfSquares< Real >::value(), ROL::LinearObjective_SimOpt< Real >::value(), ROL::LinearObjective< Real >::value(), ROL::QuadraticObjective< Real >::value(), ROL::DynamicTrackingObjective< Real >::value(), ROL::DynamicTrackingFEMObjective< Real >::value(), ROL::ZOO::Objective_Zakharov< Real >::value(), and ROL::PH_Objective< Real >::value().

template<class Real>

virtual Real ROL::Vector< Real >::norm ( ) const

pure virtual

Returns \( \| y \| \) where \(y = \mathtt{*this}\).

Returns: A nonnegative number equal to the norm of \(\mathtt{*this}\).

template<class Real>

virtual ROL::Ptr<Vector> ROL::Vector< Real >::clone ( ) const

pure virtual

Clone to make a new (uninitialized) vector.

Returns: A reference-counted pointer to the cloned vector.

Provides the means of allocating temporary memory in ROL.

template<class Real>

virtual void ROL::Vector< Real >::axpy	(	const Real	alpha,
		const Vector< Real > &	x
	)

inlinevirtual

Compute \(y \leftarrow \alpha x + y\) where \(y = \mathtt{*this}\).

Parameters

[in]	alpha	is the scaling of x.
[in]	x	is a vector.

On return \(\mathtt{*this} = \mathtt{*this} + \alpha x \). Uses clone, set, scale and plus for the computation. Please overload if a more efficient implementation is needed.

Reimplemented in ROL::RiskVector< Real >, ROL::ProfiledVector< Ordinal, Real >, ROL::SimulatedVector< Real >, ROL::PartitionedVector< Real >, ROL::StdVector< Real, Element >, ROL::StdVector< Real >, ROL::SROMVector< Real >, ROL::StdArray< Real, array_size, pool_size >, ROL::ElementwiseVector< Real >, ROL::SingletonVector< Real >, and ROL::Vector_SimOpt< Real >.

Definition at line 153 of file ROL_Vector.hpp.

References ROL::Vector< Real >::clone(), and ROL::Vector< Real >::plus().

template<class Real>

virtual void ROL::Vector< Real >::zero ( )

inlinevirtual

Set to zero vector.

Uses scale by zero for the computation. Please overload if a more efficient implementation is needed.

Reimplemented in ROL::SimulatedVector< Real >, ROL::ProfiledVector< Ordinal, Real >, ROL::PartitionedVector< Real >, ROL::StdArray< Real, array_size, pool_size >, and ROL::ElementwiseVector< Real >.

Definition at line 167 of file ROL_Vector.hpp.

References ROL::Vector< Real >::scale().

template<class Real>

virtual ROL::Ptr<Vector> ROL::Vector< Real >::basis ( const int i ) const

inlinevirtual

Return i-th basis vector.

Parameters

[in] i is the index of the basis function.

Returns: A reference-counted pointer to the basis vector with index i.

Overloading the basis is only required if the default gradient implementation is used, which computes a finite-difference approximation.

Definition at line 182 of file ROL_Vector.hpp.

References ROL_UNUSED.

Referenced by ROL::Constraint< Real >::applyAdjointJacobian(), ROL::Constraint_SimOpt< Real >::applyAdjointJacobian_1(), ROL::Constraint_SimOpt< Real >::applyAdjointJacobian_2(), ROL::Constraint< Real >::checkApplyAdjointJacobian(), ROL::computeDenseHessian(), ROL::computeDotMatrix(), ROL::Objective< Real >::gradient(), ROL::Objective_SimOpt< Real >::gradient_1(), ROL::Objective_SimOpt< Real >::gradient_2(), ROL::AugmentedLagrangianStep< Real >::initialize(), and Objective_PoissonInversion< Real >::update().

template<class Real>

virtual int ROL::Vector< Real >::dimension ( void ) const

inlinevirtual

Return dimension of the vector space.

Returns: The dimension of the vector space, i.e., the total number of basis vectors.

Overload if the basis is overloaded.

Definition at line 196 of file ROL_Vector.hpp.

Referenced by ROL::Constraint< Real >::applyAdjointJacobian(), ROL::Constraint_SimOpt< Real >::applyAdjointJacobian_1(), ROL::Constraint_SimOpt< Real >::applyAdjointJacobian_2(), ROL::StdVector< Real >::applyBinary(), ROL::StdVector< Real >::axpy(), ROL::Constraint< Real >::checkApplyAdjointJacobian(), ROL::computeDenseHessian(), ROL::computeDotMatrix(), ROL::computeScaledDenseHessian(), ROL::StdVector< Real >::dot(), ROL::Objective< Real >::gradient(), ROL::Objective_SimOpt< Real >::gradient_1(), ROL::Objective_SimOpt< Real >::gradient_2(), ROL::AugmentedLagrangianStep< Real >::initialize(), ROL::details::VectorClone< Real >::operator()(), ROL::StdVector< Real >::plus(), ROL::LinMore< Real >::run(), ROL::StdVector< Real >::set(), and ROL::Sketch< Real >::Sketch().

template<class Real>

virtual void ROL::Vector< Real >::set ( const Vector< Real > & x )

inlinevirtual

Set \(y \leftarrow x\) where \(y = \mathtt{*this}\).

Parameters

[in] x is a vector.

On return \(\mathtt{*this} = x\). Uses zero and plus methods for the computation. Please overload if a more efficient implementation is needed.

Reimplemented in H1VectorDual< Real >, H1VectorDual< Real >, H1VectorDual< Real >, H1VectorDual< Real >, H1VectorPrimal< Real >, H1VectorPrimal< Real >, H1VectorPrimal< Real >, H1VectorPrimal< Real >, L2VectorDual< Real >, L2VectorDual< Real >, L2VectorDual< Real >, L2VectorDual< Real >, L2VectorPrimal< Real >, L2VectorPrimal< Real >, L2VectorPrimal< Real >, L2VectorPrimal< Real >, ROL::ProfiledVector< Ordinal, Real >, ROL::RiskVector< Real >, ROL::ElementwiseVector< Real >, ROL::SimulatedVector< Real >, ROL::StdArray< Real, array_size, pool_size >, ROL::SROMVector< Real >, ROL::PartitionedVector< Real >, ROL::SingletonVector< Real >, ROL::StdVector< Real, Element >, and ROL::StdVector< Real >.

Definition at line 209 of file ROL_Vector.hpp.

References ROL::Vector< Real >::plus(), and ROL::Vector< Real >::zero().

template<class Real>

virtual const Vector& ROL::Vector< Real >::dual ( void ) const

inlinevirtual

Return dual representation of \(\mathtt{*this}\), for example, the result of applying a Riesz map, or change of basis, or change of memory layout.

Returns: A const reference to dual representation.

By default, returns the current object. Please overload if you need a dual representation.

Definition at line 226 of file ROL_Vector.hpp.

template<class Real>

virtual void ROL::Vector< Real >::applyUnary ( const Elementwise::UnaryFunction< Real > & f )

inlinevirtual

template<class Real>

virtual void ROL::Vector< Real >::applyBinary	(	const Elementwise::BinaryFunction< Real > &	f,
		const Vector< Real > &	x
	)

inlinevirtual

Reimplemented in ROL::RiskVector< Real >, ROL::ProfiledVector< Ordinal, Real >, ROL::SimulatedVector< Real >, ROL::RieszDualVector< Real >, ROL::PartitionedVector< Real >, ROL::StdVector< Real, Element >, ROL::StdVector< Real >, ROL::SROMVector< Real >, ROL::StdArray< Real, array_size, pool_size >, ROL::Vector_SimOpt< Real >, ROL::RieszPrimalVector< Real >, ROL::SingletonVector< Real >, and ROL::ElementwiseVector< Real >.

Definition at line 236 of file ROL_Vector.hpp.

References ROL_UNUSED.

Referenced by ROL::DiagonalOperator< Real >::apply(), ROL::BinaryConstraint< Real >::applyAdjointHessian(), ROL::ColemanLiModel< Real >::applyC(), ROL::ColemanLiModel< Real >::applyD(), ROL::DiagonalOperator< Real >::applyInverse(), ROL::ColemanLiModel< Real >::applyInverseD(), ROL::BinaryConstraint< Real >::applyJacobian(), ROL::ColemanLiModel< Real >::computeFullReflectiveStep(), ROL::ColemanLiModel< Real >::computeReflectiveStep(), ROL::LinMore< Real >::dbreakpt(), ROL::LogBarrierObjective< Real >::hessVec(), ROL::ObjectiveMMA< Real >::hessVec(), ROL::ObjectiveFromBoundConstraint< Real >::hessVec(), ROL::Bounds< Real >::project(), ROL::Bounds< Real >::projectInterior(), ROL::Bounds< Real >::pruneLowerActive(), ROL::Bounds< Real >::pruneUpperActive(), and ROL::BinaryConstraint< Real >::value().

template<class Real>

virtual Real ROL::Vector< Real >::reduce ( const Elementwise::ReductionOp< Real > & r ) const

inlinevirtual

Reimplemented in ROL::RiskVector< Real >, ROL::SimulatedVector< Real >, ROL::ProfiledVector< Ordinal, Real >, ROL::RieszDualVector< Real >, ROL::PartitionedVector< Real >, ROL::StdVector< Real, Element >, ROL::StdVector< Real >, ROL::SROMVector< Real >, ROL::Vector_SimOpt< Real >, ROL::StdArray< Real, array_size, pool_size >, ROL::RieszPrimalVector< Real >, ROL::SingletonVector< Real >, ROL::ElementwiseVector< Real >, and ROL::BatchStdVector< Real >.

Definition at line 243 of file ROL_Vector.hpp.

References ROL_UNUSED.

Referenced by ROL::LinMore< Real >::dbreakpt().

template<class Real>

virtual void ROL::Vector< Real >::print ( std::ostream & outStream ) const

inlinevirtual

Reimplemented in ROL::ProfiledVector< Ordinal, Real >, ROL::PartitionedVector< Real >, ROL::StdVector< Real, Element >, ROL::StdVector< Real >, ROL::Vector_SimOpt< Real >, ROL::StdArray< Real, array_size, pool_size >, and ROL::SingletonVector< Real >.

Definition at line 249 of file ROL_Vector.hpp.

Referenced by ROL::Algorithm< Real >::run(), and ROL::ReducedDynamicObjective< Real >::update().

template<class Real>

virtual void ROL::Vector< Real >::setScalar ( const Real C )

inlinevirtual

Set \(y \leftarrow C\) where \(C\in\mathbb{R}\).

Parameters

[in] C is a scalar.

On return \(\mathtt{*this} = C\). Uses applyUnary methods for the computation. Please overload if a more efficient implementation is needed.

Reimplemented in ROL::RiskVector< Real >, ROL::SimulatedVector< Real >, ROL::ProfiledVector< Ordinal, Real >, ROL::RieszDualVector< Real >, ROL::PartitionedVector< Real >, ROL::StdVector< Real, Element >, ROL::StdVector< Real >, ROL::Vector_SimOpt< Real >, ROL::StdArray< Real, array_size, pool_size >, ROL::RieszPrimalVector< Real >, and ROL::SingletonVector< Real >.

Definition at line 263 of file ROL_Vector.hpp.

References ROL::Vector< Real >::applyUnary().

template<class Real>

virtual void ROL::Vector< Real >::randomize	(	const Real	l = `0.0`,
		const Real	u = `1.0`
	)

inlinevirtual

Set vector to be uniform random between [l,u].

Parameters

[in]	l	is a the lower bound.
[in]	u	is a the upper bound.

On return the components of \(\mathtt{*this}\) are uniform random numbers on the interval \([l,u]\). The default implementation uses applyUnary methods for the computation. Please overload if a more efficient implementation is needed.

Reimplemented in ROL::RiskVector< Real >, ROL::SimulatedVector< Real >, ROL::ProfiledVector< Ordinal, Real >, ROL::RieszDualVector< Real >, ROL::PartitionedVector< Real >, ROL::StdVector< Real, Element >, ROL::StdVector< Real >, ROL::Vector_SimOpt< Real >, ROL::StdArray< Real, array_size, pool_size >, ROL::RieszPrimalVector< Real >, and ROL::SingletonVector< Real >.

Definition at line 280 of file ROL_Vector.hpp.

References ROL::Vector< Real >::applyUnary().

template<class Real>

virtual std::vector<Real> ROL::Vector< Real >::checkVector	(	const Vector< Real > &	x,
		const Vector< Real > &	y,
		const bool	printToStream = `true`,
		std::ostream &	outStream = `std::cout`
	)		const

inlinevirtual

Verify vector-space methods.

Parameters

[in]	x	is a vector.
[in]	y	is a vector.

Returns a vector of Reals, all of which should be close to zero. They represent consistency errors in the vector space properties, as follows:

Commutativity of addition: \(\mathtt{*this} + x = x + \mathtt{*this}\).
Associativity of addition: \(\mathtt{*this} + (x + y) = (\mathtt{*this} + x) + y\).
Identity element of addition: \(0 + x = x\).
Inverse elements of addition: \(\mathtt{*this} + (- \mathtt{*this}) = 0\).
Identity element of scalar multiplication: \( 1 \cdot \mathtt{*this} = \mathtt{*this} \).
Consistency of scalar multiplication with field multiplication: \(a (b \cdot \mathtt{*this}) = (a b) \cdot \mathtt{*this}\).
Distributivity of scalar multiplication with respect to field addition: \((a+b) \cdot \mathtt{*this} = a \cdot \mathtt{*this} + b \cdot \mathtt{*this}\).
Distributivity of scalar multiplication with respect to vector addition: \(a \cdot (\mathtt{*this} + x) = a \cdot \mathtt{*this} + a \cdot x\).
Commutativity of dot (inner) product over the field of reals: \((\mathtt{*this}, x) = (x, \mathtt{*this})\).
Additivity of dot (inner) product: \((\mathtt{*this}, x+y) = (\mathtt{*this}, x) + (\mathtt{*this}, y)\).
Consistency of scalar multiplication and norm: \(\|{\mathtt{*this}} / {\|\mathtt{*this}\|} \| = 1\).
Reflexivity: \(\mbox{dual}(\mbox{dual}(\mathtt{*this})) = \mathtt{*this}\) .

The consistency errors are defined as the norms or absolute values of the differences between the left-hand side and the right-hand side terms in the above equalities.

Definition at line 312 of file ROL_Vector.hpp.

References ROL::Vector< Real >::clone(), and ROL::Vector< Real >::zero().

Referenced by ROL::OptimizationProblem< Real >::checkMultiplierVector(), ROL::OptimizationProblem< Real >::checkSolutionVector(), and main().

The documentation for this class was generated from the following file:

ROL_Vector.hpp

Public Member Functions

Detailed Description

template<class Real> class ROL::Vector< Real >

Constructor & Destructor Documentation

Member Function Documentation

template<class Real>
class ROL::Vector< Real >