Reference documentation for deal.II version Git e413cbf8ac 2021-08-02 21:56:02 +0200
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Classes | Public Types | Public Member Functions | Static Public Member Functions | Protected Attributes | List of all members
SolverBFGS< VectorType > Class Template Reference

#include <deal.II/optimization/solver_bfgs.h>

Inheritance diagram for SolverBFGS< VectorType >:
[legend]

Classes

struct  AdditionalData
 

Public Types

using Number = typename VectorType::value_type
 
using vector_type = VectorType
 

Public Member Functions

 SolverBFGS (SolverControl &residual_control, const AdditionalData &data=AdditionalData())
 
void solve (const std::function< Number(const VectorType &x, VectorType &g)> &compute, VectorType &x)
 
boost::signals2::connection connect_line_search_slot (const std::function< Number(Number &f, VectorType &x, VectorType &g, const VectorType &p)> &slot)
 
boost::signals2::connection connect_preconditioner_slot (const std::function< void(VectorType &g, const FiniteSizeHistory< VectorType > &s, const FiniteSizeHistory< VectorType > &y)> &slot)
 
boost::signals2::connection connect (const std::function< SolverControl::State(const unsigned int iteration, const double check_value, const VectorType &current_iterate)> &slot)
 
template<class Archive >
void serialize (Archive &ar, const unsigned int version)
 
Subscriptor functionality

Classes derived from Subscriptor provide a facility to subscribe to this object. This is mostly used by the SmartPointer class.

void subscribe (std::atomic< bool > *const validity, const std::string &identifier="") const
 
void unsubscribe (std::atomic< bool > *const validity, const std::string &identifier="") const
 
unsigned int n_subscriptions () const
 
template<typename StreamType >
void list_subscribers (StreamType &stream) const
 
void list_subscribers () const
 

Static Public Member Functions

static ::ExceptionBaseExcInUse (int arg1, std::string arg2, std::string arg3)
 
static ::ExceptionBaseExcNoSubscriber (std::string arg1, std::string arg2)
 

Protected Attributes

const AdditionalData additional_data
 
boost::signals2::signal< Number(Number &f, VectorType &x, VectorType &g, const VectorType &p)> line_search_signal
 
boost::signals2::signal< void(VectorType &g, const FiniteSizeHistory< VectorType > &s, const FiniteSizeHistory< VectorType > &y)> preconditioner_signal
 
GrowingVectorMemory< VectorTypestatic_vector_memory
 
VectorMemory< VectorType > & memory
 
boost::signals2::signal< SolverControl::State(const unsigned int iteration, const double check_value, const VectorType &current_iterate), StateCombineriteration_status
 

Detailed Description

template<typename VectorType>
class SolverBFGS< VectorType >

Implement the limited memory BFGS minimization method.

This class implements a method to minimize a given function for which only the values of the function and its derivatives, but not its second derivatives are available. The BFGS method is a variation of the Newton method for function minimization in which the Hessian matrix is only approximated. In particular, the Hessian is updated using the formula of Broyden, Fletcher, Goldfarb, and Shanno (BFGS):

\begin{align*} H^{(k+1)} &= \left[ I-\rho_{(k)} s^{(k)} \otimes y^{(k)} \right] H^{(k)} \left[ I -\rho^{(k)} y^{(k)} \otimes s^{(k)} \right] + \rho^{(k)} s^{(k)} \otimes s^{(k)} \\ y^{(k)} &\dealcoloneq g^{(k+1)} - g^{(k)} \\ s^{(k)} &\dealcoloneq x^{(k+1)} - x^{(k)} \\ \rho^{(k)} &\dealcoloneq \frac{1}{y^{(k)} \cdot s^{(k)}} \end{align*}

for a symmetric positive definite \(H\). Limited memory variant is implemented via the two-loop recursion.

Definition at line 56 of file solver_bfgs.h.

Member Typedef Documentation

◆ Number

template<typename VectorType >
using SolverBFGS< VectorType >::Number = typename VectorType::value_type

Number type.

Definition at line 62 of file solver_bfgs.h.

◆ vector_type

template<class VectorType = Vector<double>>
using SolverBase< VectorType >::vector_type = VectorType
inherited

An alias for the underlying vector type

Definition at line 347 of file solver.h.

Constructor & Destructor Documentation

◆ SolverBFGS()

template<typename VectorType >
SolverBFGS< VectorType >::SolverBFGS ( SolverControl residual_control,
const AdditionalData data = AdditionalData() 
)
explicit

Constructor.

Member Function Documentation

◆ solve()

template<typename VectorType >
void SolverBFGS< VectorType >::solve ( const std::function< Number(const VectorType &x, VectorType &g)> &  compute,
VectorType x 
)

Solve the unconstrained minimization problem

\[ \min_{\mathbf x} f(\mathbf x) \]

starting from initial state x.

The function compute takes two arguments indicating the values of \(x\) and of the gradient \(g=\nabla f(\mathbf x)=\frac{\partial f}{\partial \mathbf x}\). When called, it needs to update the gradient \(g\) at the given location \(x\) and return the value of the function being minimized, i.e., \(f(\mathbf x)\).

◆ connect_line_search_slot()

template<typename VectorType >
boost::signals2::connection SolverBFGS< VectorType >::connect_line_search_slot ( const std::function< Number(Number &f, VectorType &x, VectorType &g, const VectorType &p)> &  slot)

Connect a slot to perform a custom line-search.

Given the value of function f, the current value of unknown x, the gradient g and the search direction p, return the size \(\alpha\) of the step \(x \leftarrow x + \alpha p\), and update x, g and f accordingly.

◆ connect_preconditioner_slot()

template<typename VectorType >
boost::signals2::connection SolverBFGS< VectorType >::connect_preconditioner_slot ( const std::function< void(VectorType &g, const FiniteSizeHistory< VectorType > &s, const FiniteSizeHistory< VectorType > &y)> &  slot)

Connect a slot to perform a custom preconditioning.

The preconditioner is applied inside the two loop recursion to vector g using the history of position increments s and gradient increments y.

One possibility is to use the oldest s,y pair:

const auto preconditioner = [](VectorType & g,
if (s.size() > 0)
{
const unsigned int i = s.size() - 1;
const auto yy = y[i] * y[i];
const auto sy = s[i] * y[i];
Assert(yy > 0 && sy > 0, ExcInternalError());
g *= sy / yy;
}
};

No preconditioning is performed if the code using this class has not attached anything to the signal.

◆ connect()

template<class VectorType >
boost::signals2::connection SolverBase< VectorType >::connect ( const std::function< SolverControl::State(const unsigned int iteration, const double check_value, const VectorType &current_iterate)> &  slot)
inlineinherited

Connect a function object that will be called periodically within iterative solvers. This function is used to attach monitors to iterative solvers, either to determine when convergence has happened, or simply to observe the progress of an iteration. See the documentation of this class for more information.

Parameters
slotA function object specified here will, with each call, receive the number of the current iteration, the value that is used to check for convergence (typically the residual of the current iterate with respect to the linear system to be solved) and the currently best available guess for the current iterate. Note that some solvers do not update the approximate solution in every iteration but only after convergence or failure has been determined (GMRES is an example); in such cases, the vector passed as the last argument to the signal is simply the best approximate at the time the signal is called, but not the vector that will be returned if the signal's return value indicates that the iteration should be terminated. The function object must return a SolverControl::State value that indicates whether the iteration should continue, has failed, or has succeeded. The results of all connected functions will then be combined to determine what should happen with the iteration.
Returns
A connection object that represents the connection from the signal to the function object. It can be used to disconnect the function object again from the signal. See the documentation of the BOOST Signals2 library for more information on connection management.

Definition at line 554 of file solver.h.

◆ subscribe()

void Subscriptor::subscribe ( std::atomic< bool > *const  validity,
const std::string &  identifier = "" 
) const
inherited

Subscribes a user of the object by storing the pointer validity. The subscriber may be identified by text supplied as identifier.

Definition at line 136 of file subscriptor.cc.

◆ unsubscribe()

void Subscriptor::unsubscribe ( std::atomic< bool > *const  validity,
const std::string &  identifier = "" 
) const
inherited

Unsubscribes a user from the object.

Note
The identifier and the validity pointer must be the same as the one supplied to subscribe().

Definition at line 156 of file subscriptor.cc.

◆ n_subscriptions()

unsigned int Subscriptor::n_subscriptions ( ) const
inlineinherited

Return the present number of subscriptions to this object. This allows to use this class for reference counted lifetime determination where the last one to unsubscribe also deletes the object.

Definition at line 301 of file subscriptor.h.

◆ list_subscribers() [1/2]

template<typename StreamType >
void Subscriptor::list_subscribers ( StreamType &  stream) const
inlineinherited

List the subscribers to the input stream.

Definition at line 318 of file subscriptor.h.

◆ list_subscribers() [2/2]

void Subscriptor::list_subscribers ( ) const
inherited

List the subscribers to deallog.

Definition at line 204 of file subscriptor.cc.

◆ serialize()

template<class Archive >
void Subscriptor::serialize ( Archive &  ar,
const unsigned int  version 
)
inlineinherited

Read or write the data of this object to or from a stream for the purpose of serialization using the BOOST serialization library.

This function does not actually serialize any of the member variables of this class. The reason is that what this class stores is only who subscribes to this object, but who does so at the time of storing the contents of this object does not necessarily have anything to do with who subscribes to the object when it is restored. Consequently, we do not want to overwrite the subscribers at the time of restoring, and then there is no reason to write the subscribers out in the first place.

Definition at line 310 of file subscriptor.h.

Member Data Documentation

◆ additional_data

template<typename VectorType >
const AdditionalData SolverBFGS< VectorType >::additional_data
protected

Additional data to the solver.

Definition at line 163 of file solver_bfgs.h.

◆ line_search_signal

template<typename VectorType >
boost::signals2::signal< Number(Number &f, VectorType &x, VectorType &g, const VectorType &p)> SolverBFGS< VectorType >::line_search_signal
protected

Signal used to perform line search.

Definition at line 170 of file solver_bfgs.h.

◆ preconditioner_signal

template<typename VectorType >
boost::signals2::signal<void(VectorType & g, const FiniteSizeHistory<VectorType> &s, const FiniteSizeHistory<VectorType> &y)> SolverBFGS< VectorType >::preconditioner_signal
protected

Signal used to perform preconditioning.

Definition at line 178 of file solver_bfgs.h.

◆ static_vector_memory

template<class VectorType = Vector<double>>
GrowingVectorMemory<VectorType> SolverBase< VectorType >::static_vector_memory
mutableprotectedinherited

A static vector memory object to be used whenever no such object has been given to the constructor.

Definition at line 415 of file solver.h.

◆ memory

template<class VectorType = Vector<double>>
VectorMemory<VectorType>& SolverBase< VectorType >::memory
protectedinherited

A reference to an object that provides memory for auxiliary vectors.

Definition at line 420 of file solver.h.

◆ iteration_status

template<class VectorType = Vector<double>>
boost::signals2::signal< SolverControl::State(const unsigned int iteration, const double check_value, const VectorType & current_iterate), StateCombiner> SolverBase< VectorType >::iteration_status
protectedinherited

A signal that iterative solvers can execute at the end of every iteration (or in an otherwise periodic fashion) to find out whether we should continue iterating or not. The signal may call one or more slots that each will make this determination by themselves, and the result over all slots (function calls) will be determined by the StateCombiner object.

The arguments passed to the signal are (i) the number of the current iteration; (ii) the value that is used to determine convergence (oftentimes the residual, but in other cases other quantities may be used as long as they converge to zero as the iterate approaches the solution of the linear system); and (iii) a vector that corresponds to the current best guess for the solution at the point where the signal is called. Note that some solvers do not update the approximate solution in every iteration but only after convergence or failure has been determined (GMRES is an example); in such cases, the vector passed as the last argument to the signal is simply the best approximate at the time the signal is called, but not the vector that will be returned if the signal's return value indicates that the iteration should be terminated.

Definition at line 471 of file solver.h.


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