-/* Copyright (C) 2009 Frederik Eaton [frederik at ofb dot net]
-
- This file is part of libDAI.
-
- libDAI is free software; you can redistribute it and/or modify
- it under the terms of the GNU General Public License as published by
- the Free Software Foundation; either version 2 of the License, or
- (at your option) any later version.
-
- libDAI is distributed in the hope that it will be useful,
- but WITHOUT ANY WARRANTY; without even the implied warranty of
- MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
- GNU General Public License for more details.
-
- You should have received a copy of the GNU General Public License
- along with libDAI; if not, write to the Free Software
- Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
-*/
+/* This file is part of libDAI - http://www.libdai.org/
+ *
+ * libDAI is licensed under the terms of the GNU General Public License version
+ * 2, or (at your option) any later version. libDAI is distributed without any
+ * warranty. See the file COPYING for more details.
+ *
+ * Copyright (C) 2009 Frederik Eaton [frederik at ofb dot net]
+ */
/// \file
-/// \brief Defines class BBP [\ref EaG09]
-/// \todo Improve documentation
+/// \brief Defines class BBP, which implements Back-Belief-Propagation
#ifndef ___defined_libdai_bbp_h
namespace dai {
-/// Computes the adjoint of the unnormed probability vector from the normalizer and the adjoint of the normalized probability vector @see eqn. (13) in [\ref EaG09]
-Prob unnormAdjoint( const Prob &w, Real Z_w, const Prob &adj_w );
+/// Enumeration of several cost functions that can be used with BBP
+/** \note This class is meant as a base class for BBPCostFunction, which provides additional functionality.
+ */
+DAI_ENUM(BBPCostFunctionBase,CFN_GIBBS_B,CFN_GIBBS_B2,CFN_GIBBS_EXP,CFN_GIBBS_B_FACTOR,CFN_GIBBS_B2_FACTOR,CFN_GIBBS_EXP_FACTOR,CFN_VAR_ENT,CFN_FACTOR_ENT,CFN_BETHE_ENT);
+
-/// Runs Gibbs sampling for \a iters iterations on ia.fg(), and returns state
-std::vector<size_t> getGibbsState( const InfAlg &ia, size_t iters );
+/// Predefined cost functions that can be used with BBP
+class BBPCostFunction : public BBPCostFunctionBase {
+ public:
+ /// Returns whether this cost function depends on having a Gibbs state
+ bool needGibbsState() const;
+
+ /// Evaluates cost function in state \a stateP using the information in inference algorithm \a ia
+ Real evaluate( const InfAlg &ia, const std::vector<size_t> *stateP ) const;
+
+ /// Assignment operator
+ BBPCostFunction& operator=( const BBPCostFunctionBase &x ) {
+ if( this != &x ) {
+ (BBPCostFunctionBase)*this = x;
+ }
+ return *this;
+ }
+};
/// Implements BBP (Back-Belief-Propagation) [\ref EaG09]
+/** \author Frederik Eaton
+ */
class BBP {
- protected:
- /// @name Inputs
- //@{
+ private:
+ /// \name Input variables
+ //@{
+ /// Stores a BP_dual helper object
BP_dual _bp_dual;
+ /// Pointer to the factor graph
const FactorGraph *_fg;
+ /// Pointer to the approximate inference algorithm (currently, only BP objects are supported)
const InfAlg *_ia;
- //@}
+ //@}
- /// Number of iterations done
- size_t _iters;
-
- /// @name Outputs
- //@{
+ /// \name Output variables
+ //@{
/// Variable factor adjoints
std::vector<Prob> _adj_psi_V;
/// Factor adjoints
std::vector<Prob> _adj_b_V;
/// Normalized factor belief adjoints
std::vector<Prob> _adj_b_F;
- //@}
-
- /// @name Helper quantities computed from the BP messages
- //@{
- /// _T[i][_I] (see eqn. (41) in [\ref EaG09])
- std::vector<std::vector<Prob > > _T;
- /// _U[I][_i] (see eqn. (42) in [\ref EaG09])
- std::vector<std::vector<Prob > > _U;
- /// _S[i][_I][_j] (see eqn. (43) in [\ref EaG09])
- std::vector<std::vector<std::vector<Prob > > > _S;
- /// _R[I][_i][_J] (see eqn. (44) in [\ref EaG09])
- std::vector<std::vector<std::vector<Prob > > > _R;
- //@}
-
- /// Unnormalized variable belief adjoints
- std::vector<Prob> _adj_b_V_unnorm;
- /// Unnormalized factor belief adjoints
- std::vector<Prob> _adj_b_F_unnorm;
+ //@}
+ /// \name Internal state variables
+ //@{
/// Initial variable factor adjoints
std::vector<Prob> _init_adj_psi_V;
/// Initial factor adjoints
std::vector<std::vector<Prob> > _new_adj_n;
/// Updated normalized factor->variable message adjoint (indexed [i][_I])
std::vector<std::vector<Prob> > _new_adj_m;
+ /// Unnormalized variable belief adjoints
+ std::vector<Prob> _adj_b_V_unnorm;
+ /// Unnormalized factor belief adjoints
+ std::vector<Prob> _adj_b_F_unnorm;
- /// @name Optimized indexing (for performance)
- //@{
- /// Calculates _indices, which is a cache of IndexFor @see bp.cpp
- void RegenerateInds();
-
+ /// _T[i][_I] (see eqn. (41) in [\ref EaG09])
+ std::vector<std::vector<Prob > > _T;
+ /// _U[I][_i] (see eqn. (42) in [\ref EaG09])
+ std::vector<std::vector<Prob > > _U;
+ /// _S[i][_I][_j] (see eqn. (43) in [\ref EaG09])
+ std::vector<std::vector<std::vector<Prob > > > _S;
+ /// _R[I][_i][_J] (see eqn. (44) in [\ref EaG09])
+ std::vector<std::vector<std::vector<Prob > > > _R;
+
+ /// Number of iterations done
+ size_t _iters;
+ //@}
+
+ /// \name Index cache management (for performance)
+ //@{
/// Index type
typedef std::vector<size_t> _ind_t;
/// Cached indices (indexed [i][_I])
- std::vector<std::vector<_ind_t> > _indices;
+ std::vector<std::vector<_ind_t> > _indices;
+ /// Prepares index cache _indices
+ /** \see bp.cpp
+ */
+ void RegenerateInds();
/// Returns an index from the cache
const _ind_t& _index(size_t i, size_t _I) const { return _indices[i][_I]; }
- //@}
+ //@}
- /// @name Initialization
- //@{
+ /// \name Initialization helper functions
+ //@{
/// Calculate T values; see eqn. (41) in [\ref EaG09]
void RegenerateT();
/// Calculate U values; see eqn. (42) in [\ref EaG09]
void RegenerateR();
/// Calculate _adj_b_V_unnorm and _adj_b_F_unnorm from _adj_b_V and _adj_b_F
void RegenerateInputs();
- /// Initialise members for factor adjoints (call after RegenerateInputs)
+ /// Initialise members for factor adjoints
+ /** \pre RegenerateInputs() should be called first
+ */
void RegeneratePsiAdjoints();
- /// Initialise members for message adjoints (call after RegenerateInputs) for parallel algorithm
+ /// Initialise members for message adjoints for parallel algorithm
+ /** \pre RegenerateInputs() should be called first
+ */
void RegenerateParMessageAdjoints();
- /// Initialise members for message adjoints (call after RegenerateInputs) for sequential algorithm
+ /// Initialise members for message adjoints for sequential algorithm
/** Same as RegenerateMessageAdjoints, but calls sendSeqMsgN rather
* than updating _adj_n (and friends) which are unused in the sequential algorithm.
+ * \pre RegenerateInputs() should be called first
*/
void RegenerateSeqMessageAdjoints();
- //@}
-
- /// Returns T value; see eqn. (41) in [\ref EaG09]
- DAI_ACCMUT(Prob & T(size_t i, size_t _I), { return _T[i][_I]; });
- /// Retunrs U value; see eqn. (42) in [\ref EaG09]
- DAI_ACCMUT(Prob & U(size_t I, size_t _i), { return _U[I][_i]; });
- /// Returns S value; see eqn. (43) in [\ref EaG09]
- DAI_ACCMUT(Prob & S(size_t i, size_t _I, size_t _j), { return _S[i][_I][_j]; });
- /// Returns R value; see eqn. (44) in [\ref EaG09]
- DAI_ACCMUT(Prob & R(size_t I, size_t _i, size_t _J), { return _R[I][_i][_J]; });
-
- /// @name Parallel algorithm
- //@{
+ /// Called by \a init, recalculates intermediate values
+ void Regenerate();
+ //@}
+
+ /// \name Accessors/mutators
+ //@{
+ /// Returns reference to T value; see eqn. (41) in [\ref EaG09]
+ Prob & T(size_t i, size_t _I) { return _T[i][_I]; }
+ /// Returns constant reference to T value; see eqn. (41) in [\ref EaG09]
+ const Prob & T(size_t i, size_t _I) const { return _T[i][_I]; }
+ /// Returns reference to U value; see eqn. (42) in [\ref EaG09]
+ Prob & U(size_t I, size_t _i) { return _U[I][_i]; }
+ /// Returns constant reference to U value; see eqn. (42) in [\ref EaG09]
+ const Prob & U(size_t I, size_t _i) const { return _U[I][_i]; }
+ /// Returns reference to S value; see eqn. (43) in [\ref EaG09]
+ Prob & S(size_t i, size_t _I, size_t _j) { return _S[i][_I][_j]; }
+ /// Returns constant reference to S value; see eqn. (43) in [\ref EaG09]
+ const Prob & S(size_t i, size_t _I, size_t _j) const { return _S[i][_I][_j]; }
+ /// Returns reference to R value; see eqn. (44) in [\ref EaG09]
+ Prob & R(size_t I, size_t _i, size_t _J) { return _R[I][_i][_J]; }
+ /// Returns constant reference to R value; see eqn. (44) in [\ref EaG09]
+ const Prob & R(size_t I, size_t _i, size_t _J) const { return _R[I][_i][_J]; }
+
+ /// Returns reference to variable->factor message adjoint
+ Prob& adj_n(size_t i, size_t _I) { return _adj_n[i][_I]; }
+ /// Returns constant reference to variable->factor message adjoint
+ const Prob& adj_n(size_t i, size_t _I) const { return _adj_n[i][_I]; }
+ /// Returns reference to factor->variable message adjoint
+ Prob& adj_m(size_t i, size_t _I) { return _adj_m[i][_I]; }
+ /// Returns constant reference to factor->variable message adjoint
+ const Prob& adj_m(size_t i, size_t _I) const { return _adj_m[i][_I]; }
+ //@}
+
+ /// \name Parallel algorithm
+ //@{
/// Calculates new variable->factor message adjoint
/** Increases variable factor adjoint according to eqn. (27) in [\ref EaG09] and
* calculates the new variable->factor message adjoint according to eqn. (29) in [\ref EaG09].
void upMsgM( size_t i, size_t _I );
/// Do one parallel update of all message adjoints
void doParUpdate();
- //@}
+ //@}
- /// @name Sequential algorithm
- //@{
- /// Helper function for sendSeqMsgM: increases factor->variable message adjoint by p and calculates the corresponding unnormalized adjoint
+ /// \name Sequential algorithm
+ //@{
+ /// Helper function for sendSeqMsgM(): increases factor->variable message adjoint by \a p and calculates the corresponding unnormalized adjoint
void incrSeqMsgM( size_t i, size_t _I, const Prob& p );
// DISABLED BECAUSE IT IS BUGGY:
// void updateSeqMsgM( size_t i, size_t _I );
/// Sets normalized factor->variable message adjoint and calculates the corresponding unnormalized adjoint
- void setSeqMsgM( size_t i, size_t _I, const Prob &p );
+ void setSeqMsgM( size_t i, size_t _I, const Prob &p );
/// Implements routine Send-n in Figure 5 in [\ref EaG09]
void sendSeqMsgN( size_t i, size_t _I, const Prob &f );
/// Implements routine Send-m in Figure 5 in [\ref EaG09]
void sendSeqMsgM( size_t i, size_t _I );
- //@}
+ //@}
- /// Calculates averaged L-1 norm of unnormalized message adjoints
+ /// Computes the adjoint of the unnormed probability vector from the normalizer and the adjoint of the normalized probability vector
+ /** \see eqn. (13) in [\ref EaG09]
+ */
+ Prob unnormAdjoint( const Prob &w, Real Z_w, const Prob &adj_w );
+
+ /// Calculates averaged L1 norm of unnormalized message adjoints
Real getUnMsgMag();
- /// Calculates averaged L-1 norms of current and new normalized message adjoints
+ /// Calculates averaged L1 norms of current and new normalized message adjoints
void getMsgMags( Real &s, Real &new_s );
-
- /// Sets all vectors _adj_b_F to zero
- void zero_adj_b_F() {
- _adj_b_F.clear();
- _adj_b_F.reserve( _fg->nrFactors() );
- for( size_t I = 0; I < _fg->nrFactors(); I++ )
- _adj_b_F.push_back( Prob( _fg->factor(I).states(), Real( 0.0 ) ) );
- }
-
/// Returns indices and magnitude of the largest normalized factor->variable message adjoint
void getArgmaxMsgM( size_t &i, size_t &_I, Real &mag );
/// Returns magnitude of the largest (in L1-norm) normalized factor->variable message adjoint
Real getMaxMsgM();
+
/// Calculates sum of L1 norms of all normalized factor->variable message adjoints
Real getTotalMsgM();
/// Calculates sum of L1 norms of all updated normalized factor->variable message adjoints
/// Calculates sum of L1 norms of all normalized variable->factor message adjoints
Real getTotalMsgN();
- public:
- /// Called by \a init, recalculates intermediate values
- void Regenerate();
+ /// Returns a vector of Probs (filled with zeroes) with state spaces corresponding to the factors in the factor graph \a fg
+ std::vector<Prob> getZeroAdjF( const FactorGraph &fg );
+ /// Returns a vector of Probs (filled with zeroes) with state spaces corresponding to the variables in the factor graph \a fg
+ std::vector<Prob> getZeroAdjV( const FactorGraph &fg );
- /// Constructor
+ public:
+ /// \name Constructors/destructors
+ //@{
+ /// Construct BBP object from a InfAlg \a ia and a PropertySet \a opts
+ /** \param ia should be a BP object or something compatible
+ * \param opts Parameters @see Properties
+ */
BBP( const InfAlg *ia, const PropertySet &opts ) : _bp_dual(ia), _fg(&(ia->fg())), _ia(ia) {
props.set(opts);
}
+ //@}
- /// Returns a vector of Probs (filled with zeroes) with state spaces corresponding to the factors in the factor graph fg
- std::vector<Prob> getZeroAdjF( const FactorGraph &fg );
- /// Returns a vector of Probs (filled with zeroes) with state spaces corresponding to the variables in the factor graph fg
- std::vector<Prob> getZeroAdjV( const FactorGraph &fg );
-
- /// Initializes belief adjoints and initial factor adjoints and regenerates
+ /// \name Initialization
+ //@{
+ /// Initializes from given belief adjoints \a adj_b_V, \a adj_b_F and initial factor adjoints \a adj_psi_V, \a adj_psi_F
void init( const std::vector<Prob> &adj_b_V, const std::vector<Prob> &adj_b_F, const std::vector<Prob> &adj_psi_V, const std::vector<Prob> &adj_psi_F ) {
_adj_b_V = adj_b_V;
_adj_b_F = adj_b_F;
_init_adj_psi_V = adj_psi_V;
_init_adj_psi_F = adj_psi_F;
- Regenerate();
+ Regenerate();
}
- /// Initializes belief adjoints and with zero initial factor adjoints and regenerates
+ /// Initializes from given belief adjoints \a adj_b_V and \a adj_b_F (setting initial factor adjoints to zero)
void init( const std::vector<Prob> &adj_b_V, const std::vector<Prob> &adj_b_F ) {
init( adj_b_V, adj_b_F, getZeroAdjV(*_fg), getZeroAdjF(*_fg) );
}
- /// Initializes variable belief adjoints (and sets factor belief adjoints to zero) and with zero initial factor adjoints and regenerates
- void init( const std::vector<Prob> &adj_b_V ) {
- init(adj_b_V, getZeroAdjF(*_fg));
+ /// Initializes variable belief adjoints \a adj_b_V (and sets factor belief adjoints and initial factor adjoints to zero)
+ void init
_V( const std::vector<Prob> &adj_b_V ) {
+ init( adj_b_V, getZeroAdjF(*_fg) );
}
- /// Run until change is less than given tolerance
- void run();
+ /// Initializes factor belief adjoints \a adj_b_F (and sets variable belief adjoints and initial factor adjoints to zero)
+ void init_F( const std::vector<Prob> &adj_b_F ) {
+ init( getZeroAdjV(*_fg), adj_b_F );
+ }
+
+ /// Initializes with adjoints calculated from cost function \a cfn, and state \a stateP
+ /** Uses the internal pointer to an inference algorithm in combination with the cost function and state for initialization.
+ * \param cfn Cost function used for initialization;
+ * \param stateP is a Gibbs state and can be NULL; it will be initialised using a Gibbs run.
+ */
+ void initCostFnAdj( const BBPCostFunction &cfn, const std::vector<size_t> *stateP );
+ //@}
+ /// \name BBP Algorithm
+ //@{
+ /// Perform iterative updates until change is less than given tolerance
+ void run();
+ //@}
+
+ /// \name Query results
+ //@{
+ /// Returns reference to variable factor adjoint
+ Prob& adj_psi_V(size_t i) { return _adj_psi_V[i]; }
+ /// Returns constant reference to variable factor adjoint
+ const Prob& adj_psi_V(size_t i) const { return _adj_psi_V[i]; }
+ /// Returns reference to factor adjoint
+ Prob& adj_psi_F(size_t I) { return _adj_psi_F[I]; }
+ /// Returns constant reference to factor adjoint
+ const Prob& adj_psi_F(size_t I) const { return _adj_psi_F[I]; }
+ /// Returns reference to variable belief adjoint
+ Prob& adj_b_V(size_t i) { return _adj_b_V[i]; }
+ /// Returns constant reference to variable belief adjoint
+ const Prob& adj_b_V(size_t i) const { return _adj_b_V[i]; }
+ /// Returns reference to factor belief adjoint
+ Prob& adj_b_F(size_t I) { return _adj_b_F[I]; }
+ /// Returns constant reference to factor belief adjoint
+ const Prob& adj_b_F(size_t I) const { return _adj_b_F[I]; }
/// Return number of iterations done so far
- size_t doneIters() { return _iters; }
-
- /// Returns variable factor adjoint
- DAI_ACCMUT(Prob& adj_psi_V(size_t i), { return _adj_psi_V[i]; });
- /// Returns factor adjoint
- DAI_ACCMUT(Prob& adj_psi_F(size_t I), { return _adj_psi_F[I]; });
- /// Returns variable belief adjoint
- DAI_ACCMUT(Prob& adj_b_V(size_t i), { return _adj_b_V[i]; });
- /// Returns factor belief adjoint
- DAI_ACCMUT(Prob& adj_b_F(size_t I), { return _adj_b_F[I]; });
-
- protected:
- /// Returns variable->factor message adjoint
- DAI_ACCMUT(Prob& adj_n(size_t i, size_t _I), { return _adj_n[i][_I]; });
- /// Returns factor->variable message adjoint
- DAI_ACCMUT(Prob& adj_m(size_t i, size_t _I), { return _adj_m[i][_I]; });
-
- public:
- /// Parameters of this algorithm
+ size_t Iterations() { return _iters; }
+ //@}
+
+ public:
+ /// Parameters for BBP
/* PROPERTIES(props,BBP) {
- /// Enumeration of possible update schedules
+ /// \brief Enumeration of possible update schedules
+ /// - SEQ_FIX fixed sequential updates
+ /// - SEQ_MAX maximum residual updates (inspired by [\ref EMK06])
+ /// - SEQ_BP_REV schedule used by BP, but reversed
+ /// - SEQ_BP_FWD schedule used by BP
+ /// - PAR parallel updates
DAI_ENUM(UpdateType,SEQ_FIX,SEQ_MAX,SEQ_BP_REV,SEQ_BP_FWD,PAR);
- /// Verbosity
+ /// Verbosity (amount of output sent to stderr)
size_t verbose;
/// Maximum number of iterations
size_t maxiter;
- /// Tolerance (not used for updates = SEQ_BP_REV, SEQ_BP_FWD)
- double tol;
+ /// Tolerance for convergence test
+ /// \note Not used for updates = SEQ_BP_REV, SEQ_BP_FWD
+ Real tol;
/// Damping constant (0 for none); damping = 1 - lambda where lambda is the damping constant used in [\ref EaG09]
- double damping;
+ Real damping;
/// Update schedule
UpdateType updates;
// DISABLED BECAUSE IT IS BUGGY:
// bool clean_updates;
- }
+ }
*/
-/* {{{ GENERATED CODE: DO NOT EDIT. Created by
- ./scripts/regenerate-properties include/dai/bbp.h src/bbp.cpp
+/* {{{ GENERATED CODE: DO NOT EDIT. Created by
+ ./scripts/regenerate-properties include/dai/bbp.h src/bbp.cpp
*/
struct Properties {
/// Enumeration of possible update schedules
+ /** The following update schedules are defined:
+ * - SEQ_FIX fixed sequential updates
+ * - SEQ_MAX maximum residual updates (inspired by [\ref EMK06])
+ * - SEQ_BP_REV schedule used by BP, but reversed
+ * - SEQ_BP_FWD schedule used by BP
+ * - PAR parallel updates
+ */
DAI_ENUM(UpdateType,SEQ_FIX,SEQ_MAX,SEQ_BP_REV,SEQ_BP_FWD,PAR);
- /// Verbosity
+ /// Verbosity (amount of output sent to stderr)
size_t verbose;
/// Maximum number of iterations
size_t maxiter;
- /// Tolerance (not used for updates = SEQ_BP_REV, SEQ_BP_FWD)
- double tol;
+ /// Tolerance for convergence test
+ /** \note Not used for updates = SEQ_BP_REV, SEQ_BP_FWD
+ */
+ Real tol;
/// Damping constant (0 for none); damping = 1 - lambda where lambda is the damping constant used in [\ref EaG09]
- double damping;
+ Real damping;
/// Update schedule
UpdateType updates;
/// Set members from PropertySet
+ /** \throw UNKNOWN_PROPERTY_TYPE if a Property key is not recognized
+ * \throw NOT_ALL_PROPERTIES_SPECIFIED if an expected Property is missing
+ */
void set(const PropertySet &opts);
/// Get members into PropertySet
PropertySet get() const;
};
-/// Enumeration of several cost functions that can be used with BBP.
-DAI_ENUM(bbp_cfn_t,CFN_GIBBS_B,CFN_GIBBS_B2,CFN_GIBBS_EXP,CFN_GIBBS_B_FACTOR,CFN_GIBBS_B2_FACTOR,CFN_GIBBS_EXP_FACTOR,CFN_VAR_ENT,CFN_FACTOR_ENT,CFN_BETHE_ENT);
-
-/// Initialise BBP using InfAlg, cost function, and stateP
-/** Calls bbp.init with adjoints calculated from ia.beliefV and
- * ia.beliefF. stateP is a Gibbs state and can be NULL, it will be
- * initialised using a Gibbs run of 2*fg.Iterations() iterations.
- */
-void initBBPCostFnAdj( BBP &bbp, const InfAlg &ia, bbp_cfn_t cfn_type, const std::vector<size_t> *stateP );
-
-/// Answers question: does the given cost function depend on having a Gibbs state?
-bool needGibbsState( bbp_cfn_t cfn );
-
-/// Calculate actual value of cost function (cfn_type, stateP)
-/** This function returns the actual value of the cost function whose
- * gradient with respect to singleton beliefs is given by
- * gibbsToB1Adj on the same arguments
- */
-Real getCostFn( const InfAlg &fg, bbp_cfn_t cfn_type, const std::vector<size_t> *stateP );
-
-/// Function to test the validity of adjoints computed by BBP given a state for each variable using numerical derivatives.
-/** Factors containing a variable are multiplied by psi_1 adjustments to verify accuracy of _adj_psi_V.
- * \param h controls size of perturbation.
+/// Function to verify the validity of adjoints computed by BBP using numerical differentiation.
+/** Factors containing a variable are multiplied by small adjustments to verify accuracy of calculated variable factor adjoints.
+ * \param bp BP object;
+ * \param state Global state of all variables;
+ * \param bbp_props BBP parameters;
+ * \param cfn Cost function to be used;
+ * \param h Size of perturbation.
+ * \relates BBP
*/
-double numericBBPTest( const InfAlg &bp, const std::vector<size_t> *state, const PropertySet &bbp_props, bbp_cfn_t cfn, double h );
+Real numericBBPTest( const InfAlg &bp, const std::vector<size_t> *state, const PropertySet &bbp_props, const BBPCostFunction &cfn, Real h );
} // end of namespace dai
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