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CLevenbergMarquardt.h

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/* +---------------------------------------------------------------------------+
   |          The Mobile Robot Programming Toolkit (MRPT) C++ library          |
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   |                   http://mrpt.sourceforge.net/                            |
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   |   Copyright (C) 2005-2010  University of Malaga                           |
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   |    This software was written by the Machine Perception and Intelligent    |
   |      Robotics Lab, University of Malaga (Spain).                          |
   |    Contact: Jose-Luis Blanco  <jlblanco@ctima.uma.es>                     |
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   +---------------------------------------------------------------------------+ */
#ifndef  CLevenbergMarquardt_H
#define  CLevenbergMarquardt_H

#include <mrpt/utils/CDebugOutputCapable.h>
#include <mrpt/math/CMatrixD.h>
#include <mrpt/math/utils.h>

/*---------------------------------------------------------------
        Class
  ---------------------------------------------------------------*/
namespace mrpt
{
namespace math
{
        /** An implementation of the Levenberg-Marquardt algorithm for least-square minimization.
         *
         *  Refer to the <a href="http://www.mrpt.org/Levenberg%E2%80%93Marquardt_algorithm">wiki page</a> for more details on the algorithm and usage.
         *
         *  The parameters of the template are:
         *   - NUMTYPE: The numeric type for all the operations (float, double, or long double)
         *   - USERPARAM: The type of the "y" input to the user supplied evaluation functor. Default type is a vector of NUMTYPE.
         */
        template <typename VECTORTYPE = mrpt::vector_double, class USERPARAM = VECTORTYPE >
        class CLevenbergMarquardtTempl : public mrpt::utils::CDebugOutputCapable
        {
        public:
                typedef typename VECTORTYPE::value_type  NUMTYPE;


                /** The type of the function passed to execute. The user must supply a function which evaluates the error of a given point in the solution space.
                  *  \param x The state point under examination.
                  *  \param y The same object passed to "execute" as the parameter "userParam".
                  *  \param out The vector of (non-squared) errors, of the average square root error, for the given "x". The functor code must set the size of this vector.
                  */
                typedef void (*TFunctor)(
                        const VECTORTYPE &x,
                        const USERPARAM &y,
                        VECTORTYPE &out);

                struct TResultInfo
                {
                        NUMTYPE         final_sqr_err;
                        size_t          iterations_executed;
                        CMatrixTemplateNumeric<NUMTYPE> path;   //!< Each row is the optimized value at each iteration.

                        /** This matrix can be used to obtain an estimate of the optimal parameters covariance matrix:
                          *
                          *  \f[ COV = H M H^\top \f]
                          *
                          *  With COV the covariance matrix of the optimal parameters, H this matrix, and M the covariance of the input (observations).
                          */
                        //CMatrixTemplateNumeric<NUMTYPE> H;
                };

                /** Executes the LM-method, with derivatives estimated from
                  *  "functor" Is a user-provided function which takes as input two vectors, in this order:
                  *             - x: The parameters to be optimized.
                  *             - userParam: The vector passed to the LM algorithm, unmodified.
                  *       and must return the "error vector", or the error (not squared) in each measured dimension, so the sum of the square of that output is the overall square error.
                  */
                static void     execute(
                        VECTORTYPE                      &out_optimal_x,
                        const VECTORTYPE        &x0,
                        TFunctor                        functor,
                        const VECTORTYPE        &increments,
                        const USERPARAM         &userParam,
                        TResultInfo                     &out_info,
                        bool                            verbose = false,
                        const size_t            &maxIter = 200,
                        const NUMTYPE           tau = 1e-3,
                        const NUMTYPE           e1 = 1e-8,
                        const NUMTYPE           e2 = 1e-8,
                        bool returnPath=true
                        )
                {
                        using namespace mrpt;
                        using namespace mrpt::utils;
                        using namespace mrpt::math;
                        using namespace std;

                        MRPT_START;

                        VECTORTYPE &x=out_optimal_x; // Var rename

                        // Asserts:
                        ASSERT_( increments.size() == x0.size() );

                        x=x0;                                                                   // Start with the starting point
                        VECTORTYPE      f_x;                                    // The vector error from the user function
                        CMatrixTemplateNumeric<NUMTYPE> AUX;
                        CMatrixTemplateNumeric<NUMTYPE> J;              // The Jacobian of "f"
                        CMatrixTemplateNumeric<NUMTYPE> H;              // The Hessian of "f"
                        VECTORTYPE      g;                                              // The gradient

                        // Compute the jacobian and the Hessian:
                        mrpt::math::estimateJacobian( x, functor, increments, userParam, J);
                        H.multiply_AtA(J);

                        const size_t  H_len = H.getColCount();

                        // Compute the gradient:
                        functor(x, userParam ,f_x);
                        J.multiply_Atb(f_x, g);

                        // Start iterations:
                        bool    found = math::norm_inf(g)<=e1;
                        if (verbose && found)   printf_debug("[LM] End condition: math::norm_inf(g)<=e1 :%f\n",math::norm_inf(g));

                        NUMTYPE lambda = tau * H.maximumDiagonal();
                        size_t  iter = 0;
                        NUMTYPE v = 2;

                        VECTORTYPE      h_lm;
                        VECTORTYPE      xnew, f_xnew ;
                        NUMTYPE                 F_x  = pow( math::norm( f_x ), 2);

                        const size_t    N = x.size();

                        if (returnPath) {
                                out_info.path.setSize(maxIter,N+1);
                                out_info.path.insertRow(iter,x);
                        }       else out_info.path.setSize(0,0);

                        while (!found && ++iter<maxIter)
                        {
                                // H_lm = -( H + \lambda I ) ^-1 * g
                                for (size_t k=0;k<H_len;k++)
                                        H(k,k)+= lambda;
                                        //H(k,k) *= 1+lambda;

                                H.inv_fast(AUX);
                                AUX.multiply_Ab(g,h_lm);
                                h_lm *= NUMTYPE(-1.0);

                                double h_lm_n2 = math::norm(h_lm);
                                double x_n2 = math::norm(x);

                                if (verbose) printf_debug( (format("[LM] Iter: %u x:",(unsigned)iter)+ sprintf_vector(" %f",x) + string("\n")).c_str() );

                                if (h_lm_n2<e2*(x_n2+e2))
                                {
                                        // Done:
                                        found = true;
                                        if (verbose) printf_debug("[LM] End condition: %e < %e\n", h_lm_n2, e2*(x_n2+e2) );
                                }
                                else
                                {
                                        // Improvement:
                                        xnew = x;
                                        xnew += h_lm;
                                        functor(xnew, userParam ,f_xnew );
                                        const double F_xnew = pow( math::norm(f_xnew), 2);

                                        // denom = h_lm^t * ( \lambda * h_lm - g )
                                        VECTORTYPE      tmp(h_lm);
                                        tmp *= lambda;
                                        tmp -= g;
                                        tmp*=h_lm;
                                        double denom = math::sum(tmp);
                                        double l = (F_x - F_xnew) / denom;

                                        //cout << "l:" << l << endl << tmp;

                                        if (l>0) // There is an improvement:
                                        {
                                                // Accept new point:
                                                x   = xnew;
                                                f_x = f_xnew;
                                                F_x = F_xnew;

                                                math::estimateJacobian( x, functor, increments, userParam, J);
                                                H.multiply_AtA(J);
                                                J.multiply_Atb(f_x, g);

                                                found = math::norm_inf(g)<=e1;
                                                if (verbose && found)   printf_debug("[LM] End condition: math::norm_inf(g)<=e1 : %e\n", math::norm_inf(g) );

                                                lambda *= max(0.33, 1-pow(2*l-1,3) );
                                                v = 2;
                                        }
                                        else
                                        {
                                                // Nope...
                                                lambda *= v;
                                                v*= 2;
                                        }


                                        if (returnPath) {
                                                out_info.path.insertRow(iter,x);
                                                out_info.path(iter,x.size()) = F_x;
                                        }
                                }
                        } // end while

                        // Output info:
                        out_info.final_sqr_err = F_x;
                        out_info.iterations_executed = iter;
                        if (returnPath) out_info.path.setSize(iter,N+1);

                        MRPT_END;
                }

        }; // End of class def.


        typedef CLevenbergMarquardtTempl<vector_double> CLevenbergMarquardt;  //!< The default name for the LM class is an instantiation for "double"

        } // End of namespace
} // End of namespace
#endif

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