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RandomGenerators.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 RandomGenerator_H
#define RandomGenerator_H

#include <mrpt/utils/utils_defs.h>
#include <mrpt/math/CMatrixTemplateNumeric.h>
#include <mrpt/math/ops_matrices.h>

namespace mrpt
{
        /** A namespace of pseudo-random numbers genrators of diferent distributions. The central class in this namespace is mrpt::random::CRandomGenerator
         */
        namespace random
        {
                using namespace mrpt::utils;
                using namespace mrpt::math;

                /** A thred-safe pseudo random number generator, based on an internal MT19937 randomness generator.
                  * The base algorithm for randomness is platform-independent. See http://en.wikipedia.org/wiki/Mersenne_twister
                  *
                  * For real thread-safety, each thread must create and use its own instance of this class.
                  *
                  * Single-thread programs can use the static object mrpt::random::randomGenerator
                  */
                class BASE_IMPEXP CRandomGenerator
                {
                protected:
                        /** Data used internally by the MT19937 PRNG algorithm. */
                        struct  TMT19937_data
                        {
                                TMT19937_data() : index(0), seed_initialized(false)
                                {}
                                uint32_t        MT[624];
                                uint32_t        index;
                                bool            seed_initialized;
                        } m_MT19937_data;

                        void MT19937_generateNumbers();
                        void MT19937_initializeGenerator(const uint32_t &seed);

                public:

                        /** @name Initialization
                         @{ */

                                /** Default constructor: initialize random seed based on current time */
                                CRandomGenerator() : m_MT19937_data() { randomize(); }

                                /** Constructor for providing a custom random seed to initialize the PRNG */
                                CRandomGenerator(const uint32_t seed) : m_MT19937_data() { randomize(seed); }

                                void randomize(const uint32_t seed);  //!< Initialize the PRNG from the given random seed
                                void randomize();       //!< Randomize the generators, based on current time

                        /** @} */

                        /** @name Uniform pdf
                         @{ */

                                /** Generate a uniformly distributed pseudo-random number using the MT19937 algorithm, in the whole range of 32-bit integers.
                                  *  See: http://en.wikipedia.org/wiki/Mersenne_twister */
                                uint32_t drawUniform32bit();

                                /** Generate a uniformly distributed pseudo-random number using the MT19937 algorithm, scaled to the selected range. */
                                double drawUniform( const double Min, const double Max) {
                                        return Min + (Max-Min)* drawUniform32bit() * 2.3283064370807973754314699618685e-10; // 0xFFFFFFFF ^ -1
                                }

                                /** Fills the given matrix with independent, uniformly distributed samples.
                                  * Matrix classes can be CMatrixTemplateNumeric or CMatrixFixedNumeric
                                  * \sa drawUniform
                                  */
                                template <class MAT>
                                void drawUniformMatrix(
                                        MAT &matrix,
                                        const  double unif_min = 0,
                                        const  double unif_max = 1 )
                                {
                                        for (size_t r=0;r<matrix.getRowCount();r++)
                                                for (size_t c=0;c<matrix.getColCount();c++)
                                                        matrix.get_unsafe(r,c) = static_cast<typename MAT::value_type>( drawUniform(unif_min,unif_max) );
                                }

                                /** Fills the given vector with independent, uniformly distributed samples.
                                  * \sa drawUniform
                                  */
                                template <class T>
                                void drawUniformVector(
                                        std::vector<T> & v,
                                        const  double unif_min = 0,
                                        const  double unif_max = 1 )
                                {
                                        const size_t N = v.size();
                                        for (size_t c=0;c<N;c++)
                                                v[c] = static_cast<T>( drawUniform(unif_min,unif_max) );
                                }

                        /** @} */

                        /** @name Normal/Gaussian pdf
                         @{ */

                                /** Generate a normalized (mean=0, std=1) normally distributed sample.
                                 *  \param likelihood If desired, pass a pointer to a double which will receive the likelihood of the given sample to have been obtained, that is, the value of the normal pdf at the sample value.
                                 */
                                double drawGaussian1D_normalized( double *likelihood = NULL);

                                /** Generate a normally distributed pseudo-random number.
                                 * \param mean The mean value of desired normal distribution
                                 * \param std  The standard deviation value of desired normal distribution
                                 */
                                double drawGaussian1D( const double mean, const double std ) {
                                        return mean+std*drawGaussian1D_normalized();
                                }

                                /** Fills the given matrix with independent, 1D-normally distributed samples.
                                  * Matrix classes can be CMatrixTemplateNumeric or CMatrixFixedNumeric
                                  * \sa drawGaussian1D
                                  */
                                template <class MAT>
                                void drawGaussian1DMatrix(
                                        MAT &matrix,
                                        const double mean = 0,
                                        const double std = 1 )
                                {
                                        for (size_t r=0;r<matrix.getRowCount();r++)
                                                for (size_t c=0;c<matrix.getColCount();c++)
                                                        matrix.get_unsafe(r,c) = static_cast<typename MAT::value_type>( drawGaussian1D(mean,std) );
                                }

                                /** Fills the given vector with independent, 1D-normally distributed samples.
                                  * \sa drawGaussian1D
                                  */
                                template <class T>
                                void drawGaussian1DVector(
                                        std::vector<T> & v,
                                        const double mean = 0,
                                        const double std = 1 )
                                {
                                        const size_t N = v.size();
                                        for (size_t c=0;c<N;c++)
                                                v[c] = static_cast<T>( drawGaussian1D(mean,std) );
                                }

                                /** Generate multidimensional random samples according to a given covariance matrix.
                                 *  Mean is assumed to be zero if mean==NULL.
                                 * \exception std::exception On invalid covariance matrix
                                 * \sa drawGaussianMultivariateMany
                                 */
                                 template <typename T>
                                 void  drawGaussianMultivariate(
                                        std::vector<T>          &out_result,
                                        const CMatrixTemplateNumeric<T> &cov,
                                        const std::vector<T>*  mean = NULL
                                        );

                                 /** Generate a given number of multidimensional random samples according to a given covariance matrix.
                                 * \param cov The covariance matrix where to draw the samples from.
                                 * \param desiredSamples The number of samples to generate.
                                 * \param samplesLikelihoods If desired, set to a valid pointer to a vector, where it will be stored the likelihoods of having obtained each sample: the product of the gaussian-pdf for each independent variable.
                                 * \param ret The output list of samples
                                 * \param mean The mean, or zeros if mean==NULL.
                                 *
                                 * \exception std::exception On invalid covariance matrix
                                 *
                                 * \sa drawGaussianMultivariate
                                 */
                                 template <typename VECTORLIKE, typename MATRIXLIKE>
                                 void  drawGaussianMultivariateMany(
                                        std::vector< VECTORLIKE >       &ret,
                                        size_t                                          desiredSamples,
                                        const MATRIXLIKE        &cov,
                                        const VECTORLIKE*       mean = NULL,
                                        VECTORLIKE                      *samplesLikelihoods = NULL)
                                {
                                        typename VECTORLIKE::iterator  liks_it = samplesLikelihoods ? samplesLikelihoods->begin() : typename VECTORLIKE::iterator();
                                        const size_t dim = cov.getColCount();
                                        MATRIXLIKE Z,D;

                                        MRPT_START;

                                        if (samplesLikelihoods)
                                                samplesLikelihoods->assign(desiredSamples, 0);

                                        ret.resize(desiredSamples);
                                        ASSERT_(cov.getRowCount() == cov.getColCount() )

                                        if (mean) ASSERT_(mean->size() == dim )


                                        /** Computes the eigenvalues/eigenvector decomposition of this matrix,
                                        *    so that: M = Z · D · Z<sup>T</sup>, where columns in Z are the
                                        *         eigenvectors and the diagonal matrix D contains the eigenvalues
                                        *    as diagonal elements, sorted in <i>ascending</i> order.
                                        */
                                        cov.eigenVectors( Z, D );

                                        // Scale eigenvectors with eigenvalues:
                                        // Efficient implementation of: D.Sqrt(); Z = Z * D;
                                        for (size_t i=0;i<dim;i++)
                                        {
                                                const typename VECTORLIKE::value_type eig_sqrt = std::sqrt(D.get_unsafe(i,i));
                                                for (size_t j=0;j<dim;j++)
                                                        Z.get_unsafe(j,i)*=eig_sqrt;
                                        }

                                        for (typename std::vector<VECTORLIKE>::iterator ret_it=ret.begin();ret_it!=ret.end();ret_it++)
                                        {
                                                size_t          i;
                                                double  likelihood_1, likelihood_all;

                                                // Reset vector to 0:
                                                ret_it->assign(dim,0);
                                                likelihood_all = 1.0;

                                                if (samplesLikelihoods)
                                                {
                                                        // Save likelihoods also:
                                                        // ------------------------------
                                                        for (i=0;i<dim;i++)
                                                        {
                                                                const typename VECTORLIKE::value_type   rnd = this->drawGaussian1D_normalized(&likelihood_1);
                                                                for (size_t d=0;d<dim;d++)      (*ret_it)[d]+=Z.get_unsafe(d,i)*rnd;

                                                                // Product of each independent gaussian sample:
                                                                likelihood_all *= likelihood_1;
                                                        }
                                                        if (mean)
                                                                for (size_t d=0;d<dim;d++)      (*ret_it)[d]+=(*mean)[d];

                                                        // Save the total likelihood of the generated vector:
                                                        *liks_it = static_cast<typename VECTORLIKE::value_type>(likelihood_all);
                                                        liks_it++;
                                                }
                                                else
                                                {
                                                        // DO NOT save likelihoods also, just the samples
                                                        // ----------------------------------------------------
                                                        for (i=0;i<dim;i++)
                                                        {
                                                                const typename VECTORLIKE::value_type rnd = this->drawGaussian1D_normalized();
                                                                for (size_t d=0;d<dim;d++)      (*ret_it)[d]+=Z.get_unsafe(d,i)*rnd;
                                                        }
                                                        if (mean)
                                                                for (size_t d=0;d<dim;d++)      (*ret_it)[d]+=(*mean)[d];
                                                }

                                        } // For each vector sample to generate...

                                        MRPT_END_WITH_CLEAN_UP( \
                                                printf("\nEXCEPTION: Dumping variables for debuging:\n"); \
                                                std::cout << "Z:\n" << Z << "D:\n" << D << "Cov:\n" << cov; \
                                                try \
                                                {
                                                        cov.eigenVectors(Z,D); \
                                                        std::cout << "Original Z:" << Z << "Original D:" << D;  \
                                                } \
                                                catch(...) {}; \
                                                );

                                }


                                /** Generate multidimensional random samples according to a given covariance matrix.
                                 *  Mean is assumed to be zero if mean==NULL.
                                 * \exception std::exception On invalid covariance matrix
                                 * \sa drawGaussianMultivariateMany
                                 */
                                 template <class VECTORLIKE,typename T,size_t N>
                                 void  drawGaussianMultivariate(
                                        VECTORLIKE      &out_result,
                                        const CMatrixFixedNumeric<T,N,N> &cov,
                                        const VECTORLIKE* mean = NULL
                                        )
                                {
                                        if (mean) ASSERT_(mean->size()==N)

                                        CMatrixFixedNumeric<T,N,N>      Z,D;

                                        // Set size of output vector:
                                        out_result.assign(N,0);

                                        /** Computes the eigenvalues/eigenvector decomposition of this matrix,
                                        *    so that: M = Z · D · Z<sup>T</sup>, where columns in Z are the
                                        *         eigenvectors and the diagonal matrix D contains the eigenvalues
                                        *    as diagonal elements, sorted in <i>ascending</i> order.
                                        */
                                        cov.eigenVectors( Z, D );

                                        // Scale eigenvectors with eigenvalues:
                                        // Efficient implementation of: D.Sqrt(); Z = Z * D;
                                        for (size_t i=0;i<N;i++)
                                        {
                                                const T eig_sqrt = std::sqrt(D.get_unsafe(i,i));
                                                for (size_t j=0;j<N;j++)
                                                        Z.get_unsafe(j,i)*=eig_sqrt;
                                        }


                                        for (size_t i=0;i<N;i++)
                                        {
                                                T rnd = drawGaussian1D_normalized();
                                                for (size_t d=0;d<N;d++)
                                                        out_result[d]+= ( Z(d,i)* rnd );
                                        }
                                        if (mean)
                                                for (size_t d=0;d<N;d++)
                                                        out_result[d]+= (*mean)[d];
                                }

                                /** Generate a given number of multidimensional random samples according to a given covariance matrix.
                                 * \param cov The covariance matrix where to draw the samples from.
                                 * \param desiredSamples The number of samples to generate.
                                 * \param ret The output list of samples
                                 * \param mean The mean, or zeros if mean==NULL.
                                 */
                                 template <typename T,size_t N>
                                 void  drawGaussianMultivariateMany(
                                        std::vector< std::vector<T> >   &ret,
                                        size_t                                                  desiredSamples,
                                        const CMatrixFixedNumeric<T,N,N> &cov,
                                        const std::vector<T>*                   mean = NULL )
                                {
                                        if (mean) ASSERT_(mean->size()==N)

                                        CMatrixFixedNumeric<T,N,N>      Z,D;

                                        /** Computes the eigenvalues/eigenvector decomposition of this matrix,
                                        *    so that: M = Z · D · Z<sup>T</sup>, where columns in Z are the
                                        *         eigenvectors and the diagonal matrix D contains the eigenvalues
                                        *    as diagonal elements, sorted in <i>ascending</i> order.
                                        */
                                        cov.eigenVectors( Z, D );

                                        // Scale eigenvectors with eigenvalues:
                                        // Efficient implementation of: D.Sqrt(); Z = Z * D;
                                        for (size_t i=0;i<N;i++)
                                        {
                                                const T eig_sqrt = std::sqrt(D.get_unsafe(i,i));
                                                for (size_t j=0;j<N;j++)
                                                        Z.get_unsafe(j,i)*=eig_sqrt;
                                        }

                                        // Set size of output vector:
                                        ret.resize(desiredSamples);

                                        for (size_t k=0;k<desiredSamples;k++)
                                        {
                                                ret[k].assign(N,0);
                                                for (size_t i=0;i<N;i++)
                                                {
                                                        T rnd = drawGaussian1D_normalized();
                                                        for (size_t d=0;d<N;d++)
                                                                ret[k][d]+= ( Z.get_unsafe(d,i)* rnd );
                                                }
                                                if (mean)
                                                        for (size_t d=0;d<N;d++)
                                                                ret[k][d]+= (*mean)[d];
                                        }
                                }


                        /** @} */


                        /** @name Miscellaneous
                         @{ */

                                /** Returns a random permutation of a vector: all the elements of the input vector are in the output but at random positions.
                                  */
                                template <class T>
                                void  permuteVector(
                                        const std::vector<T> &in_vector,
                                        std::vector<T>       &out_result)
                                {
                                        out_result = in_vector;
                                        std::random_shuffle( out_result.begin(),out_result.end()  );
                                }

                        /** @} */

                }; // end of CRandomGenerator --------------------------------------------------------------


                /** A static instance of a CRandomGenerator class, for use in single-thread applications */
                extern BASE_IMPEXP CRandomGenerator randomGenerator;


                /** A random number generator for usage in STL algorithms expecting a function like this (eg, random_shuffle):
                  */
                inline ptrdiff_t random_generator_for_STL(ptrdiff_t i)
                {
                        return randomGenerator.drawUniform32bit() % i;
                }

                /** Generate a normalized normally distributed pseudo-random number.
                 *  \param likelihood If desired, pass a pointer to a double which will receive the likelihood of the given sample to have been obtained, that is, the value of the normal pdf at the sample value.
                 */
                MRPT_DECLARE_DEPRECATED_FUNCTION("** deprecated **: Use mrpt::random::randomGenerator instead",
                double normalizedGaussian( double *likelihood = NULL) );

                /** Generate a normally distributed pseudo-random number.
                 * \param mean The mean value of desired normal distribution
                 * \param std  The standard deviation value of desired normal distribution
                 */
                MRPT_DECLARE_DEPRECATED_FUNCTION("** deprecated **: Use mrpt::random::randomGenerator instead",
                double RandomNormal( double mean = 0, double std = 1) );

                /** Generate a uniformly distributed pseudo-random number using the MT19937 algorithm, in the whole range of 32-bit integers.
                  *  See: http://en.wikipedia.org/wiki/Mersenne_twister
                  * \sa RandomUni, Randomize
                  */
                MRPT_DECLARE_DEPRECATED_FUNCTION("** deprecated **: Use mrpt::random::randomGenerator instead",
                uint32_t RandomUniInt() );

                /** Generate a uniformly distributed pseudo-random number using the MT19937 algorithm, scaled to the selected range.
                  *  This function uses internally RandomUniInt to generate the number, then scales it to the desired range.
                  *  Since MRPT 0.6.0 the MT19937 algorithm is used instead of C runtime library "rand" version.
                  *  See: http://en.wikipedia.org/wiki/Mersenne_twister
                  * \sa RandomUniInt, Randomize
                  */
                MRPT_DECLARE_DEPRECATED_FUNCTION("** deprecated **: Use mrpt::random::randomGenerator instead",
                double RandomUni( const double min, const double max) );

                /** Fills the given matrix with independent, uniformly distributed samples.
                  * Matrix classes can be CMatrixTemplateNumeric or CMatrixFixedNumeric
                  * \sa matrixRandomNormal
                  */
                template <class MAT>
                void matrixRandomUni(
                        MAT &matrix,
                        const  double unif_min = 0,
                        const  double unif_max = 1 )
                {
                        for (size_t r=0;r<matrix.getRowCount();r++)
                                for (size_t c=0;c<matrix.getColCount();c++)
                                        matrix.get_unsafe(r,c) = static_cast<typename MAT::value_type>( randomGenerator.drawUniform(unif_min,unif_max) );
                }

                /** Fills the given matrix with independent, uniformly distributed samples.
                  * \sa vectorRandomNormal
                  */
                template <class T>
                void vectorRandomUni(
                        std::vector<T> &v_out,
                        const  T& unif_min = 0,
                        const  T& unif_max = 1 )
                {
                        size_t n = v_out.size();
                        for (size_t r=0;r<n;r++)
                                v_out[r] = randomGenerator.drawUniform(unif_min,unif_max);
                }

                /** Fills the given matrix with independent, normally distributed samples.
                  * Matrix classes can be CMatrixTemplateNumeric or CMatrixFixedNumeric
                  * \sa matrixRandomUni
                  */
                template <class MAT>
                void matrixRandomNormal(
                        MAT &matrix,
                        const double mean = 0,
                        const double std = 1 )
                {
                        for (size_t r=0;r<matrix.getRowCount();r++)
                                for (size_t c=0;c<matrix.getColCount();c++)
                                        matrix.get_unsafe(r,c) = static_cast<typename MAT::value_type>( mean + std*randomGenerator.drawGaussian1D_normalized() );
                }

                /** Generates a random vector with independent, normally distributed samples.
                  * \sa matrixRandomUni
                  */
                template <class T>
                void vectorRandomNormal(
                        std::vector<T> &v_out,
                        const  T& mean = 0,
                        const  T& std = 1 )
                {
                        size_t n = v_out.size();
                        for (size_t r=0;r<n;r++)
                                v_out[r] = mean + std*randomGenerator.drawGaussian1D_normalized();
                }

                /** Randomize the generators.
                 *   A seed can be providen, or a current-time based seed can be used (default)
                 */
                inline void Randomize(const uint32_t seed)  {
                        randomGenerator.randomize(seed);
                }
                inline void Randomize()  {
                        randomGenerator.randomize();
                }

                /** Returns a random permutation of a vector: all the elements of the input vector are in the output but at random positions.
                  */
                template <class T>
                void  randomPermutation(
                        const std::vector<T> &in_vector,
                        std::vector<T>       &out_result)
                {
                        randomGenerator.permuteVector(in_vector,out_result);
                }


                /** Generate multidimensional random samples according to a given covariance matrix.
                 * \exception std::exception On invalid covariance matrix
                 * \sa randomNormalMultiDimensionalMany
                 */
                template <typename T>
                void  randomNormalMultiDimensional(
                        const CMatrixTemplateNumeric<T> &cov,
                        std::vector<T>          &out_result)
                 {
                        randomGenerator.drawGaussianMultivariate(out_result,cov);
                 }

                 /** Generate a given number of multidimensional random samples according to a given covariance matrix.
                 * \param cov The covariance matrix where to draw the samples from.
                 * \param desiredSamples The number of samples to generate.
                 * \param samplesLikelihoods If desired, set to a valid pointer to a vector, where it will be stored the likelihoods of having obtained each sample: the product of the gaussian-pdf for each independent variable.
                 * \param ret The output list of samples
                 *
                 * \exception std::exception On invalid covariance matrix
                 *
                 * \sa randomNormalMultiDimensional
                 */
                 template <typename T>
                 void  randomNormalMultiDimensionalMany(
                        const CMatrixTemplateNumeric<T> &cov,
                        size_t                                                  desiredSamples,
                        std::vector< std::vector<T> >   &ret,
                        std::vector<T>                                  *samplesLikelihoods = NULL)
                {
                        randomGenerator.drawGaussianMultivariateMany(ret,desiredSamples,cov,static_cast<const std::vector<T>*>(NULL),samplesLikelihoods);
                }

                /** Generate multidimensional random samples according to a given covariance matrix.
                 * \exception std::exception On invalid covariance matrix
                 * \sa randomNormalMultiDimensional
                 */
                 template <typename T,size_t N>
                 void  randomNormalMultiDimensionalMany(
                        const CMatrixFixedNumeric<T,N,N> &cov,
                        size_t                                                  desiredSamples,
                        std::vector< std::vector<T> >   &ret )
                 {
                         randomGenerator.drawGaussianMultivariateMany(ret,desiredSamples,cov);
                 }

                /** Generate multidimensional random samples according to a given covariance matrix.
                 * \exception std::exception On invalid covariance matrix
                 * \sa randomNormalMultiDimensionalMany
                 */
                 template <typename T,size_t N>
                 void  randomNormalMultiDimensional(
                        const CMatrixFixedNumeric<T,N,N> &cov,
                        std::vector<T>          &out_result)
                {
                        randomGenerator.drawGaussianMultivariate(out_result,cov);
                }


        }// End of namespace

} // End of namespace

#endif

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