RandomGenerators.h

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/* +------------------------------------------------------------------------+
   |                     Mobile Robot Programming Toolkit (MRPT)            |
   |                          http://www.mrpt.org/                          |
   |                                                                        |
   | Copyright (c) 2005-2018, Individual contributors, see AUTHORS file     |
   | See: http://www.mrpt.org/Authors - All rights reserved.                |
   | Released under BSD License. See details in http://www.mrpt.org/License |
   +------------------------------------------------------------------------+ */
#pragma once

#include <stdexcept>
#include <random>
#include <limits>
#include <vector>
#include <algorithm>
#include <cstddef>
#include <type_traits>  // remove_reference
#include <mrpt/random/random_shuffle.h>

// Frwd decl:
namespace Eigen
{
template <typename _MatrixType>
class SelfAdjointEigenSolver;
}

namespace mrpt
{
/** A namespace of pseudo-random numbers generators of diferent distributions.
 * The central class in this namespace is mrpt::random::CRandomGenerator
 * \ingroup mrpt_random_grp
 */
namespace random
{
/** 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
 * \ingroup mrpt_random_grp
  */
class CRandomGenerator
{
   protected:
    /** Data used internally by the MT19937 PRNG algorithm. */
    std::mt19937_64 m_MT19937;

    std::normal_distribution<double> m_normdistribution;
    std::uniform_int_distribution<uint32_t> m_uint32;
    std::uniform_int_distribution<uint64_t> m_uint64;

    void MT19937_initializeGenerator(const uint32_t& seed);

   public:
    /** @name Initialization
     @{ */

    /** Default constructor: initialize random seed based on current time */
    CRandomGenerator() { randomize(); }
    /** Constructor for providing a custom random seed to initialize the PRNG */
    CRandomGenerator(const uint32_t seed) { randomize(seed); }
    /** Initialize the PRNG from the given random seed */
    void randomize(const uint32_t seed);
    /** Randomize the generators, based on std::random_device */
    void randomize();

    /** @} */

    /** @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();

    /** Returns a uniformly distributed pseudo-random number by joining two
     * 32bit numbers from \a drawUniform32bit() */
    uint64_t drawUniform64bit();

    /** You can call this overloaded method with either 32 or 64bit unsigned
     * ints for the sake of general coding. */
    void drawUniformUnsignedInt(uint32_t& ret_number)
    {
        ret_number = m_uint32(m_MT19937);
    }
    void drawUniformUnsignedInt(uint64_t& ret_number)
    {
        ret_number = m_uint64(m_MT19937);
    }

    /** Return a uniform unsigned integer in the range [min_val,max_val] (both
     * inclusive) */
    template <typename T, typename U, typename V>
    void drawUniformUnsignedIntRange(
        T& ret_number, const U min_val, const V max_val)
    {
        const T range = max_val - min_val + 1;
        T rnd;
        drawUniformUnsignedInt(rnd);
        ret_number = min_val + (rnd % range);
    }

    /** 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 mrpt::math::CMatrixTemplateNumeric or
     * mrpt::math::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.rows(); r++)
            for (size_t c = 0; c < matrix.cols(); c++)
                matrix.get_unsafe(r, c) = static_cast<typename MAT::Scalar>(
                    drawUniform(unif_min, unif_max));
    }

    /** Fills the given vector with independent, uniformly distributed samples.
      * \sa drawUniform
      */
    template <class VEC>
    void drawUniformVector(
        VEC& 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<typename std::decay<decltype(v[c])>::type>(
                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();

    /** 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 mrpt::math::CMatrixTemplateNumeric or
     * mrpt::math::CMatrixFixedNumeric
      * \sa drawGaussian1D
      */
    template <class MAT>
    void drawGaussian1DMatrix(
        MAT& matrix, const double mean = 0, const double std = 1)
    {
        for (decltype(matrix.rows()) r = 0; r < matrix.rows(); r++)
            for (decltype(matrix.cols()) c = 0; c < matrix.cols(); c++)
                matrix.get_unsafe(r, c) = static_cast<typename MAT::Scalar>(
                    drawGaussian1D(mean, std));
    }

    /** Generates a random definite-positive matrix of the given size, using the
     * formula C = v*v^t + epsilon*I, with "v" being a vector of gaussian random
     * samples.
      */
    template <class MATRIX, class AUXVECTOR_T = MATRIX>
    MATRIX drawDefinitePositiveMatrix(
        const size_t dim, const double std_scale = 1.0,
        const double diagonal_epsilon = 1e-8)
    {
        AUXVECTOR_T r(dim, 1);
        drawGaussian1DMatrix(r, 0, std_scale);
        MATRIX cov;
        cov.resize(dim, dim);
        cov.multiply_AAt(r);  // random semi-definite positive matrix:
        for (size_t i = 0; i < dim; i++)
            cov(i, i) += diagonal_epsilon;  // make sure it's definite-positive
        return cov;
    }

    /** Fills the given vector with independent, 1D-normally distributed
     * samples.
      * \sa drawGaussian1D
      */
    template <class VEC>
    void drawGaussian1DVector(
        VEC& 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<std::remove_reference_t<decltype(v[c])>>(
                drawGaussian1D(mean, std));
    }

    /** Generate multidimensional random samples according to a given covariance
     * matrix.
     *  Mean is assumed to be zero if mean==nullptr.
     * \exception std::exception On invalid covariance matrix
     * \sa drawGaussianMultivariateMany
     */
    template <typename T, typename MATRIX>
    void drawGaussianMultivariate(
        std::vector<T>& out_result, const MATRIX& cov,
        const std::vector<T>* mean = nullptr)
    {
        const size_t dim = cov.cols();
        if (cov.rows() != cov.cols())
            throw std::runtime_error(
                "drawGaussianMultivariate(): cov is not square.");
        if (mean && mean->size() != dim)
            throw std::runtime_error(
                "drawGaussianMultivariate(): mean and cov sizes ");
        MATRIX Z, D;
        // Set size of output vector:
        out_result.clear();
        out_result.resize(dim, 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:
        D = D.array().sqrt().matrix();
        Z.multiply(Z, D);
        for (size_t i = 0; i < dim; i++)
        {
            T rnd = this->drawGaussian1D_normalized();
            for (size_t d = 0; d < dim; d++)
                out_result[d] += (Z.get_unsafe(d, i) * rnd);
        }
        if (mean)
            for (size_t d = 0; d < dim; d++) out_result[d] += (*mean)[d];
    }

    /** Generate multidimensional random samples according to a given covariance
     * matrix.
     *  Mean is assumed to be zero if mean==nullptr.
     * \exception std::exception On invalid covariance matrix
     * \sa drawGaussianMultivariateMany
     */
    template <class VECTORLIKE, class COVMATRIX>
    void drawGaussianMultivariate(
        VECTORLIKE& out_result, const COVMATRIX& cov,
        const VECTORLIKE* mean = nullptr)
    {
        const size_t N = cov.rows();
        if (cov.rows() != cov.cols())
            throw std::runtime_error(
                "drawGaussianMultivariate(): cov is not square.");
        if (mean && size_t(mean->size()) != N)
            throw std::runtime_error(
                "drawGaussianMultivariate(): mean and cov sizes ");

        // Compute eigenvalues/eigenvectors of cov:
        Eigen::SelfAdjointEigenSolver<typename COVMATRIX::PlainObject>
            eigensolver(cov);

        auto eigVecs = eigensolver.eigenvectors();
        auto eigVals = eigensolver.eigenvalues();

        // Scale eigenvectors with eigenvalues:
        // D.Sqrt(); Z = Z * D; (for each column)
        eigVals = eigVals.array().sqrt();
        for (typename COVMATRIX::Index i = 0; i < eigVecs.cols(); i++)
            eigVecs.col(i) *= eigVals[i];

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

        for (size_t i = 0; i < N; i++)
        {
            typename COVMATRIX::Scalar rnd = drawGaussian1D_normalized();
            for (size_t d = 0; d < N; d++)
                out_result[d] += eigVecs.coeff(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==nullptr.
     */
    template <typename VECTOR_OF_VECTORS, typename COVMATRIX>
    void drawGaussianMultivariateMany(
        VECTOR_OF_VECTORS& ret, size_t desiredSamples, const COVMATRIX& cov,
        const typename VECTOR_OF_VECTORS::value_type* mean = nullptr)
    {
        const size_t N = cov.rows();
        if (cov.rows() != cov.cols())
            throw std::runtime_error(
                "drawGaussianMultivariateMany(): cov is not square.");
        if (mean && size_t(mean->size()) != N)
            throw std::runtime_error(
                "drawGaussianMultivariateMany(): mean and cov sizes ");

        // Compute eigenvalues/eigenvectors of cov:
        Eigen::SelfAdjointEigenSolver<typename COVMATRIX::PlainObject>
            eigensolver(cov);

        typename Eigen::SelfAdjointEigenSolver<
            typename COVMATRIX::PlainObject>::MatrixType eigVecs =
            eigensolver.eigenvectors();
        typename Eigen::SelfAdjointEigenSolver<
            typename COVMATRIX::PlainObject>::RealVectorType eigVals =
            eigensolver.eigenvalues();

        // Scale eigenvectors with eigenvalues:
        // D.Sqrt(); Z = Z * D; (for each column)
        eigVals = eigVals.array().sqrt();
        for (typename COVMATRIX::Index i = 0; i < eigVecs.cols(); i++)
            eigVecs.col(i) *= eigVals[i];

        // 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++)
            {
                typename COVMATRIX::Scalar rnd = drawGaussian1D_normalized();
                for (size_t d = 0; d < N; d++)
                    ret[k][d] += eigVecs.coeff(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 VEC>
    void permuteVector(const VEC& in_vector, VEC& out_result)
    {
        out_result = in_vector;
        const size_t N = out_result.size();
        if (N > 1) mrpt::random::shuffle(&out_result[0], &out_result[N - 1]);
    }

    /** @} */

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

/** A static instance of a CRandomGenerator class, for use in single-thread
 * applications */
CRandomGenerator& getRandomGenerator();

/** 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 getRandomGenerator().drawUniform32bit() % i;
}

/** Fills the given matrix with independent, uniformly distributed samples.
  * Matrix classes can be mrpt::math::CMatrixTemplateNumeric or
 * mrpt::math::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.rows(); r++)
        for (size_t c = 0; c < matrix.cols(); c++)
            matrix.get_unsafe(r, c) = static_cast<typename MAT::Scalar>(
                getRandomGenerator().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] = getRandomGenerator().drawUniform(unif_min, unif_max);
}

/** Fills the given matrix with independent, normally distributed samples.
  * Matrix classes can be mrpt::math::CMatrixTemplateNumeric or
 * mrpt::math::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.rows(); r++)
        for (size_t c = 0; c < matrix.cols(); c++)
            matrix.get_unsafe(r, c) = static_cast<typename MAT::Scalar>(
                mean + std * getRandomGenerator().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 * getRandomGenerator().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)
{
    getRandomGenerator().randomize(seed);
}
inline void Randomize() { getRandomGenerator().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)
{
    getRandomGenerator().permuteVector(in_vector, out_result);
}

/** 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, typename MATRIX>
void randomNormalMultiDimensionalMany(
    const MATRIX& cov, size_t desiredSamples, std::vector<std::vector<T>>& ret,
    std::vector<T>* samplesLikelihoods = nullptr)
{
    getRandomGenerator().drawGaussianMultivariateMany(
        ret, desiredSamples, cov, static_cast<const std::vector<T>*>(nullptr),
        samplesLikelihoods);
}

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

}  // End of namespace
}  // End of namespace