numerical_tools.h

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/***************************************************************************
 *
 * Authors:     Carlos Oscar S. Sorzano (coss@cnb.csic.es)
 *
 * Unidad de  Bioinformatica of Centro Nacional de Biotecnologia , CSIC
 *
 * This program 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.
 *
 * This program 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 this program; if not, write to the Free Software
 * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
 * 02111-1307  USA
 *
 *  All comments concerning this program package may be sent to the
 *  e-mail address 'xmipp@cnb.csic.es'
 ***************************************************************************/
/*****************************************************************************/
/* Variable and prototype definitions for the Numerical Core                 */
/*****************************************************************************/
#ifndef CORE__NUMERICAL_TOOLS_HH
#define CORE__NUMERICAL_TOOLS_HH

#include "core/multidim_array.h"


void randomPermutation(int N, MultidimArray<int>& result);

void powellOptimizer(Matrix1D< double >& p,
                     int i0, int n,
                     double(*f)(double* , void *),
                     void *prm,
                     double ftol,
                     double& fret,
                     int& iter,
                     const Matrix1D< double >& steps,
                     bool show = false);

class GaussianInterpolator {
    MultidimArray<double> v;
    double xstep;
    double xmax;
    double ixstep;
public:
    void initialize(double xmax, int N, bool normalize=true);

    inline double getValue(double x) const {
        x=fabs(x);
        if (x>xmax) return 0;
        else
        {
            auto iaux=(int)round(x*ixstep);
            return DIRECT_A1D_ELEM(v,iaux);
        }
    }
};

double solveNonNegative(const Matrix2D< double >& A, const Matrix1D< double >& b,
                    Matrix1D< double >& result);

void solveViaCholesky(const Matrix2D< double >& A,
                        const Matrix1D< double >& b,
                        Matrix1D< double >& result);

void evaluateQuadratic(const Matrix1D< double >& x, const Matrix1D< double >& c,
                    const Matrix2D< double >& H, double& val,
                    Matrix1D< double >& grad);

void quadraticProgramming(const Matrix2D< double >& C, const Matrix1D< double >& d,
              const Matrix2D< double >& A, const Matrix1D< double >& b,
              const Matrix2D< double >& Aeq, const Matrix1D< double >& beq,
              Matrix1D< double >& bl, Matrix1D< double >& bu,
              Matrix1D< double >& x);


void leastSquare(const Matrix2D< double >& C, const Matrix1D< double >& d,
            const Matrix2D< double >& A, const Matrix1D< double >& b,
            const Matrix2D< double >& Aeq, const Matrix1D< double >& beq,
            Matrix1D< double >& bl, Matrix1D< double >& bu,
            Matrix1D< double >& x);

void regularizedLeastSquare(const Matrix2D< double >& A,
    const Matrix1D< double >& d, double lambda,
    const Matrix2D< double >& G, Matrix1D< double >& x);

template<typename T>
void solve(const Matrix2D<T>& A, const Matrix1D<T>& b, Matrix1D<T>& result)
{
    if (MAT_XSIZE(A) == 0)
        REPORT_ERROR(ERR_MATRIX_EMPTY, "Solve: Matrix is empty");

    if (MAT_XSIZE(A) != MAT_YSIZE(A))
        REPORT_ERROR(ERR_MATRIX_SIZE, "Solve: Matrix is not squared");

    if (MAT_XSIZE(A) != b.size())
        REPORT_ERROR(ERR_MATRIX_SIZE, "Solve: Different sizes of Matrix and Vector");

    if (b.isRow())
        REPORT_ERROR(ERR_MATRIX_DIM, "Solve: Not correct vector shape");

    // Perform LU decomposition and then solve
    Matrix1D< int > indx;
    T d;
    Matrix2D<T> LU;
    ludcmp(A, LU, indx, d);
    result = b;
    lubksb(LU, indx, result);
}

template<typename T>
void solveBySVD(const Matrix2D< T >& A, const Matrix1D< T >& b,
                  Matrix1D< double >& result, double tolerance);

template<typename T>
void solve(const Matrix2D<T>& A, const Matrix2D<T>& b, Matrix2D<T>& result);

// Differential Evolution Solver Class
// Based on algorithms developed by Dr. Rainer Storn & Kenneth Price
// Written By: Lester E. Godwin
//             PushCorp, Inc.
//             Dallas, Texas
//             972-840-0208 x102
//             godwin@pushcorp.com
// Created: 6/8/98
// Last Modified: 6/8/98
// Revision: 1.0

constexpr int stBest1Exp =   0;
constexpr int stRand1Exp =   1;
constexpr int stRandToBest1Exp = 2;
constexpr int stBest2Exp =   3;
constexpr int stRand2Exp =   4;
constexpr int stBest1Bin =   5;
constexpr int stRand1Bin =   6;
constexpr int stRandToBest1Bin = 7;
constexpr int stBest2Bin =   8;
constexpr int stRand2Bin =   9;

class DESolver;

typedef void(DESolver::*StrategyFunction)(int);

class DESolver
{
public:
    DESolver(int dim, int popSize);

    DESolver(const DESolver &)=delete; // Do not use the default copy constructor
    DESolver& operator=(const DESolver &)=delete; // Do not use the default copy assignment

    virtual ~DESolver(void);

    void Setup(double min[],
               double max[],
               int deStrategy,
               double diffScale,
               double crossoverProb);

    virtual bool Solve(int maxGenerations);

    virtual double EnergyFunction(double testSolution[], bool& bAtSolution) = 0;

    int Dimension() const
    {
        return nDim;
    }

    int Population() const
    {
        return nPop;
    }

    double Energy() const
    {
        return bestEnergy;
    }

    double* Solution(void)
    {
        return bestSolution;
    }

    int Generations() const
    {
        return generations;
    }

protected:
    void SelectSamples(int candidate,
                       int* r1,
                       int* r2 = nullptr,
                       int* r3 = nullptr,
                       int* r4 = nullptr,
                       int* r5 = nullptr);

    int nDim;
    int nPop;
    int generations;

    int strategy;
    StrategyFunction calcTrialSolution;
    double scale;
    double probability;

    double trialEnergy;
    double bestEnergy;

    double* trialSolution;
    double* bestSolution;
    double* popEnergy;
    double* population;
private:
    void Best1Exp(int candidate);
    void Rand1Exp(int candidate);
    void RandToBest1Exp(int candidate);
    void Best2Exp(int candidate);
    void Rand2Exp(int candidate);
    void Best1Bin(int candidate);
    void Rand1Bin(int candidate);
    void RandToBest1Bin(int candidate);
    void Best2Bin(int candidate);
    void Rand2Bin(int candidate);
};

double checkRandomness(const std::string &sequence);

double ZernikeSphericalHarmonics(int l1, int n, int l2, int m, double xr, double yr, double zr, double r);

#ifdef NEVERDEFINED

double ALegendreSphericalHarmonics(int l, int m, double xr, double yr, double zr, double rr);
#endif

void spherical_index2lnm(int idx, int &l1, int &n, int &l2, int &m, int maxl1);

int spherical_lnm2index(int l1, int n, int l2, int m, int maxl1);
#endif