linearInterpolation.hpp

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/*
  Copyright 2009, 2010, 2013 SINTEF ICT, Applied Mathematics.
  Copyright 2009, 2010 Statoil ASA.
 
  This file is part of the Open Porous Media project (OPM).
 
  OPM 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 3 of the License, or
  (at your option) any later version.
 
  OPM 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 OPM.  If not, see <http://www.gnu.org/licenses/>.
*/
 
#ifndef OPM_LINEARINTERPOLATION_HEADER_INCLUDED
#define OPM_LINEARINTERPOLATION_HEADER_INCLUDED
 
 
#include <vector>
#include <algorithm>
 
namespace Opm
{
 
    inline int tableIndex(const std::vector<double>& table, double x)
    {
    // Returns an index in an ordered table such that x is between
    // table[j] and table[j+1]. If x is out of range, first or last
    // interval is returned; Binary search.
    int n = table.size() - 1;
    if (n < 2) {
        return 0;
    }
    int jl = 0;
    int ju = n;
    bool ascend = (table[n] > table[0]);
    while (ju - jl > 1) {
        int jm = (ju + jl)/2;   // Compute a midpoint
        if ( (x >= table[jm]) == ascend) {
        jl = jm;     // Replace lower limit
        } else {
        ju = jm;     // Replace upper limit
        }
    }
    return jl;
    }
 
 
    inline double linearInterpolationDerivative(const std::vector<double>& xv,
                                                const std::vector<double>& yv, double x)
    {
        // Extrapolates if x is outside xv
    int ix1 = tableIndex(xv, x);
    int ix2 = ix1 + 1;
    return  (yv[ix2] - yv[ix1])/(xv[ix2] - xv[ix1]);
    }
 
    inline double linearInterpolation(const std::vector<double>& xv,
                                      const std::vector<double>& yv, double x)
    {
    // Extrapolates if x is outside xv
    int ix1 = tableIndex(xv, x);
    int ix2 = ix1 + 1;
    return  (yv[ix2] - yv[ix1])/(xv[ix2] - xv[ix1])*(x - xv[ix1]) + yv[ix1];
    }
 
    inline double linearInterpolationNoExtrapolation(const std::vector<double>& xv,
                                                     const std::vector<double>& yv, double x)
    {
        // Return end values if x is outside xv
        if (x < xv.front()) {
            return yv.front();
        }
        if (x > xv.back()) {
            return yv.back();
        }
 
        int ix1 = tableIndex(xv, x);
        int ix2 = ix1 + 1;
        return  (yv[ix2] - yv[ix1])/(xv[ix2] - xv[ix1])*(x - xv[ix1]) + yv[ix1];
    }
 
    inline double linearInterpolation(const std::vector<double>& xv,
                                      const std::vector<double>& yv,
                                      double x, int& ix1)
    {
    // Extrapolates if x is outside xv
    ix1 = tableIndex(xv, x);
    int ix2 = ix1 + 1;
    return (yv[ix2] - yv[ix1])/(xv[ix2] - xv[ix1])*(x - xv[ix1]) + yv[ix1];
    }
 
 
 
} // namespace Opm
 
 
 
 
 
#endif // OPM_LINEARINTERPOLATION_HEADER_INCLUDED