Tabulated1DFunction.hpp

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// -*- mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
// vi: set et ts=4 sw=4 sts=4:
/*
  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 2 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/>.
 
  Consult the COPYING file in the top-level source directory of this
  module for the precise wording of the license and the list of
  copyright holders.
*/
#ifndef OPM_TABULATED_1D_FUNCTION_HPP
#define OPM_TABULATED_1D_FUNCTION_HPP
 
#include <opm/common/OpmLog/OpmLog.hpp>
#include <opm/material/densead/Math.hpp>
 
#include <algorithm>
#include <cassert>
#include <iosfwd>
#include <stdexcept>
#include <vector>
 
namespace Opm {
 
struct SegmentIndex {
    size_t value;
};

template <class Scalar>
class Tabulated1DFunction
{
public:
    Tabulated1DFunction()
    {}

    template <class ScalarArrayX, class ScalarArrayY>
    Tabulated1DFunction(size_t nSamples,
                        const ScalarArrayX& x,
                        const ScalarArrayY& y,
                        bool sortInputs = true)
    { this->setXYArrays(nSamples, x, y, sortInputs); }

    template <class ScalarContainer>
    Tabulated1DFunction(const ScalarContainer& x,
                        const ScalarContainer& y,
                        bool sortInputs = true)
    { this->setXYContainers(x, y, sortInputs); }

    template <class PointContainer>
    explicit Tabulated1DFunction(const PointContainer& points,
                                 bool sortInputs = true)
    { this->setContainerOfTuples(points, sortInputs); }

    template <class ScalarArrayX, class ScalarArrayY>
    void setXYArrays(size_t nSamples,
                     const ScalarArrayX& x,
                     const ScalarArrayY& y,
                     bool sortInputs = true)
    {
        assert(nSamples > 1);
 
        resizeArrays_(nSamples);
        for (size_t i = 0; i < nSamples; ++i) {
            xValues_[i] = x[i];
            yValues_[i] = y[i];
        }
 
        if (sortInputs)
            sortInput_();
        else if (xValues_[0] > xValues_[numSamples() - 1])
            reverseSamplingPoints_();
    }

    template <class ScalarContainerX, class ScalarContainerY>
    void setXYContainers(const ScalarContainerX& x,
                         const ScalarContainerY& y,
                         bool sortInputs = true)
    {
        assert(x.size() == y.size());
 
        resizeArrays_(x.size());
        if (x.size() > 0) {
            std::ranges::copy(x, xValues_.begin());
            std::ranges::copy(y, yValues_.begin());
 
            if (sortInputs)
                sortInput_();
            else if (xValues_[0] > xValues_[numSamples() - 1])
                reverseSamplingPoints_();
        }
    }

    template <class PointArray>
    void setArrayOfPoints(size_t nSamples,
                          const PointArray& points,
                          bool sortInputs = true)
    {
        // a linear function with less than two sampling points? what an incredible
        // bad idea!
        assert(nSamples > 1);
 
        resizeArrays_(nSamples);
        for (size_t i = 0; i < nSamples; ++i) {
            xValues_[i] = points[i][0];
            yValues_[i] = points[i][1];
        }
 
        if (sortInputs)
            sortInput_();
        else if (xValues_[0] > xValues_[numSamples() - 1])
            reverseSamplingPoints_();
    }

    template <class XYContainer>
    void setContainerOfTuples(const XYContainer& points,
                              bool sortInputs = true)
    {
        // a linear function with less than two sampling points? what an incredible
        // bad idea!
        assert(points.size() > 1);
 
        resizeArrays_(points.size());
        typename XYContainer::const_iterator it = points.begin();
        typename XYContainer::const_iterator endIt = points.end();
        for (unsigned i = 0; it != endIt; ++i, ++it) {
            xValues_[i] = std::get<0>(*it);
            yValues_[i] = std::get<1>(*it);
        }
 
        if (sortInputs)
            sortInput_();
        else if (xValues_[0] > xValues_[numSamples() - 1])
            reverseSamplingPoints_();
    }

    size_t numSamples() const
    { return xValues_.size(); }

    Scalar xMin() const
    { return xValues_[0]; }

    Scalar xMax() const
    { return xValues_[numSamples() - 1]; }

    Scalar xAt(size_t i) const
    { return xValues_[i]; }
 
    const std::vector<Scalar>& xValues() const
    { return xValues_; }
 
    const std::vector<Scalar>& yValues() const
    { return yValues_; }

    Scalar valueAt(size_t i) const
    { return yValues_[i]; }

    template <class Evaluation>
    bool applies(const Evaluation& x) const
    { return xValues_[0] <= x && x <= xValues_[numSamples() - 1]; }

    template <class Evaluation>
    Evaluation eval(const Evaluation& x, bool extrapolate = false) const
    {
        SegmentIndex segIdx = findSegmentIndex(x, extrapolate);
        return eval(x, segIdx);
    }
 
    template <class Evaluation>
    Evaluation eval(const Evaluation& x, SegmentIndex segIdxIn) const
    {
        size_t segIdx = segIdxIn.value;
        Scalar x0 = xValues_[segIdx];
        Scalar x1 = xValues_[segIdx + 1];
 
        Scalar y0 = yValues_[segIdx];
        Scalar y1 = yValues_[segIdx + 1];
 
        return y0 + (y1 - y0)*(x - x0)/(x1 - x0);
    }

    template <class Evaluation>
    Evaluation evalDerivative(const Evaluation& x, bool extrapolate = false) const
    {
        size_t segIdx = findSegmentIndex(x, extrapolate).value;
        return evalDerivative_(x, segIdx);
    }

    template <class Evaluation>
    Evaluation evalSecondDerivative(const Evaluation&, bool = false) const
    { return 0.0; }

    template <class Evaluation>
    Evaluation evalThirdDerivative(const Evaluation&, bool = false) const
    { return 0.0; }

    int monotonic(Scalar x0, Scalar x1,
                  [[maybe_unused]] bool extrapolate = false) const
    {
        assert(x0 != x1);
 
        // make sure that x0 is smaller than x1
        if (x0 > x1)
            std::swap(x0, x1);
 
        assert(x0 < x1);
 
        int r = 3;
        if (x0 < xMin()) {
            assert(extrapolate);
 
            x0 = xMin();
        };
 
        size_t i = findSegmentIndex(x0, extrapolate).value;
        if (xValues_[i + 1] >= x1) {
            // interval is fully contained within a single function
            // segment
            updateMonotonicity_(i, r);
            return r;
        }
 
        // the first segment overlaps with the specified interval
        // partially
        updateMonotonicity_(i, r);
        ++ i;
 
        // make sure that the segments which are completly in the
        // interval [x0, x1] all exhibit the same monotonicity.
        size_t iEnd = findSegmentIndex(x1, extrapolate).value;
        for (; i < iEnd - 1; ++i) {
            updateMonotonicity_(i, r);
            if (!r)
                return 0;
        }
 
        // if the user asked for a part of the function which is
        // extrapolated, we need to check the slope at the function's
        // endpoint
        if (x1 > xMax()) {
            assert(extrapolate);
 
            Scalar m = evalDerivative_(xMax(), /*segmentIdx=*/numSamples() - 2);
            if (m < 0)
                return (r < 0 || r==3) ? -1 : 0;
            else if (m > 0)
                return r > 0 ? 1 : 0;
 
            return r;
        }
 
        // check for the last segment
        updateMonotonicity_(iEnd, r);
 
        return r;
    }

    int monotonic() const
    { return monotonic(xMin(), xMax()); }

    void printCSV(Scalar xi0, Scalar xi1, unsigned k, std::ostream& os) const;
 
    bool operator==(const Tabulated1DFunction<Scalar>& data) const {
        return xValues_ == data.xValues_ &&
               yValues_ == data.yValues_;
    }
 
    template <class Evaluation>
    SegmentIndex findSegmentIndex(const Evaluation& x, bool extrapolate = false) const
    {
        if (!isfinite(x)) {
            throw std::runtime_error("We can not search for extrapolation/interpolation "
                                     "segment in an 1D table for non-finite value " +
                                     std::to_string(getValue(x)) + " .");
        }
 
        if (!extrapolate && !applies(x))
            throw std::logic_error("Trying to evaluate a tabulated function outside of its range");
 
        // we need at least two sampling points!
        if (numSamples() < 2) {
            throw std::logic_error("We need at least two sampling points to "
                                   "do interpolation/extrapolation, "
                                   "and the table only contains " +
                                   std::to_string(numSamples()) +
                                   " sampling points");
        }
 
        if (x <= xValues_[1])
            return SegmentIndex{0};
        else if (x >= xValues_[xValues_.size() - 2])
            return SegmentIndex{xValues_.size() - 2};
        else {
            // bisection
            size_t lowerIdx = 1;
            size_t upperIdx = xValues_.size() - 2;
            while (lowerIdx + 1 < upperIdx) {
                size_t pivotIdx = (lowerIdx + upperIdx) / 2;
                if (x < xValues_[pivotIdx])
                    upperIdx = pivotIdx;
                else
                    lowerIdx = pivotIdx;
            }
 
            if (xValues_[lowerIdx] > x || x > xValues_[lowerIdx + 1]) {
                std::string msg = "Problematic interpolation/extrapolation "
                                  "segment is found for the input value " +
                                  std::to_string(Opm::getValue(x)) +
                                  "\nthe lower index of the found segment is " +
                                  std::to_string(lowerIdx) +
                                  ", the size of the table is " +
                                  std::to_string(numSamples()) +
                                  ",\nand the end values of the found segment are " +
                                  std::to_string(xValues_[lowerIdx]) +
                                  " and " +
                                  std::to_string(xValues_[lowerIdx + 1]) +
                                  ", respectively.\n";
                msg += "Outputting the problematic table for more information "
                       "(with *** marking the found segment):";
                for (size_t i = 0; i < numSamples(); ++i) {
                    if (i % 10 == 0)
                        msg += "\n";
                    if (i == lowerIdx)
                        msg += " ***";
                    msg += " " + std::to_string(xValues_[i]);
                    if (i == lowerIdx + 1)
                        msg += " ***";
                }
                msg += "\n";
                OpmLog::debug(msg);
                throw std::runtime_error(msg);
            }
            return SegmentIndex{lowerIdx};
        }
    }
 
private:
    template <class Evaluation>
    Evaluation evalDerivative_(const Evaluation& x, size_t segIdx) const
    {
 
        Scalar x0 = xValues_[segIdx];
        Scalar x1 = xValues_[segIdx + 1];
 
        Scalar y0 = yValues_[segIdx];
        Scalar y1 = yValues_[segIdx + 1];
 
        Evaluation ret = blank(x);
        ret = (y1 - y0)/(x1 - x0);
        return ret;
    }
 
    // returns the monotonicity of a segment
    //
    // The return value have the following meaning:
    //
    // 3: function is constant within interval [x0, x1]
    // 1: function is monotonously increasing in the specified interval
    // 0: function is not monotonic in the specified interval
    // -1: function is monotonously decreasing in the specified interval
    int updateMonotonicity_(size_t i, int& r) const
    {
        if (yValues_[i] < yValues_[i + 1]) {
            // monotonically increasing?
            if (r == 3 || r == 1)
                r = 1;
            else
                r = 0;
            return 1;
        }
        else if (yValues_[i] > yValues_[i + 1]) {
            // monotonically decreasing?
            if (r == 3 || r == -1)
                r = -1;
            else
                r = 0;
            return -1;
        }
 
        return 3;
    }

    struct ComparatorX_
    {
        explicit ComparatorX_(const std::vector<Scalar>& x)
            : x_(x)
        {}
 
        bool operator ()(size_t idxA, size_t idxB) const
        { return x_.at(idxA) < x_.at(idxB); }
 
        const std::vector<Scalar>& x_;
    };

    void sortInput_()
    {
        size_t n = numSamples();
 
        // create a vector containing 0...n-1
        std::vector<unsigned> idxVector(n);
        for (unsigned i = 0; i < n; ++i)
            idxVector[i] = i;
 
        // sort the indices according to the x values of the sample
        // points
        ComparatorX_ cmp(xValues_);
        std::ranges::sort(idxVector, cmp);
 
        // reorder the sample points
        std::vector<Scalar> tmpX(n), tmpY(n);
        for (size_t i = 0; i < idxVector.size(); ++ i) {
            tmpX[i] = xValues_[idxVector[i]];
            tmpY[i] = yValues_[idxVector[i]];
        }
        xValues_ = tmpX;
        yValues_ = tmpY;
    }

    void reverseSamplingPoints_()
    {
        // reverse the arrays
        size_t n = numSamples();
        for (size_t i = 0; i <= (n - 1)/2; ++i) {
            std::swap(xValues_[i], xValues_[n - i - 1]);
            std::swap(yValues_[i], yValues_[n - i - 1]);
        }
    }

    void resizeArrays_(size_t nSamples)
    {
        xValues_.resize(nSamples);
        yValues_.resize(nSamples);
    }
 
    std::vector<Scalar> xValues_;
    std::vector<Scalar> yValues_;
};
 
} // namespace Opm
 
#endif