opm-core/tests/test_spline.cpp

// -*- mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
// vi: set et ts=4 sw=4 sts=4:
/*****************************************************************************
 *   Copyright (C) 2010-2012 by Andreas Lauser                               *
 *                                                                           *
 *   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.                                     *
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 *   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.                            *
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/*!
 * \file
 *
 * \brief This is a program to test the polynomial spline interpolation.
 *
 * It just prints some function to stdout. You can look at the result
 * using the following commands:
 *
----------- snip -----------
./test_spline > spline.csv
gnuplot

gnuplot> plot "spline.csv" using 1:2 w l ti "Curve", \
              "spline.csv" using 1:3 w l ti "Derivative", \
              "spline.csv" using 1:4 w p ti "Monotonical"
----------- snap -----------


*/
#include "config.h"

#include <array>
#include <opm/core/utility/Spline.hpp>

#define GCC_VERSION (__GNUC__ * 10000 \
               + __GNUC_MINOR__ * 100 \
               + __GNUC_PATCHLEVEL__)

template <class Spline>
void testCommon(const Spline &sp,
                const double *x,
                const double *y)
{
    static double eps = 1e-10;
    static double epsFD = 1e-7;

    int n = sp.numSamples();
    for (int i = 0; i < n; ++i) {
        // sure that we hit all sampling points
        double y0 = (i>0)?sp.eval(x[i]-eps):y[0];
        double y1 = sp.eval(x[i]);
        double y2 = (i<n-1)?sp.eval(x[i]+eps):y[n-1];

        if (std::abs(y0 - y[i]) > 100*eps || std::abs(y2 - y[i]) > 100*eps)
            OPM_THROW(std::runtime_error,
                       "Spline seems to be discontinuous at sampling point " << i << "!");
        if (std::abs(y1 - y[i]) > eps)
            OPM_THROW(std::runtime_error,
                       "Spline does not capture sampling point " << i << "!");

        // make sure the derivative is continuous (assuming that the
        // second derivative is smaller than 1000)
        double d1 = sp.evalDerivative(x[i]);
        double d0 = (i>0)?sp.evalDerivative(x[i]-eps):d1;
        double d2 = (i<n-1)?sp.evalDerivative(x[i]+eps):d1;

        if (std::abs(d1 - d0) > 1000*eps || std::abs(d2 - d0) > 1000*eps)
            OPM_THROW(std::runtime_error,
                      "Spline seems to exhibit a discontinuous derivative at sampling point " << i << "!");
    }

    // make sure the derivatives are consistent with the curve
    int np = 3*n;
    for (int i = 0; i < np; ++i) {
        double xval = sp.xMin() + (sp.xMax() - sp.xMin())*i/np;

        // first derivative
        double y1 = sp.eval(xval+epsFD);
        double y0 = sp.eval(xval);

        double mFD = (y1 - y0)/epsFD;
        double m = sp.evalDerivative(xval);

        if (std::abs( mFD - m ) > 1000*epsFD)
            OPM_THROW(std::runtime_error,
                      "Derivative of spline seems to be inconsistent with cuve"
                      " (" << mFD << " - " << m << " = " << mFD - m << ")!");

        // second derivative
        y1 = sp.evalDerivative(xval+epsFD);
        y0 = sp.evalDerivative(xval);

        mFD = (y1 - y0)/epsFD;
        m = sp.evalSecondDerivative(xval);

        if (std::abs( mFD - m ) > 1000*epsFD)
            OPM_THROW(std::runtime_error,
                      "Second derivative of spline seems to be inconsistent with cuve"
                      " (" << mFD << " - " << m << " = " << mFD - m << ")!");

        // Third derivative
        y1 = sp.evalSecondDerivative(xval+epsFD);
        y0 = sp.evalSecondDerivative(xval);

        mFD = (y1 - y0)/epsFD;
        m = sp.evalThirdDerivative(xval);

        if (std::abs( mFD - m ) > 1000*epsFD)
            OPM_THROW(std::runtime_error,
                      "Third derivative of spline seems to be inconsistent with cuve"
                      " (" << mFD << " - " << m << " = " << mFD - m << ")!");
    }
}

template <class Spline>
void testFull(const Spline &sp,
              const double *x,
              const double *y,
              double m0,
              double m1)
{
    // test the common properties of splines
    testCommon(sp, x, y);

    static double eps = 1e-5;
    int n = sp.numSamples();

    // make sure the derivative at both end points is correct
    double d0 = sp.evalDerivative(x[0]);
    double d1 = sp.evalDerivative(x[n-1]);
    if (std::abs(d0 - m0) > eps)
        OPM_THROW(std::runtime_error,
                   "Invalid derivative at beginning of interval: is "
                   << d0 << " ought to be " << m0);
    if (std::abs(d1 - m1) > eps)
        OPM_THROW(std::runtime_error,
                   "Invalid derivative at end of interval: is "
                   << d1 << " ought to be " << m1);
}

template <class Spline>
void testNatural(const Spline &sp,
                 const double *x,
                 const double *y)
{
    // test the common properties of splines
    testCommon(sp, x, y);

    static double eps = 1e-5;
    int n = sp.numSamples();

    // make sure the second derivatives at both end points are 0
    double d0 = sp.evalDerivative(x[0]);
    double d1 = sp.evalDerivative(x[0] + eps);

    double d2 = sp.evalDerivative(x[n-1] - eps);
    double d3 = sp.evalDerivative(x[n-1]);

    if (std::abs(d1 - d0)/eps > 1000*eps)
        OPM_THROW(std::runtime_error,
                   "Invalid second derivative at beginning of interval: is "
                   << (d1 - d0)/eps << " ought to be 0");

    if (std::abs(d3 - d2)/eps > 1000*eps)
        OPM_THROW(std::runtime_error,
                   "Invalid second derivative at end of interval: is "
                   << (d3 - d2)/eps << " ought to be 0");
}

template <class Spline>
void testMonotonic(const Spline &sp,
                   const double *x,
                   const double *y)
{
    // test the common properties of splines
    testCommon(sp, x, y);

    int n = sp.numSamples();

    for (int i = 0; i < n - 1; ++ i) {
        // make sure that the spline is monotonic for each interval
        // between sampling points
        if (!sp.monotonic(x[i], x[i + 1]))
            OPM_THROW(std::runtime_error,
                      "Spline says it is not monotonic in interval "
                      << i << " where it should be");

        // test the intersection methods
        double d = (y[i] + y[i+1])/2;
        double interX = sp.intersectInterval(x[i], x[i+1],
                                             /*a=*/0, /*b=*/0, /*c=*/0, d);
        double interY = sp.eval(interX);
        if (std::abs(interY - d) > 1e-5)
            OPM_THROW(std::runtime_error,
                      "Spline::intersectInterval() seems to be broken: "
                      << sp.eval(interX) << " - " << d << " = " << sp.eval(interX) - d << "!");
    }

    // make sure the spline says to be monotonic on the (extrapolated)
    // left and right sides
    if (!sp.monotonic(x[0] - 1.0, (x[0] + x[1])/2, /*extrapolate=*/true))
        OPM_THROW(std::runtime_error,
                  "Spline says it is not monotonic on left side where it should be");
    if (!sp.monotonic((x[n - 2]+ x[n - 1])/2, x[n-1] + 1.0, /*extrapolate=*/true))
        OPM_THROW(std::runtime_error,
                  "Spline says it is not monotonic on right side where it should be");

    for (int i = 0; i < n - 2; ++ i) {
        // make sure that the spline says that it is non-monotonic for
        // if extrema are within the queried interval
        if (sp.monotonic((x[i] + x[i + 1])/2, (x[i + 1] + x[i + 2])/2))
            OPM_THROW(std::runtime_error,
                      "Spline says it is monotonic in interval "
                      << i << " where it should not be");
    }
}

void testAll()
{
    double x[] = { 0, 5, 7.5, 8.75, 9.375 };
    double y[] = { 10, 0, 10, 0, 10 };
    double m0 = 10;
    double m1 = -10;
    double points[][2] =
        {
            {x[0], y[0]},
            {x[1], y[1]},
            {x[2], y[2]},
            {x[3], y[3]},
            {x[4], y[4]},
        };


#if GCC_VERSION >= 40500
    std::initializer_list<const std::pair<double, double> > pointsInitList =
        {
            {x[0], y[0]},
            {x[1], y[1]},
            {x[2], y[2]},
            {x[3], y[3]},
            {x[4], y[4]},
        };
#endif

    std::vector<double> xVec;
    std::vector<double> yVec;
    std::vector<double*> pointVec;
    for (int i = 0; i < 5; ++i) {
        xVec.push_back(x[i]);
        yVec.push_back(y[i]);
        pointVec.push_back(points[i]);
    }

    /////////
    // test spline with two sampling points
    /////////

    // full spline
    { Opm::Spline<double> sp(x[0], x[1], y[0], y[1], m0, m1); sp.set(x[0],x[1],y[0],y[1],m0, m1); testFull(sp, x, y, m0, m1); };
    { Opm::Spline<double> sp(2, x, y, m0, m1); sp.setXYArrays(2, x, y, m0, m1); testFull(sp, x, y, m0, m1);  };
    { Opm::Spline<double> sp(2, points, m0, m1); sp.setArrayOfPoints(2, points, m0, m1); testFull(sp, x, y, m0, m1); };

    /////////
    // test variable length splines
    /////////

    // full spline
    { Opm::Spline<double> sp(5, x, y, m0, m1); sp.setXYArrays(5,x,y,m0, m1); testFull(sp, x, y, m0, m1);  };
    { Opm::Spline<double> sp(xVec, yVec, m0, m1); sp.setXYContainers(xVec,yVec,m0, m1); testFull(sp, x, y, m0, m1);  };
    { Opm::Spline<double> sp; sp.setArrayOfPoints(5,points,m0, m1); testFull(sp, x, y, m0, m1); };
    { Opm::Spline<double> sp; sp.setContainerOfPoints(pointVec,m0, m1); testFull(sp, x, y, m0, m1);  };
#if GCC_VERSION >= 40500
    { Opm::Spline<double> sp; sp.setContainerOfTuples(pointsInitList,m0, m1); testFull(sp, x, y, m0, m1); };
#endif

    // natural spline
    { Opm::Spline<double> sp(5, x, y); sp.setXYArrays(5,x,y); testNatural(sp, x, y);  };
    { Opm::Spline<double> sp(xVec, yVec); sp.setXYContainers(xVec,yVec); testNatural(sp, x, y); };
    { Opm::Spline<double> sp; sp.setArrayOfPoints(5,points); testNatural(sp, x, y); };
    { Opm::Spline<double> sp; sp.setContainerOfPoints(pointVec); testNatural(sp, x, y); };
#if GCC_VERSION >= 40500
    { Opm::Spline<double> sp; sp.setContainerOfTuples(pointsInitList); testNatural(sp, x, y); };
#endif
}

void plot()
{
    const int numSamples = 5;
    const int n = numSamples - 1;
    typedef std::array<double, numSamples> FV;

    double x_[] = { 0, 5, 7.5, 8.75, 10 };
    double y_[] = { 10, 0, 10, 0, 10 };
    double m1 = 10;
    double m2 = -10;
    FV &xs = *reinterpret_cast<FV*>(x_);
    FV &ys = *reinterpret_cast<FV*>(y_);

    Opm::Spline<double> spFull(xs, ys, m1, m2);
    Opm::Spline<double> spNatural(xs, ys);
    Opm::Spline<double> spPeriodic(xs, ys, /*type=*/Opm::Spline<double>::Periodic);
    Opm::Spline<double> spMonotonic(xs, ys, /*type=*/Opm::Spline<double>::Monotonic);

    testMonotonic(spMonotonic, x_, y_);

    spFull.printCSV(x_[0] - 1.00001,
                    x_[n] + 1.00001,
                    1000);
    std::cout << "\n";
    spNatural.printCSV(x_[0] - 1.00001,
                       x_[n] + 1.00001,
                       1000);
    std::cout << "\n";

    spPeriodic.printCSV(x_[0] - 1.00001,
                        x_[n] + 1.00001,
                       1000);
    std::cout << "\n";

    spMonotonic.printCSV(x_[0] - 1.00001,
                         x_[n] + 1.00001,
                         1000);
    std::cout << "\n";
}

int main()
{
    try {
        testAll();

        plot();
    }
    catch (const std::exception &e) {
        std::cout << "Caught OPM exception: " << e.what() << "\n";
    }

    return 0;
}