347 lines
12 KiB
C++
347 lines
12 KiB
C++
// -*- mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
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// vi: set et ts=4 sw=4 sts=4:
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/*****************************************************************************
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* Copyright (C) 2010-2012 by Andreas Lauser *
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* *
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* This program is free software: you can redistribute it and/or modify *
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* it under the terms of the GNU General Public License as published by *
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* the Free Software Foundation, either version 2 of the License, or *
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* (at your option) any later version. *
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* *
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* This program is distributed in the hope that it will be useful, *
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* but WITHOUT ANY WARRANTY; without even the implied warranty of *
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the *
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* GNU General Public License for more details. *
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* *
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* You should have received a copy of the GNU General Public License *
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* along with this program. If not, see <http://www.gnu.org/licenses/>. *
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*****************************************************************************/
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/*!
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* \file
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*
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* \brief This is a program to test the polynomial spline interpolation.
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*
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* It just prints some function to stdout. You can look at the result
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* using the following commands:
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*
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----------- snip -----------
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./test_spline > spline.csv
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gnuplot
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gnuplot> plot "spline.csv" using 1:2 w l ti "Curve", \
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"spline.csv" using 1:3 w l ti "Derivative", \
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"spline.csv" using 1:4 w p ti "Monotonical"
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----------- snap -----------
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*/
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#include "config.h"
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#include <array>
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#include <opm/core/utility/Spline.hpp>
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#define GCC_VERSION (__GNUC__ * 10000 \
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+ __GNUC_MINOR__ * 100 \
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+ __GNUC_PATCHLEVEL__)
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template <class Spline>
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void testCommon(const Spline &sp,
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const double *x,
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const double *y)
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{
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static double eps = 1e-10;
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static double epsFD = 1e-7;
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int n = sp.numSamples();
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for (int i = 0; i < n; ++i) {
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// sure that we hit all sampling points
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double y0 = (i>0)?sp.eval(x[i]-eps):y[0];
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double y1 = sp.eval(x[i]);
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double y2 = (i<n-1)?sp.eval(x[i]+eps):y[n-1];
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if (std::abs(y0 - y[i]) > 100*eps || std::abs(y2 - y[i]) > 100*eps)
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OPM_THROW(std::runtime_error,
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"Spline seems to be discontinuous at sampling point " << i << "!");
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if (std::abs(y1 - y[i]) > eps)
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OPM_THROW(std::runtime_error,
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"Spline does not capture sampling point " << i << "!");
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// make sure the derivative is continuous (assuming that the
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// second derivative is smaller than 1000)
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double d1 = sp.evalDerivative(x[i]);
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double d0 = (i>0)?sp.evalDerivative(x[i]-eps):d1;
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double d2 = (i<n-1)?sp.evalDerivative(x[i]+eps):d1;
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if (std::abs(d1 - d0) > 1000*eps || std::abs(d2 - d0) > 1000*eps)
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OPM_THROW(std::runtime_error,
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"Spline seems to exhibit a discontinuous derivative at sampling point " << i << "!");
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}
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// make sure the derivatives are consistent with the curve
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int np = 3*n;
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for (int i = 0; i < np; ++i) {
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double xval = sp.xMin() + (sp.xMax() - sp.xMin())*i/np;
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// first derivative
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double y1 = sp.eval(xval+epsFD);
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double y0 = sp.eval(xval);
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double mFD = (y1 - y0)/epsFD;
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double m = sp.evalDerivative(xval);
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if (std::abs( mFD - m ) > 1000*epsFD)
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OPM_THROW(std::runtime_error,
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"Derivative of spline seems to be inconsistent with cuve"
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" (" << mFD << " - " << m << " = " << mFD - m << ")!");
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// second derivative
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y1 = sp.evalDerivative(xval+epsFD);
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y0 = sp.evalDerivative(xval);
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mFD = (y1 - y0)/epsFD;
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m = sp.evalSecondDerivative(xval);
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if (std::abs( mFD - m ) > 1000*epsFD)
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OPM_THROW(std::runtime_error,
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"Second derivative of spline seems to be inconsistent with cuve"
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" (" << mFD << " - " << m << " = " << mFD - m << ")!");
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// Third derivative
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y1 = sp.evalSecondDerivative(xval+epsFD);
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y0 = sp.evalSecondDerivative(xval);
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mFD = (y1 - y0)/epsFD;
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m = sp.evalThirdDerivative(xval);
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if (std::abs( mFD - m ) > 1000*epsFD)
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OPM_THROW(std::runtime_error,
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"Third derivative of spline seems to be inconsistent with cuve"
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" (" << mFD << " - " << m << " = " << mFD - m << ")!");
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}
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}
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template <class Spline>
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void testFull(const Spline &sp,
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const double *x,
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const double *y,
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double m0,
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double m1)
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{
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// test the common properties of splines
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testCommon(sp, x, y);
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static double eps = 1e-5;
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int n = sp.numSamples();
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// make sure the derivative at both end points is correct
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double d0 = sp.evalDerivative(x[0]);
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double d1 = sp.evalDerivative(x[n-1]);
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if (std::abs(d0 - m0) > eps)
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OPM_THROW(std::runtime_error,
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"Invalid derivative at beginning of interval: is "
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<< d0 << " ought to be " << m0);
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if (std::abs(d1 - m1) > eps)
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OPM_THROW(std::runtime_error,
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"Invalid derivative at end of interval: is "
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<< d1 << " ought to be " << m1);
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}
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template <class Spline>
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void testNatural(const Spline &sp,
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const double *x,
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const double *y)
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{
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// test the common properties of splines
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testCommon(sp, x, y);
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static double eps = 1e-5;
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int n = sp.numSamples();
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// make sure the second derivatives at both end points are 0
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double d0 = sp.evalDerivative(x[0]);
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double d1 = sp.evalDerivative(x[0] + eps);
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double d2 = sp.evalDerivative(x[n-1] - eps);
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double d3 = sp.evalDerivative(x[n-1]);
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if (std::abs(d1 - d0)/eps > 1000*eps)
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OPM_THROW(std::runtime_error,
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"Invalid second derivative at beginning of interval: is "
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<< (d1 - d0)/eps << " ought to be 0");
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if (std::abs(d3 - d2)/eps > 1000*eps)
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OPM_THROW(std::runtime_error,
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"Invalid second derivative at end of interval: is "
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<< (d3 - d2)/eps << " ought to be 0");
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}
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template <class Spline>
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void testMonotonic(const Spline &sp,
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const double *x,
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const double *y)
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{
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// test the common properties of splines
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testCommon(sp, x, y);
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int n = sp.numSamples();
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for (int i = 0; i < n - 1; ++ i) {
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// make sure that the spline is monotonic for each interval
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// between sampling points
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if (!sp.monotonic(x[i], x[i + 1]))
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OPM_THROW(std::runtime_error,
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"Spline says it is not monotonic in interval "
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<< i << " where it should be");
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// test the intersection methods
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double d = (y[i] + y[i+1])/2;
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double interX = sp.intersectInterval(x[i], x[i+1],
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/*a=*/0, /*b=*/0, /*c=*/0, d);
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double interY = sp.eval(interX);
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if (std::abs(interY - d) > 1e-5)
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OPM_THROW(std::runtime_error,
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"Spline::intersectInterval() seems to be broken: "
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<< sp.eval(interX) << " - " << d << " = " << sp.eval(interX) - d << "!");
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}
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// make sure the spline says to be monotonic on the (extrapolated)
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// left and right sides
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if (!sp.monotonic(x[0] - 1.0, (x[0] + x[1])/2, /*extrapolate=*/true))
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OPM_THROW(std::runtime_error,
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"Spline says it is not monotonic on left side where it should be");
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if (!sp.monotonic((x[n - 2]+ x[n - 1])/2, x[n-1] + 1.0, /*extrapolate=*/true))
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OPM_THROW(std::runtime_error,
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"Spline says it is not monotonic on right side where it should be");
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for (int i = 0; i < n - 2; ++ i) {
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// make sure that the spline says that it is non-monotonic for
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// if extrema are within the queried interval
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if (sp.monotonic((x[i] + x[i + 1])/2, (x[i + 1] + x[i + 2])/2))
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OPM_THROW(std::runtime_error,
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"Spline says it is monotonic in interval "
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<< i << " where it should not be");
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}
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}
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void testAll()
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{
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double x[] = { 0, 5, 7.5, 8.75, 9.375 };
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double y[] = { 10, 0, 10, 0, 10 };
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double m0 = 10;
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double m1 = -10;
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double points[][2] =
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{
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{x[0], y[0]},
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{x[1], y[1]},
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{x[2], y[2]},
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{x[3], y[3]},
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{x[4], y[4]},
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};
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#if GCC_VERSION >= 40500
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std::initializer_list<const std::pair<double, double> > pointsInitList =
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{
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{x[0], y[0]},
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{x[1], y[1]},
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{x[2], y[2]},
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{x[3], y[3]},
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{x[4], y[4]},
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};
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#endif
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std::vector<double> xVec;
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std::vector<double> yVec;
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std::vector<double*> pointVec;
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for (int i = 0; i < 5; ++i) {
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xVec.push_back(x[i]);
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yVec.push_back(y[i]);
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pointVec.push_back(points[i]);
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}
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/////////
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// test spline with two sampling points
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/////////
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// full spline
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{ 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); };
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{ Opm::Spline<double> sp(2, x, y, m0, m1); sp.setXYArrays(2, x, y, m0, m1); testFull(sp, x, y, m0, m1); };
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{ Opm::Spline<double> sp(2, points, m0, m1); sp.setArrayOfPoints(2, points, m0, m1); testFull(sp, x, y, m0, m1); };
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/////////
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// test variable length splines
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/////////
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// full spline
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{ Opm::Spline<double> sp(5, x, y, m0, m1); sp.setXYArrays(5,x,y,m0, m1); testFull(sp, x, y, m0, m1); };
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{ Opm::Spline<double> sp(xVec, yVec, m0, m1); sp.setXYContainers(xVec,yVec,m0, m1); testFull(sp, x, y, m0, m1); };
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{ Opm::Spline<double> sp; sp.setArrayOfPoints(5,points,m0, m1); testFull(sp, x, y, m0, m1); };
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{ Opm::Spline<double> sp; sp.setContainerOfPoints(pointVec,m0, m1); testFull(sp, x, y, m0, m1); };
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#if GCC_VERSION >= 40500
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{ Opm::Spline<double> sp; sp.setContainerOfTuples(pointsInitList,m0, m1); testFull(sp, x, y, m0, m1); };
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#endif
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// natural spline
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{ Opm::Spline<double> sp(5, x, y); sp.setXYArrays(5,x,y); testNatural(sp, x, y); };
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{ Opm::Spline<double> sp(xVec, yVec); sp.setXYContainers(xVec,yVec); testNatural(sp, x, y); };
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{ Opm::Spline<double> sp; sp.setArrayOfPoints(5,points); testNatural(sp, x, y); };
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{ Opm::Spline<double> sp; sp.setContainerOfPoints(pointVec); testNatural(sp, x, y); };
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#if GCC_VERSION >= 40500
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{ Opm::Spline<double> sp; sp.setContainerOfTuples(pointsInitList); testNatural(sp, x, y); };
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#endif
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}
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void plot()
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{
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const int numSamples = 5;
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const int n = numSamples - 1;
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typedef std::array<double, numSamples> FV;
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double x_[] = { 0, 5, 7.5, 8.75, 10 };
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double y_[] = { 10, 0, 10, 0, 10 };
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double m1 = 10;
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double m2 = -10;
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FV &xs = *reinterpret_cast<FV*>(x_);
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FV &ys = *reinterpret_cast<FV*>(y_);
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Opm::Spline<double> spFull(xs, ys, m1, m2);
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Opm::Spline<double> spNatural(xs, ys);
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Opm::Spline<double> spPeriodic(xs, ys, /*type=*/Opm::Spline<double>::Periodic);
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Opm::Spline<double> spMonotonic(xs, ys, /*type=*/Opm::Spline<double>::Monotonic);
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testMonotonic(spMonotonic, x_, y_);
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spFull.printCSV(x_[0] - 1.00001,
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x_[n] + 1.00001,
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1000);
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std::cout << "\n";
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spNatural.printCSV(x_[0] - 1.00001,
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x_[n] + 1.00001,
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1000);
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std::cout << "\n";
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spPeriodic.printCSV(x_[0] - 1.00001,
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x_[n] + 1.00001,
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1000);
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std::cout << "\n";
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spMonotonic.printCSV(x_[0] - 1.00001,
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x_[n] + 1.00001,
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1000);
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std::cout << "\n";
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}
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int main()
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{
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try {
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testAll();
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plot();
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}
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catch (const std::exception &e) {
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std::cout << "Caught OPM exception: " << e.what() << "\n";
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}
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return 0;
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}
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