#ifndef OPENMM_SPLINEFITTER_H_ #define OPENMM_SPLINEFITTER_H_ /* -------------------------------------------------------------------------- * * OpenMM * * -------------------------------------------------------------------------- * * This is part of the OpenMM molecular simulation toolkit originating from * * Simbios, the NIH National Center for Physics-Based Simulation of * * Biological Structures at Stanford, funded under the NIH Roadmap for * * Medical Research, grant U54 GM072970. See https://simtk.org. * * * * Portions copyright (c) 2010-2014 Stanford University and the Authors. * * Authors: Peter Eastman * * Contributors: * * * * Permission is hereby granted, free of charge, to any person obtaining a * * copy of this software and associated documentation files (the "Software"), * * to deal in the Software without restriction, including without limitation * * the rights to use, copy, modify, merge, publish, distribute, sublicense, * * and/or sell copies of the Software, and to permit persons to whom the * * Software is furnished to do so, subject to the following conditions: * * * * The above copyright notice and this permission notice shall be included in * * all copies or substantial portions of the Software. * * * * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR * * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, * * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL * * THE AUTHORS, CONTRIBUTORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, * * DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR * * OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE * * USE OR OTHER DEALINGS IN THE SOFTWARE. * * -------------------------------------------------------------------------- */ #include "windowsExport.h" #include namespace OpenMM { /** * SplineFitter provides routines for performing cubic spline interpolation. */ class OPENMM_EXPORT SplineFitter { public: /** * Fit a cubic spline to a set of data points. The resulting spline interpolates all the * data points and has a continuous second derivative everywhere. The second derivatives are * identical at the end points if periodic=true or 0 at the end points if periodic=false. * * @param x the values of the independent variable at the data points to interpolate. They must * be strictly increasing: x[i] > x[i-1]. * @param y the values of the dependent variable at the data points to interpolate * @param periodic whether the interpolated function is periodic * @param deriv on exit, this contains the second derivative of the spline at each of the data points */ static void createSpline(const std::vector& x, const std::vector& y, bool periodic, std::vector& deriv); /** * Fit a natural cubic spline to a set of data points. The resulting spline interpolates all the * data points, has a continuous second derivative everywhere, and has a second derivative of 0 at * its end points. * * @param x the values of the independent variable at the data points to interpolate. They must * be strictly increasing: x[i] > x[i-1]. * @param y the values of the dependent variable at the data points to interpolate * @param deriv on exit, this contains the second derivative of the spline at each of the data points */ static void createNaturalSpline(const std::vector& x, const std::vector& y, std::vector& deriv); /** * Fit a periodic cubic spline to a set of data points. The resulting spline interpolates all the * data points, has a continuous second derivative everywhere, and has identical second derivatives * at the end points. * * @param x the values of the independent variable at the data points to interpolate. They must * be strictly increasing: x[i] > x[i-1]. * @param y the values of the dependent variable at the data points to interpolate. The first and * last entries must be identical. * @param deriv on exit, this contains the second derivative of the spline at each of the data points */ static void createPeriodicSpline(const std::vector& x, const std::vector& y, std::vector& deriv); /** * Evaluate a 1D spline generated by one of the other methods in this class. * * @param x the values of the independent variable at the data points to interpolate * @param y the values of the dependent variable at the data points to interpolate * @param deriv the vector of second derivatives that was calculated by one of the other methods * @param t the value of the independent variable at which to evaluate the spline * @return the value of the spline at the specified point */ static double evaluateSpline(const std::vector& x, const std::vector& y, const std::vector& deriv, double t); /** * Evaluate the derivative of a 1D spline generated by one of the other methods in this class. * * @param x the values of the independent variable at the data points to interpolate * @param y the values of the dependent variable at the data points to interpolate * @param deriv the vector of second derivatives that was calculated by one of the other methods * @param t the value of the independent variable at which to evaluate the spline * @return the value of the spline's derivative at the specified point */ static double evaluateSplineDerivative(const std::vector& x, const std::vector& y, const std::vector& deriv, double t); /** * Fit a cubic spline surface f(x,y) to a 2D set of data points. The resulting spline interpolates all the * data points and has a continuous second derivative everywhere. The second derivatives are identical at * the boundary if periodic=true or 0 at the boundary if periodic=false. * * @param x the values of the first independent variable at the data points to interpolate. They must * be strictly increasing: x[i] > x[i-1]. * @param y the values of the second independent variable at the data points to interpolate. They must * be strictly increasing: y[i] > y[i-1]. * @param values the values of the dependent variable at the data points to interpolate. They must be ordered * so that values[i+xsize*j] = f(x[i],y[j]), where xsize is the length of x. * @param periodic whether the interpolated function is periodic * @param c on exit, this contains the spline coefficients at each of the data points */ static void create2DSpline(const std::vector& x, const std::vector& y, const std::vector& values, bool periodic, std::vector >& c); /** * Fit a natural cubic spline surface f(x,y) to a 2D set of data points. The resulting spline interpolates all the * data points, has a continuous second derivative everywhere, and has a second derivative of 0 at the boundary. * * @param x the values of the first independent variable at the data points to interpolate. They must * be strictly increasing: x[i] > x[i-1]. * @param y the values of the second independent variable at the data points to interpolate. They must * be strictly increasing: y[i] > y[i-1]. * @param values the values of the dependent variable at the data points to interpolate. They must be ordered * so that values[i+xsize*j] = f(x[i],y[j]), where xsize is the length of x. * @param c on exit, this contains the spline coefficients at each of the data points */ static void create2DNaturalSpline(const std::vector& x, const std::vector& y, const std::vector& values, std::vector >& c); /** * Evaluate a 2D spline generated by one of the other methods in this class. * * @param x the values of the first independent variable at the data points to interpolate * @param y the values of the second independent variable at the data points to interpolate * @param values the values of the dependent variable at the data points to interpolate * @param c the vector of spline coefficients that was calculated by one of the other methods * @param u the value of the first independent variable at which to evaluate the spline * @param v the value of the second independent variable at which to evaluate the spline * @return the value of the spline at the specified point */ static double evaluate2DSpline(const std::vector& x, const std::vector& y, const std::vector& values, const std::vector >& c, double u, double v); /** * Evaluate the derivatives of a 2D spline generated by one of the other methods in this class. * * @param x the values of the first independent variable at the data points to interpolate * @param y the values of the second independent variable at the data points to interpolate * @param values the values of the dependent variable at the data points to interpolate * @param c the vector of spline coefficients that was calculated by one of the other methods * @param u the value of the first independent variable at which to evaluate the spline * @param v the value of the second independent variable at which to evaluate the spline * @param dx on exit, the x derivative of the spline at the specified point * @param dy on exit, the y derivative of the spline at the specified point */ static void evaluate2DSplineDerivatives(const std::vector& x, const std::vector& y, const std::vector& values, const std::vector >& c, double u, double v, double& dx, double& dy); /** * Fit a cubic spline surface f(x,y,z) to a 3D set of data points. The resulting spline interpolates all the * data points and has a continuous second derivative everywhere. The second derivatives are identical at * the boundary if periodic=true or 0 at the boundary if periodic=false. * * @param x the values of the first independent variable at the data points to interpolate. They must * be strictly increasing: x[i] > x[i-1]. * @param y the values of the second independent variable at the data points to interpolate. They must * be strictly increasing: y[i] > y[i-1]. * @param z the values of the third independent variable at the data points to interpolate. They must * be strictly increasing: z[i] > z[i-1]. * @param values the values of the dependent variable at the data points to interpolate. They must be ordered * so that values[i+xsize*j+xsize*ysize*k] = f(x[i],y[j],z[k]), where xsize is the length of x * and ysize is the length of y. * @param periodic whether the interpolated function is periodic * @param c on exit, this contains the spline coefficients at each of the data points */ static void create3DSpline(const std::vector& x, const std::vector& y, const std::vector& z, const std::vector& values, bool periodic, std::vector >& c); /** * Fit a natural cubic spline surface f(x,y,z) to a 3D set of data points. The resulting spline interpolates all the * data points, has a continuous second derivative everywhere, and has a second derivative of 0 at the boundary. * * @param x the values of the first independent variable at the data points to interpolate. They must * be strictly increasing: x[i] > x[i-1]. * @param y the values of the second independent variable at the data points to interpolate. They must * be strictly increasing: y[i] > y[i-1]. * @param z the values of the third independent variable at the data points to interpolate. They must * be strictly increasing: z[i] > z[i-1]. * @param values the values of the dependent variable at the data points to interpolate. They must be ordered * so that values[i+xsize*j+xsize*ysize*k] = f(x[i],y[j],z[k]), where xsize is the length of x * and ysize is the length of y. * @param c on exit, this contains the spline coefficients at each of the data points */ static void create3DNaturalSpline(const std::vector& x, const std::vector& y, const std::vector& z, const std::vector& values, std::vector >& c); /** * Evaluate a 3D spline generated by one of the other methods in this class. * * @param x the values of the first independent variable at the data points to interpolate * @param y the values of the second independent variable at the data points to interpolate * @param z the values of the third independent variable at the data points to interpolate * @param values the values of the dependent variable at the data points to interpolate * @param c the vector of spline coefficients that was calculated by one of the other methods * @param u the value of the first independent variable at which to evaluate the spline * @param v the value of the second independent variable at which to evaluate the spline * @param w the value of the third independent variable at which to evaluate the spline * @return the value of the spline at the specified point */ static double evaluate3DSpline(const std::vector& x, const std::vector& y, const std::vector& z, const std::vector& values, const std::vector >& c, double u, double v, double w); /** * Evaluate the derivatives of a 3D spline generated by one of the other methods in this class. * * @param x the values of the first independent variable at the data points to interpolate * @param y the values of the second independent variable at the data points to interpolate * @param z the values of the third independent variable at the data points to interpolate * @param values the values of the dependent variable at the data points to interpolate * @param c the vector of spline coefficients that was calculated by one of the other methods * @param u the value of the first independent variable at which to evaluate the spline * @param v the value of the second independent variable at which to evaluate the spline * @param w the value of the third independent variable at which to evaluate the spline * @param dx on exit, the x derivative of the spline at the specified point * @param dy on exit, the y derivative of the spline at the specified point * @param dz on exit, the z derivative of the spline at the specified point */ static void evaluate3DSplineDerivatives(const std::vector& x, const std::vector& y, const std::vector& z, const std::vector& values, const std::vector >& c, double u, double v, double w, double& dx, double& dy, double &dz); private: static void solveTridiagonalMatrix(const std::vector& a, const std::vector& b, const std::vector& c, const std::vector& rhs, std::vector& sol); }; } // namespace OpenMM #endif /*OPENMM_SPLINEFITTER_H_*/