include/apfel/lagrangeinterpolator.h

0001 //
0002 // APFEL++ 2017
0003 //
0004 // Author: Valerio Bertone: valerio.bertone@cern.ch
0005 //
0006
0007 #pragma once
0008
0009 #include "apfel/interpolator.h"
0010
0011 namespace apfel
0012 {
0013   /**
0014    * @brief The LagrangeInterpolator class is a specialization of the
0015    * Interpolator class using the lagrange interpolation procedure.
0016    */
0017   class LagrangeInterpolator: public Interpolator
0018   {
0019   public:
0020     /**
0021      * @brief The LagrangeInterpolator constructor.
0022      * @param gr: the x-space grid object over which interpolation takes place
0023      * @see Interpolator::Interpolator
0024      */
0025     LagrangeInterpolator(Grid const& gr);
0026
0027     /**
0028      * @brief The LagrangeInterpolator constructor.
0029      * @param gr: the x-space grid object over which interpolation takes place
0030      * @param distsubgrid: the vector of subgrids
0031      * @param distjointgrid: the joint subgrid
0032      * @see Interpolator::Interpolator
0033      * @note distjointgrid and distsubgrid are assumed to match the
0034      * structure of the grid gr.
0035      */
0036     LagrangeInterpolator(Grid                             const& gr,
0037                          std::vector<std::vector<double>> const& distsubgrid,
0038                          std::vector<double>              const& distjointgrid);
0039
0040     /**
0041      * @brief This function defines the interpolating function used by
0042      * the mother class Interpolator to perform the actual
0043      * interpolation using polynomials in log(x).
0044      * @param beta: the x-space grid index
0045      * @param lnx: the value (of the log) of the interpolation point
0046      * @param sg: the SubGrid over which the interpolant is defined
0047      * @return the interpolation weights
0048      * @see Interpolator::InterpolantLog
0049      */
0050     double InterpolantLog(int const& beta, double const& lnx, SubGrid const& sg) const;
0051
0052     /**
0053      * @brief This function defines the interpolating function used by
0054      * the mother class Interpolator to perform the
0055      * interpolation.
0056      * @param beta: the x-space grid index
0057      * @param x: the value of the interpolation point
0058      * @param sg: the SubGrid over which the interpolant is defined
0059      * @return the interpolation weights
0060      * @see Interpolator::Interpolant
0061      */
0062     double Interpolant(int const& beta, double const& x, SubGrid const& sg) const;
0063
0064     /**
0065      * @brief This function defines the derivative of the
0066      * interpolating function used by the mother class Interpolator to
0067      * perform the actual interpolation.
0068      * @param beta: the x-space grid index
0069      * @param x: the value of the interpolation point
0070      * @param sg: the SubGrid over which the interpolant is defined
0071      * @return the derivative of the interpolation weights
0072      * @see Interpolator::DerInterpolant
0073      */
0074     double DerInterpolant(int const& beta, double const& x, SubGrid const& sg) const;
0075
0076     /**
0077      * @brief This function defines the integral of the interpolating
0078      * function used by the mother class Interpolator to perform the
0079      * actual interpolation.
0080      * @param beta: the x-space grid index
0081      * @param a: the value of the lower integration bound
0082      * @param b: the value of the upper integration bound
0083      * @param sg: the SubGrid over which the interpolant is defined
0084      * @return the integral of the interpolation weights
0085      * @see Interpolator::IntInterpolant
0086      */
0087     double IntInterpolant(int const& beta, double const& a, double const& b, SubGrid const& sg) const;
0088
0089     /**
0090      * @brief This function computes the lower and upper bounds on
0091      * which the the sum over interpolants is limited.
0092      * @param x: the value in x to be interpolated
0093      * @param sg: the SubGrid over which the interpolant is defined
0094      * @return the lower and upper bounds of the grid index
0095      * @see Interpolator::SumBounds
0096      */
0097     std::array<int,2> SumBounds(double const& x, SubGrid const& sg) const;
0098   };
0099 }