formatter_barycentric_interpolation_example.cpp

// Copyright Nick Thompson, 2017

// Distributed under the Boost Software License, Version 1.0.
// (See accompanying file LICENSE_1_0.txt or
// copy at http://www.boost.org/LICENSE_1_0.txt).

#include <iostream>
#include <limits>
#include <vector>
#include <boost/math/tools/formatting.hpp>

//[barycentric_rational_example

/*`
This example shows how to use barycentric rational interpolation, using Walter Kohn's classic paper
"Solution of the Schrodinger Equation in Periodic Lattices with an Application to Metallic Lithium"
In this paper, Kohn needs to repeatedly solve an ODE (the radial Schrodinger equation) given a potential
which is only known at non-equally samples data.

If he'd only had the barycentric rational interpolant of Boost.Math!

References: Kohn, W., and N. Rostoker. "Solution of the Schrodinger equation in periodic lattices with an application to metallic lithium." Physical Review 94.5 (1954): 1111.
*/

#include <boost/math/interpolators/barycentric_rational.hpp>

int main()
{
    // The lithium potential is given in Kohn's paper, Table I:
    std::vector<double> r(45);
    std::vector<double> mrV(45);

    r[0] = 0.02; mrV[0] = 5.727;
    r[1] = 0.04, mrV[1] = 5.544;
    r[2] = 0.06, mrV[2] = 5.450;
    r[3] = 0.08, mrV[3] = 5.351;
    r[4] = 0.10, mrV[4] = 5.253;
    r[5] = 0.12, mrV[5] = 5.157;
    r[6] = 0.14, mrV[6] = 5.058;
    r[7] = 0.16, mrV[7] = 4.960;
    r[8] = 0.18, mrV[8] = 4.862;
    r[9] = 0.20, mrV[9] = 4.762;
    r[10] = 0.24, mrV[10] = 4.563;
    r[11] = 0.28, mrV[11] = 4.360;
    r[12] = 0.32, mrV[12] = 4.1584;
    r[13] = 0.36, mrV[13] = 3.9463;
    r[14] = 0.40, mrV[14] = 3.7360;
    r[15] = 0.44, mrV[15] = 3.5429;
    r[16] = 0.48, mrV[16] = 3.3797;
    r[17] = 0.52, mrV[17] = 3.2417;
    r[18] = 0.56, mrV[18] = 3.1209;
    r[19] = 0.60, mrV[19] = 3.0138;
    r[20] = 0.68, mrV[20] = 2.8342;
    r[21] = 0.76, mrV[21] = 2.6881;
    r[22] = 0.84, mrV[22] = 2.5662;
    r[23] = 0.92, mrV[23] = 2.4242;
    r[24] = 1.00, mrV[24] = 2.3766;
    r[25] = 1.08, mrV[25] = 2.3058;
    r[26] = 1.16, mrV[26] = 2.2458;
    r[27] = 1.24, mrV[27] = 2.2035;
    r[28] = 1.32, mrV[28] = 2.1661;
    r[29] = 1.40, mrV[29] = 2.1350;
    r[30] = 1.48, mrV[30] = 2.1090;
    r[31] = 1.64, mrV[31] = 2.0697;
    r[32] = 1.80, mrV[32] = 2.0466;
    r[33] = 1.96, mrV[33] = 2.0325;
    r[34] = 2.12, mrV[34] = 2.0288;
    r[35] = 2.28, mrV[35] = 2.0292;
    r[36] = 2.44, mrV[36] = 2.0228;
    r[37] = 2.60, mrV[37] = 2.0124;
    r[38] = 2.76, mrV[38] = 2.0065;
    r[39] = 2.92, mrV[39] = 2.0031;
    r[40] = 3.08, mrV[40] = 2.0015;
    r[41] = 3.24, mrV[41] = 2.0008;
    r[42] = 3.40, mrV[42] = 2.0004;
    r[43] = 3.56, mrV[43] = 2.0002;
    r[44] = 3.72, mrV[44] = 2.0001;

    // Now we want to interpolate this potential at any r:
    boost::math::barycentric_rational<double> b(r.data(), mrV.data(), r.size());

    boost::math::tools::text_printer printer(std::cout);
    printer << b << std::endl << std::endl;

    boost::math::tools::latex_printer lprinter(std::cout);
    lprinter << b << std::endl << std::endl;

    boost::math::tools::html_printer hprinter(std::cout);
    hprinter << b << std::endl << std::endl;

    boost::math::tools::docbook_printer dprinter(std::cout);
    dprinter << b << std::endl << std::endl;

}