Program Listing for File mathutil.hpp

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/*
 *      Copyright (c) 2020 Robert Shaw
 *      This file is a part of Libecpint.
 *
 *      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 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.
 */

#ifndef MATHUTILHEADERDEF
#define MATHUTILHEADERDEF

#include <vector>
#include <numeric>
#include <cmath>
#include "multiarr.hpp"

#ifndef M_PI
#define M_PI 3.14159265358979323846
#endif

#ifndef M_EULER
#define M_EULER 2.71828182845904523536
#endif

#define MAX_FAC 100
#define MAX_DFAC 200

namespace libecpint {

    constexpr double ROOT_PI = 1.772453850905516;
    constexpr double SINH_1 = 1.1752011936;
    constexpr int MAX_POW = 20;

    extern double FAC[MAX_FAC];
    extern double DFAC[MAX_DFAC];

    double pow_m2(double);
    double pow_m1(double);
    double pow_0(double);
    double pow_1(double);
    double pow_2(double);
    double pow_3(double);
    double pow_4(double);
    double pow_5(double);
    double pow_6(double);
    double pow_7(double);
    double pow_8(double);
    double pow_9(double);
    double pow_10(double);
    double pow_11(double);
    double pow_12(double);
    double pow_13(double);
    double pow_14(double);
    double pow_15(double);
    double pow_16(double);
    double pow_17(double);
    double pow_18(double);
    double pow_19(double);
    double pow_20(double);

    static double (*FAST_POW[23])(double) {pow_0, pow_1, pow_2, pow_3, pow_4, pow_5,
                                      pow_6, pow_7, pow_8, pow_9, pow_10, pow_11,
                                      pow_12, pow_13, pow_14, pow_15, pow_16, pow_17,
                                      pow_18, pow_19, pow_20, pow_m1, pow_m2};


    const double GAMMA[30] = {
        1.7724538509055,
        1.0,
        0.88622692545275,
        1.0,
        1.3293403881791,
        2.0,
        3.3233509704478,
        6.0,
        11.631728396567,
        24.0,
        52.342777784553,
        120.0,
        287.88527781504,
        720.0,
        1871.2543057978,
        5040.0,
        14034.407293483,
        40320.0,
        1.1929246199461e5,
        3.62880e5,
        1.1332783889488e6,
        3.628800e6,
        1.1899423083962e7,
        3.9916800e7,
        1.3684336546556e8,
        4.79001600e8,
        1.7105420683196e9,
        6.227020800e9,
        2.3092317922314e10,
        8.7178291200e10
    };

    TwoIndex<double> realSphericalHarmonics(int lmax, double x, double phi);

    double frobenius_norm(const TwoIndex<double>& mat);

    void initFactorials();
}

#endif