tanhDeriv.cpp

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/*
 *  Copyright (c) 2018, Martin Duy Tat
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 *     prior written permission.
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#include <gsl/gsl_integration.h>
#include <gsl/gsl_complex.h>
#include <gsl/gsl_complex_math.h>
#include <gsl/gsl_sf_pow_int.h>
#include <gsl/gsl_math.h>
#include <gsl/gsl_errno.h>
#include <gsl/gsl_sf_gamma.h>
#include "tanhDeriv.h"

namespace tanhderiv {

struct my_f_params {
    double a;
    double s0;
    double lambdaleft;
    double lambdaright;
    double r;
    int n;
};

double my_f (double x, void *p) {
    struct my_f_params *params = (struct my_f_params *)p;
    gsl_complex z = gsl_complex_add(gsl_complex_rect(params->a, 0),
                                    gsl_complex_polar(params->r, x));
    gsl_complex z1 = gsl_complex_div(gsl_complex_add(z,
                                     gsl_complex_rect(params->s0, 0)),
                                     gsl_complex_rect(params->lambdaleft, 0));
    gsl_complex z2 = gsl_complex_div(gsl_complex_sub(z,
                                     gsl_complex_rect(params->s0, 0)),
                                     gsl_complex_rect(params->lambdaright, 0));
    gsl_complex func = gsl_complex_div(gsl_complex_sub(gsl_complex_tanh(z1),
                                       gsl_complex_tanh(z2)),
                                       gsl_complex_rect(2, 0));
    func = gsl_complex_mul(func, gsl_complex_polar(1, -params->n * x));
    return gsl_sf_fact(params->n) * GSL_REAL(func)
           / (2 * M_PI * gsl_sf_pow_int(params->r, params->n));
}

double integrate(const double &a,
                 const double &s0,
                 const double &lambdaleft,
                 const double &lambdaright,
                 const int &n) {
    gsl_function F;
    double radius = gsl_hypot(a - 2, lambdaright * M_PI / 2) - 0.01;
    double radius2 = gsl_hypot(a + 2, lambdaleft * M_PI / 2) - 0.01;
    if (radius > radius2) radius = radius2;
    struct my_f_params params = {a, s0, lambdaleft, lambdaright, radius, n};
    F.function = &my_f;
    F.params = &params;
    gsl_integration_workspace *w = gsl_integration_workspace_alloc(100);
    double error = gsl_sf_pow_int(10, -12);
    double *result = new double;
    double *abserr = new double;
    gsl_set_error_handler_off();
    int status = gsl_integration_qag(&F, 0, 2 * M_PI, 0, error,
                                     100, 6, w, result, abserr);
    gsl_integration_workspace_free(w);
    double finalResult = *result;
    delete result;
    delete abserr;
    if (status) {
        return 0;
    }
    else return finalResult;
}

}