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/* Library libcerf:
* Compute complex error functions, based on a new implementation of
* Faddeeva's w_of_z. Also provide Dawson and Voigt functions.
*
* File width.c:
* Computate voigt_hwhm, using Newton's iteration.
*
* Copyright:
* (C) 2018 Forschungszentrum Jülich GmbH
*
* Licence:
* 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.
*
* Authors:
* Joachim Wuttke, Forschungszentrum Jülich, 2018
*
* Website:
* http://apps.jcns.fz-juelich.de/libcerf
*
* Revision history:
* ../CHANGELOG
*
* Man pages:
* voigt_fwhm(3)
*/
/*
This file is patched by Hans Hagen for usage in LuaMetaTeX where we don't want to exit on an
error so we intercept it.
*/
#include "cerf.h"
#include <math.h>
#include <stdio.h>
#include <stdlib.h>
double dvoigt(double x, double sigma, double gamma, double v0)
{
return voigt(x, sigma, gamma)/v0 - .5;
}
double voigt_hwhm(double sigma, double gamma, int *error)
{
*error = 0;
if (sigma == 0 && gamma == 0) {
return 0;
} else if (isnan(sigma) || isnan(gamma)) {
*error = 1;
return 0; // return NAN;
} else {
// start from an excellent approximation [Olivero & Longbothum, J Quant Spec Rad Transf 1977]:
const double eps = 1e-14;
const double hwhm0 = .5*(1.06868*gamma+sqrt(0.86743*gamma*gamma+4*2*log(2)*sigma*sigma));
const double del = eps*hwhm0;
double ret = hwhm0;
const double v0 = voigt(0, sigma, gamma);
for (int i=0; i<300; ++i) {
double val = dvoigt(ret, sigma, gamma, v0);
if (fabs(val) < 1e-15) {
return ret;
} else {
double step = -del/(dvoigt(ret+del, sigma, gamma, v0)/val-1);
double nxt = ret + step;
if (nxt < ret/3) {
*error = 2; // fprintf(stderr, "voigt_fwhm terminated because of huge deviation from 1st approx\n");
nxt = ret/3;
} else if (nxt > 2*ret) {
*error = 2; // fprintf(stderr, "voigt_fwhm terminated because of huge deviation from 1st approx\n");
nxt = 2*ret;
}
if (fabs(ret-nxt) < del) {
return nxt;
} else {
ret = nxt;
}
}
}
*error = 3; // fprintf(stderr, "voigt_fwhm failed: Newton's iteration did not converge with sigma = %f and gamma = %f\n", sigma, gamma); exit(-1);
return 0;
}
}
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