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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;
+ }
+}