Initial commit based on Ovidio version of python-scattnlay 0.3.0

COPYING

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+    Copyright (C) 2009-2013 Ovidio Peña <ovidio@bytesfall.com>
+
+    This program is free software: you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    The only additional remark is that we expect that all publications
+    describing work using this software, or all commercial products
+    using it, cite the following reference:
+    [1] O. Peña and U. Pal, "Scattering of electromagnetic radiation by
+        a multilayered sphere," Computer Physics Communications,
+        vol. 180, Nov. 2009, pp. 2348-2354.
+
+    You should have received a copy of the GNU General Public License
+    along with this program.  If not, see <http://www.gnu.org/licenses/>.
+

LICENSE

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+                    GNU GENERAL PUBLIC LICENSE
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+to choose that version for the Program.
+
+  Later license versions may give you additional or different
+permissions.  However, no additional obligations are imposed on any
+author or copyright holder as a result of your choosing to follow a
+later version.
+
+  15. Disclaimer of Warranty.
+
+  THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY
+APPLICABLE LAW.  EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT
+HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY
+OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO,
+THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
+PURPOSE.  THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM
+IS WITH YOU.  SHOULD THE PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF
+ALL NECESSARY SERVICING, REPAIR OR CORRECTION.
+
+  16. Limitation of Liability.
+
+  IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING
+WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR CONVEYS
+THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY
+GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE
+USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF
+DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD
+PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS),
+EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF
+SUCH DAMAGES.
+
+  17. Interpretation of Sections 15 and 16.
+
+  If the disclaimer of warranty and limitation of liability provided
+above cannot be given local legal effect according to their terms,
+reviewing courts shall apply local law that most closely approximates
+an absolute waiver of all civil liability in connection with the
+Program, unless a warranty or assumption of liability accompanies a
+copy of the Program in return for a fee.
+
+                     END OF TERMS AND CONDITIONS
+
+            How to Apply These Terms to Your New Programs
+
+  If you develop a new program, and you want it to be of the greatest
+possible use to the public, the best way to achieve this is to make it
+free software which everyone can redistribute and change under these terms.
+
+  To do so, attach the following notices to the program.  It is safest
+to attach them to the start of each source file to most effectively
+state the exclusion of warranty; and each file should have at least
+the "copyright" line and a pointer to where the full notice is found.
+
+    <one line to give the program's name and a brief idea of what it does.>
+    Copyright (C) <year>  <name of author>
+
+    This program is free software: you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License
+    along with this program.  If not, see <http://www.gnu.org/licenses/>.
+
+Also add information on how to contact you by electronic and paper mail.
+
+  If the program does terminal interaction, make it output a short
+notice like this when it starts in an interactive mode:
+
+    <program>  Copyright (C) <year>  <name of author>
+    This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'.
+    This is free software, and you are welcome to redistribute it
+    under certain conditions; type `show c' for details.
+
+The hypothetical commands `show w' and `show c' should show the appropriate
+parts of the General Public License.  Of course, your program's commands
+might be different; for a GUI interface, you would use an "about box".
+
+  You should also get your employer (if you work as a programmer) or school,
+if any, to sign a "copyright disclaimer" for the program, if necessary.
+For more information on this, and how to apply and follow the GNU GPL, see
+<http://www.gnu.org/licenses/>.
+
+  The GNU General Public License does not permit incorporating your program
+into proprietary programs.  If your program is a subroutine library, you
+may consider it more useful to permit linking proprietary applications with
+the library.  If this is what you want to do, use the GNU Lesser General
+Public License instead of this License.  But first, please read
+<http://www.gnu.org/philosophy/why-not-lgpl.html>.

MANIFEST.in

@@ -0,0 +1,14 @@
+include COPYING
+include LICENSE
+include README
+include CHANGES
+include MANIFEST.in
+include setup.py
+include ucomplex.h
+include nmie.h
+include py_nmie.h
+include standalone.c
+include Makefile
+include tests/python/*
+include tests/shell/*
+include debian/*

Makefile

@@ -0,0 +1,43 @@
+PYTHON=`which python`
+DESTDIR=/
+BUILDIR=$(CURDIR)/debian/python-scattnlay
+PROJECT=python-scattnlay
+VERSION=0.3.0
+
+all:
+	@echo "make source - Create source package"
+	@echo "make install - Install on local system"
+	@echo "make buildrpm - Generate a rpm package"
+	@echo "make builddeb - Generate a deb package"
+	@echo "make standalone - Create a standalone program"
+	@echo "make clean - Delete temporal files"
+
+source:
+	$(PYTHON) setup.py sdist $(COMPILE) --dist-dir=../
+
+install:
+	$(PYTHON) setup.py install --root $(DESTDIR) $(COMPILE)
+
+buildrpm:
+	#$(PYTHON) setup.py bdist_rpm --post-install=rpm/postinstall --pre-uninstall=rpm/preuninstall
+	$(PYTHON) setup.py bdist_rpm --dist-dir=../
+
+builddeb:
+	# build the source package in the parent directory
+	# then rename it to project_version.orig.tar.gz
+	$(PYTHON) setup.py sdist $(COMPILE) --dist-dir=../ --prune
+	rename -f 's/$(PROJECT)-(.*)\.tar\.gz/$(PROJECT)_$$1\.orig\.tar\.gz/' ../*
+	# build the package
+	dpkg-buildpackage -i -I -rfakeroot
+
+standalone: standalone.cc nmie.cc ucomplex.cc
+	cc standalone.cc nmie.cc ucomplex.cc -lm -o scattnlay
+	mv scattnlay ../
+
+clean:
+	$(PYTHON) setup.py clean
+	$(MAKE) -f $(CURDIR)/debian/rules clean
+	rm -rf build/ MANIFEST
+	find . -name '*.pyc' -delete
+	find . -name '*.o' -delete
+	find . -name '*.so' -delete

PKG-INFO

@@ -0,0 +1,11 @@
+Metadata-Version: 1.0
+Name: python-scattnlay
+Version: 0.3.0
+Summary: Calculation of the scattering of EM radiation by a multilayered sphere
+Home-page: http://scattering.sourceforge.net/
+Author: Ovidio Peña Rodríguez
+Author-email: ovidio@bytesfall.com
+License: GPL
+Description: The Python version of scattnlay, a computer implementation of the algorithm for the calculation of electromagnetic radiation scattering by a multilayered sphere developed by Yang. It has been shown that the program is effective, resulting in very accurate values of scattering efficiencies for a wide range of size parameters, which is a considerable improvement over previous implementations of similar algorithms. For details see: O. Pena, U. Pal, Comput. Phys. Commun. 180 (2009) 2348-2354.
+Keywords: Mie scattering,Multilayered sphere,Efficiency factors,Cross-sections
+Platform: any

README

@@ -0,0 +1,36 @@
+*******************************************************************************
+How to use scattnlay
+*******************************************************************************
+
+1. Compile Code:
+   (a) Compilation options
+	* make source - Create source package (python library)
+	* make install - Install on local system (python library)
+	* make buildrpm - Generate a rpm package (python library)
+	* make builddeb - Generate a deb package (python library)
+	* make standalone - Create a standalone program
+	* make clean - Delete temporal files
+
+*******************************************************************************
+2. Use:
+   (a) Python library
+      * Use scattnlay directly
+          from scattnlay import scattnlay
+          ...
+          x = ...
+          m = ...
+          terms, Qext, Qsca, Qabs, Qbk, Qpr, g, Albedo, S1, S2 = scattnlay(x, m)
+          ...
+
+      * Execute some of the test scripts (located in the folder 'tests/python')
+          Example:  ./test01.py
+
+   (b) Standalone program
+      * Execute scattnlay directly
+          Usage: scattnlay -l Layers x1 m1.r m1.i [x2 m2.r m2.i ...] [-c comment]
+
+      * Execute some of the test scripts (located in the folder 'tests/shell')
+          Example:  ./test01.sh > test01.csv
+
+*******************************************************************************
+

debian/changelog

@@ -0,0 +1,5 @@
+python-scattnlay (0.3.0-1) trusty; urgency=low
+
+  * Updated for Utopic Unicorn
+
+ -- Ovidio Peña Rodríguez <ovidio@bytesfall.com>  Thu, 13 November 2014 16:45:13 +0200

debian/compat

@@ -0,0 +1 @@
+7

debian/control

@@ -0,0 +1,21 @@
+Source: python-scattnlay
+Section: science
+Priority: optional
+Maintainer: Ovidio Peña Rodríguez <ovidio@bytesfall.com>
+Build-Depends: debhelper (>=7.0.0), python-numpy (>= 1.0), python-support (>= 0.6), cdbs (>= 0.4.49), python-all-dev, python-numpy-dev
+XS-Python-Version: >=2.4
+Standards-Version: 3.8.3
+
+Package: python-scattnlay
+Architecture: any
+Homepage: http://scattering.sourceforge.net/
+XB-Python-Version: ${python:Versions}
+Depends: ${shlibs:Depends}, ${misc:Depends}, ${python:Depends}, python-numpy (>= 1.0)
+Description: Calculation of the scattering of EM radiation by a multilayered sphere
+ The Python version of scattnlay, a computer implementation of the algorithm
+ for the calculation of electromagnetic radiation scattering by a multilayered
+ sphere developed by Yang. It has been shown that the program is effective,
+ resulting in very accurate values of scattering efficiencies for a wide range
+ of size parameters, which is a considerable improvement over previous
+ implementations of similar algorithms. For details see:
+ O. Peña, U. Pal, Comput. Phys. Commun. 180 (2009) 2348-2354.

debian/copyright

@@ -0,0 +1,37 @@
+This package was debianized by Ovidio Peña Rodríguez
+ on Fri, 11 Dec 2009 20:13:44 +0200.
+
+It was downloaded from http://sourceforge.net/projects/scattering/
+
+Upstream Author:
+
+    Ovidio Peña Rodríguez <ovidio@bytesfall.com>
+
+Copyright:
+
+    Copyright (C) 2009-2010 Ovidio Peña Rodríguez <ovidio@bytesfall.com>
+
+License:
+
+    This program is free software: you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    The only additional remark is that we expect that all publications
+    describing work using this software, or all commercial products
+    using it, cite the following reference:
+    [1] O. Peña and U. Pal, "Scattering of electromagnetic radiation by
+        a multilayered sphere," Computer Physics Communications,
+        vol. 180, Nov. 2009, pp. 2348-2354.
+
+    You should have received a copy of the GNU General Public License
+    along with this program.  If not, see <http://www.gnu.org/licenses/>.
+
+On Debian systems, the complete text of the GNU General
+Public License can be found in `/usr/share/common-licenses/GPL-3'.

debian/pycompat

@@ -0,0 +1 @@
+2

debian/rules

@@ -0,0 +1,12 @@
+#!/usr/bin/make -f
+# -*- makefile -*-
+
+DEB_PYTHON_SYSTEM := pysupport
+
+include /usr/share/cdbs/1/rules/debhelper.mk
+include /usr/share/cdbs/1/class/python-distutils.mk
+
+clean::
+	rm -rf build build-stamp configure-stamp build/ MANIFEST
+	dh_clean
+

debian/watch

@@ -0,0 +1,2 @@
+version=3
+http://sourceforge.net/scattering/python-scattering-(+.+)\.tar\.gz

nmie.cc

@@ -0,0 +1,809 @@
+//**********************************************************************************//
+//    Copyright (C) 2009-2015  Ovidio Pena <ovidio@bytesfall.com>                   //
+//                                                                                  //
+//    This file is part of scattnlay                                                //
+//                                                                                  //
+//    This program is free software: you can redistribute it and/or modify          //
+//    it under the terms of the GNU General Public License as published by          //
+//    the Free Software Foundation, either version 3 of the License, or             //
+//    (at your option) any later version.                                           //
+//                                                                                  //
+//    This program is distributed in the hope that it will be useful,               //
+//    but WITHOUT ANY WARRANTY; without even the implied warranty of                //
+//    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the                 //
+//    GNU General Public License for more details.                                  //
+//                                                                                  //
+//    The only additional remark is that we expect that all publications            //
+//    describing work using this software, or all commercial products               //
+//    using it, cite the following reference:                                       //
+//    [1] O. Pena and U. Pal, "Scattering of electromagnetic radiation by           //
+//        a multilayered sphere," Computer Physics Communications,                  //
+//        vol. 180, Nov. 2009, pp. 2348-2354.                                       //
+//                                                                                  //
+//    You should have received a copy of the GNU General Public License             //
+//    along with this program.  If not, see <http://www.gnu.org/licenses/>.         //
+//**********************************************************************************//
+
+//**********************************************************************************//
+// This library implements the algorithm for a multilayered sphere described by:    //
+//    [1] W. Yang, "Improved recursive algorithm for light scattering by a          //
+//        multilayered sphere,” Applied Optics,  vol. 42, Mar. 2003, pp. 1710-1720. //
+//                                                                                  //
+// You can find the description of all the used equations in:                       //
+//    [2] O. Pena and U. Pal, "Scattering of electromagnetic radiation by           //
+//        a multilayered sphere," Computer Physics Communications,                  //
+//        vol. 180, Nov. 2009, pp. 2348-2354.                                       //
+//                                                                                  //
+// Hereinafter all equations numbers refer to [2]                                   //
+//**********************************************************************************//
+#include <math.h>
+#include <stdlib.h>
+#include <stdio.h>
+#include "ucomplex.h"
+#include "nmie.h"
+
+#define round(x) ((x) >= 0 ? (int)((x) + 0.5):(int)((x) - 0.5))
+
+complex C_ZERO = {0.0, 0.0};
+complex C_ONE = {1.0, 0.0};
+complex C_I = {0.0, 1.0};
+
+int firstLayer(int L, int pl) {
+  if (pl >= 0) {
+    return pl;
+  } else {
+    return 0;
+  }
+}
+
+// Calculate Nstop - equation (17)
+int Nstop(double xL) {
+  int result;
+
+  if (xL <= 8) {
+    result = round(xL + 4*pow(xL, 1/3) + 1);
+  } else if (xL <= 4200) {
+    result = round(xL + 4.05*pow(xL, 1/3) + 2);
+  } else {
+    result = round(xL + 4*pow(xL, 1/3) + 2);
+  }
+
+  return result;
+}
+
+int Nmax(int L, int fl, int pl, double x[], complex m[]) {
+  int i, result, ri, riM1;
+
+  result = Nstop(x[L - 1]);
+  for (i = fl; i < L; i++) {
+    if (i > pl) {
+      ri = round(Cabs(RCmul(x[i], m[i])));
+    } else {
+      ri = 0;
+    }
+    if (result < ri) {
+      result = ri;
+    }
+
+    if ((i > fl) && ((i - 1) > pl)) {
+      riM1 = round(Cabs(RCmul(x[i - 1], m[i])));
+    } else {
+      riM1 = 0;
+    }
+    if (result < riM1) {
+      result = riM1;
+    }
+  }
+
+  return result + 15;
+}
+
+//**********************************************************************************//
+// This function calculates the spherical Bessel functions (jn and hn) for a given  //
+// value of r.                                                                      //
+//                                                                                  //
+// Input parameters:                                                                //
+//   r: Real argument to evaluate jn and hn                                         //
+//   n_max: Maximum number of terms to calculate jn and hn                          //
+//                                                                                  //
+// Output parameters:                                                               //
+//   jn, hn: Spherical Bessel functions (double)                                    //
+//**********************************************************************************//
+void sphericalBessel(double r, int n_max, double **j, double **h) {
+  int n;
+
+  (*j)[0] = sin(r)/r;
+  (*j)[1] = sin(r)/r/r - cos(r)/r;
+  (*h)[0] = -cos(r)/r;
+  (*h)[1] = -cos(r)/r/r - sin(r)/r;
+  for (n = 2; n < n_max; n++) {
+    (*j)[n] = (n + n + 1)*(*j)[n - 1]/r - (*j)[n - 2];
+    (*h)[n] = (n + n + 1)*(*h)[n - 1]/r - (*h)[n - 2];
+  }
+}
+
+//**********************************************************************************//
+// This function calculates the spherical Bessel functions (jn and hn) for a given  //
+// value of z.                                                                      //
+//                                                                                  //
+// Input parameters:                                                                //
+//   z: Real argument to evaluate jn and hn                                         //
+//   n_max: Maximum number of terms to calculate jn and hn                          //
+//                                                                                  //
+// Output parameters:                                                               //
+//   jn, hn: Spherical Bessel functions (complex)                                   //
+//**********************************************************************************//
+void CsphericalBessel(complex z, int n_max, complex **j, complex **h) {
+  int n;
+
+  (*j)[0] = Cdiv(Csin(z), z);
+  (*j)[1] = Csub(Cdiv(Cdiv(Csin(z), z), z), Cdiv(Ccos(z), z));
+  (*h)[0] = Csub(C_ZERO, Cdiv(Ccos(z), z));
+  (*h)[1] = Csub(C_ZERO, Cadd(Cdiv(Cdiv(Ccos(z), z), z), Cdiv(Csin(z), z)));
+  for (n = 2; n < n_max; n++) {
+    (*j)[n] = Csub(RCmul(n + n + 1, Cdiv((*j)[n - 1], z)), (*j)[n - 2]);
+    (*h)[n] = Csub(RCmul(n + n + 1, Cdiv((*h)[n - 1], z)), (*h)[n - 2]);
+  }
+}
+
+// Calculate an - equation (5)
+complex calc_an(int n, double XL, complex Ha, complex mL, complex PsiXL, complex ZetaXL, complex PsiXLM1, complex ZetaXLM1) {
+  complex Num = Csub(Cmul(Cadd(Cdiv(Ha, mL), Complex(n/XL, 0)), PsiXL), PsiXLM1);
+  complex Denom = Csub(Cmul(Cadd(Cdiv(Ha, mL), Complex(n/XL, 0)), ZetaXL), ZetaXLM1);
+
+  return Cdiv(Num, Denom);
+}
+
+// Calculate bn - equation (6)
+complex calc_bn(int n, double XL, complex Hb, complex mL, complex PsiXL, complex ZetaXL, complex PsiXLM1, complex ZetaXLM1) {
+  complex Num = Csub(Cmul(Cadd(Cmul(Hb, mL), Complex(n/XL, 0)), PsiXL), PsiXLM1);
+  complex Denom = Csub(Cmul(Cadd(Cmul(Hb, mL), Complex(n/XL, 0)), ZetaXL), ZetaXLM1);
+
+  return Cdiv(Num, Denom);
+}
+
+// Calculates S1_n - equation (25a)
+complex calc_S1_n(int n, complex an, complex bn, double Pin, double Taun) {
+  return RCmul((double)(n + n + 1)/(double)(n*n + n), Cadd(RCmul(Pin, an), RCmul(Taun, bn)));
+}
+
+// Calculates S2_n - equation (25b) (it's the same as (25a), just switches Pin and Taun)
+complex calc_S2_n(int n, complex an, complex bn, double Pin, double Taun) {
+  return calc_S1_n(n, an, bn, Taun, Pin);
+}
+
+//**********************************************************************************//
+// This function calculates the Riccati-Bessel functions (Psi and Zeta) for a       //
+// given value of z.                                                                //
+//                                                                                  //
+// Input parameters:                                                                //
+//   z: Complex argument to evaluate Psi and Zeta                                   //
+//   n_max: Maximum number of terms to calculate Psi and Zeta                       //
+//                                                                                  //
+// Output parameters:                                                               //
+//   Psi, Zeta: Riccati-Bessel functions                                            //
+//**********************************************************************************//
+void calcPsiZeta(complex z, int n_max, complex *D1, complex *D3, complex **Psi, complex **Zeta) {
+  int n;
+  complex cn;
+
+  //Upward recurrence for Psi and Zeta - equations (20a) - (21b)
+  (*Psi)[0] = Complex(sin(z.r), 0);
+  (*Zeta)[0] = Complex(sin(z.r), -cos(z.r));
+  for (n = 1; n <= n_max; n++) {
+    cn = Complex(n, 0);
+    (*Psi)[n] = Cmul((*Psi)[n - 1], Csub(Cdiv(cn, z), D1[n - 1]));
+    (*Zeta)[n] = Cmul((*Zeta)[n - 1], Csub(Cdiv(cn, z), D3[n - 1]));
+  }
+}
+
+//**********************************************************************************//
+// This function calculates the logarithmic derivatives of the Riccati-Bessel       //
+// functions (D1 and D3) for a given value of z.                                    //
+//                                                                                  //
+// Input parameters:                                                                //
+//   z: Complex argument to evaluate D1 and D3                                      //
+//   n_max: Maximum number of terms to calculate D1 and D3                          //
+//                                                                                  //
+// Output parameters:                                                               //
+//   D1, D3: Logarithmic derivatives of the Riccati-Bessel functions                //
+//**********************************************************************************//
+void calcD1D3(complex z, int n_max, complex **D1, complex **D3) {
+  int n;
+  complex cn;
+  complex *PsiZeta = (complex *) malloc((n_max + 1)*sizeof(complex));
+
+  // Downward recurrence for D1 - equations (16a) and (16b)
+  (*D1)[n_max] = C_ZERO;
+  for (n = n_max; n > 0; n--) {
+    cn = Complex(n, 0);
+    (*D1)[n - 1] = Csub(Cdiv(cn, z), Cdiv(C_ONE, Cadd((*D1)[n], Cdiv(cn, z))));
+  }
+
+  // Upward recurrence for PsiZeta and D3 - equations (18a) - (18d)
+  PsiZeta[0] = RCmul(0.5, Csub(C_ONE, Cmul(Complex(cos(2*z.r), sin(2*z.r)), Complex(exp(-2*z.i), 0))));
+  (*D3)[0] = C_I;
+  for (n = 1; n <= n_max; n++) {
+    cn = Complex(n, 0);
+    PsiZeta[n] = Cmul(PsiZeta[n - 1], Cmul(Csub(Cdiv(cn, z), (*D1)[n - 1]), Csub(Cdiv(cn, z), (*D3)[n - 1])));
+    (*D3)[n] = Cadd((*D1)[n], Cdiv(C_I, PsiZeta[n]));
+  }
+
+  free(PsiZeta);
+}
+
+//**********************************************************************************//
+// This function calculates Pi and Tau for all values of Theta.                     //
+//                                                                                  //
+// Input parameters:                                                                //
+//   n_max: Maximum number of terms to calculate Pi and Tau                         //
+//   nTheta: Number of scattering angles                                            //
+//   Theta: Array containing all the scattering angles where the scattering         //
+//          amplitudes will be calculated                                           //
+//                                                                                  //
+// Output parameters:                                                               //
+//   Pi, Tau: Angular functions Pi and Tau, as defined in equations (26a) - (26c)   //
+//**********************************************************************************//
+void calcPiTau(int n_max, int nTheta, double Theta[], double ***Pi, double ***Tau) {
+  int n, t;
+
+  for (n = 0; n < n_max; n++) {
+    //****************************************************//
+    // Equations (26a) - (26c)                            //
+    //****************************************************//
+    for (t = 0; t < nTheta; t++) {
+      if (n == 0) {
+        // Initialize Pi and Tau
+        (*Pi)[n][t] = 1.0;
+        (*Tau)[n][t] = (n + 1)*cos(Theta[t]);
+      } else {
+        // Calculate the actual values
+        (*Pi)[n][t] = ((n == 1) ?  ((n + n + 1)*cos(Theta[t])*(*Pi)[n - 1][t]/n)
+                                : (((n + n + 1)*cos(Theta[t])*(*Pi)[n - 1][t] - (n + 1)*(*Pi)[n - 2][t])/n));
+        (*Tau)[n][t] = (n + 1)*cos(Theta[t])*(*Pi)[n][t] - (n + 2)*(*Pi)[n - 1][t];
+      }
+    }
+  }
+}
+
+//**********************************************************************************//
+// This function calculates the scattering coefficients required to calculate       //
+// both the near- and far-field parameters.                                         //
+//                                                                                  //
+// Input parameters:                                                                //
+//   L: Number of layers                                                            //
+//   pl: Index of PEC layer. If there is none just send -1                          //
+//   x: Array containing the size parameters of the layers [0..L-1]                 //
+//   m: Array containing the relative refractive indexes of the layers [0..L-1]     //
+//   n_max: Maximum number of multipolar expansion terms to be used for the         //
+//          calculations. Only used if you know what you are doing, otherwise set   //
+//          this parameter to -1 and the function will calculate it.                //
+//                                                                                  //
+// Output parameters:                                                               //
+//   an, bn: Complex scattering amplitudes                                          //
+//                                                                                  //
+// Return value:                                                                    //
+//   Number of multipolar expansion terms used for the calculations                 //
+//**********************************************************************************//
+int ScattCoeff(int L, int pl, double x[], complex m[], int n_max, complex **an, complex **bn){
+  //************************************************************************//
+  // Calculate the index of the first layer. It can be either 0 (default)   //
+  // or the index of the outermost PEC layer. In the latter case all layers //
+  // below the PEC are discarded.                                           //
+  //************************************************************************//
+  int fl = firstLayer(L, pl);
+
+  if (n_max <= 0) {
+    n_max = Nmax(L, fl, pl, x, m);
+  }
+  
+  complex z1, z2, cn;
+  complex Num, Denom;
+  complex G1, G2;
+  complex Temp;
+  double Tmp;
+
+  int n, l, t;
+
+  //**************************************************************************//
+  // Note that since Fri, Nov 14, 2014 all arrays start from 0 (zero), which  //
+  // means that index = layer number - 1 or index = n - 1. The only exception //
+  // are the arrays for representing D1, D3 and Q because they need a value   //
+  // for the index 0 (zero), hence it is important to consider this shift     //
+  // between different arrays. The change was done to optimize memory usage.  //
+  //**************************************************************************//
+
+  // Allocate memory to the arrays
+  complex **D1_mlxl = (complex **) malloc(L*sizeof(complex *));
+  complex **D1_mlxlM1 = (complex **) malloc(L*sizeof(complex *));
+
+  complex **D3_mlxl = (complex **) malloc(L*sizeof(complex *));
+  complex **D3_mlxlM1 = (complex **) malloc(L*sizeof(complex *));
+
+  complex **Q = (complex **) malloc(L*sizeof(complex *));
+
+  complex **Ha = (complex **) malloc(L*sizeof(complex *));
+  complex **Hb = (complex **) malloc(L*sizeof(complex *));
+
+  for (l = 0; l < L; l++) {
+    D1_mlxl[l] = (complex *) malloc((n_max + 1)*sizeof(complex));
+    D1_mlxlM1[l] = (complex *) malloc((n_max + 1)*sizeof(complex));
+
+    D3_mlxl[l] = (complex *) malloc((n_max + 1)*sizeof(complex));
+    D3_mlxlM1[l] = (complex *) malloc((n_max + 1)*sizeof(complex));
+
+    Q[l] = (complex *) malloc((n_max + 1)*sizeof(complex));
+
+    Ha[l] = (complex *) malloc(n_max*sizeof(complex));
+    Hb[l] = (complex *) malloc(n_max*sizeof(complex));
+  }
+
+  (*an) = (complex *) malloc(n_max*sizeof(complex));
+  (*bn) = (complex *) malloc(n_max*sizeof(complex));
+
+  complex *D1XL = (complex *) malloc((n_max + 1)*sizeof(complex));
+  complex *D3XL = (complex *) malloc((n_max + 1)*sizeof(complex));
+
+  complex *PsiXL = (complex *) malloc((n_max + 1)*sizeof(complex));
+  complex *ZetaXL = (complex *) malloc((n_max + 1)*sizeof(complex));
+
+  //*************************************************//
+  // Calculate D1 and D3 for z1 in the first layer   //
+  //*************************************************//
+  if (fl == pl) {  // PEC layer
+    for (n = 0; n <= n_max; n++) {
+      D1_mlxl[fl][n] = Complex(0, -1);
+      D3_mlxl[fl][n] = C_I;
+    }
+  } else { // Regular layer
+    z1 = RCmul(x[fl], m[fl]);
+
+    // Calculate D1 and D3
+    calcD1D3(z1, n_max, &(D1_mlxl[fl]), &(D3_mlxl[fl]));
+  }
+
+  //******************************************************************//
+  // Calculate Ha and Hb in the first layer - equations (7a) and (8a) //
+  //******************************************************************//
+  for (n = 0; n < n_max; n++) {
+    Ha[fl][n] = D1_mlxl[fl][n + 1];
+    Hb[fl][n] = D1_mlxl[fl][n + 1];
+  }
+
+  //*****************************************************//
+  // Iteration from the second layer to the last one (L) //
+  //*****************************************************//
+  for (l = fl + 1; l < L; l++) {
+    //************************************************************//
+    //Calculate D1 and D3 for z1 and z2 in the layers fl+1..L     //
+    //************************************************************//
+    z1 = RCmul(x[l], m[l]);
+    z2 = RCmul(x[l - 1], m[l]);
+
+    //Calculate D1 and D3 for z1
+    calcD1D3(z1, n_max, &(D1_mlxl[l]), &(D3_mlxl[l]));
+
+    //Calculate D1 and D3 for z2
+    calcD1D3(z2, n_max, &(D1_mlxlM1[l]), &(D3_mlxlM1[l]));
+
+    //*********************************************//
+    //Calculate Q, Ha and Hb in the layers fl+1..L //
+    //*********************************************//
+
+    // Upward recurrence for Q - equations (19a) and (19b)
+    Num = RCmul(exp(-2*(z1.i - z2.i)), Complex(cos(-2*z2.r) - exp(-2*z2.i), sin(-2*z2.r)));
+    Denom = Complex(cos(-2*z1.r) - exp(-2*z1.i), sin(-2*z1.r));
+    Q[l][0] = Cdiv(Num, Denom);
+
+    for (n = 1; n <= n_max; n++) {
+      cn = Complex(n, 0);
+      Num = Cmul(Cadd(Cmul(z1, D1_mlxl[l][n]), cn), Csub(cn, Cmul(z1, D3_mlxl[l][n - 1])));
+      Denom = Cmul(Cadd(Cmul(z2, D1_mlxlM1[l][n]), cn), Csub(cn, Cmul(z2, D3_mlxlM1[l][n - 1])));
+
+      Q[l][n] = Cdiv(Cmul(RCmul((x[l - 1]*x[l - 1])/(x[l]*x[l]), Q[l][n - 1]), Num), Denom);
+    }
+
+    // Upward recurrence for Ha and Hb - equations (7b), (8b) and (12) - (15)
+    for (n = 1; n <= n_max; n++) {
+      //Ha
+      if ((l - 1) == pl) { // The layer below the current one is a PEC layer
+        G1 = RCmul(-1.0, D1_mlxlM1[l][n]);
+        G2 = RCmul(-1.0, D3_mlxlM1[l][n]);
+      } else {
+        G1 = Csub(Cmul(m[l], Ha[l - 1][n - 1]), Cmul(m[l - 1], D1_mlxlM1[l][n]));
+        G2 = Csub(Cmul(m[l], Ha[l - 1][n - 1]), Cmul(m[l - 1], D3_mlxlM1[l][n]));
+      }
+
+      Temp = Cmul(Q[l][n], G1);
+
+      Num = Csub(Cmul(G2, D1_mlxl[l][n]), Cmul(Temp, D3_mlxl[l][n]));
+      Denom = Csub(G2, Temp);
+
+      Ha[l][n - 1] = Cdiv(Num, Denom);
+
+      //Hb
+      if ((l - 1) == pl) { // The layer below the current one is a PEC layer
+        G1 = Hb[l - 1][n - 1];
+        G2 = Hb[l - 1][n - 1];
+      } else {
+        G1 = Csub(Cmul(m[l - 1], Hb[l - 1][n - 1]), Cmul(m[l], D1_mlxlM1[l][n]));
+        G2 = Csub(Cmul(m[l - 1], Hb[l - 1][n - 1]), Cmul(m[l], D3_mlxlM1[l][n]));
+      }
+
+      Temp = Cmul(Q[l][n], G1);
+
+      Num = Csub(Cmul(G2, D1_mlxl[l][n]), Cmul(Temp, D3_mlxl[l][n]));
+      Denom = Csub(G2, Temp);
+
+      Hb[l][n - 1] = Cdiv(Num, Denom);
+    }
+  }
+
+  //**************************************//
+  //Calculate D1, D3, Psi and Zeta for XL //
+  //**************************************//
+  z1 = Complex(x[L - 1], 0);
+
+  // Calculate D1XL and D3XL
+  calcD1D3(z1, n_max, &D1XL, &D3XL);
+
+  // Calculate PsiXL and ZetaXL
+  calcPsiZeta(z1, n_max, D1XL, D3XL, &PsiXL, &ZetaXL);
+
+  //*********************************************************************//
+  // Finally, we calculate the scattering coefficients (an and bn) and   //
+  // the angular functions (Pi and Tau). Note that for these arrays the  //
+  // first layer is 0 (zero), in future versions all arrays will follow  //
+  // this convention to save memory. (13 Nov, 2014)                      //
+  //*********************************************************************//
+  for (n = 0; n < n_max; n++) {
+    //********************************************************************//
+    //Expressions for calculating an and bn coefficients are not valid if //
+    //there is only one PEC layer (ie, for a simple PEC sphere).          //
+    //********************************************************************//
+    if (pl < (L - 1)) {
+      (*an)[n] = calc_an(n + 1, x[L - 1], Ha[L - 1][n], m[L - 1], PsiXL[n + 1], ZetaXL[n + 1], PsiXL[n], ZetaXL[n]);
+      (*bn)[n] = calc_bn(n + 1, x[L - 1], Hb[L - 1][n], m[L - 1], PsiXL[n + 1], ZetaXL[n + 1], PsiXL[n], ZetaXL[n]);
+    } else {
+      (*an)[n] = calc_an(n + 1, x[L - 1], C_ZERO, C_ONE, PsiXL[n + 1], ZetaXL[n + 1], PsiXL[n], ZetaXL[n]);
+      (*bn)[n] = Cdiv(PsiXL[n + 1], ZetaXL[n + 1]);
+    }
+  }
+
+  // Free the memory used for the arrays
+  for (l = 0; l < L; l++) {
+    free(D1_mlxl[l]);
+    free(D1_mlxlM1[l]);
+
+    free(D3_mlxl[l]);
+    free(D3_mlxlM1[l]);
+
+    free(Q[l]);
+
+    free(Ha[l]);
+    free(Hb[l]);
+  }
+
+  free(D1_mlxl);
+  free(D1_mlxlM1);
+
+  free(D3_mlxl);
+  free(D3_mlxlM1);
+
+  free(Q);
+
+  free(Ha);
+  free(Hb);
+
+  free(D1XL);
+  free(D3XL);
+
+  free(PsiXL);
+  free(ZetaXL);
+
+  return n_max;
+}
+
+//**********************************************************************************//
+// This function is just a wrapper to call the function 'nMieScatt' with fewer      //
+// parameters, it is here mainly for compatibility with older versions of the       //
+// program. Also, you can use it if you neither have a PEC layer nor want to define //
+// any limit for the maximum number of terms.                                       //
+//**********************************************************************************//
+
+int nMie(int L, double x[], complex m[], int nTheta, double Theta[], double *Qext, double *Qsca, double *Qabs, double *Qbk, double *Qpr, double *g, double *Albedo, complex S1[], complex S2[]) {
+
+  return nMieScatt(L, -1, x, m, nTheta, Theta, -1, Qext, Qsca, Qabs, Qbk, Qpr, g, Albedo, S1, S2);
+}
+
+//**********************************************************************************//
+// This function is just a wrapper to call the function 'nMieScatt' with fewer      //
+// parameters, it is useful if you want to include a PEC layer but not a limit      //
+// for the maximum number of terms.                                                 //
+//                                                                                  //
+// Input parameters:                                                                //
+//   L: Number of layers                                                            //
+//   pl: Index of PEC layer. If there is none just send -1                          //
+//   x: Array containing the size parameters of the layers [0..L-1]                 //
+//   m: Array containing the relative refractive indexes of the layers [0..L-1]     //
+//   nTheta: Number of scattering angles                                            //
+//   Theta: Array containing all the scattering angles where the scattering         //
+//          amplitudes will be calculated                                           //
+//                                                                                  //
+// Output parameters:                                                               //
+//   Qext: Efficiency factor for extinction                                         //
+//   Qsca: Efficiency factor for scattering                                         //
+//   Qabs: Efficiency factor for absorption (Qabs = Qext - Qsca)                    //
+//   Qbk: Efficiency factor for backscattering                                      //
+//   Qpr: Efficiency factor for the radiation pressure                              //
+//   g: Asymmetry factor (g = (Qext-Qpr)/Qsca)                                      //
+//   Albedo: Single scattering albedo (Albedo = Qsca/Qext)                          //
+//   S1, S2: Complex scattering amplitudes                                          //
+//                                                                                  //
+// Return value:                                                                    //
+//   Number of multipolar expansion terms used for the calculations                 //
+//**********************************************************************************//
+
+int nMiePEC(int L, int pl, double x[], complex m[], int nTheta, double Theta[], double *Qext, double *Qsca, double *Qabs, double *Qbk, double *Qpr, double *g, double *Albedo, complex S1[], complex S2[]) {
+
+  return nMieScatt(L, pl, x, m, nTheta, Theta, -1, Qext, Qsca, Qabs, Qbk, Qpr, g, Albedo, S1, S2);
+}
+
+//**********************************************************************************//
+// This function is just a wrapper to call the function 'nMieScatt' with fewer      //
+// parameters, it is useful if you want to include a limit for the maximum number   //
+// of terms but not a PEC layer.                                                    //
+//                                                                                  //
+// Input parameters:                                                                //
+//   L: Number of layers                                                            //
+//   x: Array containing the size parameters of the layers [0..L-1]                 //
+//   m: Array containing the relative refractive indexes of the layers [0..L-1]     //
+//   nTheta: Number of scattering angles                                            //
+//   Theta: Array containing all the scattering angles where the scattering         //
+//          amplitudes will be calculated                                           //
+//   n_max: Maximum number of multipolar expansion terms to be used for the         //
+//          calculations. Only used if you know what you are doing, otherwise set   //
+//          this parameter to -1 and the function will calculate it                 //
+//                                                                                  //
+// Output parameters:                                                               //
+//   Qext: Efficiency factor for extinction                                         //
+//   Qsca: Efficiency factor for scattering                                         //
+//   Qabs: Efficiency factor for absorption (Qabs = Qext - Qsca)                    //
+//   Qbk: Efficiency factor for backscattering                                      //
+//   Qpr: Efficiency factor for the radiation pressure                              //
+//   g: Asymmetry factor (g = (Qext-Qpr)/Qsca)                                      //
+//   Albedo: Single scattering albedo (Albedo = Qsca/Qext)                          //
+//   S1, S2: Complex scattering amplitudes                                          //
+//                                                                                  //
+// Return value:                                                                    //
+//   Number of multipolar expansion terms used for the calculations                 //
+//**********************************************************************************//
+
+int nMieMax(int L, double x[], complex m[], int nTheta, double Theta[], int n_max, double *Qext, double *Qsca, double *Qabs, double *Qbk, double *Qpr, double *g, double *Albedo, complex S1[], complex S2[]) {
+
+  return nMieScatt(L, -1, x, m, nTheta, Theta, n_max, Qext, Qsca, Qabs, Qbk, Qpr, g, Albedo, S1, S2);
+}
+
+//**********************************************************************************//
+// This function calculates the actual scattering parameters and amplitudes         //
+//                                                                                  //
+// Input parameters:                                                                //
+//   L: Number of layers                                                            //
+//   pl: Index of PEC layer. If there is none just send -1                          //
+//   x: Array containing the size parameters of the layers [0..L-1]                 //
+//   m: Array containing the relative refractive indexes of the layers [0..L-1]     //
+//   nTheta: Number of scattering angles                                            //
+//   Theta: Array containing all the scattering angles where the scattering         //
+//          amplitudes will be calculated                                           //
+//   n_max: Maximum number of multipolar expansion terms to be used for the         //
+//          calculations. Only used if you know what you are doing, otherwise set   //
+//          this parameter to -1 and the function will calculate it                 //
+//                                                                                  //
+// Output parameters:                                                               //
+//   Qext: Efficiency factor for extinction                                         //
+//   Qsca: Efficiency factor for scattering                                         //
+//   Qabs: Efficiency factor for absorption (Qabs = Qext - Qsca)                    //
+//   Qbk: Efficiency factor for backscattering                                      //
+//   Qpr: Efficiency factor for the radiation pressure                              //
+//   g: Asymmetry factor (g = (Qext-Qpr)/Qsca)                                      //
+//   Albedo: Single scattering albedo (Albedo = Qsca/Qext)                          //
+//   S1, S2: Complex scattering amplitudes                                          //
+//                                                                                  //
+// Return value:                                                                    //
+//   Number of multipolar expansion terms used for the calculations                 //
+//**********************************************************************************//
+
+int nMieScatt(int L, int pl, double x[], complex m[], int nTheta, double Theta[], int n_max, double *Qext, double *Qsca, double *Qabs, double *Qbk, double *Qpr, double *g, double *Albedo, complex S1[], complex S2[]) {
+  int i, n, t;
+  double **Pi, **Tau;
+  complex *an, *bn;
+  complex Qbktmp;
+
+  n_max = ScattCoeff(L, pl, x, m, n_max, &an, &bn);
+
+  Pi = (double **) malloc(n_max*sizeof(double *));
+  Tau = (double **) malloc(n_max*sizeof(double *));
+  for (n = 0; n < n_max; n++) {
+    Pi[n] = (double *) malloc(nTheta*sizeof(double));
+    Tau[n] = (double *) malloc(nTheta*sizeof(double));
+  }
+
+  calcPiTau(n_max, nTheta, Theta, &Pi, &Tau);
+
+  double x2 = x[L - 1]*x[L - 1];
+
+  // Initialize the scattering parameters
+  *Qext = 0;
+  *Qsca = 0;
+  *Qabs = 0;
+  *Qbk = 0;
+  Qbktmp = C_ZERO;
+  *Qpr = 0;
+  *g = 0;
+  *Albedo = 0;
+
+  // Initialize the scattering amplitudes
+  for (t = 0; t < nTheta; t++) {
+    S1[t] = C_ZERO;
+    S2[t] = C_ZERO;
+  }
+
+  // By using downward recurrence we avoid loss of precision due to float rounding errors
+  // See: https://docs.oracle.com/cd/E19957-01/806-3568/ncg_goldberg.html
+  //      http://en.wikipedia.org/wiki/Loss_of_significance
+  for (i = n_max - 2; i >= 0; i--) {
+    n = i + 1;
+    // Equation (27)
+    *Qext = *Qext + (double)(n + n + 1)*(an[i].r + bn[i].r);
+    // Equation (28)
+    *Qsca = *Qsca + (double)(n + n + 1)*(an[i].r*an[i].r + an[i].i*an[i].i + bn[i].r*bn[i].r + bn[i].i*bn[i].i);
+    // Equation (29)
+    *Qpr = *Qpr + ((n*(n + 2)/(n + 1))*((Cadd(Cmul(an[i], Conjg(an[n])), Cmul(bn[i], Conjg(bn[n])))).r) + ((double)(n + n + 1)/(n*(n + 1)))*(Cmul(an[i], Conjg(bn[i])).r));
+
+    // Equation (33)
+    Qbktmp = Cadd(Qbktmp, RCmul((double)((n + n + 1)*(1 - 2*(n % 2))), Csub(an[i], bn[i])));
+
+    //****************************************************//
+    // Calculate the scattering amplitudes (S1 and S2)    //
+    // Equations (25a) - (25b)                            //
+    //****************************************************//
+    for (t = 0; t < nTheta; t++) {
+      S1[t] = Cadd(S1[t], calc_S1_n(n, an[i], bn[i], Pi[i][t], Tau[i][t]));
+      S2[t] = Cadd(S2[t], calc_S2_n(n, an[i], bn[i], Pi[i][t], Tau[i][t]));
+    }
+  }
+
+  *Qext = 2*(*Qext)/x2;                                 // Equation (27)
+  *Qsca = 2*(*Qsca)/x2;                                 // Equation (28)
+  *Qpr = *Qext - 4*(*Qpr)/x2;                           // Equation (29)
+
+  *Qabs = *Qext - *Qsca;                                // Equation (30)
+  *Albedo = *Qsca / *Qext;                              // Equation (31)
+  *g = (*Qext - *Qpr) / *Qsca;                          // Equation (32)
+
+  *Qbk = (Qbktmp.r*Qbktmp.r + Qbktmp.i*Qbktmp.i)/x2;    // Equation (33)
+
+  // Free the memory used for the arrays
+  for (n = 0; n < n_max; n++) {
+    free(Pi[n]);
+    free(Tau[n]);
+  }
+
+  free(Pi);
+  free(Tau);
+
+  free(an);
+  free(bn);
+
+  return n_max;
+}
+
+//**********************************************************************************//
+// This function calculates complex electric and magnetic field in the surroundings //
+// and inside (TODO) the particle.                                                  //
+//                                                                                  //
+// Input parameters:                                                                //
+//   L: Number of layers                                                            //
+//   pl: Index of PEC layer. If there is none just send 0 (zero)                    //
+//   x: Array containing the size parameters of the layers [0..L-1]                 //
+//   m: Array containing the relative refractive indexes of the layers [0..L-1]     //
+//   n_max: Maximum number of multipolar expansion terms to be used for the         //
+//          calculations. Only used if you know what you are doing, otherwise set   //
+//          this parameter to 0 (zero) and the function will calculate it.          //
+//   nCoords: Number of coordinate points                                           //
+//   Coords: Array containing all coordinates where the complex electric and        //
+//           magnetic fields will be calculated                                     //
+//                                                                                  //
+// Output parameters:                                                               //
+//   E, H: Complex electric and magnetic field at the provided coordinates          //
+//                                                                                  //
+// Return value:                                                                    //
+//   Number of multipolar expansion terms used for the calculations                 //
+//**********************************************************************************//
+
+int nMieField(int L, int pl, double x[], complex m[], int n_max, int nCoords, double Xp[], double Yp[], double Zp[], complex E[], complex H[]){
+  int i, n, c;
+  double **Pi, **Tau;
+  complex *an, *bn;
+  double *Rho = (double *) malloc(nCoords*sizeof(double));
+  double *Phi = (double *) malloc(nCoords*sizeof(double));
+  double *Theta = (double *) malloc(nCoords*sizeof(double));
+
+  for (c = 0; c < nCoords; c++) {
+    Rho[c] = sqrt(Xp[c]*Xp[c] + Yp[c]*Yp[c] + Zp[c]*Zp[c]);
+    if (Rho[c] < 1e-3) {
+      Rho[c] = 1e-3;
+    }
+    Phi[c] = acos(Xp[c]/sqrt(Xp[c]*Xp[c] + Yp[c]*Yp[c]));
+    Theta[c] = acos(Xp[c]/Rho[c]);
+  }
+
+  n_max = ScattCoeff(L, pl, x, m, n_max, &an, &bn);
+
+  Pi = (double **) malloc(n_max*sizeof(double *));
+  Tau = (double **) malloc(n_max*sizeof(double *));
+  for (n = 0; n < n_max; n++) {
+    Pi[n] = (double *) malloc(nCoords*sizeof(double));
+    Tau[n] = (double *) malloc(nCoords*sizeof(double));
+  }
+
+  calcPiTau(n_max, nCoords, Theta, &Pi, &Tau);
+
+  double x2 = x[L - 1]*x[L - 1];
+
+  // Initialize the fields
+  for (c = 0; c < nCoords; c++) {
+    E[c] = C_ZERO;
+    H[c] = C_ZERO;
+  }
+
+  //*******************************************************//
+  // external scattering field = incident + scattered      //
+  // BH p.92 (4.37), 94 (4.45), 95 (4.50)                  //
+  // assume: medium is non-absorbing; refim = 0; Uabs = 0  //
+  //*******************************************************//
+
+  // Firstly the easiest case, we want the field outside the particle
+  if (Rho[c] >= x[L - 1]) {
+  }
+//  for (i = 1; i < (n_max - 1); i++) {
+//    n = i - 1;
+/*    // Equation (27)
+    *Qext = *Qext + (double)(n + n + 1)*(an[i].r + bn[i].r);
+    // Equation (28)
+    *Qsca = *Qsca + (double)(n + n + 1)*(an[i].r*an[i].r + an[i].i*an[i].i + bn[i].r*bn[i].r + bn[i].i*bn[i].i);
+    // Equation (29)
+    *Qpr = *Qpr + ((n*(n + 2)/(n + 1))*((Cadd(Cmul(an[i], Conjg(an[n])), Cmul(bn[i], Conjg(bn[n])))).r) + ((double)(n + n + 1)/(n*(n + 1)))*(Cmul(an[i], Conjg(bn[i])).r));
+
+    // Equation (33)
+    Qbktmp = Cadd(Qbktmp, RCmul((double)((n + n + 1)*(1 - 2*(n % 2))), Csub(an[i], bn[i])));
+*/
+    //****************************************************//
+    // Calculate the scattering amplitudes (S1 and S2)    //
+    // Equations (25a) - (25b)                            //
+    //****************************************************//
+/*    for (t = 0; t < nTheta; t++) {
+      S1[t] = Cadd(S1[t], calc_S1_n(n, an[i], bn[i], Pi[i][t], Tau[i][t]));
+      S2[t] = Cadd(S2[t], calc_S2_n(n, an[i], bn[i], Pi[i][t], Tau[i][t]));
+    }*/
+//  }
+
+  // Free the memory used for the arrays
+  for (n = 0; n < n_max; n++) {
+    free(Pi[n]);
+    free(Tau[n]);
+  }
+
+  free(Pi);
+  free(Tau);
+
+  free(an);
+  free(bn);
+
+  free(Rho);
+  free(Phi);
+  free(Theta);
+
+  return n_max;
+}
+

nmie.h

@@ -0,0 +1,38 @@
+//**********************************************************************************//
+//    Copyright (C) 2009-2015  Ovidio Pena <ovidio@bytesfall.com>                   //
+//                                                                                  //
+//    This file is part of scattnlay                                                //
+//                                                                                  //
+//    This program is free software: you can redistribute it and/or modify          //
+//    it under the terms of the GNU General Public License as published by          //
+//    the Free Software Foundation, either version 3 of the License, or             //
+//    (at your option) any later version.                                           //
+//                                                                                  //
+//    This program is distributed in the hope that it will be useful,               //
+//    but WITHOUT ANY WARRANTY; without even the implied warranty of                //
+//    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the                 //
+//    GNU General Public License for more details.                                  //
+//                                                                                  //
+//    The only additional remark is that we expect that all publications            //
+//    describing work using this software, or all commercial products               //
+//    using it, cite the following reference:                                       //
+//    [1] O. Pena and U. Pal, "Scattering of electromagnetic radiation by           //
+//        a multilayered sphere," Computer Physics Communications,                  //
+//        vol. 180, Nov. 2009, pp. 2348-2354.                                       //
+//                                                                                  //
+//    You should have received a copy of the GNU General Public License             //
+//    along with this program.  If not, see <http://www.gnu.org/licenses/>.         //
+//**********************************************************************************//
+
+#define VERSION "0.3.0"
+
+int nMie(int L, double x[], complex m[], int nTheta, double Theta[], double *Qext, double *Qsca, double *Qabs, double *Qbk, double *Qpr, double *g, double *Albedo, complex S1[], complex S2[]);
+
+int nMiePEC(int L, int pl, double x[], complex m[], int nTheta, double Theta[], double *Qext, double *Qsca, double *Qabs, double *Qbk, double *Qpr, double *g, double *Albedo, complex S1[], complex S2[]);
+
+int nMieMax(int L, double x[], complex m[], int nTheta, double Theta[], int n_max, double *Qext, double *Qsca, double *Qabs, double *Qbk, double *Qpr, double *g, double *Albedo, complex S1[], complex S2[]);
+
+int nMieScatt(int L, int pl, double x[], complex m[], int nTheta, double Theta[], int n_max, double *Qext, double *Qsca, double *Qabs, double *Qbk, double *Qpr, double *g, double *Albedo, complex S1[], complex S2[]);
+
+int nMieField(int L, int pl, double x[], complex m[], int n_max, int nCoords, double Xp[], double Yp[], double Zp[], complex E[], complex H[]);
+

py_nmie.cc

@@ -0,0 +1,75 @@
+//**********************************************************************************//
+//    Copyright (C) 2009-2015  Ovidio Pena <ovidio@bytesfall.com>                   //
+//                                                                                  //
+//    This file is part of scattnlay                                                //
+//                                                                                  //
+//    This program is free software: you can redistribute it and/or modify          //
+//    it under the terms of the GNU General Public License as published by          //
+//    the Free Software Foundation, either version 3 of the License, or             //
+//    (at your option) any later version.                                           //
+//                                                                                  //
+//    This program is distributed in the hope that it will be useful,               //
+//    but WITHOUT ANY WARRANTY; without even the implied warranty of                //
+//    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the                 //
+//    GNU General Public License for more details.                                  //
+//                                                                                  //
+//    The only additional remark is that we expect that all publications            //
+//    describing work using this software, or all commercial products               //
+//    using it, cite the following reference:                                       //
+//    [1] O. Pena and U. Pal, "Scattering of electromagnetic radiation by           //
+//        a multilayered sphere," Computer Physics Communications,                  //
+//        vol. 180, Nov. 2009, pp. 2348-2354.                                       //
+//                                                                                  //
+//    You should have received a copy of the GNU General Public License             //
+//    along with this program.  If not, see <http://www.gnu.org/licenses/>.         //
+//**********************************************************************************//
+
+#include <stdlib.h>
+#include <stdio.h>
+#include "ucomplex.h"
+#include "nmie.h"
+#include "py_nmie.h"
+
+//Same as nMieScatt but only uses doubles (useful for python)
+int nfMieScatt(int L, int pl, double x[], double mr[], double mi[], int nTheta, double Theta[], int n_max, double *Qext, double *Qsca, double *Qabs, double *Qbk, double *Qpr, double *g, double *Albedo, double S1r[], double S1i[], double S2r[], double S2i[]){
+  int i, result;
+  complex m[L], S1[nTheta], S2[nTheta];
+
+  for (i = 0; i < L; i++) {
+    m[i].r = mr[i];
+    m[i].i = mi[i];
+  }
+
+  result = nMieScatt(L, pl, x, m, nTheta, Theta, n_max, Qext, Qsca, Qabs, Qbk, Qpr, g, Albedo, S1, S2);
+
+  for (i = 0; i < nTheta; i++) {
+    S1r[i] = S1[i].r;
+    S1i[i] = S1[i].i;
+    S2r[i] = S2[i].r;
+    S2i[i] = S2[i].i;
+  }
+
+  return result;
+}
+
+int nfMieField(int L, int pl, double x[], double mr[], double mi[], int n_max, int nCoords, double Xp[], double Yp[], double Zp[], double Er[], double Ei[], double Hr[], double Hi[]){
+  int i, result;
+  complex m[L], E[nCoords], H[nCoords];
+
+  for (i = 0; i < L; i++) {
+    m[i].r = mr[i];
+    m[i].i = mi[i];
+  }
+
+  result = nMieField(L, pl, x, m, n_max, nCoords, Xp, Yp, Zp, E, H);
+
+  for (i = 0; i < nCoords; i++) {
+    Er[i] = E[i].r;
+    Ei[i] = E[i].i;
+    Hr[i] = H[i].r;
+    Hi[i] = H[i].i;
+  }
+
+  return result;
+}
+

py_nmie.h

@@ -0,0 +1,30 @@
+//**********************************************************************************//
+//    Copyright (C) 2009-2015  Ovidio Pena <ovidio@bytesfall.com>                   //
+//                                                                                  //
+//    This file is part of scattnlay                                                //
+//                                                                                  //
+//    This program is free software: you can redistribute it and/or modify          //
+//    it under the terms of the GNU General Public License as published by          //
+//    the Free Software Foundation, either version 3 of the License, or             //
+//    (at your option) any later version.                                           //
+//                                                                                  //
+//    This program is distributed in the hope that it will be useful,               //
+//    but WITHOUT ANY WARRANTY; without even the implied warranty of                //
+//    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the                 //
+//    GNU General Public License for more details.                                  //
+//                                                                                  //
+//    The only additional remark is that we expect that all publications            //
+//    describing work using this software, or all commercial products               //
+//    using it, cite the following reference:                                       //
+//    [1] O. Pena and U. Pal, "Scattering of electromagnetic radiation by           //
+//        a multilayered sphere," Computer Physics Communications,                  //
+//        vol. 180, Nov. 2009, pp. 2348-2354.                                       //
+//                                                                                  //
+//    You should have received a copy of the GNU General Public License             //
+//    along with this program.  If not, see <http://www.gnu.org/licenses/>.         //
+//**********************************************************************************//
+
+int nfMieScatt(int L, int pl, double x[], double mr[], double mi[], int nTheta, double Theta[], int n_max, double *Qext, double *Qsca, double *Qabs, double *Qbk, double *Qpr, double *g, double *Albedo, double S1r[], double S1i[], double S2r[], double S2i[]);
+
+int nfMieField(int L, int pl, double x[], double mr[], double mi[], int n_max, int nCoords, double Xp[], double Yp[], double Zp[], double Er[], double Ei[], double Hr[], double Hi[]);
+

setup.py

@@ -0,0 +1,57 @@
+#!/usr/bin/env python
+# -*- coding: UTF-8 -*-
+#
+#    Copyright (C) 2009-2015 Ovidio Peña Rodríguez <ovidio@bytesfall.com>
+#
+#    This file is part of python-scattnlay
+#
+#    This program is free software: you can redistribute it and/or modify
+#    it under the terms of the GNU General Public License as published by
+#    the Free Software Foundation, either version 3 of the License, or
+#    (at your option) any later version.
+#
+#    This program is distributed in the hope that it will be useful,
+#    but WITHOUT ANY WARRANTY; without even the implied warranty of
+#    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+#    GNU General Public License for more details.
+#
+#    The only additional remark is that we expect that all publications
+#    describing work using this software, or all commercial products
+#    using it, cite the following reference:
+#    [1] O. Pena and U. Pal, "Scattering of electromagnetic radiation by
+#        a multilayered sphere," Computer Physics Communications,
+#        vol. 180, Nov. 2009, pp. 2348-2354.
+#
+#    You should have received a copy of the GNU General Public License
+#    along with this program.  If not, see <http://www.gnu.org/licenses/>.
+
+__version__ = '0.3.0'
+__title__ = 'Calculation of the scattering of EM radiation by a multilayered sphere'
+__mod__ = 'python-scattnlay'
+__author__ = 'Ovidio Peña Rodríguez'
+__email__ = 'ovidio@bytesfall.com'
+__url__ = 'http://scattering.sourceforge.net/'
+
+from distutils.core import setup
+from distutils.extension import Extension
+import numpy as np
+
+setup(name = __mod__,
+      version = __version__,
+      description = __title__,
+      long_description="""The Python version of scattnlay, a computer implementation of the algorithm for the calculation of electromagnetic \
+radiation scattering by a multilayered sphere developed by Yang. It has been shown that the program is effective, \
+resulting in very accurate values of scattering efficiencies for a wide range of size parameters, which is a \
+considerable improvement over previous implementations of similar algorithms. For details see: \
+O. Pena, U. Pal, Comput. Phys. Commun. 180 (2009) 2348-2354.""",
+      author = __author__,
+      author_email = __email__,
+      maintainer = __author__,
+      maintainer_email = __email__,
+      keywords = ['Mie scattering', 'Multilayered sphere', 'Efficiency factors', 'Cross-sections'],
+      url = __url__,
+      license = 'GPL',
+      platforms = 'any',
+      ext_modules = [Extension("scattnlay", ["ucomplex.c", "nmie.c", "py_nmie.c", "scattnlay.c"], include_dirs = [np.get_include()])]
+)
+

standalone.cc

@@ -0,0 +1,136 @@
+//**********************************************************************************//
+//    Copyright (C) 2009-2013  Ovidio Pena <ovidio@bytesfall.com>                   //
+//                                                                                  //
+//    This file is part of scattnlay                                                //
+//                                                                                  //
+//    This program is free software: you can redistribute it and/or modify          //
+//    it under the terms of the GNU General Public License as published by          //
+//    the Free Software Foundation, either version 3 of the License, or             //
+//    (at your option) any later version.                                           //
+//                                                                                  //
+//    This program is distributed in the hope that it will be useful,               //
+//    but WITHOUT ANY WARRANTY; without even the implied warranty of                //
+//    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the                 //
+//    GNU General Public License for more details.                                  //
+//                                                                                  //
+//    The only additional remark is that we expect that all publications            //
+//    describing work using this software, or all commercial products               //
+//    using it, cite the following reference:                                       //
+//    [1] O. Pena and U. Pal, "Scattering of electromagnetic radiation by           //
+//        a multilayered sphere," Computer Physics Communications,                  //
+//        vol. 180, Nov. 2009, pp. 2348-2354.                                       //
+//                                                                                  //
+//    You should have received a copy of the GNU General Public License             //
+//    along with this program.  If not, see <http://www.gnu.org/licenses/>.         //
+//**********************************************************************************//
+
+#include <stdlib.h>
+#include <stdio.h>
+#include <time.h>
+#include <string.h>
+#include "ucomplex.h"
+#include "nmie.h"
+#define MAXLAYERS 1100
+#define MAXTHETA 800
+#define PI 3.14159
+
+//***********************************************************************************//
+// This is the main function of 'scattnlay', here we read the parameters as          //
+// arguments passed to the program which should be executed with the following       //
+// syntaxis:                                                                         //
+// ./scattnlay -l Layers x1 m1.r m1.i [x2 m2.r m2.i ...] [-t ti tf nt] [-c comment]  //
+//                                                                                   //
+// When all the parameters were correctly passed we setup the integer L (the         //
+// number of layers) and the arrays x and m, containing the size parameters and      //
+// refractive indexes of the layers, respectively and call the function nMie.        //
+// If the calculation is successful the results are printed with the following       //
+// format:                                                                           //
+//                                                                                   //
+//    * If no comment was passed:                                                    //
+//        'Qext, Qsca, Qabs, Qbk, Qpr, g, Albedo'                                    //
+//                                                                                   //
+//    * If a comment was passed:                                                     //
+//        'comment, Qext, Qsca, Qabs, Qbk, Qpr, g, Albedo'                           //
+//***********************************************************************************//
+int main(int argc, char *argv[]) {
+  char comment[200];
+  int has_comment = 0;
+  int i, j, L;
+  double *x, *Theta;
+  complex *m, *S1, *S2;
+  double Qext, Qabs, Qsca, Qbk, Qpr, g, Albedo;
+  double ti = 0.0, tf = 90.0;
+  int nt = 0;
+
+  if (argc < 5) {
+    printf("Insufficient parameters.\nUsage: %s -l Layers x1 m1.r m1.i [x2 m2.r m2.i ...] [-t ti tf nt] [-c comment]\n", argv[0]);
+    return -1;
+  }
+
+  strcpy(comment, "");
+  for (i = 1; i < argc; i++) {
+    if (strcmp(argv[i], "-l") == 0) {
+      i++;
+      L = atoi(argv[i]);
+      x = (double *) malloc(L*sizeof(double));
+      m = (complex *) malloc(L*sizeof(complex));
+      if (argc < 3*(L + 1)) {
+        printf("Insufficient parameters.\nUsage: %s -l Layers x1 m1.r m1.i [x2 m2.r m2.i ...] [-t ti tf nt] [-c comment]\n", argv[0]);
+        return -1;
+      } else {
+        for (j = 0; j < L; j++) {
+          i++;
+          x[j] = atof(argv[i]);
+          i++;
+          m[j].r = atof(argv[i]);
+          i++;
+          m[j].i = atof(argv[i]);
+        }
+      }
+    } else if (strcmp(argv[i], "-t") == 0) {
+      i++;
+      ti = atof(argv[i]);
+      i++;
+      tf = atof(argv[i]);
+      i++;
+      nt = atoi(argv[i]);
+      Theta = (double *) malloc(nt*sizeof(double));
+      S1 = (complex *) malloc(nt*sizeof(complex));
+      S2 = (complex *) malloc(nt*sizeof(complex));
+    } else if (strcmp(argv[i], "-c") == 0) {
+      i++;
+      strcpy(comment, argv[i]);
+      has_comment = 1;
+    } else { i++; }
+  }
+
+  if (nt < 0) {
+    printf("Error reading Theta.\n");
+    return -1;
+  } else if (nt == 1) {
+    Theta[0] = ti*PI/180.0;
+  } else {
+    for (i = 0; i < nt; i++) {
+      Theta[i] = (ti + (double)i*(tf - ti)/(nt - 1))*PI/180.0;
+    }
+  }
+
+  nMie(L, x, m, nt, Theta, &Qext, &Qsca, &Qabs, &Qbk, &Qpr, &g, &Albedo, S1, S2);
+
+  if (has_comment) {
+    printf("%6s, %+.5e, %+.5e, %+.5e, %+.5e, %+.5e, %+.5e, %+.5e\n", comment, Qext, Qsca, Qabs, Qbk, Qpr, g, Albedo);
+  } else {
+    printf("%+.5e, %+.5e, %+.5e, %+.5e, %+.5e, %+.5e, %+.5e\n", Qext, Qsca, Qabs, Qbk, Qpr, g, Albedo);
+  }
+
+  if (nt > 0) {
+    printf(" Theta,         S1.r,         S1.i,         S2.r,         S2.i\n");
+
+    for (i = 0; i < nt; i++) {
+      printf("%6.2f, %+.5e, %+.5e, %+.5e, %+.5e\n", Theta[i]*180.0/PI, S1[i].r, S1[i].i, S2[i].r, S2[i].i);
+    }
+  }
+  return 0;
+}
+
+

tests/python/scattPEC.py

@@ -0,0 +1,46 @@
+#!/usr/bin/env python
+
+# This test case calculates the differential scattering
+# cross section for different x values of a PEC sphere
+
+# The differential cross section from wave optics is:
+# d(Csca)/d(a**2*Omega) = S11(Theta)/x**2
+
+from scattnlay import scattnlay
+import numpy as np
+
+dX = 0.5
+Xmax = 5.0
+
+m = np.array([[1.0 - 1.0j]], dtype = np.complex128)
+theta = np.arange(0.0, 180.25, 0.25, dtype = np.float64)*np.pi/180.0
+
+result = theta*180.0/np.pi
+
+for xl in np.arange(dX, Xmax, dX, dtype = np.float64):
+    x = np.array([[xl]], dtype = np.float64)
+    terms, Qext, Qsca, Qabs, Qbk, Qpr, g, Albedo, S1, S2 = scattnlay(x, m, theta)
+
+    S11 = S1[0].real*S1[0].real + S1[0].imag*S1[0].imag + S2[0].real*S2[0].real + S2[0].imag*S2[0].imag
+    result = np.vstack((result, S11/(2.0*xl*xl)))
+
+result = result.transpose()
+
+try:
+    import matplotlib.pyplot as plt
+
+    plt.plot(result[ : , 0], result[ : , 1:])
+
+    ax = plt.gca()
+    ax.set_yscale('log')
+#    ax.set_ylim(1e-4, 1e3)
+
+    plt.xlabel('Theta')
+
+    plt.draw()
+    plt.show()
+finally:
+    np.savetxt("scattPEC.txt", result, fmt = "%.5f")
+    print result
+
+

tests/python/scattPEC.txt

@@ -0,0 +1,721 @@
+0.00000 0.00000 0.00065 0.02004 0.33982 2.42374 0.27467 2.91000 1.58850 3.43102
+0.25000 0.00000 0.00065 0.02004 0.33982 2.42372 0.27466 2.90986 1.58843 3.43070
+0.50000 0.00000 0.00065 0.02004 0.33980 2.42366 0.27462 2.90944 1.58821 3.42973
+0.75000 0.00000 0.00065 0.02003 0.33978 2.42356 0.27457 2.90875 1.58785 3.42813
+1.00000 0.00000 0.00065 0.02003 0.33974 2.42342 0.27449 2.90778 1.58734 3.42588
+1.25000 0.00000 0.00065 0.02003 0.33970 2.42324 0.27439 2.90653 1.58669 3.42299
+1.50000 0.00000 0.00065 0.02003 0.33964 2.42303 0.27426 2.90500 1.58589 3.41946
+1.75000 0.00000 0.00064 0.02002 0.33958 2.42277 0.27412 2.90320 1.58495 3.41529
+2.00000 0.00000 0.00064 0.02002 0.33951 2.42248 0.27395 2.90112 1.58386 3.41049
+2.25000 0.00000 0.00064 0.02002 0.33942 2.42214 0.27376 2.89877 1.58264 3.40505
+2.50000 0.00000 0.00064 0.02001 0.33933 2.42177 0.27354 2.89614 1.58127 3.39899
+2.75000 0.00000 0.00064 0.02000 0.33923 2.42136 0.27331 2.89324 1.57976 3.39230
+3.00000 0.00000 0.00064 0.02000 0.33912 2.42090 0.27305 2.89006 1.57811 3.38499
+3.25000 0.00000 0.00064 0.01999 0.33899 2.42041 0.27277 2.88661 1.57631 3.37706
+3.50000 0.00000 0.00064 0.01998 0.33886 2.41988 0.27247 2.88289 1.57438 3.36852
+3.75000 0.00000 0.00064 0.01998 0.33872 2.41931 0.27215 2.87890 1.57231 3.35936
+4.00000 0.00000 0.00064 0.01997 0.33857 2.41870 0.27181 2.87464 1.57011 3.34961
+4.25000 0.00000 0.00064 0.01996 0.33841 2.41805 0.27145 2.87011 1.56776 3.33925
+4.50000 0.00000 0.00064 0.01995 0.33824 2.41737 0.27106 2.86532 1.56529 3.32831
+4.75000 0.00000 0.00064 0.01994 0.33806 2.41664 0.27066 2.86026 1.56268 3.31677
+5.00000 0.00000 0.00064 0.01993 0.33787 2.41588 0.27024 2.85493 1.55993 3.30466
+5.25000 0.00000 0.00064 0.01992 0.33767 2.41507 0.26979 2.84934 1.55706 3.29197
+5.50000 0.00000 0.00064 0.01991 0.33746 2.41423 0.26933 2.84349 1.55405 3.27872
+5.75000 0.00000 0.00064 0.01989 0.33724 2.41335 0.26885 2.83739 1.55092 3.26491
+6.00000 0.00000 0.00064 0.01988 0.33701 2.41243 0.26835 2.83102 1.54766 3.25054
+6.25000 0.00000 0.00064 0.01987 0.33677 2.41147 0.26783 2.82440 1.54427 3.23563
+6.50000 0.00000 0.00064 0.01985 0.33653 2.41047 0.26730 2.81752 1.54077 3.22019
+6.75000 0.00000 0.00064 0.01984 0.33627 2.40944 0.26674 2.81039 1.53713 3.20421
+7.00000 0.00000 0.00064 0.01983 0.33600 2.40836 0.26617 2.80301 1.53338 3.18772
+7.25000 0.00000 0.00064 0.01981 0.33573 2.40725 0.26558 2.79538 1.52951 3.17072
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tests/python/scattSiO2.py

@@ -0,0 +1,46 @@
+#!/usr/bin/env python
+
+# This test case calculates the differential scattering
+# cross section for different x values of a SiO2 sphere
+
+# The differential cross section from wave optics is:
+# d(Csca)/d(a**2*Omega) = S11(Theta)/x**2
+
+from scattnlay import scattnlay
+import numpy as np
+
+dX = 0.5
+Xmax = 5.0
+
+m = np.array([[1.46 + 0.0j]], dtype = np.complex128)
+theta = np.arange(0.0, 180.25, 0.25, dtype = np.float64)*np.pi/180.0
+
+result = theta*180.0/np.pi
+
+for xl in np.arange(dX, Xmax, dX, dtype = np.float64):
+    x = np.array([[xl]], dtype = np.float64)
+    terms, Qext, Qsca, Qabs, Qbk, Qpr, g, Albedo, S1, S2 = scattnlay(x, m, theta)
+
+    S11 = S1[0].real*S1[0].real + S1[0].imag*S1[0].imag + S2[0].real*S2[0].real + S2[0].imag*S2[0].imag
+    result = np.vstack((result, S11/(2.0*xl*xl)))
+
+result = result.transpose()
+
+try:
+    import matplotlib.pyplot as plt
+
+    plt.plot(result[ : , 0], result[ : , 1:])
+
+    ax = plt.gca()
+    ax.set_yscale('log')
+#    ax.set_ylim(1e-4, 1e3)
+
+    plt.xlabel('Theta')
+
+    plt.draw()
+    plt.show()
+finally:
+    np.savetxt("scattSiO2.txt", result, fmt = "%.5f")
+    print result
+
+

tests/python/scattSiO2.txt

@@ -0,0 +1,721 @@
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tests/python/test01.py

@@ -0,0 +1,69 @@
+#!/usr/bin/env python
+
+# This is a test against the program n-mie (version 3a) for the test case
+# distributed by them (extended for x up to 100)
+# n-mie is based in the algorithm described in:
+# Wu Z.P., Wang Y.P.
+# Electromagnetic scattering for multilayered spheres:
+# recursive algorithms
+# Radio Science 1991. V. 26. P. 1393-1401.
+# Voshchinnikov N.V., Mathis J.S.
+# Calculating Cross Sections of Composite Interstellar Grains
+# Astrophys. J. 1999. V. 526. #1. 
+
+# The test consist in 5 layers with the following parameters
+# m1=1.8 i1.7
+# m2=0.8 i0.7
+# m3=1.2 i0.09
+# m4=2.8 i0.2
+# m5=1.5 i0.4
+
+# v1/Vt=0.1
+# v2/Vt=0.26
+# v3/Vt=0.044
+# v4/Vt=0.3666
+
+from scattnlay import scattnlay
+import numpy as np
+
+x = np.ones((400, 5), dtype = np.float64)
+x[:, 4] = np.arange(0.25, 100.25, 0.25)
+x[:, 0] = 0.1**(1.0/3.0)*x[:, 4]
+x[:, 1] = 0.36**(1.0/3.0)*x[:, 4]
+x[:, 2] = 0.404**(1.0/3.0)*x[:, 4]
+x[:, 3] = 0.7706**(1.0/3.0)*x[:, 4]
+
+m = np.ones((400, 5), dtype = np.complex128)
+m[:, 0] *= 1.8 + 1.7j
+m[:, 1] *= 0.8 + 0.7j
+m[:, 2] *= 1.2 + 0.09j
+m[:, 3] *= 2.8 + 0.2j
+m[:, 4] *= 1.5 + 0.4j
+
+terms, Qext, Qsca, Qabs, Qbk, Qpr, g, Albedo, S1, S2 = scattnlay(x, m)
+
+result = np.vstack((x[:, 4], Qext, Qsca, Qabs, Qbk, Qpr, g, Albedo)).transpose()
+
+try:
+    import matplotlib.pyplot as plt
+
+    plt.figure(1)
+    plt.subplot(311)
+    plt.plot(x[:, 4], Qext, 'k')
+    plt.ylabel('Qext')
+
+    plt.subplot(312)
+    plt.plot(x[:, 4], Qsca, 'r')
+    plt.ylabel('Qsca')
+
+    plt.subplot(313)
+    plt.plot(x[:, 4], Albedo, 'g')
+    plt.ylabel('Albedo')
+
+    plt.xlabel('X')
+
+    plt.show()
+finally:
+    np.savetxt("test01.txt", result, fmt = "%.5f")
+    print result
+

tests/python/test01.txt

@@ -0,0 +1,400 @@
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tests/python/test02.py

@@ -0,0 +1,55 @@
+#!/usr/bin/env python
+
+# This is a test against the program n-mie (version 3a) for a water sphere surrounded by soot
+# n-mie is based in the algorithm described in:
+# Wu Z.P., Wang Y.P.
+# Electromagnetic scattering for multilayered spheres:
+# recursive algorithms
+# Radio Science 1991. V. 26. P. 1393-1401.
+# Voshchinnikov N.V., Mathis J.S.
+# Calculating Cross Sections of Composite Interstellar Grains
+# Astrophys. J. 1999. V. 526. #1. 
+
+# The refractive indices of water and soot are m1 1.33 i0.00, m2 1.59 i0.66, respectively.
+# The volume fraction of soot is 0.01.
+# This test case was described in:
+# W. Yang, Appl. Opt. 42 (2003) 1710-1720.
+
+from scattnlay import scattnlay
+import numpy as np
+
+x = np.ones((400, 2), dtype = np.float64)
+x[:, 1] = np.arange(0.1, 100.0, 0.25)
+x[:, 0] = 0.99**(1.0/3.0)*x[:, 1]
+
+m = np.ones((400, 2), dtype = np.complex128)
+m[:, 0] *= 1.33
+m[:, 1] *= 1.59 + 0.66j
+
+terms, Qext, Qsca, Qabs, Qbk, Qpr, g, Albedo, S1, S2 = scattnlay(x, m)
+
+result = np.vstack((x[:, 1], Qext, Qsca, Qabs, Qbk, Qpr, g, Albedo)).transpose()
+
+try:
+    import matplotlib.pyplot as plt
+
+    plt.figure(1)
+    plt.subplot(311)
+    plt.plot(x[:, 1], Qext, 'k')
+    plt.ylabel('Qext')
+
+    plt.subplot(312)
+    plt.plot(x[:, 1], Qsca, 'r')
+    plt.ylabel('Qsca')
+
+    plt.subplot(313)
+    plt.plot(x[:, 1], Albedo, 'g')
+    plt.ylabel('Albedo')
+
+    plt.xlabel('X')
+
+    plt.show()
+finally:
+    np.savetxt("test02.txt", result, fmt = "%.5f")
+    print result
+

tests/python/test02.txt

@@ -0,0 +1,400 @@
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tests/python/test04.py

@@ -0,0 +1,57 @@
+#!/usr/bin/env python
+
+# This test case calculates the differential scattering
+# cross section from a Luneburg lens, as described in:
+# B. R. Johnson, Applied Optics 35 (1996) 3286-3296.
+
+# The Luneburg lens is a sphere of radius a, with a
+# radially-varying index of refraction, given by:
+# m(r) = [2 - (r/a)**1]**(1/2)
+
+# For the calculations, the Luneburg lens was approximated
+# as a multilayered sphere with 500 equally spaced layers.
+# The refractive index of each layer is defined to be equal to
+# m(r) at the midpoint of the layer: ml = [2 - (xm/xL)**1]**(1/2),
+# with xm = (xl-1 + xl)/2, for l = 1,2,...,L. The size
+# parameter in the lth layer is xl = l*xL/500. According to
+# geometrical optics theory, the differential cross section
+# can be expressed as:
+# d(Csca)/d(a**2*Omega) = cos(Theta)
+
+# The differential cross section from wave optics is:
+# d(Csca)/d(a**2*Omega) = S11(Theta)/x**2
+
+from scattnlay import scattnlay
+import numpy as np
+
+nL = 500.0
+Xmax = 60.0
+
+x = np.array([np.arange(1.0, nL + 1.0)*Xmax/nL], dtype = np.float64)
+m = np.array([np.sqrt((2.0 - ((x[0] - 0.5*Xmax/nL)/60.0)**2.0)) + 0.0j], dtype = np.complex128)
+
+theta = np.arange(0.0, 180.25, 0.25, dtype = np.float64)*np.pi/180.0
+
+terms, Qext, Qsca, Qabs, Qbk, Qpr, g, Albedo, S1, S2 = scattnlay(x, m, theta)
+
+S11 = S1[0].real*S1[0].real + S1[0].imag*S1[0].imag + S2[0].real*S2[0].real + S2[0].imag*S2[0].imag
+result = np.vstack((theta*180.0/np.pi, S11/(2.0*Xmax*Xmax), np.cos(theta))).transpose()
+
+try:
+    import matplotlib.pyplot as plt
+
+    plt.plot(result[ : , 0], result[ : , 1], 'k', result[ : , 0], result[ : , 2], 'r')
+
+    ax = plt.gca()
+    ax.set_yscale('log')
+    ax.set_ylim(1e-4, 1e3)
+
+    plt.xlabel('Theta')
+
+    plt.draw()
+    plt.show()
+finally:
+    np.savetxt("test04.txt", result, fmt = "%.5f")
+    print result
+
+

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tests/shell/test01.sh

@@ -0,0 +1,127 @@
+#! /bin/sh
+# This is a test against the program n-mie (version 3a) for the test case
+# distributed by them (extended for x up to 100)
+# n-mie is based in the algorithm described in:
+# Wu Z.P., Wang Y.P.
+# Electromagnetic scattering for multilayered spheres:
+# recursive algorithms
+# Radio Science 1991. V. 26. P. 1393-1401.
+# Voshchinnikov N.V., Mathis J.S.
+# Calculating Cross Sections of Composite Interstellar Grains
+# Astrophys. J. 1999. V. 526. #1. 
+# 
+# The test consist in 5 layers with the following parameters
+# m1=1.8 i1.7
+# m2=0.8 i0.7
+# m3=1.2 i0.09
+# m4=2.8 i0.2
+# m5=1.5 i0.4
+# 
+# v1/Vt=0.1
+# v2/Vt=0.26
+# v3/Vt=0.044
+# v4/Vt=0.3666
+
+PROGRAM='../../../scattnlay'
+
+$PROGRAM -l 5 0.4642 1.8000 1.7000 0.7114 0.8000 0.7000 0.7393 1.2000 0.0900 0.9168 2.8000 0.2000 1.0000 1.5000 0.4000 -c 1.0
+$PROGRAM -l 5 0.9283 1.8000 1.7000 1.4228 0.8000 0.7000 1.4785 1.2000 0.0900 1.8336 2.8000 0.2000 2.0000 1.5000 0.4000 -c 2.0
+$PROGRAM -l 5 1.3925 1.8000 1.7000 2.1341 0.8000 0.7000 2.2178 1.2000 0.0900 2.7504 2.8000 0.2000 3.0000 1.5000 0.4000 -c 3.0
+$PROGRAM -l 5 1.8566 1.8000 1.7000 2.8455 0.8000 0.7000 2.9570 1.2000 0.0900 3.6672 2.8000 0.2000 4.0000 1.5000 0.4000 -c 4.0
+$PROGRAM -l 5 2.3208 1.8000 1.7000 3.5569 0.8000 0.7000 3.6963 1.2000 0.0900 4.5840 2.8000 0.2000 5.0000 1.5000 0.4000 -c 5.0
+$PROGRAM -l 5 2.7850 1.8000 1.7000 4.2683 0.8000 0.7000 4.4355 1.2000 0.0900 5.5008 2.8000 0.2000 6.0000 1.5000 0.4000 -c 6.0
+$PROGRAM -l 5 3.2491 1.8000 1.7000 4.9797 0.8000 0.7000 5.1748 1.2000 0.0900 6.4176 2.8000 0.2000 7.0000 1.5000 0.4000 -c 7.0
+$PROGRAM -l 5 3.7133 1.8000 1.7000 5.6910 0.8000 0.7000 5.9140 1.2000 0.0900 7.3344 2.8000 0.2000 8.0000 1.5000 0.4000 -c 8.0
+$PROGRAM -l 5 4.1774 1.8000 1.7000 6.4024 0.8000 0.7000 6.6533 1.2000 0.0900 8.2512 2.8000 0.2000 9.0000 1.5000 0.4000 -c 9.0
+$PROGRAM -l 5 4.6416 1.8000 1.7000 7.1138 0.8000 0.7000 7.3925 1.2000 0.0900 9.1680 2.8000 0.2000 10.0000 1.5000 0.4000 -c 10.0
+$PROGRAM -l 5 5.1057 1.8000 1.7000 7.8252 0.8000 0.7000 8.1318 1.2000 0.0900 10.0848 2.8000 0.2000 11.0000 1.5000 0.4000 -c 11.0
+$PROGRAM -l 5 5.5699 1.8000 1.7000 8.5365 0.8000 0.7000 8.8711 1.2000 0.0900 11.0016 2.8000 0.2000 12.0000 1.5000 0.4000 -c 12.0
+$PROGRAM -l 5 6.0341 1.8000 1.7000 9.2479 0.8000 0.7000 9.6103 1.2000 0.0900 11.9184 2.8000 0.2000 13.0000 1.5000 0.4000 -c 13.0
+$PROGRAM -l 5 6.4982 1.8000 1.7000 9.9593 0.8000 0.7000 10.3496 1.2000 0.0900 12.8353 2.8000 0.2000 14.0000 1.5000 0.4000 -c 14.0
+$PROGRAM -l 5 6.9624 1.8000 1.7000 10.6707 0.8000 0.7000 11.0888 1.2000 0.0900 13.7521 2.8000 0.2000 15.0000 1.5000 0.4000 -c 15.0
+$PROGRAM -l 5 7.4265 1.8000 1.7000 11.3821 0.8000 0.7000 11.8281 1.2000 0.0900 14.6689 2.8000 0.2000 16.0000 1.5000 0.4000 -c 16.0
+$PROGRAM -l 5 7.8907 1.8000 1.7000 12.0934 0.8000 0.7000 12.5673 1.2000 0.0900 15.5857 2.8000 0.2000 17.0000 1.5000 0.4000 -c 17.0
+$PROGRAM -l 5 8.3549 1.8000 1.7000 12.8048 0.8000 0.7000 13.3066 1.2000 0.0900 16.5025 2.8000 0.2000 18.0000 1.5000 0.4000 -c 18.0
+$PROGRAM -l 5 8.8190 1.8000 1.7000 13.5162 0.8000 0.7000 14.0458 1.2000 0.0900 17.4193 2.8000 0.2000 19.0000 1.5000 0.4000 -c 19.0
+$PROGRAM -l 5 9.2832 1.8000 1.7000 14.2276 0.8000 0.7000 14.7851 1.2000 0.0900 18.3361 2.8000 0.2000 20.0000 1.5000 0.4000 -c 20.0
+$PROGRAM -l 5 9.7473 1.8000 1.7000 14.9390 0.8000 0.7000 15.5243 1.2000 0.0900 19.2529 2.8000 0.2000 21.0000 1.5000 0.4000 -c 21.0
+$PROGRAM -l 5 10.2115 1.8000 1.7000 15.6503 0.8000 0.7000 16.2636 1.2000 0.0900 20.1697 2.8000 0.2000 22.0000 1.5000 0.4000 -c 22.0
+$PROGRAM -l 5 10.6757 1.8000 1.7000 16.3617 0.8000 0.7000 17.0028 1.2000 0.0900 21.0865 2.8000 0.2000 23.0000 1.5000 0.4000 -c 23.0
+$PROGRAM -l 5 11.1398 1.8000 1.7000 17.0731 0.8000 0.7000 17.7421 1.2000 0.0900 22.0033 2.8000 0.2000 24.0000 1.5000 0.4000 -c 24.0
+$PROGRAM -l 5 11.6040 1.8000 1.7000 17.7845 0.8000 0.7000 18.4814 1.2000 0.0900 22.9201 2.8000 0.2000 25.0000 1.5000 0.4000 -c 25.0
+$PROGRAM -l 5 12.0681 1.8000 1.7000 18.4958 0.8000 0.7000 19.2206 1.2000 0.0900 23.8369 2.8000 0.2000 26.0000 1.5000 0.4000 -c 26.0
+$PROGRAM -l 5 12.5323 1.8000 1.7000 19.2072 0.8000 0.7000 19.9599 1.2000 0.0900 24.7537 2.8000 0.2000 27.0000 1.5000 0.4000 -c 27.0
+$PROGRAM -l 5 12.9964 1.8000 1.7000 19.9186 0.8000 0.7000 20.6991 1.2000 0.0900 25.6705 2.8000 0.2000 28.0000 1.5000 0.4000 -c 28.0
+$PROGRAM -l 5 13.4606 1.8000 1.7000 20.6300 0.8000 0.7000 21.4384 1.2000 0.0900 26.5873 2.8000 0.2000 29.0000 1.5000 0.4000 -c 29.0
+$PROGRAM -l 5 13.9248 1.8000 1.7000 21.3414 0.8000 0.7000 22.1776 1.2000 0.0900 27.5041 2.8000 0.2000 30.0000 1.5000 0.4000 -c 30.0
+$PROGRAM -l 5 14.3889 1.8000 1.7000 22.0527 0.8000 0.7000 22.9169 1.2000 0.0900 28.4209 2.8000 0.2000 31.0000 1.5000 0.4000 -c 31.0
+$PROGRAM -l 5 14.8531 1.8000 1.7000 22.7641 0.8000 0.7000 23.6561 1.2000 0.0900 29.3377 2.8000 0.2000 32.0000 1.5000 0.4000 -c 32.0
+$PROGRAM -l 5 15.3172 1.8000 1.7000 23.4755 0.8000 0.7000 24.3954 1.2000 0.0900 30.2545 2.8000 0.2000 33.0000 1.5000 0.4000 -c 33.0
+$PROGRAM -l 5 15.7814 1.8000 1.7000 24.1869 0.8000 0.7000 25.1346 1.2000 0.0900 31.1713 2.8000 0.2000 34.0000 1.5000 0.4000 -c 34.0
+$PROGRAM -l 5 16.2456 1.8000 1.7000 24.8983 0.8000 0.7000 25.8739 1.2000 0.0900 32.0881 2.8000 0.2000 35.0000 1.5000 0.4000 -c 35.0
+$PROGRAM -l 5 16.7097 1.8000 1.7000 25.6096 0.8000 0.7000 26.6132 1.2000 0.0900 33.0049 2.8000 0.2000 36.0000 1.5000 0.4000 -c 36.0
+$PROGRAM -l 5 17.1739 1.8000 1.7000 26.3210 0.8000 0.7000 27.3524 1.2000 0.0900 33.9217 2.8000 0.2000 37.0000 1.5000 0.4000 -c 37.0
+$PROGRAM -l 5 17.6380 1.8000 1.7000 27.0324 0.8000 0.7000 28.0917 1.2000 0.0900 34.8385 2.8000 0.2000 38.0000 1.5000 0.4000 -c 38.0
+$PROGRAM -l 5 18.1022 1.8000 1.7000 27.7438 0.8000 0.7000 28.8309 1.2000 0.0900 35.7553 2.8000 0.2000 39.0000 1.5000 0.4000 -c 39.0
+$PROGRAM -l 5 18.5664 1.8000 1.7000 28.4551 0.8000 0.7000 29.5702 1.2000 0.0900 36.6721 2.8000 0.2000 40.0000 1.5000 0.4000 -c 40.0
+$PROGRAM -l 5 19.0305 1.8000 1.7000 29.1665 0.8000 0.7000 30.3094 1.2000 0.0900 37.5889 2.8000 0.2000 41.0000 1.5000 0.4000 -c 41.0
+$PROGRAM -l 5 19.4947 1.8000 1.7000 29.8779 0.8000 0.7000 31.0487 1.2000 0.0900 38.5058 2.8000 0.2000 42.0000 1.5000 0.4000 -c 42.0
+$PROGRAM -l 5 19.9588 1.8000 1.7000 30.5893 0.8000 0.7000 31.7879 1.2000 0.0900 39.4226 2.8000 0.2000 43.0000 1.5000 0.4000 -c 43.0
+$PROGRAM -l 5 20.4230 1.8000 1.7000 31.3007 0.8000 0.7000 32.5272 1.2000 0.0900 40.3394 2.8000 0.2000 44.0000 1.5000 0.4000 -c 44.0
+$PROGRAM -l 5 20.8871 1.8000 1.7000 32.0120 0.8000 0.7000 33.2664 1.2000 0.0900 41.2562 2.8000 0.2000 45.0000 1.5000 0.4000 -c 45.0
+$PROGRAM -l 5 21.3513 1.8000 1.7000 32.7234 0.8000 0.7000 34.0057 1.2000 0.0900 42.1730 2.8000 0.2000 46.0000 1.5000 0.4000 -c 46.0
+$PROGRAM -l 5 21.8155 1.8000 1.7000 33.4348 0.8000 0.7000 34.7449 1.2000 0.0900 43.0898 2.8000 0.2000 47.0000 1.5000 0.4000 -c 47.0
+$PROGRAM -l 5 22.2796 1.8000 1.7000 34.1462 0.8000 0.7000 35.4842 1.2000 0.0900 44.0066 2.8000 0.2000 48.0000 1.5000 0.4000 -c 48.0
+$PROGRAM -l 5 22.7438 1.8000 1.7000 34.8576 0.8000 0.7000 36.2235 1.2000 0.0900 44.9234 2.8000 0.2000 49.0000 1.5000 0.4000 -c 49.0
+$PROGRAM -l 5 23.2079 1.8000 1.7000 35.5689 0.8000 0.7000 36.9627 1.2000 0.0900 45.8402 2.8000 0.2000 50.0000 1.5000 0.4000 -c 50.0
+$PROGRAM -l 5 23.6721 1.8000 1.7000 36.2803 0.8000 0.7000 37.7020 1.2000 0.0900 46.7570 2.8000 0.2000 51.0000 1.5000 0.4000 -c 51.0
+$PROGRAM -l 5 24.1363 1.8000 1.7000 36.9917 0.8000 0.7000 38.4412 1.2000 0.0900 47.6738 2.8000 0.2000 52.0000 1.5000 0.4000 -c 52.0
+$PROGRAM -l 5 24.6004 1.8000 1.7000 37.7031 0.8000 0.7000 39.1805 1.2000 0.0900 48.5906 2.8000 0.2000 53.0000 1.5000 0.4000 -c 53.0
+$PROGRAM -l 5 25.0646 1.8000 1.7000 38.4144 0.8000 0.7000 39.9197 1.2000 0.0900 49.5074 2.8000 0.2000 54.0000 1.5000 0.4000 -c 54.0
+$PROGRAM -l 5 25.5287 1.8000 1.7000 39.1258 0.8000 0.7000 40.6590 1.2000 0.0900 50.4242 2.8000 0.2000 55.0000 1.5000 0.4000 -c 55.0
+$PROGRAM -l 5 25.9929 1.8000 1.7000 39.8372 0.8000 0.7000 41.3982 1.2000 0.0900 51.3410 2.8000 0.2000 56.0000 1.5000 0.4000 -c 56.0
+$PROGRAM -l 5 26.4571 1.8000 1.7000 40.5486 0.8000 0.7000 42.1375 1.2000 0.0900 52.2578 2.8000 0.2000 57.0000 1.5000 0.4000 -c 57.0
+$PROGRAM -l 5 26.9212 1.8000 1.7000 41.2600 0.8000 0.7000 42.8767 1.2000 0.0900 53.1746 2.8000 0.2000 58.0000 1.5000 0.4000 -c 58.0
+$PROGRAM -l 5 27.3854 1.8000 1.7000 41.9713 0.8000 0.7000 43.6160 1.2000 0.0900 54.0914 2.8000 0.2000 59.0000 1.5000 0.4000 -c 59.0
+$PROGRAM -l 5 27.8495 1.8000 1.7000 42.6827 0.8000 0.7000 44.3553 1.2000 0.0900 55.0082 2.8000 0.2000 60.0000 1.5000 0.4000 -c 60.0
+$PROGRAM -l 5 28.3137 1.8000 1.7000 43.3941 0.8000 0.7000 45.0945 1.2000 0.0900 55.9250 2.8000 0.2000 61.0000 1.5000 0.4000 -c 61.0
+$PROGRAM -l 5 28.7779 1.8000 1.7000 44.1055 0.8000 0.7000 45.8338 1.2000 0.0900 56.8418 2.8000 0.2000 62.0000 1.5000 0.4000 -c 62.0
+$PROGRAM -l 5 29.2420 1.8000 1.7000 44.8169 0.8000 0.7000 46.5730 1.2000 0.0900 57.7586 2.8000 0.2000 63.0000 1.5000 0.4000 -c 63.0
+$PROGRAM -l 5 29.7062 1.8000 1.7000 45.5282 0.8000 0.7000 47.3123 1.2000 0.0900 58.6754 2.8000 0.2000 64.0000 1.5000 0.4000 -c 64.0
+$PROGRAM -l 5 30.1703 1.8000 1.7000 46.2396 0.8000 0.7000 48.0515 1.2000 0.0900 59.5922 2.8000 0.2000 65.0000 1.5000 0.4000 -c 65.0
+$PROGRAM -l 5 30.6345 1.8000 1.7000 46.9510 0.8000 0.7000 48.7908 1.2000 0.0900 60.5090 2.8000 0.2000 66.0000 1.5000 0.4000 -c 66.0
+$PROGRAM -l 5 31.0986 1.8000 1.7000 47.6624 0.8000 0.7000 49.5300 1.2000 0.0900 61.4258 2.8000 0.2000 67.0000 1.5000 0.4000 -c 67.0
+$PROGRAM -l 5 31.5628 1.8000 1.7000 48.3737 0.8000 0.7000 50.2693 1.2000 0.0900 62.3426 2.8000 0.2000 68.0000 1.5000 0.4000 -c 68.0
+$PROGRAM -l 5 32.0270 1.8000 1.7000 49.0851 0.8000 0.7000 51.0085 1.2000 0.0900 63.2595 2.8000 0.2000 69.0000 1.5000 0.4000 -c 69.0
+$PROGRAM -l 5 32.4911 1.8000 1.7000 49.7965 0.8000 0.7000 51.7478 1.2000 0.0900 64.1763 2.8000 0.2000 70.0000 1.5000 0.4000 -c 70.0
+$PROGRAM -l 5 32.9553 1.8000 1.7000 50.5079 0.8000 0.7000 52.4870 1.2000 0.0900 65.0931 2.8000 0.2000 71.0000 1.5000 0.4000 -c 71.0
+$PROGRAM -l 5 33.4194 1.8000 1.7000 51.2193 0.8000 0.7000 53.2263 1.2000 0.0900 66.0099 2.8000 0.2000 72.0000 1.5000 0.4000 -c 72.0
+$PROGRAM -l 5 33.8836 1.8000 1.7000 51.9306 0.8000 0.7000 53.9656 1.2000 0.0900 66.9267 2.8000 0.2000 73.0000 1.5000 0.4000 -c 73.0
+$PROGRAM -l 5 34.3478 1.8000 1.7000 52.6420 0.8000 0.7000 54.7048 1.2000 0.0900 67.8435 2.8000 0.2000 74.0000 1.5000 0.4000 -c 74.0
+$PROGRAM -l 5 34.8119 1.8000 1.7000 53.3534 0.8000 0.7000 55.4441 1.2000 0.0900 68.7603 2.8000 0.2000 75.0000 1.5000 0.4000 -c 75.0
+$PROGRAM -l 5 35.2761 1.8000 1.7000 54.0648 0.8000 0.7000 56.1833 1.2000 0.0900 69.6771 2.8000 0.2000 76.0000 1.5000 0.4000 -c 76.0
+$PROGRAM -l 5 35.7402 1.8000 1.7000 54.7762 0.8000 0.7000 56.9226 1.2000 0.0900 70.5939 2.8000 0.2000 77.0000 1.5000 0.4000 -c 77.0
+$PROGRAM -l 5 36.2044 1.8000 1.7000 55.4875 0.8000 0.7000 57.6618 1.2000 0.0900 71.5107 2.8000 0.2000 78.0000 1.5000 0.4000 -c 78.0
+$PROGRAM -l 5 36.6686 1.8000 1.7000 56.1989 0.8000 0.7000 58.4011 1.2000 0.0900 72.4275 2.8000 0.2000 79.0000 1.5000 0.4000 -c 79.0
+$PROGRAM -l 5 37.1327 1.8000 1.7000 56.9103 0.8000 0.7000 59.1403 1.2000 0.0900 73.3443 2.8000 0.2000 80.0000 1.5000 0.4000 -c 80.0
+$PROGRAM -l 5 37.5969 1.8000 1.7000 57.6217 0.8000 0.7000 59.8796 1.2000 0.0900 74.2611 2.8000 0.2000 81.0000 1.5000 0.4000 -c 81.0
+$PROGRAM -l 5 38.0610 1.8000 1.7000 58.3331 0.8000 0.7000 60.6188 1.2000 0.0900 75.1779 2.8000 0.2000 82.0000 1.5000 0.4000 -c 82.0
+$PROGRAM -l 5 38.5252 1.8000 1.7000 59.0444 0.8000 0.7000 61.3581 1.2000 0.0900 76.0947 2.8000 0.2000 83.0000 1.5000 0.4000 -c 83.0
+$PROGRAM -l 5 38.9893 1.8000 1.7000 59.7558 0.8000 0.7000 62.0974 1.2000 0.0900 77.0115 2.8000 0.2000 84.0000 1.5000 0.4000 -c 84.0
+$PROGRAM -l 5 39.4535 1.8000 1.7000 60.4672 0.8000 0.7000 62.8366 1.2000 0.0900 77.9283 2.8000 0.2000 85.0000 1.5000 0.4000 -c 85.0
+$PROGRAM -l 5 39.9177 1.8000 1.7000 61.1786 0.8000 0.7000 63.5759 1.2000 0.0900 78.8451 2.8000 0.2000 86.0000 1.5000 0.4000 -c 86.0
+$PROGRAM -l 5 40.3818 1.8000 1.7000 61.8899 0.8000 0.7000 64.3151 1.2000 0.0900 79.7619 2.8000 0.2000 87.0000 1.5000 0.4000 -c 87.0
+$PROGRAM -l 5 40.8460 1.8000 1.7000 62.6013 0.8000 0.7000 65.0544 1.2000 0.0900 80.6787 2.8000 0.2000 88.0000 1.5000 0.4000 -c 88.0
+$PROGRAM -l 5 41.3101 1.8000 1.7000 63.3127 0.8000 0.7000 65.7936 1.2000 0.0900 81.5955 2.8000 0.2000 89.0000 1.5000 0.4000 -c 89.0
+$PROGRAM -l 5 41.7743 1.8000 1.7000 64.0241 0.8000 0.7000 66.5329 1.2000 0.0900 82.5123 2.8000 0.2000 90.0000 1.5000 0.4000 -c 90.0
+$PROGRAM -l 5 42.2385 1.8000 1.7000 64.7355 0.8000 0.7000 67.2721 1.2000 0.0900 83.4291 2.8000 0.2000 91.0000 1.5000 0.4000 -c 91.0
+$PROGRAM -l 5 42.7026 1.8000 1.7000 65.4468 0.8000 0.7000 68.0114 1.2000 0.0900 84.3459 2.8000 0.2000 92.0000 1.5000 0.4000 -c 92.0
+$PROGRAM -l 5 43.1668 1.8000 1.7000 66.1582 0.8000 0.7000 68.7506 1.2000 0.0900 85.2627 2.8000 0.2000 93.0000 1.5000 0.4000 -c 93.0
+$PROGRAM -l 5 43.6309 1.8000 1.7000 66.8696 0.8000 0.7000 69.4899 1.2000 0.0900 86.1795 2.8000 0.2000 94.0000 1.5000 0.4000 -c 94.0
+$PROGRAM -l 5 44.0951 1.8000 1.7000 67.5810 0.8000 0.7000 70.2291 1.2000 0.0900 87.0963 2.8000 0.2000 95.0000 1.5000 0.4000 -c 95.0
+$PROGRAM -l 5 44.5593 1.8000 1.7000 68.2924 0.8000 0.7000 70.9684 1.2000 0.0900 88.0132 2.8000 0.2000 96.0000 1.5000 0.4000 -c 96.0
+$PROGRAM -l 5 45.0234 1.8000 1.7000 69.0037 0.8000 0.7000 71.7077 1.2000 0.0900 88.9300 2.8000 0.2000 97.0000 1.5000 0.4000 -c 97.0
+$PROGRAM -l 5 45.4876 1.8000 1.7000 69.7151 0.8000 0.7000 72.4469 1.2000 0.0900 89.8468 2.8000 0.2000 98.0000 1.5000 0.4000 -c 98.0
+$PROGRAM -l 5 45.9517 1.8000 1.7000 70.4265 0.8000 0.7000 73.1862 1.2000 0.0900 90.7636 2.8000 0.2000 99.0000 1.5000 0.4000 -c 99.0
+$PROGRAM -l 5 46.4159 1.8000 1.7000 71.1379 0.8000 0.7000 73.9254 1.2000 0.0900 91.6804 2.8000 0.2000 100.0000 1.5000 0.4000 -c 100.0
+

tests/shell/test02.sh

@@ -0,0 +1,120 @@
+#! /bin/sh
+# This is a test against the program n-mie (version 3a) for a water sphere surrounded by soot
+# n-mie is based in the algorithm described in:
+# Wu Z.P., Wang Y.P.
+# Electromagnetic scattering for multilayered spheres:
+# recursive algorithms
+# Radio Science 1991. V. 26. P. 1393-1401.
+# Voshchinnikov N.V., Mathis J.S.
+# Calculating Cross Sections of Composite Interstellar Grains
+# Astrophys. J. 1999. V. 526. #1. 
+# 
+# The refractive indices of water and soot are m1 1.33 i0.00, m2 1.59 i0.66, respectively.
+# The volume fraction of soot is 0.01.
+# This test case was described in:
+# W. Yang, Appl. Opt. 42 (2003) 1710-1720.
+
+PROGRAM='../../../scattnlay'
+
+$PROGRAM  -l 2 0.099668871748 1.33 0.0 0.1 1.59 0.66 -c 0.1
+$PROGRAM  -l 2 1.096357589225 1.33 0.0 1.1 1.59 0.66 -c 1.1
+$PROGRAM  -l 2 2.093046306702 1.33 0.0 2.1 1.59 0.66 -c 2.1
+$PROGRAM  -l 2 3.089735024180 1.33 0.0 3.1 1.59 0.66 -c 3.1
+$PROGRAM  -l 2 4.086423741657 1.33 0.0 4.1 1.59 0.66 -c 4.1
+$PROGRAM  -l 2 5.083112459134 1.33 0.0 5.1 1.59 0.66 -c 5.1
+$PROGRAM  -l 2 6.079801176612 1.33 0.0 6.1 1.59 0.66 -c 6.1
+$PROGRAM  -l 2 7.076489894089 1.33 0.0 7.1 1.59 0.66 -c 7.1
+$PROGRAM  -l 2 8.073178611566 1.33 0.0 8.1 1.59 0.66 -c 8.1
+$PROGRAM  -l 2 9.069867329044 1.33 0.0 9.1 1.59 0.66 -c 9.1
+$PROGRAM  -l 2 10.066556046521 1.33 0.0 10.1 1.59 0.66 -c 10.1
+$PROGRAM  -l 2 11.063244763998 1.33 0.0 11.1 1.59 0.66 -c 11.1
+$PROGRAM  -l 2 12.059933481476 1.33 0.0 12.1 1.59 0.66 -c 12.1
+$PROGRAM  -l 2 13.056622198953 1.33 0.0 13.1 1.59 0.66 -c 13.1
+$PROGRAM  -l 2 14.053310916430 1.33 0.0 14.1 1.59 0.66 -c 14.1
+$PROGRAM  -l 2 15.049999633908 1.33 0.0 15.1 1.59 0.66 -c 15.1
+$PROGRAM  -l 2 16.046688351385 1.33 0.0 16.1 1.59 0.66 -c 16.1
+$PROGRAM  -l 2 17.043377068862 1.33 0.0 17.1 1.59 0.66 -c 17.1
+$PROGRAM  -l 2 18.040065786340 1.33 0.0 18.1 1.59 0.66 -c 18.1
+$PROGRAM  -l 2 19.036754503817 1.33 0.0 19.1 1.59 0.66 -c 19.1
+$PROGRAM  -l 2 20.033443221294 1.33 0.0 20.1 1.59 0.66 -c 20.1
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+$PROGRAM  -l 2 22.026820656249 1.33 0.0 22.1 1.59 0.66 -c 22.1
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+$PROGRAM  -l 2 26.013575526159 1.33 0.0 26.1 1.59 0.66 -c 26.1
+$PROGRAM  -l 2 27.010264243636 1.33 0.0 27.1 1.59 0.66 -c 27.1
+$PROGRAM  -l 2 28.006952961113 1.33 0.0 28.1 1.59 0.66 -c 28.1
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+$PROGRAM  -l 2 46.944038593183 1.33 0.0 47.1 1.59 0.66 -c 47.1
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+$PROGRAM  -l 2 99.768540619482 1.33 0.0 100.1 1.59 0.66 -c 100.1
+

tests/shell/test02.txt

@@ -0,0 +1,400 @@
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tests/shell/test03.sh

@@ -0,0 +1,45 @@
+#!/bin/bash
+# This test explores the applicability limits of scattnlay
+# for Kai & Massoli's model:
+# L. Kai and P. Massoli, Applied Optics 33 (1994) 501-511.
+#
+# The model consists in a multilayered sphere with a radial 
+# profile of the refractive index ml = nl + i*kl given by:
+# nl = n1 + 0.5(nL - n1)(1 - cos(t*Theta)) and kl = 0.0,
+# where t = (l - 1)/(L - 1), n1 = 1.01nL, and nL = 1.33.
+# The size parameter is xl = x1 + t(xL - x1), where
+# l = 1,2,...,L, x1 = 0.001xL and L is the total number of
+# layers.
+#
+# WARNING: This test can take a LOT of time to completely run.
+
+PROGRAM='../../../scattnlay -l'
+
+numL=200
+maxL=1000
+num_xL=800
+max_xL=4000
+nL=1.33
+
+n1=$(echo "scale=5; 1.01*$nL" | bc -l)
+pi=$(echo "scale=10; 4*a(1)" | bc -l)
+
+for i in `seq 1 $numL`; # Total number of layers
+do
+  L=$(echo "scale=0; $i*$maxL/($numL)" | bc -l)
+  for j in `seq 1 $num_xL`; # Total number of size factors
+  do
+    xL=$(echo "scale=2; $j*$max_xL/($num_xL)" | bc -l)
+    x1=$(echo "scale=5; 0.001*$xL" | bc -l)
+    FULL_PROGRAM="$PROGRAM $L"
+    for l in `seq 1 $L`;
+    do
+      t=$(echo "scale=5; ($l-1)/($L-1)" | bc -l)
+      n=$(echo "scale=2; $n1+0.5*($nL-$n1)*(1-c($t*$pi))" | bc -l)
+      xl=$(echo "scale=2; $x1+$t*($xL-$x1)" | bc -l)
+      FULL_PROGRAM="$FULL_PROGRAM $xl $n 0.0"
+    done
+    FULL_PROGRAM="$FULL_PROGRAM -c L=$L,xL=$xL"
+    $FULL_PROGRAM
+  done
+done 

tests/shell/test04.py

@@ -0,0 +1,31 @@
+#! /usr/bin/python
+# This python script calculates the differential cross section
+# from the  scattering amplitudes values given by scattnlay.
+# It expects the values to be in a file named 'luneburg.txt'
+# and the output will be saved to a file named 'luneburg_fin.txt'
+
+import scipy
+import pylab
+
+def diff_scattering(Theta):
+  return scipy.cos(Theta*scipy.pi/180.0)
+
+data = scipy.loadtxt(fname = 'luneburg.txt', delimiter = ', ', skiprows = 2)
+
+S11 = data[ : , 1]*data[ : , 1] + data[ : , 2]*data[ : , 2] + data[ : , 3]*data[ : , 3] + data[ : , 4]*data[ : , 4]
+S11 = S11/7200.0
+S11 = scipy.vstack((data[ : , 0], S11, diff_scattering(data[ : , 0]))).transpose()
+
+scipy.savetxt('luneburg_fin.txt', S11)
+
+pylab.plot(S11[ : , 0], S11[ : , 1], S11[ : , 0], S11[ : , 2], color='k')
+
+ax = pylab.gca()
+ax.set_yscale('log')
+ax.set_ylim(1e-4, 1e3)
+
+pylab.draw()
+
+pylab.show()
+
+

tests/shell/test04.sh

@@ -0,0 +1,41 @@
+#!/bin/bash
+# This test case calculates the differential scattering
+# cross section from a Luneburg lens, as described in:
+# B. R. Johnson, Applied Optics 35 (1996) 3286-3296.
+#
+# The Luneburg lens is a sphere of radius a, with a
+# radially-varying index of refraction, given by:
+# m(r) = [2 - (r/a)**1]**(1/2)
+#
+# For the calculations, the Luneburg lens was approximated
+# as a multilayered sphere with 500 equally spaced layers.
+# The refractive index of each layer is defined to be equal to
+# m(r) at the midpoint of the layer: ml = [2 - (xm/xL)**1]**(1/2),
+# with xm = (xl-1 + xl)/2, for l = 1,2,...,L. The size
+# parameter in the lth layer is xl = l*xL/500. According to
+# geometrical optics theory, the differential cross section
+# can be expressed as:
+# d(Csca)/d(a**2*Omega) = cos(Theta)
+#
+# The differential cross section from wave optics is:
+# d(Csca)/d(a**2*Omega) = S11(Theta)/x**2
+
+PROGRAM='../../../scattnlay -l'
+
+L=500
+xL=60
+
+FULL_PROGRAM="$PROGRAM $L"
+for l in `seq 1 $L`; # Total number of layers
+do
+  xlM1=$(echo "scale=2; ($l-1)*$xL/$L" | bc -l)
+  xl=$(echo "scale=2; $l*$xL/$L" | bc -l)
+  xm=$(echo "scale=2; ($xlM1+$xl)/2" | bc -l)
+  ml=$(echo "scale=5; e(0.5*l(2-($xm/$xL)*($xm/$xL)))" | bc -l)
+
+  FULL_PROGRAM="$FULL_PROGRAM $xl $ml 0.0"
+done
+
+FULL_PROGRAM="$FULL_PROGRAM -t 0.0 180.0 721"
+$FULL_PROGRAM
+

tests/shell/test04.txt

@@ -0,0 +1,721 @@
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tests/shell/test05a.sh

@@ -0,0 +1,710 @@
+#! /bin/sh
+# This is a test against the experimental results for Au nanoshells published by:
+# A. M. Schwartzberg, T. Y. Olson, C. E. Talley and J. Z. Zhang,
+# J. Phys. Chem. B, 110 (2006) 19935-19944.
+#
+# This is for the first case: Rc=24.5 nm, tsh=5.7 nm
+
+PROGRAM='../../../scattnlay'
+
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tests/shell/test05b.sh

@@ -0,0 +1,710 @@
+#! /bin/sh
+# This is a test against the experimental results for Au nanoshells published by:
+# A. M. Schwartzberg, T. Y. Olson, C. E. Talley and J. Z. Zhang,
+# J. Phys. Chem. B, 110 (2006) 19935-19944.
+#
+# This is for the second case: Rc=28.0 nm, tsh=6.0 nm
+
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tests/shell/test05c.sh

@@ -0,0 +1,710 @@
+#! /bin/sh
+# This is a test against the experimental results for Au nanoshells published by:
+# A. M. Schwartzberg, T. Y. Olson, C. E. Talley and J. Z. Zhang,
+# J. Phys. Chem. B, 110 (2006) 19935-19944.
+#
+# This is for the third case: Rc=32.0 nm, tsh=5.8 nm
+
+PROGRAM='../../../scattnlay'
+
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tests/shell/test05d.sh

@@ -0,0 +1,710 @@
+#! /bin/sh
+# This is a test against the experimental results for Au nanoshells published by:
+# A. M. Schwartzberg, T. Y. Olson, C. E. Talley and J. Z. Zhang,
+# J. Phys. Chem. B, 110 (2006) 19935-19944.
+#
+# This is for the fourth case: Rc=41.0 nm, tsh=6.8 nm
+
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+
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tests/shell/test05e.sh

@@ -0,0 +1,710 @@
+#! /bin/sh
+# This is a test against the experimental results for Au nanoshells published by:
+# A. M. Schwartzberg, T. Y. Olson, C. E. Talley and J. Z. Zhang,
+# J. Phys. Chem. B, 110 (2006) 19935-19944.
+#
+# This is for the fifth case: Rc=41.0 nm, tsh=6.3 nm
+
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+
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tests/shell/test05f.sh

@@ -0,0 +1,710 @@
+#! /bin/sh
+# This is a test against the experimental results for Au nanoshells published by:
+# A. M. Schwartzberg, T. Y. Olson, C. E. Talley and J. Z. Zhang,
+# J. Phys. Chem. B, 110 (2006) 19935-19944.
+#
+# This is for the sixth case: Rc=37.0 nm, tsh=5.6 nm
+
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+
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tests/shell/test05g.sh

@@ -0,0 +1,710 @@
+#! /bin/sh
+# This is a test against the experimental results for Au nanoshells published by:
+# A. M. Schwartzberg, T. Y. Olson, C. E. Talley and J. Z. Zhang,
+# J. Phys. Chem. B, 110 (2006) 19935-19944.
+#
+# This is for the seventh case: Rc=36.0 nm, tsh=3.7 nm
+
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+
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tests/shell/test05h.sh

@@ -0,0 +1,710 @@
+#! /bin/sh
+# This is a test against the experimental results for Au nanoshells published by:
+# A. M. Schwartzberg, T. Y. Olson, C. E. Talley and J. Z. Zhang,
+# J. Phys. Chem. B, 110 (2006) 19935-19944.
+#
+# This is for the eighth case: Rc=44.0 nm, tsh=5.4 nm
+
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+
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tests/shell/test05i.sh

@@ -0,0 +1,710 @@
+#! /bin/sh
+# This is a test against the experimental results for Au nanoshells published by:
+# A. M. Schwartzberg, T. Y. Olson, C. E. Talley and J. Z. Zhang,
+# J. Phys. Chem. B, 110 (2006) 19935-19944.
+#
+# This is for the ninth case: Rc=44.0 nm, tsh=3.0 nm
+
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+
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ucomplex.cc

@@ -0,0 +1,274 @@
+//**********************************************************************************//
+//    Copyright (C) 2009-2015  Ovidio Pena <ovidio@bytesfall.com>                   //
+//                                                                                  //
+//    This file is part of scattnlay                                                //
+//                                                                                  //
+//    This program is free software: you can redistribute it and/or modify          //
+//    it under the terms of the GNU General Public License as published by          //
+//    the Free Software Foundation, either version 3 of the License, or             //
+//    (at your option) any later version.                                           //
+//                                                                                  //
+//    This program is distributed in the hope that it will be useful,               //
+//    but WITHOUT ANY WARRANTY; without even the implied warranty of                //
+//    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the                 //
+//    GNU General Public License for more details.                                  //
+//                                                                                  //
+//    The only additional remark is that we expect that all publications            //
+//    describing work using this software, or all commercial products               //
+//    using it, cite the following reference:                                       //
+//    [1] O. Pena and U. Pal, "Scattering of electromagnetic radiation by           //
+//        a multilayered sphere," Computer Physics Communications,                  //
+//        vol. 180, Nov. 2009, pp. 2348-2354.                                       //
+//                                                                                  //
+//    You should have received a copy of the GNU General Public License             //
+//    along with this program.  If not, see <http://www.gnu.org/licenses/>.         //
+//**********************************************************************************//
+
+#include <math.h>
+#include <stdlib.h>
+#include <stdio.h>
+#include "ucomplex.h"
+
+complex Cadd(complex z1, complex z2) {
+  complex zr;
+  zr.r = z1.r + z2.r;
+  zr.i = z1.i + z2.i;
+  return zr;
+}
+
+complex Csub(complex z1, complex z2) {
+  complex zr;
+  zr.r = z1.r - z2.r;
+  zr.i = z1.i - z2.i;
+  return zr;
+}
+
+complex Cmul(complex z1, complex z2) {
+  complex zr;
+  zr.r = (z1.r*z2.r) - (z1.i*z2.i);
+  zr.i = (z1.r*z2.i) + (z1.i*z2.r);
+  return zr;
+}
+
+complex RCmul(double r, complex z) {
+  complex zr;
+  zr.r = z.r*r;
+  zr.i = z.i*r;
+  return zr;
+}
+
+complex Cdiv(complex z1, complex z2) {
+/* The following algorithm is used to properly handle
+   denominator overflow:
+
+              |  a + b(d/c)   b - a(d/c)
+              |  ---------- + ----------- I     if |d| < |c|
+   a + b I    |  c + d(d/c)   c + d(d/c)
+   -------  = |
+   c + d I    |  b + a(c/d)   -a + b(c/d)
+              |  ---------- + ----------- I     if |d| >= |c|
+              |  d + c(c/d)   d + c(c/d)
+*/
+  complex zr;
+  double tmp, denom;
+
+  if(fabs(z2.r) > fabs(z2.i)) {
+    tmp = z2.i/z2.r;
+    denom = z2.r + z2.i*tmp;
+    zr.r = (z1.r + z1.i*tmp)/denom;
+    zr.i = (z1.i - z1.r*tmp)/denom;
+  } else {
+    tmp = z2.r/z2.i;
+    denom = z2.i + z2.r*tmp;
+    zr.r = (z1.i + z1.r*tmp)/denom;
+    zr.i = (-z1.r + z1.i*tmp)/denom;
+  }
+  return zr;
+}    
+
+complex Complex(double re, double im) {
+  complex zr;
+  zr.r = re;
+  zr.i = im;
+  return zr;
+}
+
+double Cabs(complex z) {
+  double r;
+  r = sqrt((z.r*z.r) + (z.i*z.i));
+  return r;
+}
+
+double Carc(complex z) {
+  double r;
+  r = atan2(z.i, z.r);
+  return r;
+}
+
+complex Conjg(complex z) {
+  complex zr;
+  zr.r = z.r;
+  zr.i = -z.i;
+  return zr;
+}
+
+complex Cinv(complex z) {
+  complex zr;
+  double denom;
+
+  denom = (z.r*z.r) + (z.i*z.i);
+  zr.r = z.r/denom;
+  zr.i = -z.i/denom;
+  return zr;
+}
+
+complex Cexp(complex z) {
+// exp(a + ib) = exp(a)*exp(ib) = exp(a)*[cos(b) + i sin(b)]
+  complex zr;
+  double expz;
+
+  expz = exp(z.r);
+  zr.r = expz*cos(z.i);
+  zr.i = expz*sin(z.i);
+  return zr;
+}
+
+complex Clog(complex z) {
+// ln( p exp(i0)) = ln(p) + i0 + 2kpi
+  complex zr;
+  zr.r = log(Cabs(z));
+  zr.i = atan2(z.i, z.r);
+  return zr;
+}
+
+complex Csqrt(complex z) {
+  complex zr;
+  double root, q;
+
+  if((z.r != 0.0) ||(z.i != 0.0)) {
+    root = sqrt(0.5*(fabs(z.r) + Cabs(z)));
+    q = z.i/(2.0*root);
+    if(z.r >= 0.0) {
+      zr.r = root;
+      zr.i = q;
+    } else if(z.i < 0.0) {
+             zr.r = -q;
+             zr.i = -root;
+           } else {
+             zr.r =  q;
+             zr.i =  root;
+           }
+    } else zr = z;
+  return zr;
+}
+
+// complex trigonometric functions
+
+// complex cosinus
+complex Ccos(complex z) {
+// cos(x+iy) = cos(x).cos(iy) - sin(x).sin(iy)
+// cos(ix) = cosh(x) et sin(ix) = i.sinh(x)
+  complex zr;
+  zr.r = cos(z.r)*cosh(z.i);
+  zr.i = -sin(z.r)*sinh(z.i);
+  return zr;
+}
+
+// complex sinus
+complex Csin(complex z) {
+// sin(x+iy) = sin(x).cos(iy) + cos(x).sin(iy)
+// cos(ix) = cosh(x) et sin(ix) = i.sinh(x)
+  complex zr;
+  zr.r = sin(z.r)*cosh(z.i);
+  zr.i = cos(z.r)*sinh(z.i);
+  return zr;
+}
+
+// tangent
+complex Ctan(complex z) {
+  return Cdiv(Csin(z), Ccos(z));
+}
+
+// Inverse trigonometric functions
+
+// complex arc cosinus
+complex Carc_cos(complex z) {
+// arccos(z) = -i.arcch(z)
+  complex temp = Carc_ch(z);
+  return Complex(temp.i, -temp.r);
+}
+
+// complex arc sinus
+complex Carc_sin(complex z) {
+// arcsin(z) = -i.arcsh(i.z)
+  complex temp = Carc_sh(Complex(-z.i, z.r));
+  return Complex(temp.i, -temp.r);
+}
+
+// complex arc tangent
+complex Carc_tan(complex z) {
+// arctg(z) = -i.arcth(i.z)
+  complex temp = Carc_th(Complex(-z.i, z.r));
+  return Complex(temp.i, -temp.r);
+}
+
+// Hyberbolic complex functions
+
+// complex hyberbolic cosinus
+complex Cch(complex z) {
+// cosh(x+iy) = cosh(x).cosh(iy) + sinh(x).sinh(iy)
+// cosh(iy) = cos(y) et sinh(iy) = i.sin(y)
+  complex zr;
+  zr.r = cosh(z.r)*cos(z.i);
+  zr.i = sinh(z.r)*sin(z.i);
+  return zr;
+}
+
+// complex hyberbolic sinus
+complex Csh(complex z) {
+// sinh(x+iy) = sinh(x).cosh(iy) + cosh(x).sinh(iy)
+// cosh(iy) = cos(y) et sinh(iy) = i.sin(y)
+  complex zr;
+  zr.r = sinh(z.r)*cos(z.i);
+  zr.i = cosh(z.r)*sin(z.i);
+  return zr;
+}
+
+// complex hyberbolic tangent
+complex Cth(complex z) {
+// th(x) = sinh(x)/cosh(x)
+// cosh(x) > 1 qq x
+  complex temp, zr;
+  temp = Cch(z);
+  zr = Csh(z);
+  return Cdiv(zr, temp);
+}
+
+// Inverse complex hyperbolic functions
+
+// complex hyperbolic arc cosinus
+complex Carc_ch(complex z) {
+//                        _________
+// arcch(z) = -/+ ln(z + V z.z - 1 )
+  complex zr;
+  complex z2 = Cmul(z, z);
+  zr = Clog(Cadd(z, Csqrt(Complex(z2.r - 1.0, z2.i))));
+  zr.r = -zr.r;
+  zr.i = -zr.i;
+  return zr;
+}
+
+// complex hyperbolic arc sinus
+complex Carc_sh(complex z) {
+//                    ________
+// arcsh(z) = ln(z + V 1 + z.z)
+  complex z2 = Cmul(z, z);
+  return Clog(Cadd(z, Csqrt(Complex(z2.r + 1.0, z2.i))));
+}
+
+// complex hyperbolic arc tangent
+complex Carc_th(complex z) {
+// arcth(z) = 1/2 ln((z + 1)/(1 - z))
+  return RCmul(0.5, Clog(Cdiv(Complex(z.r + 1.0, z.i), Complex(1.0 - z.r, -z.i))));
+}
+

ucomplex.h

@@ -0,0 +1,69 @@
+//**********************************************************************************//
+//    Copyright (C) 2009-2015  Ovidio Pena <ovidio@bytesfall.com>                   //
+//                                                                                  //
+//    This file is part of scattnlay                                                //
+//                                                                                  //
+//    This program is free software: you can redistribute it and/or modify          //
+//    it under the terms of the GNU General Public License as published by          //
+//    the Free Software Foundation, either version 3 of the License, or             //
+//    (at your option) any later version.                                           //
+//                                                                                  //
+//    This program is distributed in the hope that it will be useful,               //
+//    but WITHOUT ANY WARRANTY; without even the implied warranty of                //
+//    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the                 //
+//    GNU General Public License for more details.                                  //
+//                                                                                  //
+//    The only additional remark is that we expect that all publications            //
+//    describing work using this software, or all commercial products               //
+//    using it, cite the following reference:                                       //
+//    [1] O. Pena and U. Pal, "Scattering of electromagnetic radiation by           //
+//        a multilayered sphere," Computer Physics Communications,                  //
+//        vol. 180, Nov. 2009, pp. 2348-2354.                                       //
+//                                                                                  //
+//    You should have received a copy of the GNU General Public License             //
+//    along with this program.  If not, see <http://www.gnu.org/licenses/>.         //
+//**********************************************************************************//
+
+typedef struct COMPLEX {double r,i;} complex;
+
+// Complex functions
+complex Cadd(complex z1, complex z2);  // addition
+complex Csub(complex z1, complex z2);  // substraction
+complex Cmul(complex z1, complex z2);  // multiplication
+complex RCmul(double r, complex z);    // double*complex
+complex Cdiv(complex z1, complex z2);  // division
+complex Complex(double r, double i);   // convert to double
+
+complex Conjg(complex z);    // conjuge
+complex Cinv(complex z);     // inverse function 1/z
+
+// Complex functions with double return values
+double Cabs(complex z);      // module
+double Carc(complex z);      // argument : z1 / z = p.e^ia
+
+// Elementary functions
+complex Cexp(complex z);    // exponential
+complex Clog(complex z);    // natural logarithm
+complex Csqrt(complex z);   // square root
+
+// Complex trigonometric functions 
+complex Ccos(complex z);    // cosinus
+complex Csin(complex z);    // sinus
+complex Ctan(complex z);    // tangent
+
+// Inverse complex trigonometric functions
+complex Carc_cos(complex z);   // arc cosinus
+complex Carc_sin(complex z);   // arc sinus
+complex Carc_tan(complex z);   // arc tangent
+
+// Hyperbolic complex functions
+complex Cch(complex z);     // hyperbolic cosinus
+complex Csh(complex z);     // hyperbolic sinus
+complex Cth(complex z);     // hyperbolic tangent
+
+// Inverse hyperbolic complex functions
+complex Carc_ch(complex z); // hyperbolic arc cosinus
+complex Carc_sh(complex z); // hyperbolic arc sinus
+complex Carc_th(complex z); // hyperbolic arc tangente
+
+