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diff scripts/specfun/expint.m @ 16584:2f766ceeb03e

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Add ellipj, ellipke, and expint functions from Octave Forge * ellipj.cc, ellipke.m, expint.m: New files. * libinterp/corefcn/module.mk (COREFCN_SRC): Add ellipj.cc to the list. * scripts/specfun/module.mk (specfun_FCN_FILES): Add ellipke.m and expint.m to the list. * __unimplemented__.m (missing_functions): Remove ellipj, ellipke, and expint from the list. * arith.txi: Include ellipj, ellipke, and expint docstrings. * NEWS: Mention ellipj, ellipke, and expint.
author Mike Miller <mtmiller@ieee.org>
date Wed, 24 Apr 2013 23:22:50 -0400
parents
children 1a3bfb14b5da
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+## Copyright (C) 2006 Sylvain Pelissier <sylvain.pelissier@gmail.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.
+##
+## You should have received a copy of the GNU General Public License along with
+## this program; if not, see <http://www.gnu.org/licenses/>.
+
+## -*- texinfo -*-
+## @deftypefn {Function File} {@var{y} =} expint (@var{x})
+## Compute the exponential integral,
+## @verbatim
+##                    infinity
+##                   /
+##       expint(x) = | exp(t)/t dt
+##                   /
+##                  x
+## @end verbatim
+## @seealso{expint_E1, expint_Ei}
+## @end deftypefn
+
+function y = expint(x)
+  if (nargin != 1)
+    print_usage;
+  endif
+  y = expint_E1(x);
+endfunction
+
+## -*- texinfo -*-
+## @deftypefn {Function File} {@var{y} =} expint_E1 (@var{x})
+## Compute the exponential integral,
+## @verbatim
+##                    infinity
+##                   /
+##       expint(x) = | exp(t)/t dt
+##                   /
+##                  x
+## @end verbatim
+## @seealso{expint, expint_Ei}
+## @end deftypefn
+
+function y = expint_E1(x)
+  if (nargin != 1)
+    print_usage;
+  endif
+  y = x;
+  y(imag(x) > 0 & imag(x) != 0) = -expint_Ei(-y(imag(x) > 0 & imag(x) != 0)) -i.*pi;
+  y(imag(x) < 0 & imag(x) != 0) = -expint_Ei(-y(imag(x) < 0 & imag(x) != 0)) +i.*pi;
+  y(real(x) >= 0 & imag(x)==0) = -expint_Ei(-y(real(x) >= 0 & imag(x)==0));
+  y(real(x) < 0 & imag(x)==0) = -expint_Ei(-y(real(x) < 0 & imag(x)==0)) -i.*pi;
+endfunction
+
+## -*- texinfo -*-
+## @deftypefn {Function File} {@var{y} =} expint_Ei (@var{x})
+## Compute the exponential integral,
+## @verbatim
+##                      infinity
+##                     /
+##    expint_Ei(x) = - | exp(t)/t dt
+##                     /
+##                     -x
+## @end verbatim
+## @seealso{expint, expint_E1}
+## @end deftypefn
+
+function y = expint_Ei(x)
+  if (nargin != 1)
+    print_usage;
+  endif
+  y = zeros(size(x));
+  F = @(x) exp(-x)./x;
+  s = prod(size(x));
+  for t = 1:s;
+    if(x(t)<0 && imag(x(t)) == 0)
+      y(t) = -quad(F,-x(t),Inf);
+    else
+      if(abs(x(t)) > 2 && imag(x(t)) == 0)
+        y(t) = expint_Ei(2) - quad(F,-x(t),-2);
+      else
+        if(abs(x(t)) >= 10)
+          if(imag(x(t)) <= 0)
+            a1 = 4.03640;
+            a2 = 1.15198;
+            b1 = 5.03637;
+            b2 = 4.19160;
+            y(t) = -(x(t).^2 - a1.*x(t) + a2)./((x(t).^2-b1.*x(t)+b2).*(-x(t)).*exp(-x(t)))-i.*pi;
+          else
+            y(t) = conj(expint_Ei(conj(x(t))));
+          endif;
+        ## Serie Expansion
+        else
+          for k = 1:100;
+            y(t) = y(t) + x(t).^k./(k.*factorial(k));
+          endfor
+          y(t) = 0.577215664901532860606512090082402431 + log(x(t)) + y(t);
+        endif
+      endif
+    endif
+  endfor
+endfunction