Add a useful package (from Source forge) for octave

[CreaPhase.git] / octave_packages / specfun-1.1.0 / Ci.m

diff --git a/octave_packages/specfun-1.1.0/Ci.m b/octave_packages/specfun-1.1.0/Ci.m
new file mode 100644 (file)
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+++ b/octave_packages/specfun-1.1.0/Ci.m
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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} =} Ci (@var{z})
+## Compute the cosine integral function defined by:
+## @verbatim
+##                    Inf
+##                   /
+##           Ci(x) = | cos(t)/t dt
+##                   /
+##                   x
+## @end verbatim
+## @seealso{cosint, Si, sinint, expint, expint_Ei}
+## @end deftypefn
+
+function y = Ci(z)
+  if (nargin != 1)
+    print_usage;
+  endif
+  y = z;
+  y(z == 0) = -Inf; 
+  y(real(z) == 0 & imag(z) >0)  = 0.5*(expint_Ei(i.*y(real(z) == 0 & imag(z) >0))+expint_Ei(-i.*y(real(z) == 0 & imag(z) >0)))+ i.*pi./2;
+  y(real(z) == 0 & imag(z) <0) = 0.5*(expint_Ei(i.*y(real(z) == 0 & imag(z) <0))+expint_Ei(-i.*y(real(z) == 0 & imag(z) <0)))-i*pi./2;
+  y(real(z)>=0) = -0.5.*(expint_E1(i.*y(real(z)>=0) )+expint_E1(-i.*y(real(z)>=0) ));
+  y(real(z)<0) = -0.5.*(expint_E1(-i.*y(real(z)<0))+expint_E1(i.*y(real(z)<0)))+i*pi;
+endfunction