[Octave-cvsupdate] SF.net SVN: octave:[10290] trunk/octave-forge/main/optim

[<jpi...@us...>]

Revision: 10290
          http://octave.svn.sourceforge.net/octave/?rev=10290&view=rev
Author:   jpicarbajal
Date:     2012-04-19 09:00:48 +0000 (Thu, 19 Apr 2012)
Log Message:
-----------
optim: Numerical derivatives using the Cauchy integral. Was in worng place

Modified Paths:
--------------
    trunk/octave-forge/main/optim/DESCRIPTION

Removed Paths:
-------------
    trunk/octave-forge/main/optim/cauchy.m

Modified: trunk/octave-forge/main/optim/DESCRIPTION
===================================================================
--- trunk/octave-forge/main/optim/DESCRIPTION	2012-04-19 08:28:21 UTC (rev 10289)
+++ trunk/octave-forge/main/optim/DESCRIPTION	2012-04-19 09:00:48 UTC (rev 10290)
@@ -1,6 +1,6 @@
 Name: Optim
-Version: 1.0.18
-Date: 2011-11-30
+Version: 1.1.0
+Date: 2012-XX-XX
 Author: various authors
 Maintainer: Octave-Forge community <oct...@li...>
 Title: Optimization.

Deleted: trunk/octave-forge/main/optim/cauchy.m
===================================================================
--- trunk/octave-forge/main/optim/cauchy.m	2012-04-19 08:28:21 UTC (rev 10289)
+++ trunk/octave-forge/main/optim/cauchy.m	2012-04-19 09:00:48 UTC (rev 10290)
@@ -1,123 +0,0 @@
-## Copyright (C) 2011 Fernando Damian Nieuwveldt <fdn...@gm...>
-## 2012 Adapted by Juan Pablo Carbajal <car...@if...>
-##
-## 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,
-## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
-## GNU General Public License for more details.
-
-## -*- texinfo -*-
-## @deftypefn {Function File} {} cauchy (@var{N}, @var{r}, @var{x}, @var{f} )
-## Return the Taylor coefficients and numerical differentiation of a function
-## @var{f} for the first @var{N-1} coefficients or derivatives using the fft.
-## @var{N} is the number of points to evaluate,
-## @var{r} is the radius of convergence, needs to be chosen less then the smallest singularity,
-## @var{x} is point to evaluate the Taylor expansion or differentiation. For example,
-##
-## If @var{x} is a scalar, the function @var{f} is evaluated in a row vector
-## of length @var{N}. If @var{x} is a column vector, @var{f} is evaluated in a
-## matrix of length(x)-by-N elements and must return a matrix of the same size.
-##
-## @example
-## @group
-## d = cauchy(16,1.5,0,@(x) exp(x));
-## @result{} d(2) = 1.0000 # first (2-1) derivative of function f (index starts from zero)
-## @end group
-## @end example
-## @end deftypefn
-
-function deriv = cauchy(N, r, x, f)
-
-  if nargin != 4
-    print_usage ();
-  end
-
-  [nx m]   = size (x);
-  if m > 1
-    error('cauchy:InvalidArgument', 'The 3rd argument must be a column vector');
-  end
-
-  n        = 0:N-1;
-  th       = 2*pi*n/N;
-
-  f_p = f (bsxfun (@plus, x, r * exp (i * th) ) );
-
-  evalfft  = real(fft (f_p, [], 2));
-
-  deriv    = bsxfun (@times, evalfft, 1./(N*(r.^n)).* factorial(n)) ;
-
-endfunction
-
-%!demo
-%! # Cauchy integral formula: Application to Hermite polynomials
-%! # Author: Fernando Damian Nieuwveldt
-%! # Edited by: Juan Pablo Carbajal
-%!
-%! function g = hermite(order,x)
-%!
-%!   ## N should be bigger than order+1
-%!   N      = 32;
-%!   r      = 0.5;
-%!   Hnx    = @(t) exp ( bsxfun (@minus, kron(t(:).', x(:)) , t(:).'.^2/2) );
-%!   Hnxfft = cauchy(N, r, 0, Hnx);
-%!   g      = Hnxfft(:, order+1);
-%!
-%! endfunction
-%!
-%! t    = linspace(-1,1,30);
-%! he2  = hermite(2,t);
-%! he2_ = t.^2-1;
-%!
-%! plot(t,he2,'bo;Contour integral representation;', t,he2_,'r;Exact;');
-%! grid
-%! clear all
-%!
-%! % --------------------------------------------------------------------------
-%! % The plots compares the approximation of the Hermite polynomial using the
-%! % Cauchy integral (circles) and the corresposind polynomial H_2(x) = x.^2 - 1.
-%! % See http://en.wikipedia.org/wiki/Hermite_polynomials#Contour_integral_representation
-
-%!demo
-%! # Cauchy integral formula: Application to Hermite polynomials
-%! # Author: Fernando Damian Nieuwveldt
-%! # Edited by: Juan Pablo Carbajal
-%!
-%!  xx = sort (rand (100,1));
-%!  yy = sin (3*2*pi*xx);
-%!
-%!  # Exact first derivative derivative
-%!  diffy = 6*pi*cos (3*2*pi*xx);
-%!
-%!  np = [10 15 30 100];
-%!
-%!  for i =1:4
-%!    idx = sort(randperm (100,np(i)));
-%!    x   = xx(idx);
-%!    y   = yy(idx);
-%!
-%!    p     = spline (x,y);
-%!    yval  = ppval (ppder(p),x);
-%!    # Use the cauchy formula for computing the derivatives
-%!    deriv =  cauchy (fix (np(i)/4), .1, x, @(x) sin (3*2*pi*x));
-%!
-%!    subplot(2,2,i)
-%!    h = plot(xx,diffy,'-b;Exact;',...
-%!             x,yval,'-or;ppder solution;',...
-%!             x,deriv(:,2),'-og;Cauchy formula;');
-%!    set(h(1),'linewidth',2);
-%!    set(h(2:3),'markersize',3);
-%!
-%!    legend('Location','Northoutside','Orientation','horizontal');
-%!
-%!    if i!=1
-%!      legend('hide','Orientation','horizontal')
-%!    end
-%!  end
-%!
-%! % --------------------------------------------------------------------------
-%! % The plots compares the derivatives calculated with Cauchy and with ppder.
-%! % Each subplot shows the results with increasing number of samples.

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