The module "mloop" of the Mastrave modelling library

Copyright and license notice of the function mloop

Copyright © 2009,2010,2011,2012,2013,2014 Daniele de Rigo

The file mloop.m is part of Mastrave.

Mastrave 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.

Mastrave 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 Mastrave. If not, see http://www.gnu.org/licenses/.

Function declaration

 [transformed_obj, ...] = mloop( until_, func, obj, ... )

Description

Module for supporting tail-recursive application of a generic function handled by func to a object obj (or more objects passed following the first object obj ). The tail-recursion is implemented as a loop which is intended to address dynamic assignments so that the only possible parallelization (planned) could rely on the definition of the func handle, especially when obj is composed by a large amount of elements. The loop ends according to the until_ argument.

Input arguments

 until_             ::scalar_numel|function_handle::
                    Criterion for terminating the loop.  It may be a 
                    scalar nonnegative integer, meaning that the loop
                    is to be reapeted  until_  times.
                    It may also be a function handle.  If so, it is
                    expected to be a function whose number of input 
                    arguments is the same as the number of objects
                    passed to  @mloop .  The function must return as 
                    output a logical scalar.

 func               ::function_handle::
                    Handle of the function to be applied to  obj  and 
                    to the possible subsequently passed objects.  It
                    is expected to be a function whose number of input 
                    and output arguments is the same and is compatible
                    with the number of objects passed to  @mloop .

 obj                ::generic::
                    Object on which to apply the function handled by
                     func  until the  until_  condition terminates the 
                    loop.
                    More than one object can be passed with an 
                    arbitrary number of optional arguments.

Example of usage

   % Basic usage
   c = mloop( 1, @cumsum, [1 0 0 0 0 0 0 0 0] )
   c = mloop( 2, @cumsum, [1 0 0 0 0 0 0 0 0] )
   c = mloop( 3, @cumsum, [1 0 0 0 0 0 0 0 0] )

   % Fibonacci numbers  (sequence A000045 in OEIS: http://oeis.org/A000045)
   mloop( 10, @(x)[ x sum(x(end+[-1:0])) ], [0 1] )
   % Lucas numbers      (sequence A000032 in OEIS: http://oeis.org/A000032)
   mloop( 10, @(x)[ x sum(x(end+[-1:0])) ], [2 1] )
   % Tribonacci numbers (sequence A000073 in OEIS: http://oeis.org/A000073)
   mloop( 10, @(x)[ x sum(x(end+[-2:0])) ], [0 0 1] )

   % Implementing a cellular automata
   colormap( 'default' );
   rule  = @(x)[ x; mod( filter2( [1 1 1], x(end,:) ), 2 ) ];
   C     = mloop( 300, rule, rand(1,300)>0.5  );
   imagesc( C ); pause(3)
   C     = mloop( 300, rule, rand(1,300)>0.05 );
   imagesc( C ); pause(3)
   C     = mloop( 300, rule, rand(1,300)>0.99 );
   imagesc( C )

   % Implementing a Julia set
   [x,y] = meshgrid( linspace(-1,1,400)*pi/2 ); 
   z     = x + 1i*y;
   function [z,z0] = julia(z,z0)
      z  = z.^2 + z0;
      imagesc( 1-atan(abs(z))/pi*2 ); axis equal; pause(0.1);
   end
   mloop( 40, @julia, z, 0.37*(1+1i)  );
   mloop( 40, @julia, z, .65i         );
   mloop( 40, @julia, z, -0.8 -0.175i );
   mloop( 50, @julia, z, -0.4 +0.6i   );
   mloop( 50, @julia, z, 0.285 +0.01i );

   % A more complex example:
   % Spatially correlated noise and downsampling with binary dithering
   [D, d]         = deal( 25, 13 ) % downsampling diameter and radius
   generator_func = @(M)interp2(M,1,'spline')+.5*rand(size(M)*2-1)
   get_corrnoise  = @(n)mloop(8,generator_func,rand(n))
   norm_func      = @(M)(M-min(M(:)))/range(M(:));
   M              = norm_func( get_corrnoise(5) );
   colormap( 1 - colormap( 'gray' ) );
   subplot( 1, 3, 1 ); imagesc( M );
   Mdown          = mblk_fun( M, @(M)isfinite(M)*mean(M(:)), D ); 
   subplot( 1, 3, 2 ); imagesc( Mdown );
   Mdn            = norm_func(  Mdown ); 
   z = zeros(size(M)); z(d:D:end,d:D:end) = 1;
   % see also mfreq_matrix
   Z = double( mloop(                                                 ...
      d, @(Z,v)deal(Z|filter2(ones(3),Mdn.*Z>v),(v^.5+1/d)^2), z, 1/D ...
   ));
   subplot( 1, 3, 3 ); imagesc( Z );

See also:
   mstream, mblk_fun, func_let, mfreq_matrix



Keywords:
   tail-recursion, looping, anonymous-function



Version: 0.3.9

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