The module "mloop" of the Mastrave modelling library
Copyright © 2009,2010,2011,2012,2013,2014 Daniele de Rigo
The file mloop.m is part of Mastrave.
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[transformed_obj, ...] = mloop( until_, func, obj, ... )
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.
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.
% 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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