iterating_MATLAB_commands.m

% Iterating MATLAB Commands
% from https://nickhigham.wordpress.com/2016/05/13/iterating-matlab-commands/

% Some MATLAB commands can be ?applied to themselves?. A good example is
% help help, which provides help on the help function. For what other
% functions fun is fun fun a legal statement that produces something
% interesting? Here are some examples (by no means an exhaustive list).
%
% char char
% demo demo
% diary diary
% doc doc
% diff diff
% double double
% edit edit
% error error
% iskeyword iskeyword
% length length
% magic magic
% max max
% size size
% sort sort
% spy spy
% unique unique
% upper upper
% warning warning
% which which
%
% Can you see why these are legal and guess what the effect of these calls
% will be? Search for ?command-function duality? in the MATLAB help for
% some clues.
%
% Are there any legal triple invocations? Yes, for example
%
% and and and
% char char char
% isa isa isa
% max max max
% Indeed char can be iterated as many times as you like, but and and isa
% can be iterated three times but not twice.
%
% If you think of additional interesting examples, please add them to the
% comments below.

%% grab the folders and files on the path:

restoredefaultpath
[~,~,~,~,~,~,folders] = regexp( path , ':' );
folders = setdiff( folders , pwd );
files = {};
for f = 1:numel(folders)
    files = cat( 1 , files , dirRecurse( folders{f} ) );
end
files = unique( files );
% we know these work, but they break the rest of our search!
dangerous = { ...
    'cell.m' , ...                      size(cell cell cell) is 99 x 99,
    ...                                 size(cell cell cell cell) is 99 x 99 x 99
    ...                                 and so forth...dangerous when output isn't suppressed
    'depdir.m', ...                     at 5 and on takes considerable time
    'depfun.m', ...                     at 5 and on takes considerable time
    'matlabpath.m' , ...                breaks the path
    'memmap_data_handle_holder.m' , ... causes a segfault in 'menu menu'???
    'path.m' , ...                      breaks the path
    'spinmap.m', ...                    first argument is the duration of a while loop
    'rjr.m' ...                         second argument is ignored and gets us caught in a while loop
    };
files = setdiff( files , dangerous )';
F = numel(files);

%% check which can be run how many times

N = 10;
invocations = false(F,N);
exceptions = cell(F,N);
for n = 2:N
    for f = 1:F
        fun = files{f}(1:end-2);
        command = [ repmat([fun ' '],1,n-1) fun ];
        fprintf( 'Trying %s\n' , command );
        try
            eval( sprintf('%s' , command ) );
            invocations(f,n) = true;
        catch ME
            exceptions{f,n} = ME;
        end
    end
end
save iterating_MATLAB_commands.mat files dangerous invocations exceptions
close all

%% did we find all of Nich Higham's?

highamTwice = cellfun( @(s) [s '.m'] , { ...
    'char', 'demo', 'diary', 'doc', 'diff', 'double', 'edit', ...
    'error', 'iskeyword', 'length', 'magic', 'max' ,'size' ,'sort' , ...
    'spy' ,'unique' ,'upper' ,'warning', 'which'} , ...
    'UniformOutput', false);
highamTwice( ~ismember( highamTwice , files(invocations(:,2) ) ) )

%% find the interesting ones

% how many can be invoked for how long?
clf
plot(2:10, sum(invocations(:,2:end),1),'.-b','Linewidth',4,'Markersize',30)
hold on

% how many can uniquely be invoked that long?
maxInvocations = invocations;
for f = 1:F
    idx = find( invocations(f,:) , 1, 'last' );
    maxInvocations(f,1:idx-1) = false;
end
plot(2:10, sum(maxInvocations(:,2:end),1),'.-r','Linewidth',4,'Markersize',30)

set(gca,'FontSize',14,'FontName','Monospaced')
xlabel('Self-Invocation Count')
ylabel('Function Count')
legend('Invocations of Functions','Maximum acheived invocations')
print(gcf,'-dpng','invocations.png');

%% so what are those cool ones?

% !!! MATLAB does not have nargin/nargout information for ...
narginIssues = {'colstyle.m','enumeration.m','events.m','gcf.m', ...
    'libisloaded.m','loadobj.m','metaclass.m','properties.m', ...
    'saveobj.m','superclasses.m','ishghandle.m','ancestor.m','findobj.m'};
for n = 1:N
    fprintf( '\n---------- %i ----------\n', n );
    these = files( maxInvocations(:,n) );
    these = setdiff( these , narginIssues )';
    toPrint = cellfun( @(s) sprintf('% 2i args - %s',nargin(s(1:end-2)), [ repmat([s(1:end-2) ' '],1,n-1) s(1:end-2) ]), these , 'UniformOutput' , false);
    disp(toPrint)
end