gppretty.m

function [gene_latex_expr,full_latex_expr,expr_sym,cell_expr_sym]=gppretty(gp,ind,knockout)
%GPPRETTY GPTIPS Function to simplify multigene symbolic regression model, 
%create symbolic model objects and create LaTex versions of the expressions.
%
%   *REQUIRES SYMBOLIC MATH TOOLBOX*
%
%   Intended to simplify single and multigene symbolic regression
%   expressions created with GPTIPS using the REGRESSMULTI_FITFUN fitness 
%   function.
%
%   It is assumed that the overall symbolic model is a linear superposition
%   of the M genes weighted by regression coefficients plus a bias (offset) 
%   term.
%   I.e.
%   ypred = c0 + c1*tree1 + ... + cM*treeM'
%   where c0 = bias and c1, ..., cM are the gene weights.
%
%   GPPRETTY(GP,IND) prettifies the population member with population index
%   IND in the GPTIPS datastructure GP.
%
%   GPPRETTY(GP,''BEST'') prettifies the best individual of the run.
%
%   GPPRETTY(GP,''VALBEST'') prettifies the individual that performed best 
%   on the validation data (if it exists).
%
%   GPPRETTY can also accept an optional third argument KNOCKOUT which
%   should be a boolean vector the with same number of entries as genes in
%   the individual to be simplified. This simplifies the individual with 
%   the indicated genes removed ('knocked out'). 
%   E.g. GPPRETTY(GP,'BEST',[1 0 0 1]) knocks out the 1st and 4th genes 
%   from the best individual of run, then simplifies it. Note that the gene
%   weights are recomputed from the training data when genes are 
%   knocked out.
%
%   GENE_LATEX_EXPR = GPPRETTY(GP,''BEST'') returns a string GENE_LATEX_EXPR 
%   containing the simplified LaTeX representation of the separate genes of
%   the multigene expression formatted as a LaTeX equation array. The bias 
%   term is 'folded' in with the first gene. The genes are simplified 
%   separately.   
%
%   Remarks:
%   Each line of the LaTeX equation array is a simplified gene.
%   To be rendered, the equation array represented by the string 
%   GENE_LATEX_EXPR must be copied and pasted into the correct context in 
%   an appropriate LaTeX document, for example:
%
%   \documentclass{article}
%   \pagestyle{empty}
%   \begin{document}
%   \begin{eqnarray*}y&=& 6.565- 0.2017\,\tanh \left( {\it x_2} \right)  \left(  0.8519\,{\it x_3}-{\it x_1} \right)\\&-& 0.3174\,\tanh \left( - 0.923039\,{\it x_3}\, \left( {\it x_3}-{\it x_1} \right) -{\it x_2} \right)\end{eqnarray*}
%   \end{document}
%
%   In the above LaTeX code above the line beginning "\begin{eqnarray*}" is
%   the string GENE_LATEX_EXPR that is generated by GPPRETTY. The rest you 
%   must supply yourself.
%
%   [GENE_LATEX_EXPR,FULL_LATEX_EXPR] = GPPRETTY(GP,''BEST'') also returns 
%   FULL_LATEX_EXPR containing the simplified LaTeX representation of the 
%   combined genes of the multigene expression. That is, the genes are 
%   combined, then simplified.
%
%   Remarks:
%   Again, to be rendered, the equation represented by the string 
%   FULL_LATEX_EXPR must be copied and pasted into the correct context in 
%   an appropriate LaTeX document, for example:
%
%   \documentclass{article}
%   \pagestyle{empty}
%   \begin{document}
%   $
%   y= 7.255+ 0.2060\,{\it x_2}+ 0.2086\,{\it x_3}- 0.2086\,{\it x_1}- 0.2086\,\tanh \left( {\it x_1} \right)
%   $
%   \end{document}
%
%   Note:
%   MATLAB currently does not render LaTeX well. At time of writing a good 
%   web-based LaTeX processor that outputs high quality images is available 
%   at http://sciencesoft.at/latex/
%
%   Other usages:
%   [GENE_LATEX_EXPR,FULL_LATEX_EXPR,EXPR_SYM]=GPPRETTY(GP,''BEST'') does 
%   the above and and returns the entire simplified symbolic expression as 
%   an object of class 'sym' as EXPR_SYM
%
%   [GENE_LATEX_EXPR,FULL_LATEX_EXPR,EXPR_SYM,CELL_EXPR_SYM]=GPPRETTY(GP,''BEST'') 
%   does the above and also returns the individual simplified gene 
%   expressions as a cell array of 'sym' objects CELL_EXPR_SYM.
%
%
%   Known problems:
%   Occasionally, the underlying symbolic math software causes MATLAB to
%   crash when attempting to simplify some expressions. The cause of this
%   is currently unknown but it tends to happen with deep trees.
%
%
%   (c) Dominic Searson 2008
%
%   v1.0
%
%   See also REGRESSMULTI_FITFUN, POPBROWSER, GPREFORMAT, SYM, PRETTY, LATEX


if nargin<2
    disp('Usage is GPPRETTY(GP,IND) where IND is the population index of the desired individual');
    disp('or GPPRETTY(GP,''BEST'') to use the best individual of the run ');
    disp('or GPPRETTY(GP,''VALBEST'') uses the individual from the run that performed best on the validation set (if one is defined). ');
    return;
elseif nargin<3
   doknockout=false; 
else
    doknockout=true;
end



if license('test','symbolic_toolbox')



    %set the display precision for symbolic toolbox
    digits 4;


    if isnumeric(ind)
        


        if isempty(gp.fitness.returnvalues{ind})
            gp.fitness.returnvalues{ind}(1)=0;
            gp.fitness.returnvalues{ind}(2)=1;
        end

        %knockout genes if required, this requires that coefficients are
        %recomputed on the training data
        if doknockout
        treestrs_eval=kogene(gp.results.best.eval_individual, knockout);
        treestrs=kogene(gp.results.best.individual, knockout);
        gp.state.run_completed=false; %trick fitness function into recomputing weights
        [fitness,gp,ypred,coeffs]=feval(gp.fitness.fitfun,treestrs_eval,gp);
        gp.fitness.returnvalues{ind}=coeffs; 
        ref_tree=gpreformat(gp,treestrs);
        else
        ref_tree=gpreformat(gp,gp.pop{ind});   
        end
        
        %construct full symbolic expression using gene weights and gene expressions
        full_expr=sym(gp.fitness.returnvalues{ind}(1),'d')+sym(gp.fitness.returnvalues{ind}(2),'d')*sym(ref_tree{1});
        expr_array{1}=simple(full_expr);
        for i=2:length(ref_tree);
            gene_expr=sym(gp.fitness.returnvalues{ind}(i+1),'d')*sym(ref_tree{i});
            full_expr=full_expr+gene_expr;
            expr_array{i}=simple(gene_expr);
        end

    elseif ischar(ind) && strcmpi(ind,'best')
        

        if isempty(gp.results.best.returnvalues)
            gp.results.best.returnvalues(1)=0;
            gp.results.best.returnvalues(2)=1;
        end

        
        
        %knockout genes if required, this requires that coefficients are
        %recomputed on the training data
        if doknockout
        treestrs_eval=kogene(gp.results.best.eval_individual, knockout);
        treestrs=kogene(gp.results.best.individual, knockout);
        gp.state.run_completed=false; %trick fitness function into recomputing weights
        [fitness,gp,ypred,coeffs]=feval(gp.fitness.fitfun,treestrs_eval,gp);
        gp.results.best.returnvalues=coeffs;
        ref_tree=gpreformat(gp,treestrs);
        else
        ref_tree=gpreformat(gp,gp.results.best.individual);   
        end
        
        
        
        full_expr=sym(gp.results.best.returnvalues(1),'d')+sym(gp.results.best.returnvalues(2),'d')*sym(ref_tree{1});
        expr_array{1}=simple(full_expr);
        for i=2:length(ref_tree);
            gene_expr=sym(gp.results.best.returnvalues(i+1),'d')*sym(ref_tree{i});
            full_expr=full_expr+gene_expr;
            expr_array{i}=simple(gene_expr);
        end
       
		
		F2=full_expr;
        disp(F2);
        save F2 F2;
		
		

    elseif ischar(ind) && strcmpi(ind,'valbest')



        % check that validation data is present
        if (~isfield(gp.userdata,'xval')) || (~isfield(gp.userdata,'yval')) || ...
                isempty(gp.userdata.xval) || isempty(gp.userdata.yval)
            disp('No validation data was found. Try gppretty(gp,''best'') instead.');
            return;
        end

       

        if isempty(gp.results.valbest.returnvalues)
            gp.results.valbest.returnvalues(1)=0;
            gp.results.valbest.returnvalues(2)=1;
        end

        %knockout genes if required, this requires that coefficients are
        %recomputed on the training data
        if doknockout
        treestrs_eval=kogene(gp.results.valbest.eval_individual, knockout);
        treestrs=kogene(gp.results.valbest.individual, knockout);
        gp.state.run_completed=false; %trick fitness function into recomputing weights
        [fitness,gp,ypred,coeffs]=feval(gp.fitness.fitfun,treestrs_eval,gp);
        gp.results.valbest.returnvalues=coeffs; 
        ref_tree=gpreformat(gp,treestrs);
        else
         ref_tree=gpreformat(gp,gp.results.valbest.individual);   
        end

        full_expr=sym(gp.results.valbest.returnvalues(1),'d')+sym(gp.results.valbest.returnvalues(2),'d')*sym(ref_tree{1});
        expr_array{1}=simple(full_expr);
        for i=2:length(ref_tree);
            gene_expr=sym(gp.results.valbest.returnvalues(i+1),'d')*sym(ref_tree{i});
            full_expr=full_expr+gene_expr;
            expr_array{i}=simple(gene_expr);
        end



    else
        error('Illegal argument');
    end



    disp(' ');
    full_expr_simp=simple(full_expr);

    if nargout<1

        if length(expr_array)>1
            disp('Simplified genes:');
            disp('-----------------');
            disp(' ');
            disp('Gene 1 and bias term:');
            pretty(expr_array{1});
            disp(' ');
            for a=2:length(expr_array)
                disp(['Gene ' int2str(a) ':']);
                pretty(expr_array{a});
                disp( ' ');
            end
        end

        disp('Simplified overall GP expression:')
        disp('---------------------------------');
        pretty(full_expr_simp);
    end



    if nargout >0

        % process the LaTeX equation array
        % line up the initial '=' and subsequent '+' and '-' symbols
        % that mark the start of a new gene using &s
        exprs=expr_array;
        latex_expr=['y=&&' deblank(latex(exprs{1}))]; %creates line up point for genes
        
        pat='x(\d+)';


        latex_expr=regexprep(latex_expr,pat,'x_{$1}');
         %latex_expr=strrep(latex_expr,'x','x_'); %adds a subscript markup for input vars

        for i=2:length(exprs)
            lex=deblank(latex(exprs{i}));
            latex_expr=regexprep(latex_expr,pat,'x_{$1}');
        
            if lex(1)=='-'
                lex=lex(2:end);
                lex=['&-&' lex]; %lines up the genes
                latex_expr=[latex_expr '\\' lex]; %starts next line in array

            else
                lex=lex(2:end);
                lex=['&+&' lex];
                latex_expr=[latex_expr '\\' lex];
            end
        end

        gene_latex_expr=['\begin{eqnarray*}' latex_expr '\end{eqnarray*}'];
    end


    if nargout>1
        full_latex_expr=['y=' deblank(latex(full_expr_simp))];
        full_latex_expr=regexprep(full_latex_expr,pat,'x_{$1}');
        
    end

    if nargout>2
        expr_sym=full_expr_simp;
    end

    if nargout >3
        cell_expr_sym=expr_array;
    end

    %set display precision back to 32
    digits 32;


else

    disp('You need the Symbolic Math Toolbox to use this function.');
end