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gppretty.m
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function [exprSym,geneExprSym,fullLatexExpr,geneLatexExpr] = gppretty(gp,ID,knockout,separateBias,fastMode,useAlias)
%GPPRETTY Simplify and prettify a multigene symbolic regression model.
%
% Simplifies single and multigene symbolic regression models created with
% GPTIPS using the REGRESSMULTI_FITFUN fitness function (and variants
% thereof with file name beginning 'REGRESSMULTI').
%
% GPPRETTY(GP,ID) simplifies the model with numeric population identifier
% ID in the GPTIPS datastructure GP.
%
% GPPRETTY(GP,'best') simplifies the best model of the run (as evaluated
% on the training data).
%
% GPPRETTY(GP,'valbest') simplifies the model that performed best on the
% validation data (if it exists).
%
% GPPRETTY(GP,'testbest') simplifies the model that performed best on the
% test data (if it exists).
%
% GPPRETTY(GP,GPMODEL) prettifies the multigene regression model
% structure GPMODEL (i.e. the struct created by the function
% GPMODEL2STRUCT or by the function GENES2GPMODEL).
%
% EXPRSYM = GPPRETTY(GP,'best') does the above and and returns the entire
% simplified symbolic expression as an object of class SYM as EXPRSYM.
%
% [EXPRSYM,GENEEXPRSYM] = GPPRETTY(GP,'best') also returns the individual
% simplified gene expressions as a cell array of SYM objects GENEEXPRSYM.
%
% Advanced:
%
% 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 model of the run, then simplifies it. Note that the gene
% weights are recomputed from the training data when genes are knocked
% out.
%
% [EXPRSYM,GENEEXPRSYM,FULLLATEXEXPR] = GPPRETTY(GP,'best') also returns
% FULLLATEXEXPR containing the simplified LaTeX representation of the
% combined genes of the multigene equation. That is, the genes are
% combined, then simplified.
%
% [EXPRSYM,GENEEXPRSYM,FULLLATEXEXPR,GENELATEXEXPR = GPPRETTY(GP,'best')
% returns a string GENELATEXEXPR containing the simplified LaTeX
% representation of the separate genes of the multigene equation
% formatted as a LaTeX equation array. The bias term is 'folded' in with
% the first gene. The genes are simplified separately and are displayed
% on different lines of the LaTex expression.
%
% Remarks on precision and simplification:
%
% In GPTIPS 2 symbolic expressions are now simplified directly using the
% MuPAD engine's 'Simplify' method (instead of the MATLAB SIMPLE function
% used in GPTIPS v1).
%
% This is due to:
%
% (a) ongoing problems with SIMPLE causing MATLAB to hang occasionally.
%
% (b) the 'SIMPLE' method is now deprecated by MATLAB (R2014b).
%
% GPPRETTY by default displays expressions with 4 digits of 'accuracy'.
%
% You can also use the GPMODEL2SYM function to return the GPTIPS
% expresssion as a SYM object. You can then use the Symbolic Math Toolbox
% VPA function to control the display precision. E.g.
%
% EQ = GPMODEL2SYM(GP,'best');
% EQ_TWO_DIGITS = VPA(S,2)
%
% In the previous version of GPTIPS, symbolic math objects were created
% from GPTIPS expressions using a fixed precision method (i.e. 4 digits).
% This could sometimes lead to undesirable numerical properties if using
% the SYM form of the model directly.
%
% In GPTIPS 2 this has been rectified, symbolic math objects are always
% created and stored with 'full' precision but are displayed by GPPRETTY,
% GPMODELREPORT, HTMLEQUATION, VPA etc. to a controlled number of
% significant digits. See SYM/VPA for more information.
%
% Remarks on LaTex:
%
% The LaTeX equation represented by the string GENELATEXEXPR 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 GENELATEXEXPR that is generated by GPPRETTY. The rest you
% must supply yourself.
%
% Again, the equation represented by the string FULLLATEXEXPR 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}
%
% Copyright (c) 2009-2015 Dominic Searson
%
% GPTIPS 2
%
% See also GPSIMPLIFY, GPMODEL2MFILE, GPMODEL2SYM, GPMODELREPORT,
% GPMODEL2STRUCT, GPMODEL2FUNC, SYM/PRETTY, SYM/VPA, SYM/SIMPLIFY
if nargin < 2
disp('Usage is GPPRETTY(GP,ID) where ID is the population identifer 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). ');
disp('or GPPRETTY(GP,''TESTBEST'') uses the individual from the run that performed best on the test set (if one is defined). ');
return;
end
verReallyOld = verLessThan('matlab', '7.7.0');
%Set the max number of steps for each Mupad SIMPLIFY function call to
%take. The MuPAD default is 100. Edit this to to take more or less steps.
%This doesn't seem have any effect on old (<7.7) versions of MATLAB)
simplifySteps = 100;
if nargin < 3 || isempty(knockout)
knockout = 0;
end
if nargin < 4 || isempty(separateBias)
separateBias = false;
end
if nargin < 5 || isempty(fastMode)
fastMode = false;
end
if nargin < 6 || isempty(useAlias)
useAlias = true;
end
if isempty(knockout) || ~any(knockout)
doknockout = false;
else
doknockout = true;
end
if gp.info.toolbox.symbolic
if isnumeric(ID)
if ID > gp.runcontrol.pop_size || ID < 1
error('Supplied population index is invalid.');
end
%if no return values
if isempty(gp.fitness.returnvalues{ID})
if gp.genes.multigene
error('No gene weights were computed for this model. This is probably because one or more genes gave a non-finite output on the training data.');
else %if single gene/regular GP (e.g. quartic poly) then set bias = 0 and weight = 1
gp.fitness.returnvalues{ID}(1) = 0;
gp.fitness.returnvalues{ID}(2) = 1;
end
end
%knockout genes if required
if doknockout
treestrs_eval = kogene(gp.results.best.eval_individual, knockout);
treestrs = kogene(gp.results.best.individual, knockout);
gp.state.run_completed = false; %force fitness function into recomputing weights
[~,gp,coeffs] = feval(gp.fitness.fitfun,treestrs_eval,gp);
gp.fitness.returnvalues{ID} = coeffs;
evalTree = gpreformat(gp,treestrs,useAlias);
else
evalTree = gpreformat(gp,gp.pop{ID},useAlias);
end
%construct full symbolic expression using gene weights and gene expressions
if separateBias %bias is kept as a separate "gene"
fullExpr = sym(gp.fitness.returnvalues{ID}(1));
exprArray = cell(1, numel(evalTree)+1);
exprArray{1} = gpsimplify(fullExpr,simplifySteps,verReallyOld,fastMode);
for i=1:length(evalTree);
geneExpr = gp.fitness.returnvalues{ID}(i+1)*sym(evalTree{i});
fullExpr = fullExpr + geneExpr;
exprArray{i+1} = gpsimplify(geneExpr,simplifySteps,verReallyOld,fastMode);
end
else %normal processing where bias is folded into first gene
fullExpr = gp.fitness.returnvalues{ID}(1) + gp.fitness.returnvalues{ID}(2)*sym(evalTree{1});
exprArray = cell(1, numel(evalTree));
exprArray{1} = gpsimplify(fullExpr,simplifySteps,verReallyOld,fastMode);
for i=2:length(evalTree);
geneExpr = gp.fitness.returnvalues{ID}(i+1) * sym(evalTree{i});
fullExpr = fullExpr + geneExpr;
exprArray{i} = gpsimplify(geneExpr,simplifySteps,verReallyOld,fastMode);
end
end
elseif ischar(ID) && strcmpi(ID,'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
[~,gp,coeffs] = feval(gp.fitness.fitfun,treestrs_eval,gp);
gp.results.best.returnvalues = coeffs;
evalTree = gpreformat(gp,treestrs,useAlias);
else
evalTree = gpreformat(gp,gp.results.best.individual,useAlias);
end
if separateBias %bias is kept as a separate "gene"
fullExpr = sym(gp.results.best.returnvalues(1));
exprArray{1} = gpsimplify(fullExpr,simplifySteps,verReallyOld,fastMode);
for i=1:length(evalTree);
geneExpr = gp.results.best.returnvalues(i+1) * sym(evalTree{i});
fullExpr = fullExpr + geneExpr;
exprArray{i+1} = gpsimplify(geneExpr,simplifySteps,verReallyOld,fastMode);
end
else
fullExpr = gp.results.best.returnvalues(1) + gp.results.best.returnvalues(2)*sym(evalTree{1});
exprArray{1} = gpsimplify(fullExpr,simplifySteps,verReallyOld,fastMode);
for i=2:length(evalTree);
geneExpr = gp.results.best.returnvalues(i+1) * sym(evalTree{i});
fullExpr = fullExpr+geneExpr;
exprArray{i} = gpsimplify(geneExpr,simplifySteps,verReallyOld,fastMode);
end
end
elseif ischar(ID) && strcmpi(ID,'valbest')
% check that validation data is present
if ~isfield(gp.results,'valbest')
error('No validation data was found.');
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;
[~,gp,coeffs] = feval(gp.fitness.fitfun,treestrs_eval,gp);
gp.results.valbest.returnvalues = coeffs;
evalTree = gpreformat(gp,treestrs,useAlias);
else
evalTree = gpreformat(gp,gp.results.valbest.individual,useAlias);
end
if separateBias %bias is kept as a separate "gene"
fullExpr = sym(gp.results.valbest.returnvalues(1));
exprArray{1} = gpsimplify(fullExpr,simplifySteps,verReallyOld,fastMode);
for i=1:length(evalTree);
geneExpr = gp.results.valbest.returnvalues(i+1)*sym(evalTree{i});
fullExpr = fullExpr+geneExpr;
exprArray{i+1} = gpsimplify(geneExpr,simplifySteps,verReallyOld,fastMode);
end
else %normal processing (bias folded into first gene)
fullExpr = gp.results.valbest.returnvalues(1) + gp.results.valbest.returnvalues(2)*sym(evalTree{1});
exprArray{1} = gpsimplify(fullExpr,simplifySteps,verReallyOld,fastMode);
for i=2:length(evalTree);
geneExpr = gp.results.valbest.returnvalues(i+1) * sym(evalTree{i});
fullExpr = fullExpr+geneExpr;
exprArray{i} = gpsimplify(geneExpr,simplifySteps,verReallyOld,fastMode);
end
end
elseif ischar(ID) && strcmpi(ID,'testbest')
% check that validation data is present
if ~isfield(gp.results,'testbest')
error('No test data was found.');
end
if isempty(gp.results.testbest.returnvalues)
gp.results.testbest.returnvalues(1) = 0;
gp.results.testbest.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.testbest.eval_individual, knockout);
treestrs = kogene(gp.results.testbest.individual, knockout);
gp.state.run_completed = false;
[~,gp,coeffs] = feval(gp.fitness.fitfun,treestrs_eval,gp);
gp.results.testbest.returnvalues = coeffs;
evalTree = gpreformat(gp,treestrs,useAlias);
else
evalTree = gpreformat(gp,gp.results.testbest.individual,useAlias);
end
if separateBias %bias is kept as a separate "gene"
fullExpr = sym(gp.results.testbest.returnvalues(1));
exprArray{1} = gpsimplify(fullExpr,simplifySteps,verReallyOld,fastMode);
for i=1:length(evalTree);
geneExpr = gp.results.testbest.returnvalues(i+1)*sym(evalTree{i});
fullExpr = fullExpr+geneExpr;
exprArray{i+1} = gpsimplify(geneExpr,simplifySteps,verReallyOld,fastMode);
end
else %normal processing (bias folded into first gene)
fullExpr = gp.results.testbest.returnvalues(1) + gp.results.testbest.returnvalues(2)*sym(evalTree{1});
exprArray{1} = gpsimplify(fullExpr,simplifySteps,verReallyOld,fastMode);
for i=2:length(evalTree);
geneExpr = gp.results.testbest.returnvalues(i+1) * sym(evalTree{i});
fullExpr = fullExpr+geneExpr;
exprArray{i} = gpsimplify(geneExpr,simplifySteps,verReallyOld,fastMode);
end
end
elseif iscell(ID) %process cell array of encoded trees and rntVals
%used, for instance, by gpgenes2model.m
numGenes = numel(ID) - 1;
evalTree = gpreformat(gp,{ID{1:numGenes}},useAlias);
rtnVals = ID{end};
fullExpr = rtnVals(1) + rtnVals(2)*sym(evalTree{1});
exprArray = cell(1, numel(evalTree)+1);
exprArray{1} = sym(rtnVals(1));
for i=1:length(evalTree);
geneExpr = rtnVals(i+1) * sym(evalTree{i});
fullExpr = fullExpr + geneExpr;
exprArray{i+1} = gpsimplify(geneExpr,simplifySteps,verReallyOld,fastMode);
end
%or process a gpmodel struct
elseif isa(ID,'struct') && isfield(ID,'source') &&...
(strcmpi(ID.source,'gpmodel2struct') || strcmpi(ID.source,'genes2GPmodel') );
exprArray = ID.genes.geneSyms;
fullExpr = ID.sym;
else
error('Illegal argument or unrecognised model selector');
end
%simplify the overall expression
try
fullExprSimplified = gpsimplify(fullExpr,2*simplifySteps,verReallyOld,fastMode);
catch
fullExprSimplified = fullExpr;
end
%et the display precision via Mupad
if ~verReallyOld
existingPrecision = char(feval(symengine,'Pref::outputDigits'));
evalin(symengine,'Pref::outputDigits(4)');
end
if nargout < 1
if length(exprArray) > 1
disp(' ');
disp('Simplified genes');
disp('----------------');
disp(' ');
disp('Gene 1 and bias term');
pretty(vpa(exprArray{1},4));
disp(' ');
for a=2:length(exprArray)
disp(['Gene ' int2str(a)]);
pretty(vpa(exprArray{a},4));
disp( ' ');
end
end
disp('Simplified overall GP expression')
disp('--------------------------------');
pretty(vpa(fullExprSimplified,4));
end
if nargout > 0
exprSym = fullExprSimplified;
end
if nargout > 1
geneExprSym = exprArray;
end
if nargout > 2
%process the LaTeX equation array line up the initial '=' and
%subsequent '+' and '-' symbols that mark the start of a new gene
%using &s
exprs = exprArray;
latexExpr = ['y=&&' deblank(latex(vpa(exprs{1},4)))]; %creates line up point for genes
pat='x(\d+)';
latexExpr = regexprep(latexExpr,pat,'x_{$1}');
for i=2:length(exprs)
lex = deblank(latex(vpa(exprs{i},4)));
latexExpr = regexprep(latexExpr,pat,'x_{$1}');
if lex(1) == '-'
lex = lex(2:end);
lex = ['&-&' lex]; %lines up the genes
latexExpr = [latexExpr '\\' lex]; %starts next line in array
else
lex = lex(2:end);
lex = ['&+&' lex];
latexExpr = [latexExpr '\\' lex];
end
end
geneLatexExpr = ['\begin{eqnarray*}' latexExpr '\end{eqnarray*}'];
end
if nargout > 2
fullLatexExpr = ['y=' deblank(latex(vpa(fullExprSimplified,4)))];
fullLatexExpr = regexprep(fullLatexExpr,pat,'x_{$1}');
end
%reset display precision to what it was
if ~verReallyOld
evalin(symengine,['Pref::outputDigits(' existingPrecision ')']);
end
else
error('The Symbolic Math Toolbox is required to use this function.');
end