consider cyclic replacements in SBML Export

Update to improve compatibility of SBML as a export format:
* add check if CONDITIONS can be mapped to initAssignments in SBML
* add fnction to help fix dependent conditions
* improve encoding of conditions and initial values in SBML

arFramework3/ImportExport/arCheckSBMLCompatibilty.m

@@ -0,0 +1,83 @@
+function [qSBMLCompatible, pProblemCond] = arCheckSBMLCompatibilty(m)
+% ARCHECHECKSBMLCOMPATIBILTY checks if CONDITIONS in model.def are SBML compatible
+%
+% BACKGROUND:
+% CONDITIONS in model.def correspond to replacements of the original model parameters
+% with numerical values of mathematical expressions. In SBML this is best represented as
+% "initialAssignment" rules. However, there is an important difference how CONDITIONS
+% and initialAssignment rules are applied:
+%   - CONDITIONS are applied exactly once and independently of each other
+%   - initialAssignment rules are combined to form a set of equations that are solved
+%     simultaneously
+%
+% This means that conditions should be encoded as initialAssignment rules*, but cannot
+% be translated directly in all cases. Specifically, there must not be any dependencies
+% between the conditions. This means, a parameter that is repalced must not appear in
+% any mathematical expression on the RHS of the replacements.
+%
+% * See arExportSBML_fullmodel.m
+%
+% EXAMPLE OF DIFFERENT BEHAVIOR:
+% consider the expression expr = "p1*x^p2"
+%
+% d2d:
+%   CONDITIONS
+%   p1   "2"
+%   p2   "p1*2"
+%
+%   The expression after replacements becomes: "2*x^(2*p1)"
+% 
+% SBML:
+%   <listOfInitialAssignments>
+%       <initialAssignment symbol="p1">
+%           <math xmlns="http://www.w3.org/1998/Math/MathML">
+%               <cn> 2 </cn>
+%           </math>
+%       </initialAssignment>
+%       <initialAssignment symbol="p2">
+%           <math xmlns="http://www.w3.org/1998/Math/MathML">
+%               <apply>
+%                   <times/>
+%                   <ci> p1 </ci>
+%                   <cn> 2 </cn>
+%               </apply>
+%           </math>
+%       </initialAssignment>
+%   </listOfInitialAssignments>
+%
+%   The expression after replacements becomes: "2*x^(4)"
+%   This is because the assignment p1<-2 is also applied within the assignment p2<-p1*2 
+
+arguments
+    m (1,1) double {mustBeInteger, mustBePositive} = 1
+end
+
+
+global ar
+
+% identify parameters that are replaced in the conditions
+modelP = ar.model(m).p';
+modelFPsym = arSym(ar.model(m).fp);
+modelFP = cellstr(string(arSym(ar.model(m).fp)));
+qReplaced = ~strcmp(modelP, modelFP);
+
+% identify which of the replaced parameters also appear in modelFP expressions
+fpParams = unique(cellstr(string(symvar(modelFPsym(qReplaced)))));
+qReplacedAndInFP = ismember(modelP, fpParams) & qReplaced;
+
+% exclude init parameters that do not appear in the model equations
+qStateInit = ismember(modelP, ar.model(m).px0);
+qInModelEquations = ismember(modelP, union(ar.model(m).pu, ar.model(m).pv));
+qPureStateInit = qStateInit & ~qInModelEquations;
+
+% exclude compartment size parameters
+% Compartment size parameters do not pose a problem, because they are not used in SBML.
+% Instead compartment valume is assigned directly to the compartment ID in the SBML file.
+qCompSizeParam = ismember(ar.model(m).p', ar.model(m).pc);
+
+% final array of parameters with problematic replacements
+qProblemCond = qReplacedAndInFP & ~qCompSizeParam & ~qPureStateInit;
+pProblemCond = modelP(qProblemCond);
+
+% Flag that indicates if the model is SBML compatible
+qSBMLCompatible = ~any(qProblemCond);