[SOSlib-devel] piecewise evaluation and abs differentiation

[Rainer M. <ra...@tb...>]

hi

just for the record, and if someone is interested:

i have just commited a new processAST.c file

a) repaired and generalized piecewise evaluation:

a1) piecewise for the simple piece/otherwise case was implemented wrong
a2) a general solution for multiple pieces w or w/o otherwise statements

I have added the new code for piecewise evaluation below, in case 
someone finds the time to check this.


b) repaired differentiation of abs function:

f(x) = abs(a(x))
df/dx = sig(a(x)) * da/dx

we have decided to set sig(a(x)) to 0 if a(x) = 0, i.e. sig(0) = 0,
even though the signum function is actually not defined at 0.

Alternatively we could either set sig(0) to +1
or forget about differentiation of abs and use CVODE's internal 
approximation instead.

Any opinions?

Rainer



   case AST_FUNCTION_PIECEWISE:
     /** Piecewise: */
     found = 0;
     /** Go through n pieces with 2 AST children for each piece, */
     for ( i=0; i<(childnum-1); i=i+2 )
     {
       if ( evaluateAST(child(n, i+1), data) )
       {
 	found++;
 	result = evaluateAST(child(n, i), data);
       }
     }
     /** odd number of AST children: if no piece was true, otherwise 
remains */
     /* i should be equal to childnum for even number piecewise AST
        and equal to childnum-1 for odd numbered piecewise ASTs */
     if ( i == childnum-1 && found == 0 )
     {
       found++;
       result = evaluateAST(child(n, i), data);
     }
     if ( found == 0 )
       SolverError_error(ERROR_ERROR_TYPE,
 			SOLVER_ERROR_AST_EVALUATION_FAILED_PIECEWISE,
 			"Piecewise function failed; no true piece");
     if ( found > 1 )
       SolverError_error(ERROR_ERROR_TYPE,
 			SOLVER_ERROR_AST_EVALUATION_FAILED_PIECEWISE,
 			"Piecewise function failed; several true pieces");
     break;