The OPTLSO Procedure

This example further illustrates the use of external data sets that are specified in the OBJECTIVE= option. For this example, a data set that contains randomly generated observations is used to estimate the parameters for the Johnson family of distributions (Bowman and Shenton, 1983). The objective is the log likelihood for the family, which involves four variables, :

where

Here, denotes the value of d in the kth observation of the data set that is generated by the following DATA step.

 data sudata;
    n=20000;
    theta=-1;
    sigma=1;
    delta=3;
    gamma=5;
    rngSeed=123;
    do i = 1 to n;
       z = rannor(rngSeed);
       a = exp( (z - gamma)/delta );
       d = sigma * ( (a**2 - 1)/(2*a) ) + theta;
       output;
    end;
    keep d;
 run;

This generates a data set called sudata that contains observations. You can modify n to increase or decrease the computational work per function evaluation. The following call to PROC FCMP defines the corresponding FCMP function definition:

proc fcmp outlib=sasuser.myfuncs.mypkg;
   function jsu(x4,x2,f1);
      return (20000*(log(x4) - log(x2)) + f1);
   endsub;

   function jsu1(x1,x2,x3,x4,d);
      yk = (d - x1)/x2;
      zk = yk + sqrt(1 + yk**2);
      return (-0.5*(x3 + x4*log(zk))**2 -0.5*log(1 + yk**2));
   endsub;
run;
options cmplib = sasuser.myfuncs;

In the following steps, the assumption for the definition of jsu and jsu1 is that jsu1 is called once for each line of data (in this case 20,000 times) and cumulatively summed. The resulting value is then provided to the function jsu for a final calculation, which is called only once per evaluation of .

 data objdata;
    input _id_ $ _function_ $ _sense_ $ _dataset_ $;
    datalines;
 f1 jsu1 .   sudata
 f  jsu  max .
 ;

 data vardata;
    input _id_ $ _lb_ _ub_;
    datalines;
 x1  .     .
 x2  1e-12 .
 x3  .     .
 x4  1e-12 .
 ;

 proc optlso
    primalout = solution
    objective = objdata
    variables = vardata
    logfreq   = 100
    maxgen    = 1000;
    performance nodes=4 nthreads=8;
 run;

Output 3.8.1 shows the output from running these steps.