*  This is file MARSINVD.SAS  ;
options noovp;
title 'Martian Invasion Data';
DATA raw;
  infile marsinvd;
  input time I;
*   Grid Search   ;
proc NLIN;
   parameters Imax=10 to 30 by 2 T=10 to 30 by 2;
   model I=Imax*(cos(2*3.14159*time/T)+1)/2;
         DER.Imax=(cos(2*3.14159*time/T)+1)/2;
         DER.T=Imax*sin(2*3.14159*time/T)*(3.14159*time/T**2);
   output OUT=PlotGrid  PREDICTED=Ihat  RESIDUAL=resid;
proc PLOT data=PlotGrid;
   plot I*time='+'  Ihat*time='P' / OVERLAY VPOS=25;
   plot resid*time / VREF=0 VPOS=25;
*   Steepest descent    ;
*   Good first guess    ;
*   Global minimum      ;
proc NLIN METHOD=GRADIENT CONVERGENCE=.005 data=raw;
   parameters Imax=20  T=20;
   model I=Imax*(cos(2*3.14159*time/T)+1)/2;
         DER.Imax=(cos(2*3.14159*time/T)+1)/2;
         DER.T=Imax*sin(2*3.14159*time/T)*(3.14159*time/T**2);
   output OUT=PlotG1  PREDICTED=Ihat  RESIDUAL=resid;
proc PLOT data=PlotG1;
   plot I*time='+'  Ihat*time='P' / OVERLAY VPOS=25;
   plot resid*time / VREF=0 VPOS=25;
*   Gauss - Newton    ;
proc NLIN METHOD=GAUSS CONVERGENCE=.00000001 data=raw;
   parameters Imax=20  T=20;
   model I=Imax*(cos(2*3.14159*time/T)+1)/2;
         DER.Imax=(cos(2*3.14159*time/T)+1)/2;
         DER.T=Imax*sin(2*3.14159*time/T)*(3.14159*time/T**2);
   output OUT=PlotGaus  PREDICTED=Ihat  RESIDUAL=resid;
proc PLOT data=PlotGaus;
   plot I*time='+'  Ihat*time='P' / OVERLAY VPOS=25;
   plot resid*time / VREF=0 VPOS=25;
*   Marquardt  ;
proc NLIN METHOD=MARQUARDT CONVERGENCE=.00000001 data=raw;
   parameters Imax=20  T=20;
   model I=Imax*(cos(2*3.14159*time/T)+1)/2;
         DER.Imax=(cos(2*3.14159*time/T)+1)/2;
         DER.T=Imax*sin(2*3.14159*time/T)*(3.14159*time/T**2);
   output OUT=PlotMarq  PREDICTED=Ihat  RESIDUAL=resid;
proc PLOT data=PlotMarq;
   plot I*time='+'  Ihat*time='P' / OVERLAY VPOS=25;
   plot resid*time / VREF=0 VPOS=25;