USE meanandvar
USE gnuplot
! This example generates a plot of the evolving estimates of the variance
! of the estimate of the mean for a simple prescribed process

#include <time.h>
srand[INTEGER(time(NULL))] ! select different initial seed every time the program is run

REAL procstate=0.5
REAL FUNCTION process() ! simple first-order dynamical system with lorentzian spectrum
  procstate=0.9∗~+0.1∗RAND()
  RESULT=procstate
END process

MEANANDVAR accum
mvinit(accum) ! initialize mean and variance accumulator

DO dum=process() FOR 1000 TIMES ! skip initial transient

RANGE 1E3,1E6,0,0.14 ! prepare to plot results
set logscale x
STARTLINE
DRAW 1E6,0.0834 ! the exact variance is 0.0834/nt
DRAW 1E3,0.0834
LOOP FOR 1000 TIMES
  DO meanandvar[accum,process()] FOR 1000 TIMES ! accumulate samples
  DRAW accum.nt,accum.nt∗accum.var
REPEAT
SHOWGRAPH
READ ! keep plot displayed until Enter is pressed