# Markov Chains in Maple

The following is a procedure for Maple that simulates a Markov chain by executing a specified number of trials:

```MarkovSim := proc(Mat, startstage, ntrials)
local count, nvisit, a, i, j, firstAbsorbingStage, run, stage, sumQuant;
count:=Vector(ColumnDimension(Mat));
nvisit:=Vector(ColumnDimension(Mat));
firstAbsorbingStage:=0;
for i from 1 to ColumnDimension(Mat) do
for j from 1 to RowDimension(Mat) do
if Mat[j,i]>=1.0 then firstAbsorbingStage:=i; break; fi;
od;
if firstAbsorbingStage>0 then break; fi;
od;
for i from 1 to ColumnDimension(Mat) do count[i]:=0; od;
for run from 1 to ntrials do
for i from 1 to ColumnDimension(Mat) do nvisit[i]:=0; od;
nvisit[startstage]:=1;
stage:=startstage;
while stage
a:=rand()/10.^12;
sumQuant:=0;
for i from 1 to RowDimension(Mat) do
if a<(sumQuant+Mat[i,stage]) and a>sumQuant then
stage:=i; nvisit[i]:=nvisit[i]+1; break;
fi;
sumQuant:=sumQuant+Mat[i,stage];
od;
od;
count:=count+nvisit;
od;
printf("Average number of steps in different stages before absorption:\n");
for i from 1 to firstAbsorbingStage-1 do printf("%g ", count[i]/ntrials); od;
j:=0; printf("\n");
for i from 1 to ColumnDimension(Mat) do j:=j+count[i]; od;
printf("Average number of steps until absorption:\n %g", j/ntrials);
end proc:```