<form>

<P>

Input probability matrix P

(P_ij, transition probability from i to j.):

<BR>

<textarea id="TEXTAREA1" name="textin" rows="20" style="width:100%;">

0.6 0.4

0.3 0.7

</textarea>

<P>

<input onclick="b_clk(this.form)" type="button" value="calculate" name="b">

probability vector in stable state:

<BR>

<textarea name="textout" rows="10" style="width:100%;">

</textarea>

<P>

<input onclick="c_clk(this.form)" type="button" value="calculate" name="c">

<input type="text" size="3" value="2" name="textin2">

'th power of probability matrix

<BR>

<textarea name="textout2" rows="20" style="width:100%;"></textarea>

</form>

<script type="text/javascript">

<!--

function init()

{

//document.forms[0].textin.value="0.6 0.4\n0.3 0.7";

//document.forms[0].textin2.value="2";

}

function b_clk(form)

{

form.textout.value = markov(form.textin.value);

}

function c_clk(form)

{

form.textout2.value = mpower(form.textin.value, form.textin2.value);

}

function mpower(c, v)

{

var p=to_matrix(c);

var n=p.length;

var pp=new Array(n);

var sum=new Array(n);

var i,j,k,l;

for (i=0; i<n; i++) {

pp[i]=new Array(n);

sum[i]=new Array(n);

for (j=0; j<n; j++) {

pp[i][j]=p[i][j];

sum[i][j]=0;

}

}

for (l=1; l<v; l++) {

for (i=0; i<n; i++)

for (j=0; j<n; j++)

sum[i][j]=0;

for (i=0; i<n; i++)

for (j=0; j<n; j++)

for (k=0; k<n; k++)

sum[i][j]+=pp[i][k]*p[k][j];

for (i=0; i<n; i++)

for (j=0; j<n; j++)

pp[i][j]=sum[i][j];

}

return print2dmf(pp, 2)

}

function replaceall(str,c,cc)

{

while(str.indexOf(c) > -1)

str=str.replace(c,cc);

}

function to_matrix(c)

{

//obtain array p[][] from strings c

var i,j;

var cin=c;

replaceall(cin,"\t"," ");

replaceall(cin,","," ");

replaceall(cin," "," ");

var n=0;

var cl=cin.split("\n");

for (i=0; i<cl.length; i++) {

while(cl[i].indexOf(" ") == 0)

cl[i]=cl[i].replace(" ","");

//replaceall(cl[i],"\r","*");

//replaceall(cl[i],"\n","**");

//alert(cl[i]+cl[i].length);

if (cl[i].length <= 1)

break;

var cc=cl[i].split(" ");

n++;

//if (cc.length <= 0)

// break;

//n=i+1;

}

var p=new Array(n);

for (i=0; i<n; i++) {

p[i]=new Array(n);

var cc=cl[i].split(" ");

for (j=0; j<n; j++)

p[i][j]=Number(cc[j]);

}

return p;

}

function markov(c)

{

var i,j;

var p=to_matrix(c);

var n=p.length;

//alert("p=\n"+print2dm(p,n,n));

//add normalization condition

m=n+1;

var a=new Array(m);

for (i=0; i<m; i++) {

a[i]=new Array(m);

for (j=0; j<m; j++)

a[i][j]=0;

}

for (j=0; j<m; j++)

a[0][j]=1;

//copy transverse of p-1 to a

for (i=0; i<n; i++)

for (j=0; j<n; j++) {

if (i!=j)

a[i+1][j]=p[j][i];

else

a[i+1][j]=p[j][i]-1;

}

//alert("a=\n"+print2dm(a,m,m));

var f=new Array(n);

gaussj(a,n,f);

return print1dmf(f, 3);

}

function print1dm(a)

{

return print1dmf(a,-1);

}

function print1dmf(a, l)

{

//var res = "n=" + String(a.length) + "\n\n";

var i,j;

var res="";

for (i=0; i<a.length; i++)

res += String(i+1)+": " + pfmt(a[i],l)+"\n";

return res;

}

function print2dm(a)

{

return print2dmf(a,-1);

}

function print2dmf(a, l)

{

var i,j,k;

var res="";

for (i=0; i<a.length; i++) {

for (j=0; j<a[i].length; j++)

res += pfmt(a[i][j],l)+" ";

res += "\n";

}

return res;

}

function pfmt(v, l)

{

if (l<0)

return String(v);

var i;

var a=1;

for (i=0; i<l; i++)

a *= 10;

var s = String(Math.round(v*a)/a);

for (i=0; i<l+2-s.length; i++)

s += " ";

return s;

}

function gaussj(a,n,f)

{

var m=n+1;

var i,j,k;

//implicit pivoting

for (i=0; i<m; i++) {

amx=Math.abs(a[i][0]);

for (j=1; j<n; j++) {

if (amx < Math.abs(a[i][j]) )

amx=Math.abs(a[i][j]);

}

for (j=0; j<m; j++)

a[i][j] /= amx;

}

for (i=0; i<n; i++) {

//alert("i="+String(i));

//select pivot

if (i>0) {

var r=i;

for (k=i+1; k<m; k++) {

if ( Math.abs(a[r][i]) < Math.abs(a[k][i]) )

r=k;

}

//alert("piot="+r);

for (j=0; j<m; j++) {

t=a[i][j];

a[i][j]=a[r][j];

a[r][j]=t;

}

}

//normalize line i

var d = a[i][i];

for (j=i; j<m; j++)

a[i][j] /= d;

//alert("ai2=\n"+print2dm(a));

//subtract line i from k!=i.

for (k=0; k<m; k++) {

if(k != i) {

d=a[k][i];

for (j=i; j<m; j++)

a[k][j] -= d*a[i][j];

}

}

//alert("ai3=\n"+print2dm(a));

}

for (i=0; i<n; i++)

f[i]=a[i][m-1];

return;

}

//

-->

</script>

</P>