Supporting algorithm (PHP alternative) 13.php

<?php

//##############################################################################################
//# John Wiley & Sons, Inc.                                                                    #
//#                                                                                            #
//# Book:   Markov Chains: From Theory To Implementation And Experimentation                   #
//# Author: Dr. Paul Gagniuc                                                                   #
//# Data:   01/09/2016                                                                         #
//#                                                                                            #
//# Description:                                                                               #
//# Supporting algorithm 13. Prediction framework based on a 4x4 transition matrix.            #
//# Known transition probability values are directly used from a transition matrix             #
//# for highlighting the behavior of a Markov Chain. A variable number of states               #
//# and configurations can be tested. For instance, a diagram with three states can            #
//# be molded on the algorithm. However, since the framework is made for a total of            #
//# 4 states the following modifications are required: all Jar(n, 4) elements are              #
//# set to zero (Jar(1, 4)=0; Jar(2, 4)=0; Jar(3, 4)=0; and Jar(4, 4)=0). Furthermore,         #
//# the molding of a diagram with two states on this framework involves two                    #
//# modifications: all Jar(n, 4) elements are set to zero and all Jar(n, 3) elements           #
//# are set to zero. Any type of diagram configuration can be tested by following two          #
//# rules: 1) the absence of an arrow is indicated by zero, and 2) any value greater           #
//# than zero and less than or equal to 1 indicates an arrow.                                  #
//##############################################################################################

$Jar = array();
$v = array();

$Jar[1][1] = 1;
$Jar[1][2] = 0;
$Jar[1][3] = 0;
$Jar[1][4] = 0;

$Jar[2][1] = 0.5;
$Jar[2][2] = 0;
$Jar[2][3] = 0.5;
$Jar[2][4] = 0;

$Jar[3][1] = 0;
$Jar[3][2] = 0.5;
$Jar[3][3] = 0;
$Jar[3][4] = 0.5;

$Jar[4][1] = 0;
$Jar[4][2] = 0;
$Jar[4][3] = 1;
$Jar[4][4] = 0;

$chain = 5;

$v[0][0] = 0;
$v[1][0] = 0;
$v[2][0] = 0;
$v[3][0] = 1;

$v[0][1] = 0;
$v[1][1] = 0;
$v[2][1] = 0;
$v[3][1] = 0;

for($k=1; $k<=$chain; $k++){

    for($i=0; $i<=3; $i++){
        for($j=0; $j<=3; $j++){
           $v[$i][1] = $v[$i][1] + ($v[$j][0] * $Jar[$j + 1][$i + 1]);
        }
    }

for($i=0; $i<=3; $i++){
    $v[$i][0] = $v[$i][1];
    $v[$i][1] = 0;
}
    $A = $v[0][0];
    $B = $v[1][0];
    $C = $v[2][0];
    $D = $v[3][0];

echo "Step(".$k.")=[".$A."|".$B."|".$C."|".$D."]</br>";
}
?>