function matrixreduce($A, $rref = false, $frac = false)
{
include_once "fractions.php";
// number of rows
$N = count($A);
$M = count($A[0]);
$pivots = array();
if ($N > 10) {
global $myrights;
if ($myrights > 10) {
echo "You really shouldn't use matrixreduce for matrices bigger than 10 rows.";
}
}
for ($r = 0; $r < $N; $r++) {
for ($c = 0; $c < $M; $c++) {
$A[$r][$c] = fractionparse($A[$r][$c]);
}
}
$r = 0;
$c = 0;
while ($r < $N && $c < $M) {
if ($A[$r][$c][0] == 0) {
//swap only if there's a 0 entry
$max = $p;
for ($i = $r + 1; $i < $N; $i++) {
if (abs($A[$i][$c][0] / $A[$i][$c][1]) > abs($A[$max][$c][0] / $A[$max][$c][1])) {
$max = $i;
}
}
if ($max != $p) {
$temp = $A[$r];
$A[$r] = $A[$max];
$A[$max] = $temp;
}
}
if (abs($A[$r][$c][0] / $A[$r][$c][1]) <= 1.0E-10) {
$c++;
continue;
}
//scale pivot row
if ($rref) {
$divisor = $A[$r][$c];
for ($j = $c; $j < $M; $j++) {
$A[$r][$j] = fractiondivide($A[$r][$j], $divisor);
}
}
for ($i = $rref ? 0 : $r + 1; $i < $N; $i++) {
if ($i == $r) {
continue;
}
$mult = fractiondivide($A[$i][$c], $A[$r][$c]);
if ($mult[0] == 0) {
continue;
}
for ($j = $c; $j < $M; $j++) {
//echo "Entry $i,$j: ".fractionreduce($A[$i][$j]).' - '.fractionreduce( $mult).'*'.fractionreduce($A[$r][$j]).'<br/>';
$A[$i][$j] = fractionsubtract($A[$i][$j], fractionmultiply($mult, $A[$r][$j]));
}
}
$r++;
$c++;
}
for ($r = 0; $r < $N; $r++) {
for ($c = 0; $c < $M; $c++) {
if ($frac) {
$A[$r][$c] = fractionreduce($A[$r][$c]);
} else {
$A[$r][$c] = $A[$r][$c][0] / $A[$r][$c][1];
}
}
}
return $A;
}
function simplexreadsolutionarray($sma, $type, $showfractions = 1)
{
// process arguments -----------------------------------------------
$type = verifytype("simplexreadsolution", $type, "max");
if (is_null($type)) {
return null;
}
// showfractions
$showfractions = verifyshowfraction("simplexreadsolution", $showfractions, 1);
// Done processing arguments ---------------------------------------
//
// if we have 3 constraints with 2 variables then we will have:
//
// x1, x2, s1, s2, s3, f, obj
// 0 1 2 3 4 5 6
// rows = 4 --> slacks = 4 (3 slacks + 1 objectives)
// lastrow =3
// cols = 7
// lastcol = 6
// startcol = 6-4 = 2 --> lastcol-rows // start column of slacks
// endcol = 2+3 = 5 --> startcol + lastrow
$solution = array();
$rows = count($sma);
$cols = count($sma[0]);
$lastrow = $rows - 1;
$lastcol = $cols - 1;
$objectiveposition = $lastcol - 1;
$dualplusobjective = count($sma) + 1;
$var = $lastcol - $rows;
// number of x variables
if ($type == "min") {
for ($c = 0; $c < $var; $c++) {
$solution[$c] = 0;
$columnsolutionfound = true;
$zerorow = -1;
// not found
if ($sma[$lastrow][$c][0] == 0) {
for ($r = 0; $r < $lastrow; $r++) {
if ($sma[$r][$c][0] != 0 && $sma[$r][$c][0] != 1) {
$columnsolutionfound = false;
break;
// This should break out of the for r loop
}
if ($sma[$r][$c][0] == $sma[$r][$c][1]) {
if ($zerorow != -1) {
$columnsolutionfound = false;
break;
// This should break out of the for r loop
} else {
$zerorow = $r;
}
}
}
if ($columnsolutionfound) {
if ($showfractions == 1) {
$solution[$c] = fractionreduce($sma[$zerorow][$lastcol]);
} else {
$solution[$c] = fractiontodecimal($sma[$zerorow][$lastcol]);
}
}
}
}
for ($c = $var; $c < $dualplusobjective + 1; $c++) {
if ($showfractions == 1) {
$solution[$c] = fractionreduce($sma[$lastrow][$c]);
} else {
$solution[$c] = fractiontodecimal($sma[$lastrow][$c]);
}
}
} else {
for ($c = 0; $c < $lastcol - 1; $c++) {
$solution[$c] = 0;
$columnsolutionfound = true;
$zerorow = -1;
// not found
if ($sma[$lastrow][$c][0] == 0) {
for ($r = 0; $r < $lastrow; $r++) {
if ($sma[$r][$c][0] != 0 && $sma[$r][$c][0] != 1) {
$columnsolutionfound = false;
}
if ($sma[$r][$c][0] == $sma[$r][$c][1]) {
if ($zerorow != -1) {
$columnsolutionfound = false;
} else {
$zerorow = $r;
}
}
}
if ($columnsolutionfound) {
if ($showfractions == 1) {
$solution[$c] = fractionreduce($sma[$zerorow][$lastcol]);
} else {
$solution[$c] = fractiontodecimal($sma[$zerorow][$lastcol]);
}
}
}
}
}
if ($showfractions == 1) {
$solution[$objectiveposition] = fractionreduce($sma[$lastrow][$lastcol]);
} else {
$solution[$objectiveposition] = fractiontodecimal($sma[$lastrow][$lastcol]);
}
$solution[$lastcol] = "Yes";
// objective reached
for ($c = 0; $c < count($sma[0]); $c++) {
if ($sma[$lastrow][$c][0] < 0) {
$solution[$lastcol] = "No";
break;
}
}
return $solution;
}
function fractionpower($f, $p)
{
if (!is_array($f)) {
$f = fractionparse($f);
}
$fracarr = false;
if (is_array($args[0])) {
$fracarr = true;
}
$num = pow($f[0], $p);
$denom = pow($f[1], $p);
return fractionreduce($num, $denom, $fracarr);
}
