Solving Determinates in PHP

[cooldude832]

I know it could be done, but image a 20x20 matrix, that is a ton of minors to do, anyone got an idea on discovering the most 0ed row/column to expand upon.  The expansion is fairly easily, but I was wondering if it could be made faster by finding the path of least resistance, or if that is just a waste of power?

[Orio]

You could do something like this- it chooses the most 0ed column/row and from there you can continue.

 

<?php

//$matrix is a ($matrix_size)X($matrix_size) matrix

$matrix_size = 20;

$max1 = $max1_v = 0;
$max2 = $max2_v = 0;
$transpose = array();

for($i=0; $i<$matrix_size; $i++)
for($j=0; $j<$matrix_size; $j++)
	$transpose[$j][$i] = $matrix[$i][$j];

for($i=0; $i<$matrix_size; $i++)
if ($max1_v < $temp=count(array_keys($matrix[$i], 0)))
{
	$max1_v = $temp;
	$max1 = $i;
}

for($i=0; $i<$matrix_size; $i++)
{
if ($max2_v < $temp=count(array_keys($transpose[$i], 0)))
{
	$max2_v = $temp;
	$max2 = $i;
}
}


if($max1_v < $max2_v)  //Remember- the output is between 0 to ($matrix_size-1)
echo "Use column $max2";
else
echo "Use row $max1";

?>

 

Orio.

[sasa]

try

<?php
function deter($a, $i = -1){
if ($i < 0) $i = count($a) -1;
if ($i==0) return $a[0][0];
$j = $i;
$sig = 1;
while ($a[$j][$i] == 0 and $j-- > -1);
if ($i != $j and $a[$j][$i] != 0) {
	$tmp = $a[$i];
	$a[$i] = $a[$j];
	$a[$j] = $tmp;
	$sig *= -1;
}
else if($a[$j][$i] == 0) return 0;
$b = $a[$i][$i];
for ($row = $i -1; $row >= 0; $row--){
	$c = -$a[$row][$i] / $b;
	for ($k = 0; $k < $i; $k++){
		$a[$row][$k] += $a[$i][$k] * $c;
	}
}
return $out = $b * deter($a, $i - 1) * $sig;
}
$matr = array(
array(0,2,0),
array(3,4,2),
array(6,0,0)
);
echo deter($matr);
?>

[corbin]

Whoa.... We did that in Algebra 2 the other day (I'm in 10th grade lol)....

 

Hmmm would diagonals or minors be faster PHP wise.... I guess minors would be since it would be a lot less math (especially with 20x20 matrices and what not)....

 

Bleh idk....

 

Hmmm.... I contributed nothing to this thread.... oh well ;p.

[cooldude832]

yeah you learn them early, but my application to them is figuring out linear dependencies of non-first order diffy Qs, so your education now will help later.

[corbin]

I don't even know what a non-first order differential equation is lol.....  (Guess that's what the abbreviations were ;p)

 

 

[cooldude832]

abbrivations??? 

[Barand]

No, abbreviations

 

As in

diffy Qs

[cooldude832]

Diffy as in Differential thought that was pretty straight forward.

[Barand]

I agree completely.

 

Most of us would have thought the term "abbrivations abbreviations" pretty straightforward too, so why query it, having just abbreviated "differential equations" to "diffy Qs"

 

All corbin wanted was confirmation that that was what you meant.

[corbin]

lol just curious if I guessed that right since that sounded oddly familiar.... No idea why though.... haha...  Didn't mean to start a discussion about it ;p.