# 4x4 Matrix Solver (Multiplication)

## Recommended Posts

Good day, guys... it seems I'm messing up my algorithm to multiply two(2) 4x4 Matrix and put it in a table. Can somebody point out what's wrong with my code? THANKS IN ADVANCE!!!

Here's the situation. I'm getting values from two(2) 4x4 tables, multiply them, and store them in another table. Here's the "math" part of my code:

``` <?php

echo "<br/><br/><br/><br/><br/><br/><br/><br/><br/>";

\$i=0;

for(\$row = 0; \$row < 4; \$row++){

for(\$column = 0; \$column < 4; \$column++){

\$sum = 0;
for(\$ctr = 0; \$ctr < 4; \$ctr++){

\$sum = \$sum + (\$cell[\$i][\$row][\$ctr] * \$cell[\$i+1][\$ctr][\$row]);

}

\$sol[\$i][\$row][\$column] = \$sum;

}

}

?>

<table width="50" border="5" align = "left" cellpadding="5">
<tr>
<td><?php echo \$sol[\$i][0][0] ?></td>
<td><?php echo \$sol[\$i][0][1] ?></td>
<td><?php echo \$sol[\$i][0][2] ?></td>
<td><?php echo \$sol[\$i][0][3] ?></td>
</tr>
<tr>
<td><?php echo \$sol[\$i][1][0] ?></td>
<td><?php echo \$sol[\$i][1][1] ?></td>
<td><?php echo \$sol[\$i][1][2] ?></td>
<td><?php echo \$sol[\$i][1][3] ?></td>
</tr>
<tr>
<td><?php echo \$sol[\$i][2][0] ?></td>
<td><?php echo \$sol[\$i][2][1] ?></td>
<td><?php echo \$sol[\$i][2][2] ?></td>
<td><?php echo \$sol[\$i][2][3] ?></td>
</tr>
<tr>
<td><?php echo \$sol[\$i][3][0] ?></td>
<td><?php echo \$sol[\$i][3][1] ?></td>
<td><?php echo \$sol[\$i][3][2] ?></td>
<td><?php echo \$sol[\$i][3][3] ?></td>
</tr>
</table>   ```

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That's not all your code. Can you post the whole thing?

##### Share on other sites

change

`\$sum = \$sum + (\$cell[\$i][\$row][\$ctr] * \$cell[\$i+1][\$ctr][\$row]);`

to

`\$sum = \$sum + (\$cell[\$i][\$row][\$ctr] * \$cell[\$i+1][\$ctr][\$column]);`

##### Share on other sites

change

`\$sum = \$sum + (\$cell[\$i][\$row][\$ctr] * \$cell[\$i+1][\$ctr][\$row]);`

to

`\$sum = \$sum + (\$cell[\$i][\$row][\$ctr] * \$cell[\$i+1][\$ctr][\$column]);`

THANKS! So that's why it gives the wrong solution. I multiplied it in the with the wrong row/column! THANK YOU SO MUCH!!!

That's not all your code. Can you post the whole thing?

Sure, cuz I need help for something more than just this. Hehe. Here's my code. After that multiplication, I should copy the succeeding 4 matrices and place it beside my solution. Then I multiply the first 2 again, until one matrix is left. Any idea how will I do it? By the way, here's the 'string':

rotx(90);trans(2,1,-1);roty(90);rotz(90);trans(1,-1,2);roty(90)

...THANKS!

```<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
<html xmlns="http://www.w3.org/1999/xhtml">
<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
<title>Matrix Solver</title>

<body>

<?php
\$transformation = \$_POST['string'];

\$transbits = explode(";",\$transformation);

for(\$i=0; \$i<count(\$transbits);\$i++){

if(strcmp(substr(\$transbits[\$i],0,5),"trans")==0){

preg_match('#\((.*?)\)#', \$transbits[\$i], \$match);
\$extrans = explode(",",\$match[1]);
?>

<tr>
<td><?php \$cell[\$i][0][0] = 1; echo \$cell[\$i][0][0] ?></td>
<td><?php \$cell[\$i][0][1] = 0; echo \$cell[\$i][0][1] ?></td>
<td><?php \$cell[\$i][0][2] = 0; echo \$cell[\$i][0][2] ?></td>
<td><?php \$cell[\$i][0][3] = \$extrans[0]; echo \$cell[\$i][0][3] ?></td>
</tr>
<tr>
<td><?php \$cell[\$i][1][0] = 0; echo \$cell[\$i][1][0] ?></td>
<td><?php \$cell[\$i][1][1] = 1; echo \$cell[\$i][1][1] ?></td>
<td><?php \$cell[\$i][1][2] = 0; echo \$cell[\$i][1][2] ?></td>
<td><?php \$cell[\$i][1][3] = \$extrans[1]; echo \$cell[\$i][1][3] ?></td>
</tr>
<tr>
<td><?php \$cell[\$i][2][0] = 0; echo \$cell[\$i][2][0] ?></td>
<td><?php \$cell[\$i][2][1] = 0; echo \$cell[\$i][2][1] ?></td>
<td><?php \$cell[\$i][2][2] = 1; echo \$cell[\$i][2][2] ?></td>
<td><?php \$cell[\$i][2][3] = \$extrans[2]; echo \$cell[\$i][2][3] ?></td>
</tr>
<tr>
<td><?php \$cell[\$i][3][0] = 0; echo \$cell[\$i][3][0] ?></td>
<td><?php \$cell[\$i][3][1] = 0; echo \$cell[\$i][3][1] ?></td>
<td><?php \$cell[\$i][3][2] = 0; echo \$cell[\$i][3][2] ?></td>
<td><?php \$cell[\$i][3][3] = 1; echo \$cell[\$i][3][3] ?></td>
</tr>
</table>
<?php

}

else if(strcmp(substr(\$transbits[\$i],0,3),"rot")==0){

preg_match('#\((.*?)\)#', \$transbits[\$i], \$match);
//echo "\$match[1] <br/>";

if (strcmp(substr(\$transbits[\$i],3,1),"x")==0){
?>

<tr>
<td><?php \$cell[\$i][0][0] = 1; echo \$cell[\$i][0][0] ?></td>
<td><?php \$cell[\$i][0][1] = 0; echo \$cell[\$i][0][1] ?></td>
<td><?php \$cell[\$i][0][2] = 0; echo \$cell[\$i][0][2] ?></td>
<td><?php \$cell[\$i][0][3] = 0; echo \$cell[\$i][0][3] ?></td>
</tr>
<tr>
<td><?php \$cell[\$i][1][0] = 0; echo \$cell[\$i][1][0] ?></td>
<td><?php \$cell[\$i][1][1] = intval(cos(deg2rad(\$match[1]))); echo \$cell[\$i][1][1] ?></td>
<td><?php \$cell[\$i][1][2] = intval(-sin(deg2rad(\$match[1]))); echo \$cell[\$i][1][2] ?></td>
<td><?php \$cell[\$i][1][3] = 0; echo \$cell[\$i][1][3] ?></td>
</tr>
<tr>
<td><?php \$cell[\$i][2][0] = 0; echo \$cell[\$i][2][0] ?></td>
<td><?php \$cell[\$i][2][1] = intval(sin(deg2rad(\$match[1]))); echo \$cell[\$i][2][1] ?></td>
<td><?php \$cell[\$i][2][2] = intval(cos(deg2rad(\$match[1]))); echo \$cell[\$i][2][2] ?></td>
<td><?php \$cell[\$i][2][3] = 0; echo \$cell[\$i][2][3] ?></td>
</tr>
<tr>
<td><?php \$cell[\$i][3][0] = 0; echo \$cell[\$i][3][0] ?></td>
<td><?php \$cell[\$i][3][1] = 0; echo \$cell[\$i][3][1] ?></td>
<td><?php \$cell[\$i][3][2] = 0; echo \$cell[\$i][3][2] ?></td>
<td><?php \$cell[\$i][3][3] = 1; echo \$cell[\$i][3][3] ?></td>
</tr>
</table>

<?php

}

else if (strcmp(substr(\$transbits[\$i],3,1),"y")==0){

?>

<tr>
<td><?php \$cell[\$i][0][0] = intval(cos(deg2rad(\$match[1]))); echo \$cell[\$i][0][0] ?></td>
<td><?php \$cell[\$i][0][1] = 0; echo \$cell[\$i][0][1] ?></td>
<td><?php \$cell[\$i][0][2] = intval(sin(deg2rad(\$match[1]))); echo \$cell[\$i][0][2] ?></td>
<td><?php \$cell[\$i][0][3] = 0; echo \$cell[\$i][0][3] ?></td>
</tr>
<tr>
<td><?php \$cell[\$i][1][0] = 0; echo \$cell[\$i][1][0] ?></td>
<td><?php \$cell[\$i][1][1] = 1; echo \$cell[\$i][1][1] ?></td>
<td><?php \$cell[\$i][1][2] = 0; echo \$cell[\$i][1][2] ?></td>
<td><?php \$cell[\$i][1][3] = 0; echo \$cell[\$i][1][3] ?></td>
</tr>
<tr>
<td><?php \$cell[\$i][2][0] = intval(-sin(deg2rad(\$match[1]))); echo \$cell[\$i][2][0] ?></td>
<td><?php \$cell[\$i][2][1] = 0; echo \$cell[\$i][2][1] ?></td>
<td><?php \$cell[\$i][2][2] = intval(cos(deg2rad(\$match[1]))); echo \$cell[\$i][2][2] ?></td>
<td><?php \$cell[\$i][2][3] = 0; echo \$cell[\$i][2][3] ?></td>
</tr>
<tr>
<td><?php \$cell[\$i][3][0] = 0; echo \$cell[\$i][3][0] ?></td>
<td><?php \$cell[\$i][3][1] = 0; echo \$cell[\$i][3][1] ?></td>
<td><?php \$cell[\$i][3][2] = 0; echo \$cell[\$i][3][2] ?></td>
<td><?php \$cell[\$i][3][3] = 1; echo \$cell[\$i][3][3] ?></td>
</tr>
</table>

<?php
}

else if (strcmp(substr(\$transbits[\$i],3,1),"z")==0){
?>

<tr>
<td><?php \$cell[\$i][0][0] = intval(cos(deg2rad(\$match[1]))); echo \$cell[\$i][0][0] ?></td>
<td><?php \$cell[\$i][0][1] = intval(-sin(deg2rad(\$match[1]))); echo \$cell[\$i][0][1] ?></td>
<td><?php \$cell[\$i][0][2] = 0; echo \$cell[\$i][0][2] ?></td>
<td><?php \$cell[\$i][0][3] = 0; echo \$cell[\$i][0][3] ?></td>
</tr>
<tr>
<td><?php \$cell[\$i][1][0] = intval(sin(deg2rad(\$match[1]))); echo \$cell[\$i][1][0] ?></td>
<td><?php \$cell[\$i][1][1] = intval(cos(deg2rad(\$match[1]))); echo \$cell[\$i][1][1] ?></td>
<td><?php \$cell[\$i][1][2] = 0; echo \$cell[\$i][1][2] ?></td>
<td><?php \$cell[\$i][1][3] = 0; echo \$cell[\$i][1][3] ?></td>
</tr>
<tr>
<td><?php \$cell[\$i][2][0] = 0; echo \$cell[\$i][2][0] ?></td>
<td><?php \$cell[\$i][2][1] = 0; echo \$cell[\$i][2][1] ?></td>
<td><?php \$cell[\$i][2][2] = 1; echo \$cell[\$i][2][2] ?></td>
<td><?php \$cell[\$i][2][3] = 0; echo \$cell[\$i][2][3] ?></td>
</tr>
<tr>
<td><?php \$cell[\$i][3][0] = 0; echo \$cell[\$i][3][0] ?></td>
<td><?php \$cell[\$i][3][1] = 0; echo \$cell[\$i][3][1] ?></td>
<td><?php \$cell[\$i][3][2] = 0; echo \$cell[\$i][3][2] ?></td>
<td><?php \$cell[\$i][3][3] = 1; echo \$cell[\$i][3][3] ?></td>
</tr>
</table>

<?php
}

}

}

?>

<?php

echo "<br/><br/><br/><br/><br/><br/><br/><br/><br/>";

\$i=0;

for(\$row = 0; \$row < 4; \$row++){

for(\$column = 0; \$column < 4; \$column++){

\$sum = 0;
for(\$ctr = 0; \$ctr < 4; \$ctr++){

\$sum = \$sum + (\$cell[\$i][\$row][\$ctr] * \$cell[\$i+1][\$ctr][\$column]);

}

\$sol[\$i][\$row][\$column] = \$sum;

}

}

?>

<table width="50" border="5" align = "left" cellpadding="5">
<tr>
<td><?php echo \$sol[\$i][0][0] ?></td>
<td><?php echo \$sol[\$i][0][1] ?></td>
<td><?php echo \$sol[\$i][0][2] ?></td>
<td><?php echo \$sol[\$i][0][3] ?></td>
</tr>
<tr>
<td><?php echo \$sol[\$i][1][0] ?></td>
<td><?php echo \$sol[\$i][1][1] ?></td>
<td><?php echo \$sol[\$i][1][2] ?></td>
<td><?php echo \$sol[\$i][1][3] ?></td>
</tr>
<tr>
<td><?php echo \$sol[\$i][2][0] ?></td>
<td><?php echo \$sol[\$i][2][1] ?></td>
<td><?php echo \$sol[\$i][2][2] ?></td>
<td><?php echo \$sol[\$i][2][3] ?></td>
</tr>
<tr>
<td><?php echo \$sol[\$i][3][0] ?></td>
<td><?php echo \$sol[\$i][3][1] ?></td>
<td><?php echo \$sol[\$i][3][2] ?></td>
<td><?php echo \$sol[\$i][3][3] ?></td>
</tr>
</table>

</body>
</html>```

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HI! I'm almost finished with my code. And I need one last help. I don't think I'm doing this correctly in the 2nd iteration when \$i = 1? And how Do I get rid of the last (unnecessary and empty) matrix? THANKS!

```<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
<html xmlns="http://www.w3.org/1999/xhtml">
<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
<title>Matrix Solver</title>

<body>

<?php
\$transformation = \$_POST['string'];

\$transbits = explode(";",\$transformation);

for(\$i=0; \$i<count(\$transbits);\$i++){

if(strcmp(substr(\$transbits[\$i],0,5),"trans")==0){

preg_match('#\((.*?)\)#', \$transbits[\$i], \$match);
\$extrans = explode(",",\$match[1]);
?>

<tr>
<td><?php \$cell[\$i][0][0] = 1; echo \$cell[\$i][0][0] ?></td>
<td><?php \$cell[\$i][0][1] = 0; echo \$cell[\$i][0][1] ?></td>
<td><?php \$cell[\$i][0][2] = 0; echo \$cell[\$i][0][2] ?></td>
<td><?php \$cell[\$i][0][3] = \$extrans[0]; echo \$cell[\$i][0][3] ?></td>
</tr>
<tr>
<td><?php \$cell[\$i][1][0] = 0; echo \$cell[\$i][1][0] ?></td>
<td><?php \$cell[\$i][1][1] = 1; echo \$cell[\$i][1][1] ?></td>
<td><?php \$cell[\$i][1][2] = 0; echo \$cell[\$i][1][2] ?></td>
<td><?php \$cell[\$i][1][3] = \$extrans[1]; echo \$cell[\$i][1][3] ?></td>
</tr>
<tr>
<td><?php \$cell[\$i][2][0] = 0; echo \$cell[\$i][2][0] ?></td>
<td><?php \$cell[\$i][2][1] = 0; echo \$cell[\$i][2][1] ?></td>
<td><?php \$cell[\$i][2][2] = 1; echo \$cell[\$i][2][2] ?></td>
<td><?php \$cell[\$i][2][3] = \$extrans[2]; echo \$cell[\$i][2][3] ?></td>
</tr>
<tr>
<td><?php \$cell[\$i][3][0] = 0; echo \$cell[\$i][3][0] ?></td>
<td><?php \$cell[\$i][3][1] = 0; echo \$cell[\$i][3][1] ?></td>
<td><?php \$cell[\$i][3][2] = 0; echo \$cell[\$i][3][2] ?></td>
<td><?php \$cell[\$i][3][3] = 1; echo \$cell[\$i][3][3] ?></td>
</tr>
</table>
<?php

}

else if(strcmp(substr(\$transbits[\$i],0,3),"rot")==0){

preg_match('#\((.*?)\)#', \$transbits[\$i], \$match);
//echo "\$match[1] <br/>";

if (strcmp(substr(\$transbits[\$i],3,1),"x")==0){
?>

<tr>
<td><?php \$cell[\$i][0][0] = 1; echo \$cell[\$i][0][0] ?></td>
<td><?php \$cell[\$i][0][1] = 0; echo \$cell[\$i][0][1] ?></td>
<td><?php \$cell[\$i][0][2] = 0; echo \$cell[\$i][0][2] ?></td>
<td><?php \$cell[\$i][0][3] = 0; echo \$cell[\$i][0][3] ?></td>
</tr>
<tr>
<td><?php \$cell[\$i][1][0] = 0; echo \$cell[\$i][1][0] ?></td>
<td><?php \$cell[\$i][1][1] = intval(cos(deg2rad(\$match[1]))); echo \$cell[\$i][1][1] ?></td>
<td><?php \$cell[\$i][1][2] = intval(-sin(deg2rad(\$match[1]))); echo \$cell[\$i][1][2] ?></td>
<td><?php \$cell[\$i][1][3] = 0; echo \$cell[\$i][1][3] ?></td>
</tr>
<tr>
<td><?php \$cell[\$i][2][0] = 0; echo \$cell[\$i][2][0] ?></td>
<td><?php \$cell[\$i][2][1] = intval(sin(deg2rad(\$match[1]))); echo \$cell[\$i][2][1] ?></td>
<td><?php \$cell[\$i][2][2] = intval(cos(deg2rad(\$match[1]))); echo \$cell[\$i][2][2] ?></td>
<td><?php \$cell[\$i][2][3] = 0; echo \$cell[\$i][2][3] ?></td>
</tr>
<tr>
<td><?php \$cell[\$i][3][0] = 0; echo \$cell[\$i][3][0] ?></td>
<td><?php \$cell[\$i][3][1] = 0; echo \$cell[\$i][3][1] ?></td>
<td><?php \$cell[\$i][3][2] = 0; echo \$cell[\$i][3][2] ?></td>
<td><?php \$cell[\$i][3][3] = 1; echo \$cell[\$i][3][3] ?></td>
</tr>
</table>

<?php

}

else if (strcmp(substr(\$transbits[\$i],3,1),"y")==0){

?>

<tr>
<td><?php \$cell[\$i][0][0] = intval(cos(deg2rad(\$match[1]))); echo \$cell[\$i][0][0] ?></td>
<td><?php \$cell[\$i][0][1] = 0; echo \$cell[\$i][0][1] ?></td>
<td><?php \$cell[\$i][0][2] = intval(sin(deg2rad(\$match[1]))); echo \$cell[\$i][0][2] ?></td>
<td><?php \$cell[\$i][0][3] = 0; echo \$cell[\$i][0][3] ?></td>
</tr>
<tr>
<td><?php \$cell[\$i][1][0] = 0; echo \$cell[\$i][1][0] ?></td>
<td><?php \$cell[\$i][1][1] = 1; echo \$cell[\$i][1][1] ?></td>
<td><?php \$cell[\$i][1][2] = 0; echo \$cell[\$i][1][2] ?></td>
<td><?php \$cell[\$i][1][3] = 0; echo \$cell[\$i][1][3] ?></td>
</tr>
<tr>
<td><?php \$cell[\$i][2][0] = intval(-sin(deg2rad(\$match[1]))); echo \$cell[\$i][2][0] ?></td>
<td><?php \$cell[\$i][2][1] = 0; echo \$cell[\$i][2][1] ?></td>
<td><?php \$cell[\$i][2][2] = intval(cos(deg2rad(\$match[1]))); echo \$cell[\$i][2][2] ?></td>
<td><?php \$cell[\$i][2][3] = 0; echo \$cell[\$i][2][3] ?></td>
</tr>
<tr>
<td><?php \$cell[\$i][3][0] = 0; echo \$cell[\$i][3][0] ?></td>
<td><?php \$cell[\$i][3][1] = 0; echo \$cell[\$i][3][1] ?></td>
<td><?php \$cell[\$i][3][2] = 0; echo \$cell[\$i][3][2] ?></td>
<td><?php \$cell[\$i][3][3] = 1; echo \$cell[\$i][3][3] ?></td>
</tr>
</table>

<?php
}

else if (strcmp(substr(\$transbits[\$i],3,1),"z")==0){
?>

<tr>
<td><?php \$cell[\$i][0][0] = intval(cos(deg2rad(\$match[1]))); echo \$cell[\$i][0][0] ?></td>
<td><?php \$cell[\$i][0][1] = intval(-sin(deg2rad(\$match[1]))); echo \$cell[\$i][0][1] ?></td>
<td><?php \$cell[\$i][0][2] = 0; echo \$cell[\$i][0][2] ?></td>
<td><?php \$cell[\$i][0][3] = 0; echo \$cell[\$i][0][3] ?></td>
</tr>
<tr>
<td><?php \$cell[\$i][1][0] = intval(sin(deg2rad(\$match[1]))); echo \$cell[\$i][1][0] ?></td>
<td><?php \$cell[\$i][1][1] = intval(cos(deg2rad(\$match[1]))); echo \$cell[\$i][1][1] ?></td>
<td><?php \$cell[\$i][1][2] = 0; echo \$cell[\$i][1][2] ?></td>
<td><?php \$cell[\$i][1][3] = 0; echo \$cell[\$i][1][3] ?></td>
</tr>
<tr>
<td><?php \$cell[\$i][2][0] = 0; echo \$cell[\$i][2][0] ?></td>
<td><?php \$cell[\$i][2][1] = 0; echo \$cell[\$i][2][1] ?></td>
<td><?php \$cell[\$i][2][2] = 1; echo \$cell[\$i][2][2] ?></td>
<td><?php \$cell[\$i][2][3] = 0; echo \$cell[\$i][2][3] ?></td>
</tr>
<tr>
<td><?php \$cell[\$i][3][0] = 0; echo \$cell[\$i][3][0] ?></td>
<td><?php \$cell[\$i][3][1] = 0; echo \$cell[\$i][3][1] ?></td>
<td><?php \$cell[\$i][3][2] = 0; echo \$cell[\$i][3][2] ?></td>
<td><?php \$cell[\$i][3][3] = 1; echo \$cell[\$i][3][3] ?></td>
</tr>
</table>

<?php
}

}

}

?>

<?php

for(\$i=0; \$i<count(\$transbits);\$i++){

echo "<br/><br/><br/><br/><br/><br/><br/><br/><br/>";

for(\$row = 0; \$row < 4; \$row++){

for(\$column = 0; \$column < 4; \$column++){

\$sum = 0;
for(\$ctr = 0; \$ctr < 4; \$ctr++){

\$sum = \$sum + (\$cell[\$i][\$row][\$ctr] * \$cell[\$i+1][\$ctr][\$column]);

}

\$cell[\$i][\$row][\$column] = \$sum;

}

}
?>

<table width="50" border="5" align = "left" cellpadding="5">
<tr>
<td><?php echo \$cell[\$i][0][0] ?></td>
<td><?php echo \$cell[\$i][0][1] ?></td>
<td><?php echo \$cell[\$i][0][2] ?></td>
<td><?php echo \$cell[\$i][0][3] ?></td>
</tr>
<tr>
<td><?php echo \$cell[\$i][1][0] ?></td>
<td><?php echo \$cell[\$i][1][1] ?></td>
<td><?php echo \$cell[\$i][1][2] ?></td>
<td><?php echo \$cell[\$i][1][3] ?></td>
</tr>
<tr>
<td><?php echo \$cell[\$i][2][0] ?></td>
<td><?php echo \$cell[\$i][2][1] ?></td>
<td><?php echo \$cell[\$i][2][2] ?></td>
<td><?php echo \$cell[\$i][2][3] ?></td>
</tr>
<tr>
<td><?php echo \$cell[\$i][3][0] ?></td>
<td><?php echo \$cell[\$i][3][1] ?></td>
<td><?php echo \$cell[\$i][3][2] ?></td>
<td><?php echo \$cell[\$i][3][3] ?></td>
</tr>
</table>

<?php

for(\$j=\$i+2; \$j<(count(\$transbits));\$j++){

?>

<table width="50" border="5" align = "left" cellpadding="5">
<tr>
<td><?php echo \$cell[\$j][0][0] ?></td>
<td><?php echo \$cell[\$j][0][1] ?></td>
<td><?php echo \$cell[\$j][0][2] ?></td>
<td><?php echo \$cell[\$j][0][3] ?></td>
</tr>
<tr>
<td><?php echo \$cell[\$j][1][0] ?></td>
<td><?php echo \$cell[\$j][1][1] ?></td>
<td><?php echo \$cell[\$j][1][2] ?></td>
<td><?php echo \$cell[\$j][1][3] ?></td>
</tr>
<tr>
<td><?php echo \$cell[\$j][2][0] ?></td>
<td><?php echo \$cell[\$j][2][1] ?></td>
<td><?php echo \$cell[\$j][2][2] ?></td>
<td><?php echo \$cell[\$j][2][3] ?></td>
</tr>
<tr>
<td><?php echo \$cell[\$j][3][0] ?></td>
<td><?php echo \$cell[\$j][3][1] ?></td>
<td><?php echo \$cell[\$j][3][2] ?></td>
<td><?php echo \$cell[\$j][3][3] ?></td>
</tr>
</table>

<?php
}

}

?>

</body>
</html>```

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