PHP inverse to matrix

Question

I saw this question and expressed this idea.

Is there an efficient way to do this in PHP?

EDIT

Best with demo?

Answer 1

You can use the Math_Matrix pear pack for this.

Answer 2

This package claims to be able to do what you are looking for.

Answer 3

/**
* matrix_inverse
*
* Matrix Inverse
* Guass-Jordan Elimination Method
* Reduced Row Eshelon Form (RREF)
*
* In linear algebra an n-by-n (square) matrix A is called invertible (some
* authors use nonsingular or nondegenerate) if there exists an n-by-n matrix    B
* such that AB = BA = In where In denotes the n-by-n identity matrix and the
* multiplication used is ordinary matrix multiplication. If this is the case,
* then the matrix B is uniquely determined by A and is called the inverse of A,
* denoted by A-1. It follows from the theory of matrices that if for finite
* square matrices A and B, then also non-square matrices (m-by-n matrices for
* which m ? n) do not have an inverse. However, in some cases such a matrix may
* have a left inverse or right inverse. If A is m-by-n and the rank of A is
* equal to n, then A has a left inverse: an n-by-m matrix B such that BA = I.
* If A has rank m, then it has a right inverse: an n-by-m matrix B such that
* AB = I.
*
* A square matrix that is not invertible is called singular or degenerate. A
* square matrix is singular if and only if its determinant is 0. Singular
* matrices are rare in the sense that if you pick a random square matrix over
* a continuous uniform distribution on its entries, it will almost surely not
* be singular.
*
* While the most common case is that of matrices over the real or complex
* numbers, all these definitions can be given for matrices over any commutative
* ring. However, in this case the condition for a square matrix to be
* invertible is that its determinant is invertible in the ring, which in
* general is a much stricter requirement than being nonzero. The conditions for
* existence of left-inverse resp. right-inverse are more complicated since a
* notion of rank does not exist over rings.
*/
public function matrix_inverse($m1)
{
    $rows = $this->rows($m1);
    $cols = $this->columns($m1);
    if ($rows != $cols)
    {
        die("Matrim1 is not square. Can not be inverted.");
    }

    $m2 = $this->eye($rows);

    for ($j = 0; $j < $cols; $j++)
    {
        $factor = $m1[$j][$j];
        if ($this->debug)
        {
            fms_writeln('Divide Row [' . $j . '] by ' . $m1[$j][$j] . ' (to
                                                  give us a "1" in the desired position):');
        }
        $m1 = $this->rref_div($m1, $j, $factor);
        $m2 = $this->rref_div($m2, $j, $factor);
        if ($this->debug)
        {
            $this->disp2($m1, $m2);
        }
        for ($i = 0; $i < $rows; $i++)
        {
            if ($i != $j)
            {
                $factor = $m1[$i][$j];
                if ($this->debug)
                {
                    $this->writeln('Row[' . $i . '] - ' . number_format($factor, 4) . ' ×
                                                Row[' . $j . '] (to give us 0 in the desired position):');
                }
                $m1 = $this->rref_sub($m1, $i, $factor, $j);
                $m2 = $this->rref_sub($m2, $i, $factor, $j);
                if ($this->debug)
                {
                    $this->disp2($m1, $m2);
                }
            }
        }
    }
    return $m2;
}

Answer 4

open source PHP, .

, ,

<?php
include_once ("Matrix.class.php");
$matrixA = new Matrix(array(array(0, 1), array(2, 6)));
echo $matrixA->getInverse()->getMathMl();
?>

Answer 5

https://gist.github.com/unix1/7510208 identity_matrix() invert()