我正是需要这个，但我找不到行列式函数，所以我自己做了一个。Cramer 规则函数也是如此。也许它会帮助某人。
/**
* $matrix must be 2-dimensional n x n array in following format
* $matrix = array(array(1,2,3),array(1,2,3),array(1,2,3))
*/
function determinant($matrix = array()) {
// dimension control - n x n
foreach ($matrix as $row) {
if (sizeof($matrix) != sizeof($row)) {
return false;
}
}
// count 1x1 and 2x2 manually - rest by recursive function
$dimension = sizeof($matrix);
if ($dimension == 1) {
return $matrix[0][0];
}
if ($dimension == 2) {
return ($matrix[0][0] * $matrix[1][1] - $matrix[0][1] * $matrix[1][0]);
}
// cycles for submatrixes calculations
$sum = 0;
for ($i = 0; $i < $dimension; $i++) {
// for each "$i", you will create a smaller matrix based on the original matrix
// by removing the first row and the "i"th column.
$smallMatrix = array();
for ($j = 0; $j < $dimension - 1; $j++) {
$smallMatrix[$j] = array();
for ($k = 0; $k < $dimension; $k++) {
if ($k < $i) $smallMatrix[$j][$k] = $matrix[$j + 1][$k];
if ($k > $i) $smallMatrix[$j][$k - 1] = $matrix[$j + 1][$k];
}
}
// after creating the smaller matrix, multiply the "i"th element in the first
// row by the determinant of the smaller matrix.
// odd position is plus, even is minus - the index from 0 so it's oppositely
if ($i % 2 == 0){
$sum += $matrix[0][$i] * determinant($smallMatrix);
} else {
$sum -= $matrix[0][$i] * determinant($smallMatrix);
}
}
return $sum;
}
/**
* left side of equations - parameters:
* $leftMatrix must be 2-dimensional n x n array in following format
* $leftMatrix = array(array(1,2,3),array(1,2,3),array(1,2,3))
* right side of equations - results:
* $rightMatrix must be in format
* $rightMatrix = array(1,2,3);
*/
function equationSystem($leftMatrix = array(), $rightMatrix = array()) {
// matrixes and dimension check
if (!is_array($leftMatrix) || !is_array($rightMatrix)) {
return false;
}
if (sizeof($leftMatrix) != sizeof($rightMatrix)) {
return false;
}
$M = determinant($leftMatrix);
if (!$M) {
return false;
}
$x = array();
foreach ($rightMatrix as $rk => $rv) {
$xMatrix = $leftMatrix;
foreach ($rightMatrix as $rMk => $rMv) {
$xMatrix[$rMk][$rk] = $rMv;
}
$x[$rk] = determinant($xMatrix) / $M;
}
return $x;
}