class CartesianService
{
    public static function cartezianIterator($inputArray)
    {
        $maximumPosition = array_map('count', $inputArray);
        $position        = array_pad([], count($inputArray), 0);
        while (false !== ($item = self::buildItemAtPosition($inputArray, $position))) {
            yield $item;
            $position = self::incrementPosition($position, $maximumPosition);
        }
    }
    private static function buildItemAtPosition($inputArray, $positions)
    {
        if ($positions[0] >= count($inputArray[0])) {
            return false;
        }
        $item = [];
        foreach ($inputArray as $rowIndex => $row) {
            $position = $positions[$rowIndex];
            $item[] = $row[$position];
        }
        return $item;
    }
    private static function incrementPosition($position, $maximumPosition)
    {
        $digitToIncrement = count($position) - 1;
        do {
            ++$position[$digitToIncrement];
            if ($position[$digitToIncrement] < $maximumPosition[$digitToIncrement] || 0 === $digitToIncrement) {
                //no overflow
                break;
            }
            //overflow, reset to zero and increment parent digit
            $position[$digitToIncrement] = 0;
            --$digitToIncrement;
        } while ($digitToIncrement >= 0);
        return $position;
    }
}

使用

foreach (CartesianService::cartezianIterator(array_values($cartesian_arr)) as $item) {
     var_dump($item);
     }