Magento: Check if Customer Logged in

//LOAD MAGENTO
 
require_once 'YOUR_PATH_TO_MAGENTO/app/Mage.php';
umask(0);
Mage::app('YOUR_WEBSITE_CODE', 'website');

//GET SESSION DATA
Mage::getSingleton('core/session', array('name'=>'frontend'));
$session = Mage::getSingleton('customer/session', array('name'=>'frontend'));

$customer_data = Mage::getModel('customer/customer')->$session->id);

//CHECK IF LOGGED IN
if($session->isLoggedIn()){
echo 'Welcome ' . $customer_data->firstname . " " . $customer_data->lastname;
}
else {
echo "Access Denied: Sorry, but this page is for registered members only.";
exit;
}