Google Analytics and XML namespace issue - php

Question

I have looked through several posts on how to parse the namespace of a Google Analytics api feed (XML file) in PHP. They all say I need to have this bit of code:
$properties = $item->children('http://schemas.google.com/analytics/2009');
(or something similar, all involving the URL "http://schemas.google.com/analytics/2009")
The problem is, however, that I then get an error:
Fatal error: Call to a member function children() on a non-object
It seems as though the schemas.google.com doesn't exist, but I can't find where I need to be pointing to... any ideas?
Here's a snippet of the XML file I'm working with:
<?xml version="1.0" encoding="UTF-8"?>
<feed xmlns="http://www.w3.org/2005/Atom" xmlns:dxp="http://schemas.google.com/analytics/2009" xmlns:openSearch="http://a9.com/-/spec/opensearch/1.1/">
<id>https://www.googleapis.com/analytics/v2.4/data?ids=ga:42418300&dimensions=ga:pagePath&metrics=ga:pageviews,ga:uniquePageviews&sort=-ga:pageviews&start-date=2013-12-01&end-date=2014-01-01&max-results=10</id>
<updated>2014-01-03T22:21:31.057Z</updated>
<title type="text">Google Analytics Data for View (Profile) xxxxxxx</title>
<link rel="self" type="application/atom+xml" href="https://www.googleapis.com/analytics/v2.4/data?ids=ga:42418300&dimensions=ga:pagePath&metrics=ga:pageviews,ga:uniquePageviews&sort=-ga:pageviews&start-date=2013-12-01&end-date=2014-01-01&max-results=10"/>
<link rel="next" type="application/atom+xml" href="https://www.googleapis.com/analytics/v2.4/data?ids=ga:42418300&dimensions=ga:pagePath&metrics=ga:pageviews,ga:uniquePageviews&sort=-ga:pageviews&start-date=2013-12-01&end-date=2014-01-01&start-index=11&max-results=10"/>
<author>
<name>Google Analytics</name>
</author>
<generator>Google Analytics</generator>
<openSearch:totalResults>4826</openSearch:totalResults>
<openSearch:startIndex>1</openSearch:startIndex>
<openSearch:itemsPerPage>10</openSearch:itemsPerPage>
<dxp:aggregates>
<dxp:metric name="ga:pageviews" type="integer" value="166656"/>
<dxp:metric name="ga:uniquePageviews" type="integer" value="132895"/>
</dxp:aggregates>
<dxp:containsSampledData>false</dxp:containsSampledData>
<dxp:dataSource>
<dxp:property name="ga:profileId" value="xxxxxxxx"/>
<dxp:property name="ga:webPropertyId" value="UA-xxxxxxxx-1"/>
<dxp:property name="ga:accountName" value="Provost"/>
<dxp:tableId>ga:42418300</dxp:tableId>
<dxp:tableName>WebSite</dxp:tableName>
</dxp:dataSource>
<dxp:endDate>2014-01-01</dxp:endDate>
<dxp:startDate>2013-12-01</dxp:startDate>
<entry>
<id>https://www.googleapis.com/analytics/v2.4/data?ids=ga:42418300&ga:pagePath=/&start-date=2013-12-01&end-date=2014-01-01</id>
<updated>2014-01-03T22:21:31.057Z</updated>
<title type="text">ga:pagePath=/</title>
<link rel="alternate" type="text/html" href="http://www.google.com/analytics"/>
<dxp:dimension name="ga:pagePath" value="/"/>
<dxp:metric name="ga:pageviews" type="integer" value="38197"/>
<dxp:metric name="ga:uniquePageviews" type="integer" value="29385"/>
</entry>
<entry>
<id>https://www.googleapis.com/analytics/v2.4/data?ids=ga:42418300&ga:pagePath=/page2/&start-date=2013-12-01&end-date=2014-01-01</id>
<updated>2014-01-03T22:21:31.057Z</updated>
<title type="text">ga:pagePath=/page2/</title>
<link rel="alternate" type="text/html" href="http://www.google.com/analytics"/>
<dxp:dimension name="ga:pagePath" value="/page2/"/>
<dxp:metric name="ga:pageviews" type="integer" value="13964"/>
<dxp:metric name="ga:uniquePageviews" type="integer" value="10974"/>
</entry>
Here's my PHP so far:
<?php
//ini_set('auto_detect_line_endings',TRUE);
$xml = simplexml_load_file("/ga-feed.xml");
$namespaces = $xml->getNamespaces(true);
foreach ($xml->entry as $key => $value) {
$value->registerXPathNamespace('dxp', 'http://schemas.google.com/analytics/2009');
echo $value->xpath('dxp:metric[pageviews]') . "<br />\n";
}
?>
Eventually, I need to be able run some calculations with pageviews and unique pageviews (show top 4 sites, a 5th "Other" would be a combination of all the other sites) against the overall pageviews/unique pageviews. Am I at least going in a semi-correct direction?
Update: In my foreach, I removed "feed" so it just says $xml->entry as $key, and now it will display a list of text:
Array
Array
Array
Array
Array
Array
Array
Array
Array
Array
Not quite what I'm looking for... but progress? lol