title: AngularJS update input manually does not trigger change in the model
body: <p>When I am changing a value of an input element from plain JavaScript then the angular model is not updated. Is there any way to trigger somehow this update by firing some event manually after the change? </p>
  
  <pre><code>&lt;body ng-controller="MainCtrl"&gt;
    &lt;script&gt;
      function changeValue() {
        var e = document.getElementById("field");
        e.value = "updated value";
      }
    &lt;/script&gt;
  
    field: &lt;input type="text" id="field" ng-model="field"&gt;{{field}}
    &lt;br&gt;
    &lt;button onclick="changeValue()"&gt;Change the value&lt;/button&gt;
  
  &lt;/body&gt;
  </code></pre>
  
  <p>Complete example can be found on <a href="http://plnkr.co/edit/q0PfooK9tTQGTvT4PaxL?p=preview">plunkr</a>. After clicking the button I would expect that the <code>{{field}}</code> is updated somehow. Is there a way doing this?</p>