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<dt>Revision</dt> <dd><a href="http://trac.webkit.org/projects/webkit/changeset/192107">192107</a></dd>
<dt>Author</dt> <dd>commit-queue@webkit.org</dd>
<dt>Date</dt> <dd>2015-11-06 09:55:08 -0800 (Fri, 06 Nov 2015)</dd>
</dl>

<h3>Log Message</h3>
<pre>Initialize the graphics benchmark's Kalman filter with estimated 60 FPS
https://bugs.webkit.org/show_bug.cgi?id=150965

Patch by Said Abou-Hallawa &lt;sabouhallawa@apple.com&gt; on 2015-11-06
Reviewed by Darin Adler.

This should give the benchmark more accurate reading at warmup time. And
hence we can safely reduce the test running time to be 10 seconds.

* Animometer/runner/animometer.html:
Add &quot;defer&quot; back when loading resources/animometer.js since this script
depends on many other scripts and we need to wait till the page is parsed.
Also change the default test interval to be 10 seconds.

* Animometer/runner/resources/graph.js:
(graph): Make the test results curves smoother.

* Animometer/tests/resources/main.js:
(Animator): Initialize the Kalman filter with 60 FPS which should be true
if the test page is empty.

(Animator.prototype.animate):
* Animometer/tests/resources/math.js:
(KalmanEstimator): Fix the initial value of _vecX_est.
    _vecX_est[0] = current FPS (= 60FPS when the test page is empty)
    _vecX_est[1] = first time derivative of FPS (=0; FPS has been constant).
    _vecX_est[2] = second time derivative of FPS (=0; since _vecX_est[1]=0).
(KalmanEstimator.prototype.estimate): Add some comments.</pre>

<h3>Modified Paths</h3>
<ul>
<li><a href="#trunkPerformanceTestsAnimometerrunneranimometerhtml">trunk/PerformanceTests/Animometer/runner/animometer.html</a></li>
<li><a href="#trunkPerformanceTestsAnimometerrunnerresourcesgraphjs">trunk/PerformanceTests/Animometer/runner/resources/graph.js</a></li>
<li><a href="#trunkPerformanceTestsAnimometertestsresourcesmainjs">trunk/PerformanceTests/Animometer/tests/resources/main.js</a></li>
<li><a href="#trunkPerformanceTestsAnimometertestsresourcesmathjs">trunk/PerformanceTests/Animometer/tests/resources/math.js</a></li>
<li><a href="#trunkPerformanceTestsChangeLog">trunk/PerformanceTests/ChangeLog</a></li>
</ul>

</div>
<div id="patch">
<h3>Diff</h3>
<a id="trunkPerformanceTestsAnimometerrunneranimometerhtml"></a>
<div class="modfile"><h4>Modified: trunk/PerformanceTests/Animometer/runner/animometer.html (192106 => 192107)</h4>
<pre class="diff"><span>
<span class="info">--- trunk/PerformanceTests/Animometer/runner/animometer.html        2015-11-06 16:58:31 UTC (rev 192106)
+++ trunk/PerformanceTests/Animometer/runner/animometer.html        2015-11-06 17:55:08 UTC (rev 192107)
</span><span class="lines">@@ -7,7 +7,7 @@
</span><span class="cx">     &lt;script src=&quot;../resources/extensions.js&quot;&gt;&lt;/script&gt;
</span><span class="cx">     &lt;script src=&quot;resources/tests.js&quot;&gt;&lt;/script&gt;
</span><span class="cx">     &lt;script src=&quot;resources/benchmark-runner.js&quot;&gt;&lt;/script&gt;
</span><del>-    &lt;script src=&quot;resources/animometer.js&quot;&gt;&lt;/script&gt;
</del><ins>+    &lt;script src=&quot;resources/animometer.js&quot; defer&gt;&lt;/script&gt;
</ins><span class="cx">     &lt;script src=&quot;resources/d3.min.js&quot;&gt;&lt;/script&gt;
</span><span class="cx">     &lt;script src=&quot;resources/graph.js&quot;&gt;&lt;/script&gt;
</span><span class="cx"> &lt;/head&gt;
</span><span class="lines">@@ -27,7 +27,7 @@
</span><span class="cx">             &lt;/suites&gt;
</span><span class="cx">             &lt;options&gt;
</span><span class="cx">                 &lt;h2&gt;Options:&lt;/h2&gt;
</span><del>-                &lt;label&gt;Test interval: &lt;input id=&quot;test-interval&quot; type=&quot;number&quot; value=&quot;30&quot;&gt; seconds&lt;/label&gt;&lt;br&gt;
</del><ins>+                &lt;label&gt;Test interval: &lt;input id=&quot;test-interval&quot; type=&quot;number&quot; value=&quot;10&quot;&gt; seconds&lt;/label&gt;&lt;br&gt;
</ins><span class="cx">                 &lt;label&gt;Frame rate: &lt;input id=&quot;frame-rate&quot; type=&quot;number&quot; value=&quot;50&quot;&gt; fps&lt;/label&gt;&lt;br&gt;
</span><span class="cx">                 &lt;label&gt;&lt;input id=&quot;estimated-frame-rate&quot; type=&quot;checkbox&quot; checked&gt; Estimated Frame Rate&lt;/label&gt;&lt;br&gt;
</span><span class="cx">                 &lt;label&gt;&lt;input id=&quot;fix-test-complexity&quot; type=&quot;checkbox&quot;&gt; Fix test complexity after warmup&lt;/label&gt;&lt;br&gt;
</span></span></pre></div>
<a id="trunkPerformanceTestsAnimometerrunnerresourcesgraphjs"></a>
<div class="modfile"><h4>Modified: trunk/PerformanceTests/Animometer/runner/resources/graph.js (192106 => 192107)</h4>
<pre class="diff"><span>
<span class="info">--- trunk/PerformanceTests/Animometer/runner/resources/graph.js        2015-11-06 16:58:31 UTC (rev 192106)
+++ trunk/PerformanceTests/Animometer/runner/resources/graph.js        2015-11-06 17:55:08 UTC (rev 192107)
</span><span class="lines">@@ -30,10 +30,12 @@
</span><span class="cx">             .orient(&quot;right&quot;);
</span><span class="cx"> 
</span><span class="cx">     var lineLeft = d3.svg.line()
</span><ins>+            .interpolate(&quot;basis&quot;)
</ins><span class="cx">             .x(function(d) { return x(d.timeOffset); })
</span><span class="cx">             .y(function(d) { return yLeft(d.values[0]); });
</span><span class="cx"> 
</span><span class="cx">     var lineRight = d3.svg.line()
</span><ins>+            .interpolate(&quot;basis&quot;)
</ins><span class="cx">             .x(function(d) { return x(d.timeOffset); })
</span><span class="cx">             .y(function(d) { return yRight(d.values[1]); });
</span><span class="cx"> 
</span></span></pre></div>
<a id="trunkPerformanceTestsAnimometertestsresourcesmainjs"></a>
<div class="modfile"><h4>Modified: trunk/PerformanceTests/Animometer/tests/resources/main.js (192106 => 192107)</h4>
<pre class="diff"><span>
<span class="info">--- trunk/PerformanceTests/Animometer/tests/resources/main.js        2015-11-06 16:58:31 UTC (rev 192106)
+++ trunk/PerformanceTests/Animometer/tests/resources/main.js        2015-11-06 17:55:08 UTC (rev 192107)
</span><span class="lines">@@ -67,7 +67,7 @@
</span><span class="cx">     this._measureFrameCount = 3; 
</span><span class="cx">     this._referenceTime = 0;
</span><span class="cx">     this._currentTimeOffset = 0;
</span><del>-    this._estimator = new KalmanEstimator();
</del><ins>+    this._estimator = new KalmanEstimator(60);
</ins><span class="cx"> }
</span><span class="cx"> 
</span><span class="cx"> Animator.prototype =
</span><span class="lines">@@ -110,7 +110,7 @@
</span><span class="cx">          
</span><span class="cx">         // Use Kalman filter to get a more non-fluctuating frame rate.
</span><span class="cx">         if (this._benchmark.options[&quot;estimated-frame-rate&quot;])
</span><del>-            currentFrameRate = this._estimator.estimate(measureTimeDelta, currentFrameRate);
</del><ins>+            currentFrameRate = this._estimator.estimate(currentFrameRate);
</ins><span class="cx">         
</span><span class="cx">         // Adjust the test to reach the desired FPS.
</span><span class="cx">         var result = this._benchmark.update(this._currentTimeOffset, this.timeDelta(), currentFrameRate);
</span></span></pre></div>
<a id="trunkPerformanceTestsAnimometertestsresourcesmathjs"></a>
<div class="modfile"><h4>Modified: trunk/PerformanceTests/Animometer/tests/resources/math.js (192106 => 192107)</h4>
<pre class="diff"><span>
<span class="info">--- trunk/PerformanceTests/Animometer/tests/resources/math.js        2015-11-06 16:58:31 UTC (rev 192106)
+++ trunk/PerformanceTests/Animometer/tests/resources/math.js        2015-11-06 17:55:08 UTC (rev 192107)
</span><span class="lines">@@ -233,42 +233,55 @@
</span><span class="cx">     }
</span><span class="cx"> }
</span><span class="cx"> 
</span><del>-function KalmanEstimator()
</del><ins>+function KalmanEstimator(initX)
</ins><span class="cx"> {
</span><ins>+    // Initialize state transition matrix
</ins><span class="cx">     this._matA = Matrix3.identity();
</span><ins>+    this._matA[Matrix3.pos(0, 2)] = 1;
</ins><span class="cx">     
</span><ins>+    // Initialize measurement matrix
</ins><span class="cx">     this._vecH = Vector3.zeros();
</span><span class="cx">     this._vecH[0] = 1;
</span><span class="cx">     
</span><span class="cx">     this._matQ = Matrix3.identity();
</span><span class="cx">     this._R = 1000;
</span><span class="cx">     
</span><del>-    this._vecX_est = Vector3.ones();
</del><ins>+    // Initial state conditions
+    this._vecX_est = Vector3.zeros();
+    this._vecX_est[0] = initX;
</ins><span class="cx">     this._matP_est = Matrix3.zeros();
</span><span class="cx"> }
</span><span class="cx"> 
</span><span class="cx"> KalmanEstimator.prototype =
</span><span class="cx"> {
</span><del>-    estimate: function(timeDelta, current)
</del><ins>+    estimate: function(current)
</ins><span class="cx">     {
</span><del>-        // Update the transition matrix.
-        this._matA[Matrix3.pos(0, 2)] = 1;
-
-        // Predicted state and covariance.
</del><ins>+        // Project the state ahead
+        //  X_prd(k) = A * X_est(k-1)
</ins><span class="cx">         var vecX_prd = Matrix3.multiplyVector3(this._matA, this._vecX_est);
</span><ins>+        
+        // Project the error covariance ahead
+        //  P_prd(k) = A * P_est(k-1) * A' + Q
</ins><span class="cx">         var matP_prd = Matrix3.add(Matrix3.multiplyMatrix3(Matrix3.multiplyMatrix3(this._matA, this._matP_est), Matrix3.transpose(this._matA)), this._matQ);
</span><span class="cx"> 
</span><del>-        // Estimation.
</del><ins>+        // Compute Kalman gain
+        //  B = H * P_prd(k)';
+        //  S = B * H' + R;
+        //  K(k) = (S \ B)';
</ins><span class="cx">         var vecB = Vector3.multiplyMatrix3(this._vecH, Matrix3.transpose(matP_prd));
</span><span class="cx">         var S = Vector3.multiplyVector3(vecB, this._vecH) + this._R;
</span><del>-
</del><span class="cx">         var vecGain = Vector3.scale(1/S, vecB);
</span><span class="cx">         
</span><del>-        // Estimated state and covariance.
</del><ins>+        // Update the estimate via z(k)
+        //  X_est(k) = x_prd + K(k) * (z(k) - H * X_prd(k));
</ins><span class="cx">         this._vecX_est = Vector3.add(vecX_prd, Vector3.scale(current - Vector3.multiplyVector3(this._vecH, vecX_prd), vecGain));
</span><ins>+        
+        // Update the error covariance
+        //  P_est(k) = P_prd(k) - K(k) * H * P_prd(k);
</ins><span class="cx">         this._matP_est = Matrix3.subtract(matP_prd, Matrix3.scale(Vector3.multiplyVector3(vecGain, this._vecH), matP_prd));
</span><span class="cx"> 
</span><span class="cx">         // Compute the estimated measurement.
</span><ins>+        //  y = H * X_est(k);
</ins><span class="cx">         return Vector3.multiplyVector3(this._vecH,  this._vecX_est);
</span><span class="cx">     }
</span><span class="cx"> }
</span></span></pre></div>
<a id="trunkPerformanceTestsChangeLog"></a>
<div class="modfile"><h4>Modified: trunk/PerformanceTests/ChangeLog (192106 => 192107)</h4>
<pre class="diff"><span>
<span class="info">--- trunk/PerformanceTests/ChangeLog        2015-11-06 16:58:31 UTC (rev 192106)
+++ trunk/PerformanceTests/ChangeLog        2015-11-06 17:55:08 UTC (rev 192107)
</span><span class="lines">@@ -1,3 +1,33 @@
</span><ins>+2015-11-06  Said Abou-Hallawa  &lt;sabouhallawa@apple.com&gt;
+
+        Initialize the graphics benchmark's Kalman filter with estimated 60 FPS
+        https://bugs.webkit.org/show_bug.cgi?id=150965
+
+        Reviewed by Darin Adler.
+
+        This should give the benchmark more accurate reading at warmup time. And
+        hence we can safely reduce the test running time to be 10 seconds.
+
+        * Animometer/runner/animometer.html:
+        Add &quot;defer&quot; back when loading resources/animometer.js since this script
+        depends on many other scripts and we need to wait till the page is parsed.
+        Also change the default test interval to be 10 seconds.
+        
+        * Animometer/runner/resources/graph.js:
+        (graph): Make the test results curves smoother.
+        
+        * Animometer/tests/resources/main.js:
+        (Animator): Initialize the Kalman filter with 60 FPS which should be true
+        if the test page is empty.
+        
+        (Animator.prototype.animate):
+        * Animometer/tests/resources/math.js:
+        (KalmanEstimator): Fix the initial value of _vecX_est.
+            _vecX_est[0] = current FPS (= 60FPS when the test page is empty)
+            _vecX_est[1] = first time derivative of FPS (=0; FPS has been constant).
+            _vecX_est[2] = second time derivative of FPS (=0; since _vecX_est[1]=0).
+        (KalmanEstimator.prototype.estimate): Add some comments.
+
</ins><span class="cx"> 2015-11-04  Said Abou-Hallawa  &lt;sabouhallawa@apple.com&gt;
</span><span class="cx"> 
</span><span class="cx">         Remove &quot;defer&quot; from the scripts' references in the graphics benchmark home page 
</span></span></pre>
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