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<title>[15338] CalendarServer/trunk/contrib/performance</title>
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<dl class="meta">
<dt>Revision</dt> <dd><a href="http://trac.calendarserver.org//changeset/15338">15338</a></dd>
<dt>Author</dt> <dd>cdaboo@apple.com</dd>
<dt>Date</dt> <dd>2015-11-19 13:44:28 -0800 (Thu, 19 Nov 2015)</dd>
</dl>
<h3>Log Message</h3>
<pre>LogNormal visualization and curve fitting.</pre>
<h3>Modified Paths</h3>
<ul>
<li><a href="#CalendarServertrunkcontribperformancestatspy">CalendarServer/trunk/contrib/performance/stats.py</a></li>
</ul>
<h3>Added Paths</h3>
<ul>
<li><a href="#CalendarServertrunkcontribperformancestats_analysispy">CalendarServer/trunk/contrib/performance/stats_analysis.py</a></li>
</ul>
</div>
<div id="patch">
<h3>Diff</h3>
<a id="CalendarServertrunkcontribperformancestatspy"></a>
<div class="modfile"><h4>Modified: CalendarServer/trunk/contrib/performance/stats.py (15337 => 15338)</h4>
<pre class="diff"><span>
<span class="info">--- CalendarServer/trunk/contrib/performance/stats.py 2015-11-19 20:00:29 UTC (rev 15337)
+++ CalendarServer/trunk/contrib/performance/stats.py 2015-11-19 21:44:28 UTC (rev 15338)
</span><span class="lines">@@ -298,6 +298,8 @@
</span><span class="cx"> else:
</span><span class="cx"> raise ValueError("When using mode one of median or mean must be defined")
</span><span class="cx">
</span><ins>+ self._mode = mode
+ self._median = median
</ins><span class="cx"> self._mu = mu
</span><span class="cx"> self._sigma = sigma
</span><span class="cx"> self._scale = scale
</span><span class="lines">@@ -470,28 +472,3 @@
</span><span class="cx"> return prop
</span><span class="cx">
</span><span class="cx"> return None
</span><del>-
-if __name__ == '__main__':
-
- import matplotlib.pyplot as plt
- from collections import defaultdict
- mode_val = 6.0
- median_val = 8.0
- distribution = LogNormalDistribution(mode=mode_val, median=median_val, maximum=60)
- result = defaultdict(int)
- for i in range(1000000):
- s = int(distribution.sample())
- result[s] += 1
-
- total = 0
- for k, v in sorted(result.items(), key=lambda x: x[0]):
- print("%d\t%.5f" % (k, float(v) / result[1]))
- total += k * v
-
- print("Average: %.2f" % (float(total) / sum(result.values()),))
-
- x, y = zip(*sorted(result.items()))
- plt.plot(x, y)
- plt.xlabel("Samples")
- plt.ylabel("LogNormal")
- plt.show()
</del></span></pre></div>
<a id="CalendarServertrunkcontribperformancestats_analysispy"></a>
<div class="addfile"><h4>Added: CalendarServer/trunk/contrib/performance/stats_analysis.py (0 => 15338)</h4>
<pre class="diff"><span>
<span class="info">--- CalendarServer/trunk/contrib/performance/stats_analysis.py (rev 0)
+++ CalendarServer/trunk/contrib/performance/stats_analysis.py 2015-11-19 21:44:28 UTC (rev 15338)
</span><span class="lines">@@ -0,0 +1,229 @@
</span><ins>+##
+# Copyright (c) 2015 Apple Inc. All rights reserved.
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+# http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+##
+
+
+from collections import defaultdict, namedtuple
+from contrib.performance.stats import LogNormalDistribution
+from scipy.optimize import curve_fit
+import itertools
+import matplotlib.pyplot as plt
+import numpy as np
+import os
+
+
+class LogNormal(object):
+
+ Params = namedtuple("Params", ("mu", "sigma", "scale_x", "scale_y"))
+
+ @staticmethod
+ def fn(x, mu, sigma, scale_x, scale_y):
+ """
+ Calculate the LogNormal F(x) value for the given parameters.
+
+ @param x: x value to use
+ @type x: L{float}
+ @param mu: mean
+ @type mu: L{float}
+ @param sigma: standard deviation
+ @type sigma: L{float}
+ @param scale_x: X-scaling factor (to make mode == 1.0)
+ @type scale_x: L{float}
+ @param scale_y: Y-scaling factor for peak height
+ @type scale_y: L{float}
+ """
+ return scale_y * (
+ np.exp(-(np.log(x / scale_x) - mu) ** 2 / (2 * sigma ** 2)) /
+ (x / scale_x * sigma * np.sqrt(2 * np.pi))
+ )
+
+
+ @staticmethod
+ def estimate(x, y):
+ """
+ Given a set of x-y data that is likely a LogNormal distribution, try and estimate the mode
+ and median, and then derive mu, sigma, scale_x and scale_y values.
+
+ @param x: sequence of values
+ @type x: L{list} of L{float}
+ @param y: sequence of values
+ @type y: L{list} of L{float}
+ """
+ estimate_mode = 0.0
+ estimate_median = 0.0
+ max_y = 0.0
+ accumulated_y = 0.0
+ half_y = sum(y) / 2.0
+ for x_val, y_val in itertools.izip(x, y):
+ if y_val > max_y:
+ max_y = y_val
+ estimate_mode = x_val
+ accumulated_y += y_val
+ if half_y is not None and accumulated_y > half_y:
+ estimate_median = x_val
+ half_y = None
+
+ estimate_scale_x = estimate_mode - 0.5
+ estimate_mode = 1.0
+ estimate_median /= estimate_scale_x
+ estimate_mu = np.log(estimate_median)
+ estimate_sigma = np.sqrt(np.log(estimate_median) - np.log(estimate_mode))
+
+ peak_y = LogNormal.fn(estimate_scale_x, estimate_mu, estimate_sigma, estimate_scale_x, 1.0)
+ estimate_scale_y = max(y) / peak_y
+ return (
+ estimate_mode, estimate_median,
+ LogNormal.Params(estimate_mu, estimate_sigma, estimate_scale_x, estimate_scale_y),
+ )
+
+
+ @staticmethod
+ def plot(min_x, max_x, params, color):
+ """
+ Plot a LogNormal distribution over the specified x-axis range using the supplied
+ distribution parameters.
+
+ @param min_x: minimum x-axis value
+ @type min_x: L{float}
+ @param max_x: maximum x-asix value
+ @type max_x: L{float}
+ @param params: distribution parameters
+ @type params: L{LogNormal.Params}
+ @param color: color to use for line in plot
+ @type color: L{str}
+ """
+ xl = np.linspace(min_x, max_x, 10000)
+ yl = (
+ np.exp(-(np.log(xl / params.scale_x) - params.mu) ** 2 / (2 * params.sigma ** 2)) /
+ (xl / params.scale_x * params.sigma * np.sqrt(2 * np.pi))
+ )
+
+ plt.plot(xl, params.scale_y * yl, linewidth=2, color=color)
+
+
+ @staticmethod
+ def plotCSV(path, cutoff, bucket, color):
+ """
+ Plot data from a CSV file.
+
+ @param path: file to read from
+ @type path: L{str}
+ @param cutoff: maximum x-value to process
+ @type cutoff: L{float}
+ @param bucket: size of x-value buckets to use
+ @type bucket: L{int}
+ @param color: color to use for line in plot
+ @type color: L{str}
+ """
+ with open(os.path.expanduser(path)) as f:
+ data = f.read()
+ result = defaultdict(int)
+ for line in data.splitlines():
+ sp = line.split(",")
+ x_val = int(sp[0])
+ y_val = int(sp[1])
+ if x_val < cutoff:
+ result[(x_val / bucket) * bucket] += y_val
+
+ x, y = zip(*sorted(result.items()))
+ plt.plot(x, y)
+ return (x, y,)
+
+
+ @staticmethod
+ def distributionPlot(mode, median, maximum, color):
+ """
+ Plot data from a randomly generated LogNornal distribution.
+
+ @param mode: distribution mode
+ @type mode: L{float}
+ @param median: distribution median
+ @type median: L{float}
+ @param maximum: highest x-value to allow
+ @type maximum: L{float}
+ @param color: color to use for line in plot
+ @type color: L{str}
+ """
+ distribution = LogNormalDistribution(mode=mode, median=median, maximum=maximum)
+ result = defaultdict(int)
+ for _ignore in range(1000000):
+ s = int(distribution.sample()) + 0.5
+ result[s] += 1
+
+ x, y = zip(*sorted(result.items()))
+ plt.plot(x, y, color=color)
+
+ peak_y = LogNormal.fn(distribution._scale, distribution._mu, distribution._sigma, distribution._scale, 1.0)
+ scale_y = sum(sorted(y, reverse=True)[0:100]) / 100.0 / peak_y
+
+ return (x, y, LogNormal.Params(distribution._mu, distribution._sigma, distribution._scale, scale_y),)
+
+
+ @staticmethod
+ def fit(x, y):
+ """
+ Try and fit a LogNormal distribution to the supplied x-y data.
+
+ @param x: sequence of values
+ @type x: L{list} of L{float}
+ @param y: sequence of values
+ @type y: L{list} of L{float}
+ """
+ estimate_mode, estimate_median, estimate_params = LogNormal.estimate(x, y)
+
+ print("\n==== Estimates")
+ print("mode: {}".format(estimate_mode * estimate_params.scale_x))
+ print("median: {}".format(estimate_median * estimate_params.scale_x))
+ print("mu: {}".format(estimate_params.mu))
+ print("sigma: {}".format(estimate_params.sigma))
+ print("scale_x: {}".format(estimate_params.scale_x))
+ print("scale_y: {}".format(estimate_params.scale_y))
+
+ popt, _ignore_pcov = curve_fit(LogNormal.fn, x, y, (
+ estimate_params.mu, estimate_params.sigma, estimate_params.scale_x, estimate_params.scale_y,
+ ))
+
+ print("\n==== Fit results")
+ print("mode: {:.2f}".format(popt[2] * np.exp(popt[0] - popt[1] ** 2)))
+ print("median: {:.2f}".format(popt[2] * np.exp(popt[0])))
+ print("mu: {:.2f}".format(popt[0]))
+ print("sigma: {:.2f}".format(popt[1]))
+ print("scale_x: {:.2f}".format(popt[2]))
+ print("scale_y: {:.2f}".format(popt[3]))
+
+ return (
+ LogNormal.Params(*popt),
+ estimate_params,
+ )
+
+
+
+if __name__ == '__main__':
+
+ #x, y = LogNormal.plotCSV("~/data.txt", 10000, 10, color="b")
+ #estimate_mode, estimate_median, estimate_params = LogNormal.estimate(x, y)
+
+ mode_val = 450
+ median_val = 650
+ x, y, estimate_params = LogNormal.distributionPlot(mode_val, median_val, 10000, color="b")
+
+ LogNormal.plot(1, 10000, estimate_params, color="g")
+
+ popt, estimate = LogNormal.fit(x, y)
+ LogNormal.plot(1, 10000, popt, color="r")
+
+ plt.xlabel("Samples")
+ plt.ylabel("LogNormal")
+ plt.show()
</ins></span></pre>
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