chutten/release_spinners_frequencies.ipynb Secret

## release_spinners_frequencies.ipynb
{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Egregious Spinners on Release 49 and their Frequencies of Occurence"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Unable to parse whitelist (/home/hadoop/anaconda2/lib/python2.7/site-packages/moztelemetry/histogram-whitelists.json). Assuming all histograms are acceptable.\n",
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING: pylab import has clobbered these variables: ['Annotation', 'Figure']\n",
      "`%matplotlib` prevents importing * from pylab and numpy\n"
     ]
    }
   ],
   "source": [
    "import ujson as json\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import plotly.plotly as py\n",
    "from plotly.graph_objs import *\n",
    "import IPython\n",
    "\n",
    "from moztelemetry import get_pings, get_pings_properties, get_one_ping_per_client, get_clients_history, get_records\n",
    "\n",
    "%pylab inline\n",
    "IPython.core.pylabtools.figsize(16, 7)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "224"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sc.defaultParallelism"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "pings = get_pings(sc, app=\"Firefox\", channel=\"release\", build_id=(\"20160916101415\", \"20160922113459\"), submission_date=\"20160928\", fraction=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2399803"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pings.count()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "subset = get_pings_properties(pings, [\"clientId\",\n",
    "                                      \"environment/system/os/name\",\n",
    "                                      \"environment/system/memoryMB\",\n",
    "                                      \"environment/system/cpu/speedMHz\",\n",
    "                                      \"environment/addons/activeAddons\",\n",
    "                                      \"payload/histograms/GC_MAX_PAUSE_MS\",\n",
    "                                      \"payload/histograms/CYCLE_COLLECTOR_MAX_PAUSE\",\n",
    "                                      \"payload/histograms/FX_TAB_SWITCH_SPINNER_VISIBLE_LONG_MS\"], with_processes=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "acceptable_addons = set([\n",
    "        \"e10srollout@mozilla.org\",\n",
    "        \"firefox@getpocket.com\",\n",
    "        \"webcompat@mozilla.org\",\n",
    "    ])\n",
    "\n",
    "def no_addons(p):\n",
    "    return p[\"environment/addons/activeAddons\"] is None or \\\n",
    "        len(p[\"environment/addons/activeAddons\"]) == 0 or \\\n",
    "        len(set(p[\"environment/addons/activeAddons\"].keys()) | acceptable_addons) == len(acceptable_addons)\n",
    "\n",
    "acceptable = subset.filter(no_addons)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "subset = acceptable"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "713515"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ping_count = subset.count()\n",
    "ping_count"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "76742"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "spinning_pings = subset.filter(lambda p: p[\"payload/histograms/FX_TAB_SWITCH_SPINNER_VISIBLE_LONG_MS\"] is not None)\n",
    "spinning_pings.count()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "203728"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "client_count = get_one_ping_per_client(subset).count()\n",
    "client_count"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "52600"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "spinning_clients_count = get_one_ping_per_client(spinning_pings).count()\n",
    "spinning_clients_count"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "17670"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hgram = \"payload/histograms/FX_TAB_SWITCH_SPINNER_VISIBLE_LONG_MS\"\n",
    "def has_longish_spinner(p):\n",
    "    if p[hgram] is None:\n",
    "        return False\n",
    "    for bucket, count in p[hgram].iteritems():\n",
    "        if bucket > 1000 and count > 0:\n",
    "            return True\n",
    "    return False\n",
    "\n",
    "longish_spinning_pings = spinning_pings.filter(has_longish_spinner)\n",
    "longish_spinning_pings.count()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "14630"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "longish_spinning_clients = get_one_ping_per_client(longish_spinning_pings)\n",
    "longish_spinning_clients.count()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Check frequencies of spinners per client, per bucket"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "client_spinner_freq = spinning_pings \\\n",
    "    .flatMap(lambda p: [((p[\"clientId\"], bucket), p[hgram][bucket]) for bucket in p[hgram].keys()]) \\\n",
    "    .reduceByKey(lambda a,b: a+b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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oZYZsc3MzGxsb+3rtYC8otd8PDAAAQD+tr69nfX09x44d2/NrFzJzO29mbgEAAMarlzO3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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa10c94f890>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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PAAAA9sV27nP7gCTfl+SZSZ7dPX5+P5MCYFjMdzEG6pixUMusqu2cuf3WJPds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\n3AIAADB4/z+v2mrGhVSnkQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa10ce48ad0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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Zuf2WJF/cWvuH/U4Gju/mLOIo8tGju/rjDwAAMBA7WZb80iRPbq19cDkpnZxl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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa10ce48850>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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2xZTjKW4BAAAGaiWfc1tVz03y+iR3r6qrq+rxrbXrk1yQ5NIk70jyvGkLWwAAANjuwIvb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\nfD5nnnk011xzfP5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u6+sPOj4A5nf55ZcvOwSYmzxmKOQy6+owZm4vTvLgrTuq6pQkv9zt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\nP7RTGP1YNYtxAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa0ffd6e750>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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quD0v8+L284ft6yR5Y5L7JHlHklcleWh3v2GP8yluAQAAJmoln3NbVc9M8ookn1dVb6mq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\nS1U9oruvTvKoJC9M8rokz+r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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa0ffe07350>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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v4e1eVT0kyYOS3CzJr3X3yw/zeAAAAKy23fTcXqdnXpjkgYcUz+ZxXtTdj0ny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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa0ffe07210>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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Zxe0BeEySc4bvb5HkXpmvaE6S2fD1ROOrrp9pqy9hY2PD2PhIx9t7YlYhHmPjRcdb21Yl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\n5oLv3QM5/28AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa106fe71d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "limit = 50\n",
    "\n",
    "for bucket in spinning_pings.take(1)[0][hgram].keys():\n",
    "    bucket_client_spinner_freq = client_spinner_freq \\\n",
    "        .filter(lambda x: x[0][1] == bucket) \\\n",
    "        .map(lambda x: x[1] if x[1] < limit else limit) # cap to a max of `limit` spinners\n",
    "    bucket_spinner_series = pd.Series(bucket_client_spinner_freq.collect())\n",
    "    bucket_spinner_series.hist(bins=limit, log=True, width=1)\n",
    "    plt.xlim(0, limit)\n",
    "    plt.title(\"Spinners of length %d\" % bucket)\n",
    "    plt.xlabel(\"Number of spinners ( %d total )\" % bucket_spinner_series.sum())\n",
    "    plt.ylabel(\"Number of clients\")\n",
    "    plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.11"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}

## release_spinners_frequencies.py

# coding: utf-8

# ### Egregious Spinners on Release 49 and their Frequencies of Occurence

# In[1]:

import ujson as json
import matplotlib.pyplot as plt
import pandas as pd
import numpy as np
import plotly.plotly as py
from plotly.graph_objs import *
import IPython

from moztelemetry import get_pings, get_pings_properties, get_one_ping_per_client, get_clients_history, get_records

get_ipython().magic(u'pylab inline')
IPython.core.pylabtools.figsize(16, 7)


# In[2]:

sc.defaultParallelism


# In[5]:

pings = get_pings(sc, app="Firefox", channel="release", build_id=("20160916101415", "20160922113459"), submission_date="20160928", fraction=1)


# In[6]:

pings.count()


# In[7]:

subset = get_pings_properties(pings, ["clientId",
                                      "environment/system/os/name",
                                      "environment/system/memoryMB",
                                      "environment/system/cpu/speedMHz",
                                      "environment/addons/activeAddons",
                                      "payload/histograms/GC_MAX_PAUSE_MS",
                                      "payload/histograms/CYCLE_COLLECTOR_MAX_PAUSE",
                                      "payload/histograms/FX_TAB_SWITCH_SPINNER_VISIBLE_LONG_MS"], with_processes=True)


# In[8]:

acceptable_addons = set([
        "e10srollout@mozilla.org",
        "firefox@getpocket.com",
        "webcompat@mozilla.org",
    ])

def no_addons(p):
    return p["environment/addons/activeAddons"] is None or         len(p["environment/addons/activeAddons"]) == 0 or         len(set(p["environment/addons/activeAddons"].keys()) | acceptable_addons) == len(acceptable_addons)

acceptable = subset.filter(no_addons)


# In[9]:

subset = acceptable


# In[10]:

ping_count = subset.count()
ping_count


# In[11]:

spinning_pings = subset.filter(lambda p: p["payload/histograms/FX_TAB_SWITCH_SPINNER_VISIBLE_LONG_MS"] is not None)
spinning_pings.count()


# In[12]:

client_count = get_one_ping_per_client(subset).count()
client_count


# In[13]:

spinning_clients_count = get_one_ping_per_client(spinning_pings).count()
spinning_clients_count


# In[14]:

hgram = "payload/histograms/FX_TAB_SWITCH_SPINNER_VISIBLE_LONG_MS"
def has_longish_spinner(p):
    if p[hgram] is None:
        return False
    for bucket, count in p[hgram].iteritems():
        if bucket > 1000 and count > 0:
            return True
    return False

longish_spinning_pings = spinning_pings.filter(has_longish_spinner)
longish_spinning_pings.count()


# In[15]:

longish_spinning_clients = get_one_ping_per_client(longish_spinning_pings)
longish_spinning_clients.count()


# #### Check frequencies of spinners per client, per bucket

# In[16]:

client_spinner_freq = spinning_pings     .flatMap(lambda p: [((p["clientId"], bucket), p[hgram][bucket]) for bucket in p[hgram].keys()])     .reduceByKey(lambda a,b: a+b)


# In[17]:

limit = 50

for bucket in spinning_pings.take(1)[0][hgram].keys():
    bucket_client_spinner_freq = client_spinner_freq         .filter(lambda x: x[0][1] == bucket)         .map(lambda x: x[1] if x[1] < limit else limit) # cap to a max of `limit` spinners
    bucket_spinner_series = pd.Series(bucket_client_spinner_freq.collect())
    bucket_spinner_series.hist(bins=limit, log=True, width=1)
    plt.xlim(0, limit)
    plt.title("Spinners of length %d" % bucket)
    plt.xlabel("Number of spinners ( %d total )" % bucket_spinner_series.sum())
    plt.ylabel("Number of clients")
    plt.show()

	# coding: utf-8

	# ### Egregious Spinners on Release 49 and their Frequencies of Occurence

	# In[1]:

	import ujson as json
	import matplotlib.pyplot as plt
	import pandas as pd
	import numpy as np
	import plotly.plotly as py
	from plotly.graph_objs import *
	import IPython

	from moztelemetry import get_pings, get_pings_properties, get_one_ping_per_client, get_clients_history, get_records

	get_ipython().magic(u'pylab inline')
	IPython.core.pylabtools.figsize(16, 7)


	# In[2]:

	sc.defaultParallelism


	# In[5]:

	pings = get_pings(sc, app="Firefox", channel="release", build_id=("20160916101415", "20160922113459"), submission_date="20160928", fraction=1)


	# In[6]:

	pings.count()


	# In[7]:

	subset = get_pings_properties(pings, ["clientId",
	"environment/system/os/name",
	"environment/system/memoryMB",
	"environment/system/cpu/speedMHz",
	"environment/addons/activeAddons",
	"payload/histograms/GC_MAX_PAUSE_MS",
	"payload/histograms/CYCLE_COLLECTOR_MAX_PAUSE",
	"payload/histograms/FX_TAB_SWITCH_SPINNER_VISIBLE_LONG_MS"], with_processes=True)


	# In[8]:

	acceptable_addons = set([
	"e10srollout@mozilla.org",
	"firefox@getpocket.com",
	"webcompat@mozilla.org",
	])

	def no_addons(p):
	return p["environment/addons/activeAddons"] is None or len(p["environment/addons/activeAddons"]) == 0 or len(set(p["environment/addons/activeAddons"].keys()) \| acceptable_addons) == len(acceptable_addons)

	acceptable = subset.filter(no_addons)


	# In[9]:

	subset = acceptable


	# In[10]:

	ping_count = subset.count()
	ping_count


	# In[11]:

	spinning_pings = subset.filter(lambda p: p["payload/histograms/FX_TAB_SWITCH_SPINNER_VISIBLE_LONG_MS"] is not None)
	spinning_pings.count()


	# In[12]:

	client_count = get_one_ping_per_client(subset).count()
	client_count


	# In[13]:

	spinning_clients_count = get_one_ping_per_client(spinning_pings).count()
	spinning_clients_count


	# In[14]:

	hgram = "payload/histograms/FX_TAB_SWITCH_SPINNER_VISIBLE_LONG_MS"
	def has_longish_spinner(p):
	if p[hgram] is None:
	return False
	for bucket, count in p[hgram].iteritems():
	if bucket > 1000 and count > 0:
	return True
	return False

	longish_spinning_pings = spinning_pings.filter(has_longish_spinner)
	longish_spinning_pings.count()


	# In[15]:

	longish_spinning_clients = get_one_ping_per_client(longish_spinning_pings)
	longish_spinning_clients.count()


	# #### Check frequencies of spinners per client, per bucket

	# In[16]:

	client_spinner_freq = spinning_pings .flatMap(lambda p: [((p["clientId"], bucket), p[hgram][bucket]) for bucket in p[hgram].keys()]) .reduceByKey(lambda a,b: a+b)


	# In[17]:

	limit = 50

	for bucket in spinning_pings.take(1)[0][hgram].keys():
	bucket_client_spinner_freq = client_spinner_freq .filter(lambda x: x[0][1] == bucket) .map(lambda x: x[1] if x[1] < limit else limit) # cap to a max of `limit` spinners
	bucket_spinner_series = pd.Series(bucket_client_spinner_freq.collect())
	bucket_spinner_series.hist(bins=limit, log=True, width=1)
	plt.xlim(0, limit)
	plt.title("Spinners of length %d" % bucket)
	plt.xlabel("Number of spinners ( %d total )" % bucket_spinner_series.sum())
	plt.ylabel("Number of clients")
	plt.show()