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    "# 12. Stochastic simulation of biological circuits\n",
    "\n",
    "(c) 2019 Justin Bois and Michael Elowitz. With the exception of pasted graphics, where the source is noted, this work is licensed under a [Creative Commons Attribution License CC-BY 4.0](https://creativecommons.org/licenses/by/4.0/). All code contained herein is licensed under an [MIT license](https://opensource.org/licenses/MIT).\n",
    "\n",
    "This document was prepared at [Caltech](http://www.caltech.edu) with financial support from the [Donna and Benjamin M. Rosen Bioengineering Center](http://rosen.caltech.edu).\n",
    "\n",
    "<img src=\"figs/caltech_rosen.png\">\n",
    "\n",
    "<hr>\n",
    "<br/>"
   ]
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  {
   "cell_type": "markdown",
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   "source": [
    "#### Concepts\n",
    "- Sampling out of probability distributions is a useful way to computational determine their properties.\n",
    "- Master equations can equivalently be defined in terms of a set of moves and associated propensities and updates.\n",
    "- The Gillespie algorithm enables sampling out of probability distributions described by master equations.\n",
    "\n",
    "#### Techniques\n",
    "- Application of the Gillespie algorithm.\n",
    "- Profiling of code for optimization.\n",
    "\n",
    "<br />\n",
    "\n",
    "<hr>"
   ]
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Possible fixes:\\n\"+\n     \"</p>\\n\"+\n     \"<ul>\\n\"+\n     \"<li>re-rerun `output_notebook()` to attempt to load from CDN again, or</li>\\n\"+\n     \"<li>use INLINE resources instead, as so:</li>\\n\"+\n     \"</ul>\\n\"+\n     \"<code>\\n\"+\n     \"from bokeh.resources import INLINE\\n\"+\n     \"output_notebook(resources=INLINE)\\n\"+\n     \"</code>\\n\"+\n     \"</div>\"}};\n\n  function display_loaded() {\n    var el = document.getElementById(\"1001\");\n    if (el != null) {\n      el.textContent = \"BokehJS is loading...\";\n    }\n    if (root.Bokeh !== undefined) {\n      if (el != null) {\n        el.textContent = \"BokehJS \" + root.Bokeh.version + \" successfully loaded.\";\n      }\n    } else if (Date.now() < root._bokeh_timeout) {\n      setTimeout(display_loaded, 100)\n    }\n  }\n\n\n  function run_callbacks() {\n    try {\n      root._bokeh_onload_callbacks.forEach(function(callback) {\n        if (callback != null)\n          callback();\n      });\n    } finally {\n      delete root._bokeh_onload_callbacks\n    }\n    console.debug(\"Bokeh: all callbacks have finished\");\n  }\n\n  function load_libs(css_urls, js_urls, callback) {\n    if (css_urls == null) css_urls = [];\n    if (js_urls == null) js_urls = [];\n\n    root._bokeh_onload_callbacks.push(callback);\n    if (root._bokeh_is_loading > 0) {\n      console.debug(\"Bokeh: BokehJS is being loaded, scheduling callback at\", now());\n      return null;\n    }\n    if (js_urls == null || js_urls.length === 0) {\n      run_callbacks();\n      return null;\n    }\n    console.debug(\"Bokeh: BokehJS not loaded, scheduling load and callback at\", now());\n    root._bokeh_is_loading = css_urls.length + js_urls.length;\n\n    function on_load() {\n      root._bokeh_is_loading--;\n      if (root._bokeh_is_loading === 0) {\n        console.debug(\"Bokeh: all BokehJS libraries/stylesheets loaded\");\n        run_callbacks()\n      }\n    }\n\n    function on_error() {\n      console.error(\"failed to load \" + url);\n    }\n\n    for (var i = 0; i < css_urls.length; i++) {\n      var url = css_urls[i];\n      const element = document.createElement(\"link\");\n      element.onload = on_load;\n      element.onerror = on_error;\n      element.rel = \"stylesheet\";\n      element.type = \"text/css\";\n      element.href = url;\n      console.debug(\"Bokeh: injecting link tag for BokehJS stylesheet: \", url);\n      document.body.appendChild(element);\n    }\n\n    for (var i = 0; i < js_urls.length; i++) {\n      var url = js_urls[i];\n      var element = document.createElement('script');\n      element.onload = on_load;\n      element.onerror = on_error;\n      element.async = false;\n      element.src = url;\n      console.debug(\"Bokeh: injecting script tag for BokehJS library: \", url);\n      document.head.appendChild(element);\n    }\n  };var element = document.getElementById(\"1001\");\n  if (element == null) {\n    console.error(\"Bokeh: ERROR: autoload.js configured with elementid '1001' but no matching script tag was found. \")\n    return false;\n  }\n\n  function inject_raw_css(css) {\n    const element = document.createElement(\"style\");\n    element.appendChild(document.createTextNode(css));\n    document.body.appendChild(element);\n  }\n\n  var js_urls = [\"https://cdn.pydata.org/bokeh/release/bokeh-1.1.0.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-widgets-1.1.0.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-tables-1.1.0.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-gl-1.1.0.min.js\"];\n  var css_urls = [\"https://cdn.pydata.org/bokeh/release/bokeh-1.1.0.min.css\", \"https://cdn.pydata.org/bokeh/release/bokeh-widgets-1.1.0.min.css\", \"https://cdn.pydata.org/bokeh/release/bokeh-tables-1.1.0.min.css\"];\n\n  var inline_js = [\n    function(Bokeh) {\n      Bokeh.set_log_level(\"info\");\n    },\n    \n    function(Bokeh) {\n      \n    },\n    function(Bokeh) {} // ensure no trailing comma for IE\n  ];\n\n  function run_inline_js() {\n    \n    if ((root.Bokeh !== undefined) || (force === true)) {\n      for (var i = 0; i < inline_js.length; i++) {\n        inline_js[i].call(root, root.Bokeh);\n      }if (force === true) {\n        display_loaded();\n      }} else if (Date.now() < root._bokeh_timeout) {\n      setTimeout(run_inline_js, 100);\n    } else if (!root._bokeh_failed_load) {\n      console.log(\"Bokeh: BokehJS failed to load within specified timeout.\");\n      root._bokeh_failed_load = true;\n    } else if (force !== true) {\n      var cell = $(document.getElementById(\"1001\")).parents('.cell').data().cell;\n      cell.output_area.append_execute_result(NB_LOAD_WARNING)\n    }\n\n  }\n\n  if (root._bokeh_is_loading === 0) {\n    console.debug(\"Bokeh: BokehJS loaded, going straight to plotting\");\n    run_inline_js();\n  } else {\n    load_libs(css_urls, js_urls, function() {\n      console.debug(\"Bokeh: BokehJS plotting callback run at\", now());\n      run_inline_js();\n    });\n  }\n}(window));"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import multiprocessing\n",
    "import tqdm\n",
    "\n",
    "import numpy as np\n",
    "import scipy.stats as st\n",
    "import numba\n",
    "\n",
    "import biocircuits\n",
    "\n",
    "# Plotting modules\n",
    "import bokeh.io\n",
    "import bokeh.plotting\n",
    "\n",
    "bokeh.io.output_notebook()\n",
    "\n",
    "# Line profiler (can install with conda install line_profiler)\n",
    "%load_ext line_profiler"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Sampling out of master equations\n",
    "\n",
    "For some stories, we know the probability distribution. For example, if the story is that we are doing $n$ independent coin flips, each with probability $p$ of landing heads, the number $h$ of heads is Binomially distributed. We could prove that this is the case, or look it up in a book. But sometimes, it is too difficult (or impossible) to prove what the distribution is, so we can numerically compute its properties by **sampling** out of the distribution. Sampling involved using a random number generator to *simulate* the story that generates the distribution. So, if you know the story and you have a computer handy, you can sample to be able to get a plot of your distribution, though you will not get the analytical form.\n",
    "\n",
    "Let's demonstrate this with the Binomial distribution. We will take $n = 25$ and $p = 0.25$ and compute $P(h \\mid n, p)$, the probability of getting $h$ heads in $n$ flips, each with probability $p$ of landing heads. We will draw 10, 30, 100, and 300 samples and plot them versus the expected Binomial distribution."
   ]
  },
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Application\",\"version\":\"1.1.0\"}};\n",
       "  var render_items = [{\"docid\":\"8b7e0727-b4cb-4e3e-a2d8-eaafc2ff1f57\",\"roots\":{\"1225\":\"35c0443c-01af-41a3-971d-78e78c3ed014\"}}];\n",
       "  root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
       "\n",
       "  }\n",
       "  if (root.Bokeh !== undefined) {\n",
       "    embed_document(root);\n",
       "  } else {\n",
       "    var attempts = 0;\n",
       "    var timer = setInterval(function(root) {\n",
       "      if (root.Bokeh !== undefined) {\n",
       "        embed_document(root);\n",
       "        clearInterval(timer);\n",
       "      }\n",
       "      attempts++;\n",
       "      if (attempts > 100) {\n",
       "        console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n",
       "        clearInterval(timer);\n",
       "      }\n",
       "    }, 10, root)\n",
       "  }\n",
       "})(window);"
      ],
      "application/vnd.bokehjs_exec.v0+json": ""
     },
     "metadata": {
      "application/vnd.bokehjs_exec.v0+json": {
       "id": "1225"
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def simulate_coinflips(n, p, size=1):\n",
    "    \"\"\"\n",
    "    Simulate n_samples sets of n coin flips with prob. p of heads.\n",
    "    \"\"\"\n",
    "    n_heads = np.empty(size, dtype=int)\n",
    "    for i in range(size):\n",
    "        n_heads[i] = np.sum(np.random.random(size=n) < p)\n",
    "    return n_heads\n",
    "\n",
    "size = (30, 100, 1000, 10000)\n",
    "n = 25\n",
    "p = 0.25\n",
    "h_plot = np.arange(26)\n",
    "theor_dist = st.binom.pmf(h_plot, n, p)\n",
    "\n",
    "plots = []\n",
    "for n_samp in size:\n",
    "    plot = bokeh.plotting.figure(plot_height=200,\n",
    "                                 plot_width=300,\n",
    "                                 x_axis_label='h',\n",
    "                                 y_axis_label='P(h)',\n",
    "                                 title=f'{n_samp} samples')\n",
    "    h = simulate_coinflips(n, p, size=n_samp)\n",
    "    plot.circle(h_plot, theor_dist)\n",
    "    plot.circle(np.arange(h.max()+1), np.bincount(h)/n_samp, color='orange')\n",
    "    plots.append(plot)\n",
    "    \n",
    "bokeh.io.show(bokeh.layouts.gridplot(plots, ncols=2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we can see, if we *sample* out of the probability distribution, we can approximately calculate the actual distribution. If we sample enough, the approximation is very good.\n",
    "\n",
    "Sampling is such a powerful strategy that highly efficient algorithms with convenient APIs have been developed to sample out of named probability distributions. For example, we could have used `np.random.binom()` as a drop-in (and _much_ more efficient) replacement for the `simulate_coinflips()` function above.\n",
    "\n",
    "We will use the same strategy for solving master equations. We will find a way to *sample* out of the distribution that is governed by the master equation. This technique was pioneered by Dan Gillespie in the last 70s. For that reason, these sampling techniques are often called **Gillespie simulations**. The algorithm is sometimes referred to as a **stochastic simulation algorithm**, or SSA.\n",
    "\n",
    "Here, we will explore how this algorithm works by looking at simple production of a protein."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The dynamical equations\n",
    "\n",
    "For simple protein production, we have the following reactions.\n",
    "\n",
    "\\begin{align}\n",
    "\\text{DNA} \\rightarrow \\text{mRNA} \\rightarrow \\text{protein}\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Macroscale equations\n",
    "As we've seen before, the deterministic dynamics, which describe mean concentrations over a large population of cells, are described by the ODEs\n",
    "\n",
    "\\begin{align}\n",
    "\\frac{\\mathrm{d}m}{\\mathrm{d}t} &= \\beta_m - \\gamma_m m, \\\\[1em]\n",
    "\\frac{\\mathrm{d}p}{\\mathrm{d}t} &= \\beta_p m - \\gamma_p p.\n",
    "\\end{align}\n",
    "\n",
    "The same equations should hold if $m$ and $p$ represent the mean *numbers* of cells; we would just have to appropriately rescale the constants. Assuming the $m$ and $p$ are now numbers (so we are not free to pick their units), we can nondimensionalize using $\\gamma_m$ to nondimensionalize time. This leads to redefinition of parameters and variables\n",
    "\n",
    "\\begin{align}\n",
    "&\\beta_m/\\gamma_m \\to \\beta_m, \\\\[1em]\n",
    "&\\beta_p/\\gamma_m \\to \\beta_p, \\\\[1em]\n",
    "&\\gamma_m t \\to t.\n",
    "\\end{align}\n",
    "\n",
    "The dimensionless equations are\n",
    "\n",
    "\\begin{align}\n",
    "\\frac{\\mathrm{d}m}{\\mathrm{d}t} &= \\beta_m - m, \\\\[1em]\n",
    "\\frac{\\mathrm{d}p}{\\mathrm{d}t} &= \\beta_p m - \\gamma p,\n",
    "\\end{align}\n",
    "\n",
    "with $\\gamma = \\gamma_p/\\gamma_m$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The Master equation\n",
    "\n",
    "We can write a master equation for these dynamics.  In this case, each state is defined by an mRNA copy number $m$ and a protein copy number $p$.  So, we will write a master equation for $P(m, p, t)$.\n",
    "\n",
    "\\begin{align}\n",
    "\\frac{\\mathrm{d}P(m,p,t)}{\\mathrm{d}t} &= \\beta_m P(m-1,p,t) + (m+1)P(m+1,p,t) - \\beta_m P(m,p,t) - mP(m,p,t) \\nonumber \\\\[1em]\n",
    "&+\\beta_p mP(m,p-1,t) + \\gamma_p (p+1)P(m,p+1,t) - \\beta_p mP(m,p,t) - \\gamma p P(m,p,t).\n",
    "\\end{align}\n",
    "\n",
    "We implicitly define $P(m, p, t) = 0$ if $m < 0$ or $p < 0$. This is the master equation we will sample from using the stochastic simulation algorithm (SSA) or Gillespie algorithm."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The Gillespie algorithm\n",
    "\n",
    "The transition probabilities are also called **propensities** in the context of stochastic simulation. The propensity for a given transition, say indexed $i$, is denoted as $a_i$. The equivalence to notation we introduced for master equations is that if transition $i$ results in the change of state from $n'$ to $n$, then $a_i = W(n\\mid n')$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To cast this problem for a Gillespie simulation, we can write each change of state (moving either the copy number of mRNA or protein up or down by 1 in this case) and their respective propensities.\n",
    "\n",
    "\\begin{align}\n",
    "\\begin{array}{ll}\n",
    "\\text{reaction, }r_i & \\text{propensity, } a_i \\\\\n",
    "m \\rightarrow m+1,\\;\\;\\;\\; & \\beta_m \\\\[0.3em]\n",
    "m \\rightarrow m-1, \\;\\;\\;\\; & m\\\\[0.3em]\n",
    "p \\rightarrow p+1, \\;\\;\\;\\; & \\beta_p m \\\\[0.3em]\n",
    "p \\rightarrow p-1, \\;\\;\\;\\; & \\gamma p.\n",
    "\\end{array}\n",
    "\\end{align}\n",
    "\n",
    "We will not carefully prove that the Gillespie algorithm samples from the probability distribution governed by the master equation, but will state the principles behind it.  The basic idea is that events (such as those outlined above) are rare, discrete, separate events.  I.e., each event is an arrival of a Poisson process.  The Gillespie algorithm starts with some state, $(m_0,p_0)$.  Then a state change, *any* state change, will happen in some time $\\Delta t$ that has a certain probability distribution (which we will show is Exponential momentarily).  The probability that the state change that happens is reaction $j$ is proportional to $a_j$.  That is to say, state changes with high propensities are more likely to occur.  Thus, choosing which of the $n$ state changes happens in $\\Delta t$ is a matter of drawing an integer $j$ in $[1,n]$ where the probability of drawing $j$ is\n",
    "\n",
    "\\begin{align}\n",
    "\\frac{a_j}{\\sum_i a_i}.\n",
    "\\end{align}\n",
    "\n",
    "Now, how do we determine how long the state change took?  The probability density function describing that a *given* state change $i$ takes place in time $t$ is\n",
    "\n",
    "\\begin{align}\n",
    "P(t\\mid a_i) = a_i\\, \\mathrm{e}^{-a_i t},\n",
    "\\end{align}\n",
    "\n",
    "since the time it takes for arrival of a [Poisson process](https://en.wikipedia.org/wiki/Poisson_point_process) is [Exponentially distributed](https://en.wikipedia.org/wiki/Exponential_distribution). The probability that it has *not* arrived in time $\\Delta t$ is the probability that the arrival time is greater than $\\Delta t$, given by the complementary cumulative distribution function for the Exponential distribution.\n",
    "\n",
    "\\begin{align}\n",
    "P(t > \\Delta t\\mid a_i) = \\int_{\\Delta t}^\\infty \\mathrm{d}t\\,P(t\\mid a_i) = \\mathrm{e}^{-a_i \\Delta t}.\n",
    "\\end{align}\n",
    "\n",
    "Now, say we have $n$ processes that arrive in time $t_1, t_2, \\ldots$.  The probability that *none* of them arrive before $\\Delta t$ is\n",
    "\n",
    "\\begin{align}\n",
    "P(t_1 > \\Delta t, t_2 > \\Delta t, \\ldots) &=\n",
    "P(t_1 > \\Delta t) P(t_2 > \\Delta t) \\cdots =\n",
    "\\prod_i \\mathrm{e}^{-a_i \\Delta t} \n",
    "= \\mathrm{exp}\\left[-\\Delta t \\sum_i a_i\\right].\n",
    "\\end{align}\n",
    "\n",
    "This is the same as the probability of a single Poisson process with $a = \\sum_i a_i$ not arriving before $\\Delta t$. So, the probability that it *does* arrive in $\\Delta t$ is Exponentially distributed with mean $\\left(\\sum_i a_i\\right)^{-1}$.\n",
    "\n",
    "So, we know how to choose a state change and we also know how long it takes.\n",
    "The Gillespie algorithm then proceeds as follows.\n",
    "\n",
    ">1. Choose an initial condition, e.g., $m = p = 0$.\n",
    "2. Calculate the propensity for each of the enumerated state changes.  The propensities may be functions of $m$ and $p$, so they need to be recalculated for every $m$ and $p$ we encounter.\n",
    "3. Choose how much time the reaction will take by drawing out of an exponential distribution with a mean equal to $\\left(\\sum_i a_i\\right.)^{-1}$.  This means that a change arises from a Poisson process.\n",
    "4. Choose what state change will happen by drawing a sample out of the discrete distribution where $P_i = \\left.a_i\\middle/\\left(\\sum_i a_i\\right)\\right.$.  In other words, the probability that a state change will be chosen is proportional to its propensity.\n",
    "5. Increment time by the time step you chose in step 3.\n",
    "6. Update the states according to the state change you choose in step 4.\n",
    "7. If $t$ is less than your pre-determined stopping time, go to step 2. Else stop.\n",
    "\n",
    "Gillespie proved that this algorithm samples the probability distribution described by the master equation in his seminal papers in [1976](https://doi.org/10.1016/0021-9991(76)90041-3) and [1977](http://doi.org/10.1021/j100540a008). (We recommend reading the latter.) You can also read a concise discussion of how the algorithm samples the master equation in [section 4.2 of Del Vecchio and Murray](http://www.cds.caltech.edu/~murray/books/AM08/pdf/bfs-stochastic_14Sep14.pdf)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Coding up the Gillespie simulation\n",
    "\n",
    "To code up the Gillespie simulation, we first make an an array that gives the changes in the counts of $m$ and $p$ for each of the four reactions.  This is a way of encoding the updates in the particle counts that we get from choosing the respective state changes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Column 0 is change in m, column 1 is change in p\n",
    "simple_update = np.array([[1, 0],   # Make mRNA transcript\n",
    "                          [-1, 0],  # Degrade mRNA\n",
    "                          [0, 1],   # Make protein\n",
    "                          [0, -1]], # Degrade protein\n",
    "                         dtype=np.int)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we make a function that updates the array of propensities for each of the four reactions. We update the propensities (which are passed into the function as an argument) instead of instantiating them and returning them to save on memory allocation while running the code. It has the added benefit that it forces you to keep track of the indices corresponding to the update matrix. This helps prevent bugs. It will naturally be a function of the current population of molecules. It may in general also be a function of time, so we explicitly allow for time dependence (even though we will not use it in this simple example) as well."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def simple_propensity(propensities, population, t, beta_m, beta_p, gamma):\n",
    "    \"\"\"Updates an array of propensities given a set of parameters\n",
    "    and an array of populations.\n",
    "    \"\"\"\n",
    "    # Unpack population\n",
    "    m, p = population\n",
    "    \n",
    "    # Update propensities\n",
    "    propensities[0] = beta_m      # Make mRNA transcript\n",
    "    propensities[1] = m           # Degrade mRNA\n",
    "    propensities[2] = beta_p * m  # Make protein\n",
    "    propensities[3] = gamma * p   # Degrade protein"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Making a draw\n",
    "\n",
    "Finally, we write a general function that draws a choice of reaction and the time interval for that reaction.  This is the heart of the Gillespie algorithm, so we will take some time to discuss speed.  First, to get the time interval, we sample a random number from an exponential distribution with mean $\\left(\\sum_i a_i\\right)^{-1}$.  This is easily done using the `np.random.exponential()` function.  \n",
    "\n",
    "Next, we have to select which reaction will take place.  This amounts to drawing a sample over the discrete distribution where $P_i = a_i\\left(\\sum_i a_i\\right)^{-1}$, or the probability of each reaction is proportional to its propensity.  This can be done using `scipy.stats.rv_discrete`, which allows specification of an arbitrary discrete distribution.  We will write a function to do this."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def sample_discrete_scipy(probs):\n",
    "    \"\"\"Randomly sample an index with probability given by probs.\"\"\"\n",
    "    return st.rv_discrete(values=(range(len(probs)), probs)).rvs()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is a nice one-liner, but is it fast? There may be significant overhead in setting up the `scipy.stats` discrete random variable object to sample from each time. Remember, we can't just do this once because the array `probs` changes with each step in the SSA because the propensities change. We will therefore write a less elegant, but maybe faster way of doing it.  \n",
    "\n",
    "Another way to sample the distribution is to generate a uniformly distributed random number $q$, with $0 < q < 1$ and return the value $j$ such that\n",
    "\n",
    "\\begin{align}\n",
    "\\sum_{i=0}^{j-1} p_i < q < \\sum_{i=0}^{j}p_i.\n",
    "\\end{align}\n",
    "\n",
    "We'll code this up."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def sample_discrete(probs):\n",
    "    \"\"\"Randomly sample an index with probability given by probs.\"\"\"\n",
    "    # Generate random number\n",
    "    q = np.random.rand()\n",
    "    \n",
    "    # Find index\n",
    "    i = 0\n",
    "    p_sum = 0.0\n",
    "    while p_sum < q:\n",
    "        p_sum += probs[i]\n",
    "        i += 1\n",
    "    return i - 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's compare the speeds using the `%timeit` magic function. This is a useful tool to help diagnose slow spots in your code."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Result from scipy.stats:\n",
      "577 µs ± 7.76 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)\n",
      "\n",
      "Result from hand-coded method:\n",
      "1.72 µs ± 21.5 ns per loop (mean ± std. dev. of 7 runs, 1000000 loops each)\n"
     ]
    }
   ],
   "source": [
    "# Make dummy probs\n",
    "probs = np.array([0.1, 0.3, 0.4, 0.05, 0.15])\n",
    "\n",
    "print('Result from scipy.stats:')\n",
    "%timeit sample_discrete_scipy(probs)\n",
    "\n",
    "print('\\nResult from hand-coded method:')\n",
    "%timeit sample_discrete(probs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Wow!  The less concise method is a couple of orders of magnitude faster!  So, we will ditch using `scipy.stats`, and use our hand-built sampler instead.\n",
    "\n",
    "Now we can write a function to do our draws."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def gillespie_draw(propensity_func, propensities, population, t, args=()):\n",
    "    \"\"\"\n",
    "    Draws a reaction and the time it took to do that reaction.\n",
    "    \n",
    "    Parameters\n",
    "    ----------\n",
    "    propensity_func : function\n",
    "        Function with call signature propensity_func(population, t, *args)\n",
    "        used for computing propensities. This function must return\n",
    "        an array of propensities.\n",
    "    population : ndarray\n",
    "        Current population of particles\n",
    "    t : float\n",
    "        Value of the current time.\n",
    "    args : tuple, default ()\n",
    "        Arguments to be passed to `propensity_func`.\n",
    "        \n",
    "    Returns\n",
    "    -------\n",
    "    rxn : int\n",
    "        Index of reaction that occured.\n",
    "    time : float\n",
    "        Time it took for the reaction to occur.\n",
    "    \"\"\"\n",
    "    # Compute propensities\n",
    "    propensity_func(propensities, population, t, *args)\n",
    "    \n",
    "    # Sum of propensities\n",
    "    props_sum = propensities.sum()\n",
    "    \n",
    "    # Compute next time\n",
    "    time = np.random.exponential(1.0 / props_sum)\n",
    "    \n",
    "    # Compute discrete probabilities of each reaction\n",
    "    rxn_probs = propensities / props_sum\n",
    "    \n",
    "    # Draw reaction from this distribution\n",
    "    rxn = sample_discrete(rxn_probs)\n",
    "    \n",
    "    return rxn, time"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## SSA time stepping\n",
    "\n",
    "Now we are ready to write our main SSA loop.  We will only keep the counts at pre-specified time points. This saves on RAM, and we really only care about the values at given time points anyhow.\n",
    "\n",
    "Note that this function is generic. All we need to specify our system are:\n",
    "* A function to compute the propensities\n",
    "* How the updates for a given reaction are made\n",
    "* Initial population\n",
    "\n",
    "Additionally, we specify necessary parameters, an initial condition, and the time points at which we want to store our samples. So, providing the propensity function and update are analogous to providing the time derivatives when using `scipy.integrate.odeint()`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def gillespie_ssa(propensity_func, update, population_0, time_points, args=()):\n",
    "    \"\"\"\n",
    "    Uses the Gillespie stochastic simulation algorithm to sample\n",
    "    from probability distribution of particle counts over time.\n",
    "    \n",
    "    Parameters\n",
    "    ----------\n",
    "    propensity_func : function\n",
    "        Function of the form f(params, t, population) that takes the current\n",
    "        population of particle counts and return an array of propensities\n",
    "        for each reaction.\n",
    "    update : ndarray, shape (num_reactions, num_chemical_species)\n",
    "        Entry i, j gives the change in particle counts of species j\n",
    "        for chemical reaction i.\n",
    "    population_0 : array_like, shape (num_chemical_species)\n",
    "        Array of initial populations of all chemical species.\n",
    "    time_points : array_like, shape (num_time_points,)\n",
    "        Array of points in time for which to sample the probability\n",
    "        distribution.\n",
    "    args : tuple, default ()\n",
    "        The set of parameters to be passed to propensity_func.        \n",
    "\n",
    "    Returns\n",
    "    -------\n",
    "    sample : ndarray, shape (num_time_points, num_chemical_species)\n",
    "        Entry i, j is the count of chemical species j at time\n",
    "        time_points[i].\n",
    "    \"\"\"\n",
    "\n",
    "    # Initialize output\n",
    "    pop_out = np.empty((len(time_points), update.shape[1]), dtype=np.int)\n",
    "\n",
    "    # Initialize and perform simulation\n",
    "    i_time = 1\n",
    "    i = 0\n",
    "    t = time_points[0]\n",
    "    population = population_0.copy()\n",
    "    pop_out[0,:] = population\n",
    "    propensities = np.zeros(update.shape[0])\n",
    "    while i < len(time_points):\n",
    "        while t < time_points[i_time]:\n",
    "            # draw the event and time step\n",
    "            event, dt = gillespie_draw(propensity_func, propensities, population, t, args)\n",
    "                \n",
    "            # Update the population\n",
    "            population_previous = population.copy()\n",
    "            population += update[event,:]\n",
    "                \n",
    "            # Increment time\n",
    "            t += dt\n",
    "\n",
    "        # Update the index\n",
    "        i = np.searchsorted(time_points > t, True)\n",
    "        \n",
    "        # Update the population\n",
    "        pop_out[i_time:min(i,len(time_points))] = population_previous\n",
    "        \n",
    "        # Increment index\n",
    "        i_time = i\n",
    "                           \n",
    "    return pop_out"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Running and parsing results\n",
    "\n",
    "We can now run a set of SSA simulations and plot the results.  We will run 100 trajectories and store them, using $\\beta_p = \\beta_m = 10$ and $\\gamma = 0.4$. We will also use the nifty package `tqdm` to give a progress bar so we know how long it is taking."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
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       "version_major": 2,
       "version_minor": 0
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      "text/plain": [
       "HBox(children=(IntProgress(value=0), HTML(value='')))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "# Specify parameters for calculation\n",
    "args = (10.0, 10.0, 0.4)\n",
    "time_points = np.linspace(0, 50, 101)\n",
    "population_0 = np.array([0, 0], dtype=int)\n",
    "size = 100\n",
    "\n",
    "# Seed random number generator for reproducibility\n",
    "np.random.seed(42)\n",
    "\n",
    "# Initialize output array\n",
    "samples = np.empty((size, len(time_points), 2), dtype=int)\n",
    "\n",
    "# Run the calculations\n",
    "for i in tqdm.tqdm_notebook(range(size)):\n",
    "    samples[i,:,:] = gillespie_ssa(simple_propensity, simple_update,\n",
    "                                population_0, time_points, args=args)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We now have our samples, so we can plot the trajectories. For visualization, we will plot every trajectory as a thin blue line, and then the average of the trajectories as a thick orange line."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
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       "  var render_items = [{\"docid\":\"f0604565-ba38-44b3-baf9-e351cc55d076\",\"roots\":{\"3003\":\"90db7fde-d314-44b5-97f5-fd2e2bd87bee\"}}];\n",
       "  root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
       "\n",
       "  }\n",
       "  if (root.Bokeh !== undefined) {\n",
       "    embed_document(root);\n",
       "  } else {\n",
       "    var attempts = 0;\n",
       "    var timer = setInterval(function(root) {\n",
       "      if (root.Bokeh !== undefined) {\n",
       "        embed_document(root);\n",
       "        clearInterval(timer);\n",
       "      }\n",
       "      attempts++;\n",
       "      if (attempts > 100) {\n",
       "        console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n",
       "        clearInterval(timer);\n",
       "      }\n",
       "    }, 10, root)\n",
       "  }\n",
       "})(window);"
      ],
      "application/vnd.bokehjs_exec.v0+json": ""
     },
     "metadata": {
      "application/vnd.bokehjs_exec.v0+json": {
       "id": "3003"
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Set up plots\n",
    "plots = [bokeh.plotting.figure(plot_width=300,\n",
    "                               plot_height=200,\n",
    "                               x_axis_label='dimensionless time',\n",
    "                               y_axis_label='number of mRNAs'),\n",
    "         bokeh.plotting.figure(plot_width=300,\n",
    "                               plot_height=200,\n",
    "                               x_axis_label='dimensionless time',\n",
    "                               y_axis_label='number of proteins')]\n",
    "\n",
    "# Plot trajectories and mean\n",
    "for i in [0, 1]:\n",
    "    for x in samples[:,:,i]:\n",
    "        plots[i].line(time_points, x, line_width=0.3, \n",
    "                      alpha=0.2, line_join='bevel')\n",
    "    plots[i].line(time_points, samples[:,:,i].mean(axis=0),\n",
    "                  line_width=6, color='orange', line_join='bevel')\n",
    "\n",
    "# Link axes\n",
    "plots[0].x_range = plots[1].x_range\n",
    "\n",
    "bokeh.io.show(bokeh.layouts.gridplot(plots, ncols=2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also compute the steady state properties by considering the end of the simulation.  The last 50 time points are at steady state, so we will average over them."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mRNA mean copy number = 10.0748\n",
      "protein mean copy number = 251.6994\n",
      "\n",
      "mRNA variance = 10.26200496\n",
      "protein variance = 2145.33703964\n",
      "\n",
      "mRNA noise = 0.317965262817717\n",
      "protein noise = 0.18402023679851773\n"
     ]
    }
   ],
   "source": [
    "print('mRNA mean copy number =', samples[:,-50:,0].mean())\n",
    "print('protein mean copy number =', samples[:,-50:,1].mean())\n",
    "print('\\nmRNA variance =', samples[:,-50:,0].std()**2)\n",
    "print('protein variance =', samples[:,-50:,1].std()**2)\n",
    "print('\\nmRNA noise =', samples[:,-50:,0].std() / samples[:,-50:,0].mean())\n",
    "print('protein noise =', samples[:,-50:,1].std() / samples[:,-50:,1].mean())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, we can compute the steady state probability distributions. To plot them, we plot the empirical cumulative distribution function (ECDF) from the sampling.  The theoretical distribution for mRNA is Poisson, which is overlayed in orange."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
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       "\n",
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\",\"dtype\":\"float64\",\"shape\":[5000]}},\"selected\":{\"id\":\"6069\",\"type\":\"Selection\"},\"selection_policy\":{\"id\":\"6068\",\"type\":\"UnionRenderers\"}},\"id\":\"6046\",\"type\":\"ColumnDataSource\"},{\"attributes\":{\"children\":[[{\"id\":\"5970\",\"subtype\":\"Figure\",\"type\":\"Plot\"},0,0],[{\"id\":\"6013\",\"subtype\":\"Figure\",\"type\":\"Plot\"},0,1]]},\"id\":\"6071\",\"type\":\"GridBox\"},{\"attributes\":{},\"id\":\"5991\",\"type\":\"WheelZoomTool\"},{\"attributes\":{\"data_source\":{\"id\":\"6008\",\"type\":\"ColumnDataSource\"},\"glyph\":{\"id\":\"6009\",\"type\":\"Circle\"},\"hover_glyph\":null,\"muted_glyph\":null,\"nonselection_glyph\":{\"id\":\"6010\",\"type\":\"Circle\"},\"selection_glyph\":null,\"view\":{\"id\":\"6012\",\"type\":\"CDSView\"}},\"id\":\"6011\",\"type\":\"GlyphRenderer\"},{\"attributes\":{\"active_drag\":\"auto\",\"active_inspect\":\"auto\",\"active_multi\":null,\"active_scroll\":\"auto\",\"active_tap\":\"auto\",\"tools\":[{\"id\":\"6033\",\"type\":\"PanTool\"},{\"id\":\"6034\",\"type\":\"WheelZoomTool\"},{\"id\":\"6035\",\"type\":\"BoxZoomTool\"},{\"id\":\"6036\",\"type\":\"SaveTool\"},{\"id\":\"6037\",\"type\":\"ResetTool\"},{\"id\":\"6038\",\"type\":\"HelpTool\"}]},\"id\":\"6039\",\"type\":\"Toolbar\"},{\"attributes\":{\"dimension\":1,\"ticker\":{\"id\":\"5986\",\"type\":\"BasicTicker\"}},\"id\":\"5989\",\"type\":\"Grid\"},{\"attributes\":{},\"id\":\"5990\",\"type\":\"PanTool\"},{\"attributes\":{\"fill_alpha\":{\"value\":0.1},\"fill_color\":{\"value\":\"#1f77b4\"},\"line_alpha\":{\"value\":0.1},\"line_color\":{\"value\":\"#1f77b4\"},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"6010\",\"type\":\"Circle\"},{\"attributes\":{\"source\":{\"id\":\"6046\",\"type\":\"ColumnDataSource\"}},\"id\":\"6050\",\"type\":\"CDSView\"},{\"attributes\":{},\"id\":\"5993\",\"type\":\"SaveTool\"},{\"attributes\":{\"fill_color\":{\"value\":\"orange\"},\"line_color\":{\"value\":\"orange\"},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"6009\",\"type\":\"Circle\"},{\"attributes\":{},\"id\":\"6024\",\"type\":\"BasicTicker\"},{\"attributes\":{},\"id\":\"5981\",\"type\":\"BasicTicker\"},{\"attributes\":{\"callback\":null},\"id\":\"6015\",\"type\":\"DataRange1d\"},{\"attributes\":{},\"id\":\"6052\",\"type\":\"BasicTickFormatter\"},{\"attributes\":{\"callback\":null},\"id\":\"5972\",\"type\":\"DataRange1d\"},{\"attributes\":{},\"id\":\"6021\",\"type\":\"LinearScale\"},{\"attributes\":{\"data_source\":{\"id\":\"6003\",\"type\":\"ColumnDataSource\"},\"glyph\":{\"id\":\"6004\",\"type\":\"Circle\"},\"hover_glyph\":null,\"muted_glyph\":null,\"nonselection_glyph\":{\"id\":\"6005\",\"type\":\"Circle\"},\"selection_glyph\":null,\"view\":{\"id\":\"6007\",\"type\":\"CDSView\"}},\"id\":\"6006\",\"type\":\"GlyphRenderer\"},{\"attributes\":{\"callback\":null},\"id\":\"6017\",\"type\":\"DataRange1d\"},{\"attributes\":{},\"id\":\"6054\",\"type\":\"BasicTickFormatter\"},{\"attributes\":{\"bottom_units\":\"screen\",\"fill_alpha\":{\"value\":0.5},\"fill_color\":{\"value\":\"lightgrey\"},\"left_units\":\"screen\",\"level\":\"overlay\",\"line_alpha\":{\"value\":1.0},\"line_color\":{\"value\":\"black\"},\"line_dash\":[4,4],\"line_width\":{\"value\":2},\"render_mode\":\"css\",\"right_units\":\"screen\",\"top_units\":\"screen\"},\"id\":\"6056\",\"type\":\"BoxAnnotation\"},{\"attributes\":{},\"id\":\"6019\",\"type\":\"LinearScale\"},{\"attributes\":{\"source\":{\"id\":\"6003\",\"type\":\"ColumnDataSource\"}},\"id\":\"6007\",\"type\":\"CDSView\"},{\"attributes\":{},\"id\":\"6057\",\"type\":\"UnionRenderers\"}],\"root_ids\":[\"6074\"]},\"title\":\"Bokeh Application\",\"version\":\"1.1.0\"}};\n",
       "  var render_items = [{\"docid\":\"9fb05d93-9d43-4e3d-94a8-0f6b41286f66\",\"roots\":{\"6074\":\"82b3916a-5f41-4fd4-9e0c-6fad1870dc2b\"}}];\n",
       "  root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
       "\n",
       "  }\n",
       "  if (root.Bokeh !== undefined) {\n",
       "    embed_document(root);\n",
       "  } else {\n",
       "    var attempts = 0;\n",
       "    var timer = setInterval(function(root) {\n",
       "      if (root.Bokeh !== undefined) {\n",
       "        embed_document(root);\n",
       "        clearInterval(timer);\n",
       "      }\n",
       "      attempts++;\n",
       "      if (attempts > 100) {\n",
       "        console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n",
       "        clearInterval(timer);\n",
       "      }\n",
       "    }, 10, root)\n",
       "  }\n",
       "})(window);"
      ],
      "application/vnd.bokehjs_exec.v0+json": ""
     },
     "metadata": {
      "application/vnd.bokehjs_exec.v0+json": {
       "id": "6074"
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# mRNA ECDF\n",
    "p_m = biocircuits.viz.ecdf(samples[:,-50:,0].flatten(),\n",
    "                           plot_width=300,\n",
    "                           plot_height=200,\n",
    "                           x_axis_label='mRNA copy number')\n",
    "\n",
    "# Theoretial mRNA CDF (Poisson)\n",
    "p_m.circle(np.arange(25), st.poisson.cdf(np.arange(25), args[0]), color='orange')\n",
    "\n",
    "# protein ECDF\n",
    "p_p = biocircuits.viz.ecdf(samples[:,-50:,1].flatten(),\n",
    "                           plot_width=300,\n",
    "                           plot_height=200,\n",
    "                           x_axis_label='protein copy number')\n",
    "\n",
    "bokeh.io.show(bokeh.layouts.gridplot([p_m, p_p], ncols=2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we expect, the mRNA copy number matches the Poisson distribution. We also managed to get a distribution for the protein copy number that we could plot. So, you now have the basic tools for doing Gillespie simulations. You just need to code the propensity function and the update, and you're on your way! (Note, though, that this only works for Gillespie simulations where the states are defined by particle counts, which should suffice for this course.)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Implementation in the biocircuits package\n",
    "\n",
    "This algorithm is implemented in the biocircuits package. A significant speed boost is achieved by [just-in-time compliation](https://en.wikipedia.org/wiki/Just-in-time_compilation) using [Numba](http://numba.pydata.org). To utilize this feature, you need to just-in-time compile (JIT) your propensity function. You can insist that everything is compiled (and therefore skips the comparably slow Python interpreter) by using the <font style=\"font-family: monospace;\">@numba.njit</font> decorator. In many cases, like in this one for simple gene expression, that is all you have to do."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "@numba.njit\n",
    "def simple_propensity(propensities, population, t, beta_m, beta_p, gamma):\n",
    "    \"\"\"Updates an array of propensities given a set of parameters\n",
    "    and an array of populations.\n",
    "    \"\"\"\n",
    "    # Unpack population\n",
    "    m, p = population\n",
    "    \n",
    "    # Update propensities\n",
    "    propensities[0] = beta_m      # Make mRNA transcript\n",
    "    propensities[1] = m           # Degrade mRNA\n",
    "    propensities[2] = beta_p * m  # Make protein\n",
    "    propensities[3] = gamma * p   # Degrade protein"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can also utilize more threads and do the Gillespie simulations in parallel if you like. Because of the speed boosts, we will take more samples using the biocircuits implementation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "samples = biocircuits.gillespie_ssa(simple_propensity, \n",
    "                                    simple_update, \n",
    "                                    population_0, \n",
    "                                    time_points, \n",
    "                                    size=1000, \n",
    "                                    args=args,\n",
    "                                    n_threads=4,\n",
    "                                    progress_bar=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We now have 4000 trajectories, and we can again make the plots as we did before. With so many trajectories, though, we should not show them all, since there would be too many glyphs on the plot. We therefore thin out the samples for plotting, taking only every 100th trajectory."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
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       "  var render_items = [{\"docid\":\"bfb579de-06d9-48ae-b4f4-7dcb3f3e32a5\",\"roots\":{\"7316\":\"fcb6b767-39aa-4ae2-be8d-9320dadd1d6a\"}}];\n",
       "  root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
       "\n",
       "  }\n",
       "  if (root.Bokeh !== undefined) {\n",
       "    embed_document(root);\n",
       "  } else {\n",
       "    var attempts = 0;\n",
       "    var timer = setInterval(function(root) {\n",
       "      if (root.Bokeh !== undefined) {\n",
       "        embed_document(root);\n",
       "        clearInterval(timer);\n",
       "      }\n",
       "      attempts++;\n",
       "      if (attempts > 100) {\n",
       "        console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n",
       "        clearInterval(timer);\n",
       "      }\n",
       "    }, 10, root)\n",
       "  }\n",
       "})(window);"
      ],
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     },
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       "id": "7316"
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     "output_type": "display_data"
    }
   ],
   "source": [
    "# Set up plots\n",
    "plots = [bokeh.plotting.figure(plot_width=300,\n",
    "                               plot_height=200,\n",
    "                               x_axis_label='dimensionless time',\n",
    "                               y_axis_label='number of mRNAs'),\n",
    "         bokeh.plotting.figure(plot_width=300,\n",
    "                               plot_height=200,\n",
    "                               x_axis_label='dimensionless time',\n",
    "                               y_axis_label='number of proteins')]\n",
    "\n",
    "# Plot trajectories and mean\n",
    "for i in [0, 1]:\n",
    "    for x in samples[::100,:,i]:\n",
    "        plots[i].line(time_points, x, line_width=0.3, \n",
    "                      alpha=0.2, line_join='bevel')\n",
    "    plots[i].line(time_points, samples[:,:,i].mean(axis=0),\n",
    "                  line_width=6, color='orange', line_join='bevel')\n",
    "\n",
    "# Link axes\n",
    "plots[0].x_range = plots[1].x_range\n",
    "\n",
    "bokeh.io.show(bokeh.layouts.gridplot(plots, ncols=2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Simulating the repressilator\n",
    "\n",
    "We have seen a structure to how we can set up Gillespie simulations; we need to specify the propensities and updates, along with an initial population. It helps clarify the system being simulated and also avoids bugs if we make tables for\n",
    "\n",
    "1. The species whose populations we are describing;\n",
    "2. The update-propensity pairs;\n",
    "3. The parameter values.\n",
    "\n",
    "After constructing the tables, coding up the update and propensity functions is much easier.\n",
    "\n",
    "To demonstrate this procedure, we will perform a Gillespie simulation for the repressilator, as described in [Elowitz and Leibler](https://doi.org/10.1038/35002125). We will consider both RNA and DNA in a repressilator where gene 1 represses gene 2, gene 2 repressed gene 3, and gene 3 repressed gene 1. We explicitly consider mRNA and protein. A repressor binds its operon with chemical rate constant $k_r$, and an operon may have zero, one, or two repressors bound. The unbinding rate of a repressor when one is bound is $k_{u,1}$ and that of a repressor when two are bound if $k_{u,2}$, with $k_{u,2} < k_{u,1}$ to capture cooperativity. Transcription happens when no repressors are bound to a promoter region with rate constant $k_{m,u}$ and happens when one or two repressors are bound with rate $k_{m,o}$.\n",
    "\n",
    "As we build the simulation, let's start with a table of the populations we are keeping track of.\n",
    "\n",
    "|index|description | variable|\n",
    "|:----:|:------ |:------: |\n",
    "|0|gene 1 mRNA copy number | `m1`|\n",
    "|1|gene 1 protein copy number | `p1`|\n",
    "|2|gene 2 mRNA copy number | `m2`|\n",
    "|3|gene 2 protein copy number | `p2`|\n",
    "|4|gene 3 mRNA copy number | `m3`|\n",
    "|5|gene 3 protein copy number | `p3`|\n",
    "|6|Number of repressors bound to promoter of gene 3| `n1`|\n",
    "|7|Number of repressors bound to promoter of gene 1| `n2`|\n",
    "|8|Number of repressors bound to promoter of gene 2| `n3`|"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that we labeled each species with an index, which corresponds to its position in the array of populations in the simulation.\n",
    "\n",
    "Next, we can set up a table of updates and propensities for the moves we allow in the Gillespie simulation. We also assign an index to each entry here, as this helps keep track of everything.\n",
    "\n",
    "|index|description | update | propensity|\n",
    "|:----|:------ |:------ | :----:|\n",
    "|0|transcription of gene 1 mRNA| `m1 ⟶ m1 + 1`| `kmu*(n3 == 0) + kmo*(n3 > 0)`|\n",
    "|1|transcription of gene 2 mRNA| `m2 ⟶ m2 + 1`| `kmu*(n1 == 0) + kmo*(n1 > 0)`|\n",
    "|2|transcription of gene 3 mRNA| `m3 ⟶ m3 + 1`| `kmu*(n2 == 0) + kmo*(n2 > 0)`|\n",
    "|3|translation of gene 1 protein| `p1 ⟶ p1 + 1`| `kp * m1`|\n",
    "|4|translation of gene 1 protein| `p2 ⟶ p2 + 1`| `kp * m2`|\n",
    "|5|translation of gene 1 protein| `p3 ⟶ p3 + 1`| `kp * m3`|\n",
    "|6|degradation of gene 1 mRNA| `m1 ⟶ m1 - 1`| `gamma_m * m1`|\n",
    "|7|degradation of gene 2 mRNA| `m2 ⟶ m2 - 1`| `gamma_m * m2`|\n",
    "|8|degradation of gene 3 mRNA| `m3 ⟶ m3 - 1`| `gamma_m * m3`|\n",
    "|9|degradation of unbound gene 1 protein| `p1 ⟶ p1 - 1` | `gamma_p * p1`|\n",
    "|10|degradation of unbound gene 2 protein| `p2 ⟶ p2 - 1` | `gamma_p * p2`|\n",
    "|11|degradation of unbound gene 3 protein| `p3 ⟶ p3 - 1` | `gamma_p * p3`|\n",
    "|12|degradation of bound gene 1 protein| `n1 ⟶ n1 - 1` | `gamma_p * n1`|\n",
    "|13|degradation of bound gene 2 protein| `n2 ⟶ n2 - 1` | `gamma_p * n2`|\n",
    "|14|degradation of bound gene 3 protein| `n3 ⟶ n3 - 1` | `gamma_p * n3`|\n",
    "|15|binding of protein to gene 1 operator| `n3 ⟶ n3 + 1`, `p3 ⟶ p3 - 1`| `kr * p3 * (n3 < 2)`|\n",
    "|16|binding of protein to gene 2 operator| `n1 ⟶ n1 + 1`, `p1 ⟶ p1 - 1`| `kr * p1 * (n1 < 2)`|\n",
    "|17|binding of protein to gene 3 operator| `n2 ⟶ n2 + 1`, `p2 ⟶ p2 - 1`| `kr * p2 * (n2 < 2)`|\n",
    "|18|unbinding of protein to gene 1 operator| `n3 ⟶ n3 - 1`, `p3 ⟶ p3 + 1`| `ku1*(n3 == 1) + 2*ku2*(n3 == 2)`|\n",
    "|19|unbinding of protein to gene 2 operator| `n1 ⟶ n1 - 1`, `p1 ⟶ p1 + 1`| `ku1*(n1 == 1) + 2*ku2*(n1 == 2)`|\n",
    "|20|unbinding of protein to gene 3 operator| `n2 ⟶ n2 - 1`, `p2 ⟶ p2 + 1`| `ku1*(n2 == 1) + 2*ku2*(n2 == 2)`|"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, we have parameters that were introduced in the propensities, so we should have a table defining them.\n",
    "\n",
    "|parameter| value | units |\n",
    "|:----|:------ |:------: |\n",
    "|`kmu`| 0.5 | 1/sec|\n",
    "|`kmo`|5×10$^{-4}$  | 1/sec|\n",
    "|`kp`| 0.167 | 1/molec-sec|\n",
    "|`gamma_m`| 0.005776 | 1/sec|\n",
    "|`gamma_p`| 0.001155 | 1/sec|\n",
    "| `kr` | 1 | 1/molec-sec|\n",
    "| `ku1` | 224 | 1/sec|\n",
    "| `ku2` | 9 | 1/sec|\n",
    "\n",
    "We have now clearly defined all of our parameters, updates, and propensities. With the initial population, out simulation is not completely defined. In practice, we recommend constructing tables like this (and including them in your publications!) if you are going to do Gillespie simulations in your work.\n",
    "\n",
    "We are now tasked with coding up the propensities and the updates. Starting with the propensities, we recall that the biocircuits module requires a call signature of `propensity(propensities, population, t, *args)`, where the `args` are the parameters. We find that it is clearest to list the arguments one at a time in the function definition. It is also much clearer to unpack the population into individual variables than to use indexing. Finally, when returning the array of propensities, we recommend having one propensity for each line indexed in order."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "@numba.njit\n",
    "def repressilator_propensity(propensities, population, t, \n",
    "                             kmu,\n",
    "                             kmo,\n",
    "                             kp,\n",
    "                             gamma_m,\n",
    "                             gamma_p,\n",
    "                             kr,\n",
    "                             ku1,\n",
    "                             ku2):\n",
    "    m1, p1, m2, p2, m3, p3, n1, n2, n3 = population\n",
    "    \n",
    "    propensities[0] = kmu if n3 == 0 else kmo\n",
    "    propensities[1] = kmu if n1 == 0 else kmo\n",
    "    propensities[2] = kmu if n2 == 0 else kmo\n",
    "    propensities[3] = kp * m1                \n",
    "    propensities[4] = kp * m2                \n",
    "    propensities[5] = kp * m3                \n",
    "    propensities[6] = gamma_m * m1           \n",
    "    propensities[7] = gamma_m * m2           \n",
    "    propensities[8] = gamma_m * m3           \n",
    "    propensities[9] = gamma_p * p1           \n",
    "    propensities[10] = gamma_p * p2          \n",
    "    propensities[11] = gamma_p * p3          \n",
    "    propensities[12] = gamma_p * n1          \n",
    "    propensities[13] = gamma_p * n2          \n",
    "    propensities[14] = gamma_p * n3          \n",
    "    propensities[15] = kr * p3 * (n3 < 2)    \n",
    "    propensities[16] = kr * p1 * (n1 < 2)    \n",
    "    propensities[17] = kr * p2 * (n2 < 2)    \n",
    "    propensities[18] = ku1*(n3==1) + 2*ku2*(n3==2)\n",
    "    propensities[19] = ku1*(n1==1) + 2*ku2*(n1==2)\n",
    "    propensities[20] = ku1*(n2==1) + 2*ku2*(n2==2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, we can code up the update. The update is a matrix where entry `i,j` is the change in species `i` due to move `j`. Since we have indexes both the species and the moves (in the update/propensity table), we can include the indices when we define the update for clarity."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "repressilator_update = np.array([\n",
    "    # 0   1   2   3   4   5   6   7   8\n",
    "    [ 1,  0,  0,  0,  0,  0,  0,  0,  0], # 0\n",
    "    [ 0,  0,  1,  0,  0,  0,  0,  0,  0], # 1\n",
    "    [ 0,  0,  0,  0,  1,  0,  0,  0,  0], # 2\n",
    "    [ 0,  1,  0,  0,  0,  0,  0,  0,  0], # 3\n",
    "    [ 0,  0,  0,  1,  0,  0,  0,  0,  0], # 4\n",
    "    [ 0,  0,  0,  0,  0,  1,  0,  0,  0], # 5\n",
    "    [-1,  0,  0,  0,  0,  0,  0,  0,  0], # 6\n",
    "    [ 0,  0, -1,  0,  0,  0,  0,  0,  0], # 7\n",
    "    [ 0,  0,  0,  0, -1,  0,  0,  0,  0], # 8\n",
    "    [ 0, -1,  0,  0,  0,  0,  0,  0,  0], # 9\n",
    "    [ 0,  0,  0, -1,  0,  0,  0,  0,  0], # 10\n",
    "    [ 0,  0,  0,  0,  0, -1,  0,  0,  0], # 11\n",
    "    [ 0,  0,  0,  0,  0,  0, -1,  0,  0], # 12\n",
    "    [ 0,  0,  0,  0,  0,  0,  0, -1,  0], # 13\n",
    "    [ 0,  0,  0,  0,  0,  0,  0,  0, -1], # 14\n",
    "    [ 0,  0,  0,  0,  0, -1,  0,  0,  1], # 15\n",
    "    [ 0, -1,  0,  0,  0,  0,  1,  0,  0], # 16\n",
    "    [ 0,  0,  0, -1,  0,  0,  0,  1,  0], # 17\n",
    "    [ 0,  0,  0,  0,  0,  1,  0,  0, -1], # 18\n",
    "    [ 0,  1,  0,  0,  0,  0, -1,  0,  0], # 19\n",
    "    [ 0,  0,  0,  1,  0,  0,  0, -1,  0], # 20\n",
    "    ], dtype=int)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we specify the parameter values according to the parameter table. Remember that we need to package them in a tuple, after defining them."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Parameter values\n",
    "kmu = 0.5\n",
    "kmo = 5e-4\n",
    "kp = 0.167\n",
    "gamma_m = 0.005776\n",
    "gamma_p = 0.001155\n",
    "kr = 1.0\n",
    "ku1 = 224.0\n",
    "ku2 = 9.0\n",
    "\n",
    "repressilator_args = (kmu,\n",
    "                      kmo,\n",
    "                      kp,\n",
    "                      gamma_m,\n",
    "                      gamma_p,\n",
    "                      kr,\n",
    "                      ku1,\n",
    "                      ku2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, we specify the initial population and the time points we want for the sampling."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "# State with 10 copies of everything, nothing bound to operators\n",
    "repressilator_pop_0 = np.array([10, 10, 10, 10, 10, 10, 0, 0, 0], dtype=int)\n",
    "\n",
    "repressilator_time_points = np.linspace(0, 80000, 4001)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And we are all set to perform the calculation. We will make a single trace and then plot it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
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copy number\",\"formatter\":{\"id\":\"9742\",\"type\":\"BasicTickFormatter\"},\"ticker\":{\"id\":\"9054\",\"type\":\"BasicTicker\"}},\"id\":\"9053\",\"type\":\"LinearAxis\"},{\"attributes\":{},\"id\":\"9062\",\"type\":\"ResetTool\"},{\"attributes\":{},\"id\":\"9747\",\"type\":\"UnionRenderers\"},{\"attributes\":{},\"id\":\"9054\",\"type\":\"BasicTicker\"},{\"attributes\":{\"bottom_units\":\"screen\",\"fill_alpha\":{\"value\":0.5},\"fill_color\":{\"value\":\"lightgrey\"},\"left_units\":\"screen\",\"level\":\"overlay\",\"line_alpha\":{\"value\":1.0},\"line_color\":{\"value\":\"black\"},\"line_dash\":[4,4],\"line_width\":{\"value\":2},\"render_mode\":\"css\",\"right_units\":\"screen\",\"top_units\":\"screen\"},\"id\":\"9746\",\"type\":\"BoxAnnotation\"},{\"attributes\":{\"line_alpha\":0.1,\"line_color\":\"#1f77b4\",\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"9083\",\"type\":\"Line\"},{\"attributes\":{\"dimension\":1,\"ticker\":{\"id\":\"9054\",\"type\":\"BasicTicker\"}},\"id\":\"9057\",\"type\":\"Grid\"},{\"attributes\":{},\"id\":\"9751\",\"type\":\"UnionRenderers\"}],\"root_ids\":[\"9039\"]},\"title\":\"Bokeh Application\",\"version\":\"1.1.0\"}};\n",
       "  var render_items = [{\"docid\":\"f2d3e563-2e66-40c1-87d8-97c65e5a5c3d\",\"roots\":{\"9039\":\"84c8cb35-4ab1-4fc0-854e-04b0c83d83ef\"}}];\n",
       "  root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
       "\n",
       "  }\n",
       "  if (root.Bokeh !== undefined) {\n",
       "    embed_document(root);\n",
       "  } else {\n",
       "    var attempts = 0;\n",
       "    var timer = setInterval(function(root) {\n",
       "      if (root.Bokeh !== undefined) {\n",
       "        embed_document(root);\n",
       "        clearInterval(timer);\n",
       "      }\n",
       "      attempts++;\n",
       "      if (attempts > 100) {\n",
       "        console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n",
       "        clearInterval(timer);\n",
       "      }\n",
       "    }, 10, root)\n",
       "  }\n",
       "})(window);"
      ],
      "application/vnd.bokehjs_exec.v0+json": ""
     },
     "metadata": {
      "application/vnd.bokehjs_exec.v0+json": {
       "id": "9039"
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Perform the Gillespie simulation\n",
    "pop = biocircuits.gillespie_ssa(repressilator_propensity, \n",
    "                                repressilator_update, \n",
    "                                repressilator_pop_0, \n",
    "                                repressilator_time_points, \n",
    "                                args=repressilator_args)\n",
    "\n",
    "\n",
    "# Make plot\n",
    "colors = bokeh.palettes.d3['Category10'][3]\n",
    "p = bokeh.plotting.figure(height=250, width=600, \n",
    "                          x_axis_label='time (min)',\n",
    "                          y_axis_label='protein copy number')\n",
    "for c, i in enumerate([1, 3, 5]):\n",
    "    p.line(repressilator_time_points/60, \n",
    "           pop[0,:,i], color=colors[c])\n",
    "\n",
    "bokeh.io.show(p)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We observe the oscillations, but the amplitudes are highly variable."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Increasing speed\n",
    "\n",
    "*In this last section of the tutorial, we briefly discuss some strategies for boosting the speed of your Gillespie simulation. There are no major conceptual topics here, and this section may be skipped.*\n",
    "\n",
    "The calculation we implemented without JITting is much slower than the version in the biocircuits package. Still, the algorithm in that package implements a rather naive version of the Gillespie algorithm.\n",
    "\n",
    "An obvious speed improvement can be made by only recalculating the propensity for copy numbers we have not visited. For example, for simple gene expression, we do not need to recompute the propensity for mRNA decay if the previous move was a protein decay. The propensity for mRNA decay is the same it was at the previous step. Gibson and Bruck developed the [next reaction method](http://doi.org/10.1021/jp993732q), which makes these improvements, among others, and can result in significant speed-up for complicated sets of reactions. Instead of wading into the algorithmic details, we will instead investigate how we can speed up our implementation of the direct Gillespie algorithm. (These speed boosts are all implemented in the biocircuits package.)\n",
    "\n",
    "We will first remake the non-JITted version of the propensity function to test its speed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "def simple_propensity(propensities, population, t, beta_m, beta_p, gamma):\n",
    "    \"\"\"Updates an array of propensities given a set of parameters\n",
    "    and an array of populations.\n",
    "    \"\"\"\n",
    "    # Unpack population\n",
    "    m, p = population\n",
    "    \n",
    "    # Update propensities\n",
    "    propensities[0] = beta_m      # Make mRNA transcript\n",
    "    propensities[1] = m           # Degrade mRNA\n",
    "    propensities[2] = beta_p * m  # Make protein\n",
    "    propensities[3] = gamma * p   # Degrade protein"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's do some profiling to see what took so long.  We will use the magic function `%lprun` to profile runs of SSAs.  The output has line wrapping, so it is kind of hard to read in a Jupyter notebook, unfortunately."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "*** Profile printout saved to text file 'lp_results.txt'. \n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Timer unit: 1e-06 s\n",
       "\n",
       "Total time: 0.344129 s\n",
       "File: <ipython-input-9-8202fdcc5b63>\n",
       "Function: gillespie_ssa at line 1\n",
       "\n",
       "Line #      Hits         Time  Per Hit   % Time  Line Contents\n",
       "==============================================================\n",
       "     1                                           def gillespie_ssa(propensity_func, update, population_0, time_points, args=()):\n",
       "     2                                               \"\"\"\n",
       "     3                                               Uses the Gillespie stochastic simulation algorithm to sample\n",
       "     4                                               from probability distribution of particle counts over time.\n",
       "     5                                               \n",
       "     6                                               Parameters\n",
       "     7                                               ----------\n",
       "     8                                               propensity_func : function\n",
       "     9                                                   Function of the form f(params, t, population) that takes the current\n",
       "    10                                                   population of particle counts and return an array of propensities\n",
       "    11                                                   for each reaction.\n",
       "    12                                               update : ndarray, shape (num_reactions, num_chemical_species)\n",
       "    13                                                   Entry i, j gives the change in particle counts of species j\n",
       "    14                                                   for chemical reaction i.\n",
       "    15                                               population_0 : array_like, shape (num_chemical_species)\n",
       "    16                                                   Array of initial populations of all chemical species.\n",
       "    17                                               time_points : array_like, shape (num_time_points,)\n",
       "    18                                                   Array of points in time for which to sample the probability\n",
       "    19                                                   distribution.\n",
       "    20                                               args : tuple, default ()\n",
       "    21                                                   The set of parameters to be passed to propensity_func.        \n",
       "    22                                           \n",
       "    23                                               Returns\n",
       "    24                                               -------\n",
       "    25                                               sample : ndarray, shape (num_time_points, num_chemical_species)\n",
       "    26                                                   Entry i, j is the count of chemical species j at time\n",
       "    27                                                   time_points[i].\n",
       "    28                                               \"\"\"\n",
       "    29                                           \n",
       "    30                                               # Initialize output\n",
       "    31         1         16.0     16.0      0.0      pop_out = np.empty((len(time_points), update.shape[1]), dtype=np.int)\n",
       "    32                                           \n",
       "    33                                               # Initialize and perform simulation\n",
       "    34         1          2.0      2.0      0.0      i_time = 1\n",
       "    35         1          1.0      1.0      0.0      i = 0\n",
       "    36         1          3.0      3.0      0.0      t = time_points[0]\n",
       "    37         1         10.0     10.0      0.0      population = population_0.copy()\n",
       "    38         1          6.0      6.0      0.0      pop_out[0,:] = population\n",
       "    39         1          5.0      5.0      0.0      propensities = np.zeros(update.shape[0])\n",
       "    40       101        109.0      1.1      0.0      while i < len(time_points):\n",
       "    41      9329       8487.0      0.9      2.5          while t < time_points[i_time]:\n",
       "    42                                                       # draw the event and time step\n",
       "    43      9229     274680.0     29.8     79.8              event, dt = gillespie_draw(propensity_func, propensities, population, t, args)\n",
       "    44                                                           \n",
       "    45                                                       # Update the population\n",
       "    46      9229      21588.0      2.3      6.3              population_previous = population.copy()\n",
       "    47      9229      30218.0      3.3      8.8              population += update[event,:]\n",
       "    48                                                           \n",
       "    49                                                       # Increment time\n",
       "    50      9229       7156.0      0.8      2.1              t += dt\n",
       "    51                                           \n",
       "    52                                                   # Update the index\n",
       "    53       100       1168.0     11.7      0.3          i = np.searchsorted(time_points > t, True)\n",
       "    54                                                   \n",
       "    55                                                   # Update the population\n",
       "    56       100        609.0      6.1      0.2          pop_out[i_time:min(i,len(time_points))] = population_previous\n",
       "    57                                                   \n",
       "    58                                                   # Increment index\n",
       "    59       100         70.0      0.7      0.0          i_time = i\n",
       "    60                                                                      \n",
       "    61         1          1.0      1.0      0.0      return pop_out"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%lprun -T lp_results.txt -f gillespie_ssa gillespie_ssa(\\\n",
    "        simple_propensity, simple_update, population_0, time_points, args)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see that 80% of the time is spent doing draws.  Nothing else is really worth looking at.  Let's see how we can improve our draw speed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "*** Profile printout saved to text file 'lp_results.txt'. \n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Timer unit: 1e-06 s\n",
       "\n",
       "Total time: 0.281033 s\n",
       "File: <ipython-input-8-45f2423df14c>\n",
       "Function: gillespie_draw at line 1\n",
       "\n",
       "Line #      Hits         Time  Per Hit   % Time  Line Contents\n",
       "==============================================================\n",
       "     1                                           def gillespie_draw(propensity_func, propensities, population, t, args=()):\n",
       "     2                                               \"\"\"\n",
       "     3                                               Draws a reaction and the time it took to do that reaction.\n",
       "     4                                               \n",
       "     5                                               Parameters\n",
       "     6                                               ----------\n",
       "     7                                               propensity_func : function\n",
       "     8                                                   Function with call signature propensity_func(population, t, *args)\n",
       "     9                                                   used for computing propensities. This function must return\n",
       "    10                                                   an array of propensities.\n",
       "    11                                               population : ndarray\n",
       "    12                                                   Current population of particles\n",
       "    13                                               t : float\n",
       "    14                                                   Value of the current time.\n",
       "    15                                               args : tuple, default ()\n",
       "    16                                                   Arguments to be passed to `propensity_func`.\n",
       "    17                                                   \n",
       "    18                                               Returns\n",
       "    19                                               -------\n",
       "    20                                               rxn : int\n",
       "    21                                                   Index of reaction that occured.\n",
       "    22                                               time : float\n",
       "    23                                                   Time it took for the reaction to occur.\n",
       "    24                                               \"\"\"\n",
       "    25                                               # Compute propensities\n",
       "    26     10000     108070.0     10.8     38.5      propensity_func(propensities, population, t, *args)\n",
       "    27                                               \n",
       "    28                                               # Sum of propensities\n",
       "    29     10000      46277.0      4.6     16.5      props_sum = propensities.sum()\n",
       "    30                                               \n",
       "    31                                               # Compute next time\n",
       "    32     10000      46984.0      4.7     16.7      time = np.random.exponential(1.0 / props_sum)\n",
       "    33                                               \n",
       "    34                                               # Compute discrete probabilities of each reaction\n",
       "    35     10000      26205.0      2.6      9.3      rxn_probs = propensities / props_sum\n",
       "    36                                               \n",
       "    37                                               # Draw reaction from this distribution\n",
       "    38     10000      48705.0      4.9     17.3      rxn = sample_discrete(rxn_probs)\n",
       "    39                                               \n",
       "    40     10000       4792.0      0.5      1.7      return rxn, time"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "propensities = np.ones(4)\n",
    "\n",
    "%lprun -T lp_results.txt -f gillespie_draw \\\n",
    "        [gillespie_draw(simple_propensity, propensities, population_0, 0, args) \\\n",
    "            for _ in range(10000)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The propensity function is taking the most time. We will focus on improving that."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Speed boost by JIT compilation with Numba\n",
    "\n",
    "As we have seen [Numba](https://numba.pydata.org) is a package that does LLVM optimized just-in-time compilation of Python code.  The speed-ups can be substantial.  We will use `numba` to compile the parts of the code that we can.  For many functions, we just need to decorate the function with\n",
    "\n",
    "    @numba.jit()\n",
    "\n",
    "and that is it.  If possible, we can use the `nopython=True` keyword argument to get more speed because the compiler can assume that all of the code is JIT-able. Note that using <font style=\"font-family:monospace;\">@numba.njit</font> is equivalent to using <font style=\"font-family:monospace;\">@numba.jit(nopython=True)</font>.\n",
    "\n",
    "We can speed that up by sacrificing some readability and directly accessing the arrays instead of setting up views, as we have been doing."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Old propensity function:\n",
      "6.54 µs ± 106 ns per loop (mean ± std. dev. of 7 runs, 100000 loops each)\n",
      "\n",
      "Numba'd propensity function:\n",
      "702 ns ± 7.82 ns per loop (mean ± std. dev. of 7 runs, 1000000 loops each)\n"
     ]
    }
   ],
   "source": [
    "@numba.njit\n",
    "def simple_propensity_numba(propensities, population, t, beta_m, beta_p, gamma):\n",
    "    \"\"\"Updates an array of propensities given a set of parameters\n",
    "    and an array of populations.\n",
    "    \"\"\"\n",
    "    # Unpack population\n",
    "    m, p = population\n",
    "    \n",
    "    # Update propensities\n",
    "    propensities[0] = beta_m      # Make mRNA transcript\n",
    "    propensities[1] = m           # Degrade mRNA\n",
    "    propensities[2] = beta_p * m  # Make protein\n",
    "    propensities[3] = gamma * p   # Degrade protein\n",
    "\n",
    "# Check speeds\n",
    "print('Old propensity function:')\n",
    "%timeit simple_propensity(propensities, population_0, 0, *args)\n",
    "\n",
    "print('\\nNumba\\'d propensity function:')\n",
    "%timeit simple_propensity_numba(propensities, population_0, 0, *args)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We got some speed up! Nice! \n",
    "\n",
    "Now, we also saw that the sums and division of arrays are slow.  Let's optimize the sum operation using `numba`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "NumPy sum:\n",
      "2.05 µs ± 41.2 ns per loop (mean ± std. dev. of 7 runs, 100000 loops each)\n",
      "\n",
      "Numba sum:\n",
      "303 ns ± 4.63 ns per loop (mean ± std. dev. of 7 runs, 1000000 loops each)\n"
     ]
    }
   ],
   "source": [
    "@numba.jit(nopython=True)\n",
    "def sum_numba(ar):\n",
    "    return ar.sum()\n",
    "\n",
    "# Make dummy array for testing\n",
    "ar = np.array([0.3, 0.4, 0.3, 0.2, 0.15])\n",
    "\n",
    "print('\\nNumPy sum:')\n",
    "%timeit ar.sum()\n",
    "\n",
    "print('\\nNumba sum:')\n",
    "%timeit sum_numba(ar)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We get another speed boost, though we should note that this speed boost in the sum is due to `numba` optimizing sums of a certain size.  For sums over large numbers of entries, `numba`'s performance will not exceed NumPy's by much at all.\n",
    "\n",
    "Finally, we will speed up the sampling of the discrete distribution.  We will do this in two ways.  First, we notice that the division operation on the propensities took a fair amount of time when we profiled the code.  We do not need it; we can instead sample from an unnormalized discrete distribution.  Secondly, we can use `numba` to accelerate the while loop in the sampling."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Result from hand-coded method:\n",
      "1.77 µs ± 55.3 ns per loop (mean ± std. dev. of 7 runs, 1000000 loops each)\n",
      "\n",
      "Results from numba'd version:\n",
      "365 ns ± 14.4 ns per loop (mean ± std. dev. of 7 runs, 1000000 loops each)\n"
     ]
    }
   ],
   "source": [
    "@numba.njit\n",
    "def sample_discrete_numba(probs, probs_sum):\n",
    "    q = np.random.rand() * probs_sum\n",
    "\n",
    "    i = 0\n",
    "    p_sum = 0.0\n",
    "    while p_sum < q:\n",
    "        p_sum += probs[i]\n",
    "        i += 1\n",
    "    return i - 1\n",
    "\n",
    "# Make dummy unnormalized probs\n",
    "probs = np.array([0.1, 0.3, 0.4, 0.05, 0.15, 0.6])\n",
    "probs_sum = sum_numba(probs)\n",
    "\n",
    "print('Result from hand-coded method:')\n",
    "%timeit sample_discrete(probs)\n",
    "\n",
    "print(\"\\nResults from numba'd version:\")\n",
    "%timeit sample_discrete_numba(probs, probs_sum)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We get a speed-up of about a factor of three.  Let's now make a new `gillespie_draw()` function that is faster.  The fast propensity function is just an argument to the fast draw-er."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Old Gillespie draw:\n",
      "17.7 µs ± 260 ns per loop (mean ± std. dev. of 7 runs, 100000 loops each)\n",
      "\n",
      "Fast Gillespie draw:\n",
      "3.5 µs ± 65.1 ns per loop (mean ± std. dev. of 7 runs, 100000 loops each)\n"
     ]
    }
   ],
   "source": [
    "def gillespie_draw_fast(propensity_func, propensities, population, t, args):\n",
    "    \"\"\"\n",
    "    Draws a reaction and the time it took to do that reaction.\n",
    "    \"\"\"\n",
    "    # Compute propensities\n",
    "    propensity_func(propensities, population, t, *args)\n",
    "    \n",
    "    # Sum of propensities\n",
    "    props_sum = sum_numba(propensities)\n",
    "    \n",
    "    # Compute time\n",
    "    time = np.random.exponential(1 / props_sum)\n",
    "\n",
    "    # Draw reaction given propensities\n",
    "    rxn = sample_discrete_numba(propensities, props_sum)\n",
    "    \n",
    "    return rxn, time\n",
    "\n",
    "print('Old Gillespie draw:')\n",
    "%timeit gillespie_draw(simple_propensity, propensities, population_0, 0.0, args)\n",
    "\n",
    "print('\\nFast Gillespie draw:')\n",
    "%timeit gillespie_draw_fast(simple_propensity_numba, propensities, population_0, 0.0, args)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So, our optimization got us another speed boost.  Let's adjust our SSA function to include the fast draws."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def gillespie_ssa_fast(propensity_func, update, population_0, \n",
    "                       time_points, args=()):\n",
    "    \"\"\"\n",
    "    Uses the Gillespie stochastic simulation algorithm to sample\n",
    "    from proability distribution of particle counts over time.\n",
    "    \n",
    "    Parameters\n",
    "    ----------\n",
    "    propensity_func : function\n",
    "        Function of the form f(params, population) that takes the current\n",
    "        population of particle counts and return an array of propensities\n",
    "        for each reaction.\n",
    "    update : ndarray, shape (num_reactions, num_chemical_species)\n",
    "        Entry i, j gives the change in particle counts of species j\n",
    "        for chemical reaction i.\n",
    "    population_0 : array_like, shape (num_chemical_species)\n",
    "        Array of initial populations of all chemical species.\n",
    "    time_points : array_like, shape (num_time_points,)\n",
    "        Array of points in time for which to sample the probability\n",
    "        distribution.\n",
    "    args : tuple, default ()\n",
    "        The set of parameters to be passed to propensity_func. \n",
    "        \n",
    "    Returns\n",
    "    -------\n",
    "    rxn : int\n",
    "        Index of reaction that occured.\n",
    "    time : float\n",
    "        Time it took for the reaction to occur.        \n",
    "    Returns\n",
    "    -------\n",
    "    sample : ndarray, shape (num_time_points, num_chemical_species)\n",
    "        Entry i, j is the count of chemical species j at time\n",
    "        time_points[i].\n",
    "    \"\"\"\n",
    "\n",
    "    # Initialize output\n",
    "    pop_out = np.empty((len(time_points), update.shape[1]), dtype=np.int)\n",
    "\n",
    "    # Initialize and perform simulation\n",
    "    i_time = 1\n",
    "    i = 0\n",
    "    t = time_points[0]\n",
    "    population = population_0.copy()\n",
    "    pop_out[0,:] = population\n",
    "    propensities = np.zeros(update.shape[0])\n",
    "    while i < len(time_points):\n",
    "        while t < time_points[i_time]:\n",
    "            # draw the event and time step\n",
    "            event, dt = gillespie_draw_fast(propensity_func, \n",
    "                                            propensities, population, t, args)\n",
    "                \n",
    "            # Update the population\n",
    "            population_previous = population.copy()\n",
    "            population += update[event,:]\n",
    "                \n",
    "            # Increment time\n",
    "            t += dt\n",
    "\n",
    "        # Update the index\n",
    "        i = np.searchsorted(time_points > t, True)\n",
    "        \n",
    "        # Update the population\n",
    "        pop_out[i_time:min(i,len(time_points))] = population_previous\n",
    "        \n",
    "        # Increment index\n",
    "        i_time = i\n",
    "                           \n",
    "    return pop_out"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can test the speed of the two SSAs."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Gillespie SSA:\n",
      "235 ms ± 14 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)\n",
      "\n",
      "Fast Gillespie SSA:\n",
      "73.2 ms ± 1.54 ms per loop (mean ± std. dev. of 7 runs, 10 loops each)\n"
     ]
    }
   ],
   "source": [
    "print('Gillespie SSA:')\n",
    "%timeit gillespie_ssa(simple_propensity, simple_update, \\\n",
    "                      population_0, time_points, args)\n",
    "\n",
    "print('\\nFast Gillespie SSA:')\n",
    "%timeit gillespie_ssa_fast(simple_propensity_numba, simple_update,\\\n",
    "                           population_0, time_points, args)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So, we are now faster with not too much work. This is still a general solver that you can use with any propensity function and update.\n",
    "\n",
    "We have constructed a generic tool for doing Gillespie simulations.  Specifically, we pass a propensity function into the algorithm. Passing a function as an argument precludes use of `numba`. This means that we cannot just-in-time compile the entire Gillespie simulation. We could insist that our propensity function be encoded in a global function `prop_func()`, then we can fully JIT compile the entire simulation. (Note that there are ways to get around this insistence on a global function, and the `biocircuits` package does not rely on such a global function, but for the purposes of this demonstration, it is convenient.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "@numba.njit\n",
    "def prop_func(propensities, population, t, beta_m, beta_p, gamma):\n",
    "    \"\"\"Updates an array of propensities given a set of parameters\n",
    "    and an array of populations.\n",
    "    \"\"\"\n",
    "    # Unpack population\n",
    "    m, p = population\n",
    "    \n",
    "    # Update propensities\n",
    "    propensities[0] = beta_m      # Make mRNA transcript\n",
    "    propensities[1] = m           # Degrade mRNA\n",
    "    propensities[2] = beta_p * m  # Make protein\n",
    "    propensities[3] = gamma * p   # Degrade protein\n",
    "\n",
    "\n",
    "@numba.njit\n",
    "def gillespie_draw_numba(propensities, population, t, args):\n",
    "    \"\"\"\n",
    "    Draws a reaction and the time it took to do that reaction.\n",
    "    \n",
    "    Assumes that there is a globally scoped function\n",
    "    `prop_func` that is Numba'd with nopython=True.\n",
    "    \"\"\"\n",
    "    # Compute propensities\n",
    "    prop_func(propensities, population, t, *args)\n",
    "\n",
    "    # Sum of propensities\n",
    "    props_sum = np.sum(propensities)\n",
    "    \n",
    "    # Compute time\n",
    "    time = np.random.exponential(1 / props_sum)\n",
    "    \n",
    "    # Draw reaction given propensities\n",
    "    rxn = sample_discrete_numba(propensities, props_sum)\n",
    "\n",
    "    return rxn, time\n",
    "\n",
    "\n",
    "@numba.njit\n",
    "def gillespie_ssa_numba(update, population_0, time_points, args):\n",
    "    \"\"\"\n",
    "    Uses the Gillespie stochastic simulation algorithm to sample\n",
    "    from proability distribution of particle counts over time.\n",
    "    \n",
    "    Parameters\n",
    "    ----------\n",
    "    update : ndarray, shape (num_reactions, num_chemical_species)\n",
    "        Entry i, j gives the change in particle counts of species j\n",
    "        for chemical reaction i.\n",
    "    population_0 : array_like, shape (num_chemical_species)\n",
    "        Array of initial populations of all chemical species.\n",
    "    time_points : array_like, shape (num_time_points,)\n",
    "        Array of points in time for which to sample the probability\n",
    "        distribution.\n",
    "    args : tuple, default ()\n",
    "        The set of parameters to be passed to propensity_func.\n",
    "        \n",
    "    Returns\n",
    "    -------\n",
    "    sample : ndarray, shape (num_time_points, num_chemical_species)\n",
    "        Entry i, j is the count of chemical species j at time\n",
    "        time_points[i].\n",
    "        \n",
    "    Notes\n",
    "    -----\n",
    "    .. Assumes that there is a globally scoped function\n",
    "       `propensity_func` that is Numba'd with nopython=True.\n",
    "    \"\"\"\n",
    "    # Initialize output\n",
    "    pop_out = np.empty((len(time_points), update.shape[1]), dtype=np.int64)\n",
    "\n",
    "    # Initialize and perform simulation\n",
    "    i_time = 1\n",
    "    i = 0\n",
    "    t = time_points[0]\n",
    "    population = population_0.copy()\n",
    "    pop_out[0,:] = population\n",
    "    propensities = np.zeros(update.shape[0])\n",
    "    while i < len(time_points):\n",
    "        while t < time_points[i_time]:\n",
    "            # draw the event and time step\n",
    "            event, dt = gillespie_draw_numba(propensities, population, t, args)\n",
    "                \n",
    "            # Update the population\n",
    "            population_previous = population.copy()\n",
    "            population += update[event,:]\n",
    "                \n",
    "            # Increment time\n",
    "            t += dt\n",
    "\n",
    "        # Update the index (Have to be careful about types for Numba)\n",
    "        i = np.searchsorted((time_points > t).astype(np.int64), 1)\n",
    "\n",
    "        # Update the population\n",
    "        for j in np.arange(i_time, min(i, len(time_points))):\n",
    "            pop_out[j,:] = population_previous\n",
    "        \n",
    "        # Increment index\n",
    "        i_time = i\n",
    "                           \n",
    "    return pop_out"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's test the speed of all three of our functions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Gillespie SSA:\n",
      "243 ms ± 13.3 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)\n",
      "\n",
      "Fast Gillespie SSA:\n",
      "75.3 ms ± 4.69 ms per loop (mean ± std. dev. of 7 runs, 10 loops each)\n",
      "\n",
      "Totally numba'd Gillespie SSA:\n",
      "3.2 ms ± 147 µs per loop (mean ± std. dev. of 7 runs, 1 loop each)\n"
     ]
    }
   ],
   "source": [
    "print('Gillespie SSA:')\n",
    "%timeit gillespie_ssa(simple_propensity, simple_update, \\\n",
    "                      population_0, time_points, args)\n",
    "\n",
    "print('\\nFast Gillespie SSA:')\n",
    "%timeit gillespie_ssa_fast(simple_propensity_numba, simple_update,\\\n",
    "                            population_0, time_points, args)\n",
    "\n",
    "print('\\nTotally numba\\'d Gillespie SSA:')\n",
    "%timeit gillespie_ssa_numba(simple_update, population_0, time_points, args)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We got an extra order of magnitude speed boost by totally JIT compiling everything. The speed up is significant, so we should probably use Numba'd code, which is what the `biocircuits` module uses."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Parallel Gillespie simulations\n",
    "\n",
    "Sampling by the Gillespie algorithm is trivially parallelizable. We can use the `multiprocessing` module to parallelize the computation. Syntactically, we need to specify a function that takes a single argument. Below, we set up a parallel calculation of Gillespie simulations for our specific example."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def gillespie_fn(args):\n",
    "    return gillespie_ssa_numba(*args)\n",
    "    \n",
    "def gillespie_parallel(fn, update, population_0, time_points, args,\n",
    "                       n_simulations, n_threads):\n",
    "    \"\"\"\n",
    "    Convenience function to do parallel Gillespie simulations.\n",
    "    \"\"\"\n",
    "    input_args = (update, population_0, time_points, args)\n",
    "\n",
    "    with multiprocessing.Pool(n_threads) as p:\n",
    "        populations = p.map(fn, [input_args]*n_simulations)\n",
    "        \n",
    "    return np.array(populations)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We are paying some overhead in setting up the parallelization.  Let's time it to see how we do with four threads. _Note_: Your machine have have fewer than four cores, which means that you cannot parallelize the code more than this."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "numba'd Gillespie SSA:\n",
      "3.61 s ± 181 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)\n",
      "\n",
      "Parallel numba'd Gillespie SSA:\n",
      "1.87 s ± 8.95 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)\n"
     ]
    }
   ],
   "source": [
    "n_simulations = 1000\n",
    "\n",
    "print('\\nnumba\\'d Gillespie SSA:')\n",
    "%timeit [gillespie_ssa_numba(simple_update, population_0, time_points, args) \\\n",
    "            for _ in range(n_simulations)]\n",
    "\n",
    "print('\\nParallel numba\\'d Gillespie SSA:')\n",
    "%timeit gillespie_parallel(gillespie_fn, simple_update, population_0, time_points,\\\n",
    "                           args, n_simulations, 2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We get a factor of two speed boost from two cores. This brings our total speed boost from the optimization to near two orders of magnitude.\n",
    "\n",
    "If we insist on *exact* sampling out of a probability distribution defined by a master question, we can get significant speed boosts by switching to the [Gibson and Bruck algorithm](http://doi.org/10.1021/jp993732q). If we are willing to *approximately* sample out of the probability distribution, there are many fast, approximate methods (e.g., [Salis and Kaznessis](https://doi.org/10.1063%2F1.1835951)) available."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Computing environment"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "tags": [
     "remove_input"
    ]
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPython 3.7.3\n",
      "IPython 7.5.0\n",
      "\n",
      "numpy 1.16.3\n",
      "scipy 1.2.1\n",
      "numba 0.43.1\n",
      "bokeh 1.1.0\n",
      "jupyterlab 0.35.5\n",
      "tqdm 4.31.1\n",
      "biocircuits 0.0.10\n"
     ]
    }
   ],
   "source": [
    "%load_ext watermark\n",
    "%watermark -v -p numpy,scipy,numba,bokeh,jupyterlab,tqdm,biocircuits"
   ]
  }
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