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   "source": [
    "# Modeling and Simulation in Python\n",
    "\n",
    "Chapter 17\n",
    "\n",
    "Copyright 2017 Allen Downey\n",
    "\n",
    "License: [Creative Commons Attribution 4.0 International](https://creativecommons.org/licenses/by/4.0)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Configure Jupyter so figures appear in the notebook\n",
    "%matplotlib inline\n",
    "\n",
    "# Configure Jupyter to display the assigned value after an assignment\n",
    "%config InteractiveShell.ast_node_interactivity='last_expr_or_assign'\n",
    "\n",
    "# import functions from the modsim.py module\n",
    "from modsim import *"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Data\n",
    "\n",
    "We have data from Pacini and Bergman (1986), \"MINMOD: a computer program to calculate insulin sensitivity and pancreatic responsivity from the frequently sampled intravenous glucose tolerance test\", *Computer Methods and Programs in Biomedicine*, 23: 113-122.."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = pd.read_csv('data/glucose_insulin.csv', index_col='time')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's what the glucose time series looks like."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "plot(data.glucose, 'bo', label='glucose')\n",
    "decorate(xlabel='Time (min)',\n",
    "         ylabel='Concentration (mg/dL)')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And the insulin time series."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "plot(data.insulin, 'go', label='insulin')\n",
    "decorate(xlabel='Time (min)',\n",
    "         ylabel='Concentration ($\\mu$U/mL)')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For the book, I put them in a single figure, using `subplot`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "subplot(2, 1, 1)\n",
    "plot(data.glucose, 'bo', label='glucose')\n",
    "decorate(ylabel='Concentration (mg/dL)')\n",
    "\n",
    "subplot(2, 1, 2)\n",
    "plot(data.insulin, 'go', label='insulin')\n",
    "decorate(xlabel='Time (min)',\n",
    "         ylabel='Concentration ($\\mu$U/mL)')\n",
    "\n",
    "savefig('figs/chap17-fig01.pdf')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Interpolation\n",
    "\n",
    "We have measurements of insulin concentration at discrete points in time, but we need to estimate it at intervening points.  We'll use `interpolate`, which takes a `Series` and returns a function:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The return value from `interpolate` is a function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "I = interpolate(data.insulin)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can use the result, `I`, to estimate the insulin level at any point in time."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "I(7)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`I` can also take an array of time and return an array of estimates:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "t_0 = get_first_label(data)\n",
    "t_end = get_last_label(data)\n",
    "ts = linrange(t_0, t_end, endpoint=True)\n",
    "I(ts)\n",
    "type(ts)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's what the interpolated values look like."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "plot(data.insulin, 'go', label='insulin data')\n",
    "plot(ts, I(ts), color='green', label='interpolated')\n",
    "\n",
    "decorate(xlabel='Time (min)',\n",
    "         ylabel='Concentration ($\\mu$U/mL)')\n",
    "\n",
    "savefig('figs/chap17-fig02.pdf')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise:** [Read the documentation](https://docs.scipy.org/doc/scipy/reference/generated/scipy.interpolate.interp1d.html) of `scipy.interpolate.interp1d`.  Pass a keyword argument to `interpolate` to specify one of the other kinds of interpolation, and run the code again to see what it looks like. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Solution goes here"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise:** Interpolate the glucose data and generate a plot, similar to the previous one, that shows the data points and the interpolated curve evaluated at the time values in `ts`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Solution goes here"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Under the hood"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "source_code(interpolate)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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