{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# STAT540: Computing in Statistics\n",
    "# Python Lecture 3: Defining Functions, Plotting with Matplotlib, and Conditional Programming\"\n",
    "\n",
    "---\n",
    "\n",
    "\n",
    "## Outline\n",
    "\n",
    "1. Making plots with Matplotlib\n",
    "2. Defining new functions\n",
    "3. Conditional programming (`if` / `elif` / `else`)\n",
    "4. Putting it together: piecewise functions\n",
    "5. Practice\n",
    "\n",
    "## Making Plots: Getting Started\n",
    "\n",
    "To make plots, we import **matplotlib** --- the most widely used Python plotting library ([matplotlib.org](https://matplotlib.org))."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "x = np.linspace(0, 2*np.pi, 361)\n",
    "sinx = np.sin(x)\n",
    "plt.plot(x, sinx)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- `plt.plot(x, y)` draws a line plot\n",
    "- `plt.show()` displays the figure\n",
    "\n",
    "## Result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "fig-height": 3,
    "fig-width": 6.5
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#| echo: false\n",
    "#| eval: true\n",
    "#| out-width: 90%\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "x = np.linspace(0, 2*np.pi, 361)\n",
    "sinx = np.sin(x)\n",
    "plt.plot(x, sinx)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Adding Features and a Legend"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "u = np.random.random(30) * 2*np.pi\n",
    "v = 0.8*np.sin(u) + 0.2*np.cos(u) + np.random.normal(0, 1/3, u.size)\n",
    "\n",
    "x  = np.linspace(0, 2*np.pi, 361)\n",
    "fx = 0.8*np.sin(x) + 0.2*np.cos(x)\n",
    "\n",
    "plt.figure()  # start a new, empty figure\n",
    "plt.plot(u, v, 'bo', label='observations')\n",
    "plt.plot(x, fx, label='true function')\n",
    "plt.xlabel(\"x\"); plt.ylabel(\"response\")\n",
    "plt.title(\"Demo plot\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A `label=` on each plotted feature builds the legend automatically.\n",
    "\n",
    "## Result \n",
    "\\small"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "fig-height": 3,
    "fig-width": 6.5
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#| echo: false\n",
    "#| eval: true\n",
    "#| out-width: 90%\n",
    "u = np.random.random(30) * 2*np.pi\n",
    "v = 0.8*np.sin(u) + 0.2*np.cos(u) + np.random.normal(0, 1/3, u.size)\n",
    "\n",
    "x  = np.linspace(0, 2*np.pi, 361)\n",
    "fx = 0.8*np.sin(x) + 0.2*np.cos(x)\n",
    "\n",
    "plt.figure()  # start a new, empty figure\n",
    "plt.plot(u, v, 'bo', label='observations')\n",
    "plt.plot(x, fx, label='true function')\n",
    "plt.xlabel(\"x\"); plt.ylabel(\"response\")\n",
    "plt.title(\"Demo plot\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The Figure/Axes Approach\n",
    "\n",
    "The more flexible --- and more common in tutorials --- way to build a plot: set up a **figure** and a set of **axes** first, then add to the axes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(10, 5))\n",
    "ax.plot(u, v, 'bo', label='Observations')\n",
    "ax.plot(x, fx, label='True function', linestyle=\"--\")\n",
    "ax.set_xlabel(\"x\")\n",
    "ax.set_ylabel(\"Response\")\n",
    "ax.set_title(\"Demo plot\")\n",
    "ax.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Because a new figure is created, plotting commands never get appended to a previous plot by accident.\n",
    "\n",
    "## Result "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "fig-height": 3,
    "fig-width": 6.5
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#| echo: false\n",
    "#| eval: true\n",
    "#| out-width: 90%\n",
    "fig, ax = plt.subplots(figsize=(10, 5))\n",
    "ax.plot(u, v, 'bo', label='Observations')\n",
    "ax.plot(x, fx, label='True function', linestyle=\"--\")\n",
    "ax.set_xlabel(\"x\")\n",
    "ax.set_ylabel(\"Response\")\n",
    "ax.set_title(\"Demo plot\")\n",
    "ax.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Multi-Panel Figures\n",
    "\n",
    "Setting up the figure first lets us build figures with several panels (each panel is an **axes**):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(10, 4))\n",
    "\n",
    "ax1.plot(u, v, 'bo', label='observations')\n",
    "ax1.set_title(\"Demo plot\"); ax1.legend()\n",
    "\n",
    "ax2.plot(x, fx, 'g', label='true function')\n",
    "ax2.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "fig-height": 3,
    "fig-width": 6.5
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#| echo: false\n",
    "#| eval: true\n",
    "#| out-width: 90%\n",
    "fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(10, 4))\n",
    "\n",
    "ax1.plot(u, v, 'bo', label='observations')\n",
    "ax1.set_title(\"Demo plot\"); ax1.legend()\n",
    "\n",
    "ax2.plot(x, fx, 'g', label='true function')\n",
    "ax2.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A \"mosaic\" arrangement (`plt.subplot_mosaic`) allows even more flexible panel layouts, with panels referenced by name instead of position.\n",
    "\n",
    "## Outline\n",
    "\n",
    "1. Making plots with Matplotlib\n",
    "2. **Defining new functions**\n",
    "3. Conditional programming (`if` / `elif` / `else`)\n",
    "4. Putting it together: piecewise functions\n",
    "5. Practice\n",
    "\n",
    "## Defining a Simple Function\n",
    "\n",
    "A one-liner function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8414709848078965"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#| echo: true\n",
    "#| eval: true\n",
    "def f(x): return x * np.sin(x)\n",
    "\n",
    "f(1)   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "::: {.callout-note}\n",
    "**Key rule:** A Python function must `return` a value explicitly, or it\n",
    "returns nothing!\n",
    ":::\n",
    "\n",
    "## Defining a Python Function\n",
    "With more than one line, we **indent** the body --- no curly braces as in R. The function ends when the indentation stops."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "#| echo: true\n",
    "#| eval: true\n",
    "def hyp(a, b):\n",
    "    csq = a**2 + b**2\n",
    "    c = np.sqrt(csq)\n",
    "    return c"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Returning Multiple Values\n",
    "\n",
    "List every object to return, separated by commas:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "#| echo: true\n",
    "#| eval: true\n",
    "def eucl(r, th):\n",
    "    x = r * np.cos(th)\n",
    "    y = r * np.sin(th)\n",
    "    return x, y\n",
    "\n",
    "x, y = eucl(2, np.pi/3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Python automatically packages multiple return values into a tuple, which we can unpack on the left-hand side --- just as we did with multiple assignment earlier.\n",
    "\n",
    "## Default Argument Values\n",
    "\n",
    "Default values work just as they do in R:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "#| echo: true\n",
    "#| eval: true\n",
    "def logistic(x, a=0, b=1):\n",
    "    l   = a + x*b\n",
    "    val = np.exp(l) / (1 + np.exp(l))\n",
    "    return val\n",
    "\n",
    "x   = np.linspace(-4, 4, 200)\n",
    "fx1 = logistic(x)               # uses defaults a=0, b=1\n",
    "fx2 = logistic(x, a=-2, b=3)    # override the defaults"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Arguments can be supplied positionally or by name (`a=-2`); naming them makes calls more readable.\n",
    "\n",
    "## Outline\n",
    "\n",
    "1. Making plots with Matplotlib\n",
    "2. Defining new functions\n",
    "3. **Conditional programming (`if` / `elif` / `else`)**\n",
    "4. Putting it together: piecewise functions\n",
    "5. Practice\n",
    "\n",
    "## `if` / `else`\n",
    "\n",
    "The logic of conditional programming is the same in every language --- only the syntax changes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "#| echo: true\n",
    "#| eval: true\n",
    "def rolldice():\n",
    "    r1 = np.random.choice(np.arange(1, 7), 1)\n",
    "    r2 = np.random.choice(np.arange(1, 7), 1)\n",
    "\n",
    "    if r1 == r2:\n",
    "        print(\"Doubles!\")\n",
    "    else:\n",
    "        print(\"No match.\")\n",
    "\n",
    "    print(r1, r2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Just as with functions and loops, the body of an `if`/`else` block is defined by **indentation**, not braces.\n",
    "\n",
    "## `elif`: \"Else If\"\n",
    "\n",
    "Python spells \"else if\" as a single word, `elif`:\n",
    "\\small"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "def rolldice():\n",
    "    r1 = np.random.choice(np.arange(1, 7), 1)\n",
    "    r2 = np.random.choice(np.arange(1, 7), 1)\n",
    "\n",
    "    if r1 == r2:\n",
    "        if r1 == 1:\n",
    "            print(\"Snake-eyes!\")\n",
    "        elif r1 == 6:\n",
    "            print(\"Can't beat it!\")\n",
    "        else:\n",
    "            print(\"Doubles!\")\n",
    "    elif (r1 + r2) <= 7:\n",
    "        print(\"Sad rollin'.\")\n",
    "    else:\n",
    "        print(\"Mighty fine!\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Conditions can be **nested** just like in R.\n",
    "\n",
    "## Booleans as Numbers\n",
    "\n",
    "The function `bool()` coerces its argument to `True`/`False`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "bool(1)   # True\n",
    "bool(0)   # False"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Just as in R, a logical value coerces to $0$ or $1$ in arithmetic. This lets us write **piecewise-defined functions** compactly, without an explicit `if` statement, using indicator-style expressions.\n",
    "\n",
    "## Outline\n",
    "\n",
    "1. Making plots with Matplotlib\n",
    "2. Defining new functions\n",
    "3. Conditional programming (`if` / `elif` / `else`)\n",
    "4. **Putting it together: piecewise functions**\n",
    "5. Practice\n",
    "\n",
    "## Example: Soft-Thresholding\n",
    "\n",
    "$$\n",
    "S(x, \\lambda) = \\begin{cases}\n",
    "x + \\lambda, & x < -\\lambda \\\\\n",
    "0,            & -\\lambda \\le x \\le \\lambda \\\\\n",
    "x - \\lambda,  & \\lambda < x\n",
    "\\end{cases}\n",
    "\\quad (\\lambda > 0)\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def softthresh(x, lam):\n",
    "    return (x + lam)*(x < -lam) + (x - lam)*(x > lam)\n",
    "\n",
    "x  = np.linspace(-2, 2, 200)\n",
    "fx = softthresh(x, lam=1)\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(8, 4))\n",
    "ax.plot(x, fx)\n",
    "ax.axhline(0, linestyle=\"--\", linewidth=0.5)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The boolean expressions `(x < -lam)` etc. act as $0/1$ indicators.\n",
    "\n",
    "## Result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#| echo: false\n",
    "#| eval: true\n",
    "def softthresh(x, lam):\n",
    "    return (x + lam)*(x < -lam) + (x - lam)*(x > lam)\n",
    "\n",
    "x  = np.linspace(-2, 2, 200)\n",
    "fx = softthresh(x, lam=1)\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(8, 4))\n",
    "ax.plot(x, fx)\n",
    "ax.axhline(0, linestyle=\"--\", linewidth=0.5)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example: A Bivariate Density Surface"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def bivn(z1, z2, rho=0):\n",
    "    r = 1 - rho**2\n",
    "    a = 1 / (2*np.pi*np.sqrt(r))\n",
    "    b = (z1**2 - 2*rho*z1*z2 + z2**2) / r\n",
    "    return a * np.exp(-b/2)\n",
    "\n",
    "gs = 50\n",
    "z       = np.linspace(-3, 3, gs)\n",
    "X, Y    = np.meshgrid(z, z)       # build a 2-d grid from 1-d grids\n",
    "Z       = bivn(X, Y, rho=-0.5)   # evaluate the function on the grid\n",
    "\n",
    "fig = plt.figure(figsize=(8, 8))\n",
    "ax  = fig.add_subplot(projection='3d')\n",
    "ax.plot_surface(X, Y, Z, cmap=plt.cm.YlGnBu_r)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Result "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "fig-height": 2,
    "fig-width": 6.4
   },
   "outputs": [],
   "source": [
    "#| echo: false\n",
    "#| eval: true\n",
    "#| out-width: 90%\n",
    "def bivn(z1, z2, rho=0):\n",
    "    r = 1 - rho**2\n",
    "    a = 1 / (2*np.pi*np.sqrt(r))\n",
    "    b = (z1**2 - 2*rho*z1*z2 + z2**2) / r\n",
    "    return a * np.exp(-b/2)\n",
    "\n",
    "gs = 50\n",
    "z       = np.linspace(-3, 3, gs)\n",
    "X, Y    = np.meshgrid(z, z)       # build a 2-d grid from 1-d grids\n",
    "Z       = bivn(X, Y, rho=-0.5)   # evaluate the function on the grid\n",
    "\n",
    "fig = plt.figure(figsize=(8, 8))\n",
    "ax  = fig.add_subplot(projection='3d')\n",
    "ax.plot_surface(X, Y, Z, cmap=plt.cm.YlGnBu_r)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Outline\n",
    "\n",
    "1. Making plots with Matplotlib\n",
    "2. Defining new functions\n",
    "3. Conditional programming (`if` / `elif` / `else`)\n",
    "4. Putting it together: piecewise functions\n",
    "5. **Practice**\n",
    "\n",
    "## Practice: Write a function for Bootstrap Median\n",
    "\\scriptsize"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'estimate': 29.6,\n",
       " 'ci_lower': 29.4,\n",
       " 'ci_upper': 29.8,\n",
       " 'boot_dist': array([29.5, 29.9, 29.7, ..., 29.8, 29.5, 29.5])}"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#| echo: true\n",
    "#| eval: true\n",
    "def bootstrap_ci(x, n_boot=2000, seed=42, alpha=0.05):\n",
    "    rng = np.random.default_rng(seed)     \n",
    "    x = np.asarray(x, dtype=float)\n",
    "    n = x.size\n",
    "    obs_median = float(np.median(x))\n",
    "    boot_meds = np.empty(n_boot)          # pre-allocate storage\n",
    "\n",
    "    for b in range(n_boot):\n",
    "        idx = rng.integers(0, n, size=n)  # 0-based, high exclusive\n",
    "        x_star = x[idx]\n",
    "        boot_meds[b] = np.median(x_star)\n",
    "\n",
    "    lo, hi = np.quantile(boot_meds, [alpha/2, 1 - alpha/2])\n",
    "    return {\"estimate\": obs_median, \"ci_lower\": float(lo),\n",
    "            \"ci_upper\": float(hi), \"boot_dist\": boot_meds}\n",
    "bmi = np.round(np.random.default_rng(1).gamma(30.0, 1.0, size=5000), 1)\n",
    "res = bootstrap_ci(bmi, n_boot=2000, seed=42)\n",
    "res"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Practice: Read Code\n",
    "\n",
    "Predict the output of the following code before running it.\n",
    "\\small"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#| echo: true\n",
    "#| eval: false\n",
    "def star(p, s):\n",
    "    th = np.linspace(np.pi/2, np.pi/2 + 2*np.pi*s, s*p + 1)\n",
    "    x  = np.cos(th[::s])\n",
    "    y  = np.sin(th[::s])\n",
    "    return x, y\n",
    "\n",
    "x, y = star(5, 2)\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(4, 4))\n",
    "ax.set_aspect('equal')\n",
    "ax.axis('off')\n",
    "ax.plot(x, y)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 1.57079633  2.82743339  4.08407045  5.34070751  6.59734457  7.85398163\n",
      "  9.1106187  10.36725576 11.62389282 12.88052988 14.13716694]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([ 1.57079633,  4.08407045,  6.59734457,  9.1106187 , 11.62389282,\n",
       "       14.13716694])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p=5\n",
    "s=2\n",
    "th = np.linspace(np.pi/2, np.pi/2 + 2*np.pi*s, s*p + 1)\n",
    "print(th)\n",
    "th.size\n",
    "th[::s]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#| echo: false\n",
    "#| eval: true\n",
    "def star(p, s):\n",
    "    th = np.linspace(np.pi/2, np.pi/2 + 2*np.pi*s, s*p + 1)\n",
    "    x  = np.cos(th[::s])\n",
    "    y  = np.sin(th[::s])\n",
    "    return x, y\n",
    "\n",
    "x, y = star(5, 2)\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(4, 4))\n",
    "ax.set_aspect('equal')\n",
    "ax.axis('off')\n",
    "ax.plot(x, y)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![Star polygons](star.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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