feat: add image of distributions

examples/01_Simulation.ipynb

@@ -1497,45 +1497,16 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "We can also define the shape of the noise to be uniform or triangular instead of normal. This example demonstrates a uniform process noise distribution."
+    "We can also define the shape of the noise to be uniform or triangular instead of normal. The image below shows the shapes of these distributions.\n",
+    "\n",
+    "![Graphs of normal, triangular, and uniform distributions](distributions.png \"Distributions\")"
    ]
   },
   {
-   "cell_type": "code",
-   "execution_count": null,
+   "cell_type": "markdown",
    "metadata": {},
-   "outputs": [],
    "source": [
-    "# TODO: Add screenshot of shapes of distribution\n",
-    "\n",
-    "import numpy as np\n",
-    "import matplotlib.pyplot as plt\n",
-    "from scipy.stats import norm, triang, uniform\n",
-    "\n",
-    "x=np.linspace(-4, 4, 1000)\n",
-    "norm_pdf = norm.pdf(x, loc=0, scale=1)\n",
-    "triang_pdf = triang.pdf(x, c=0.5, loc=-4, scale=8)\n",
-    "uni_pdf = uniform.pdf(x, loc=-4, scale=8)\n",
-    "\n",
-    "fig, ax = plt.subplots(1, 3, figsize=(14, 4))\n",
-    "\n",
-    "ax[0].plot(x, norm_pdf)\n",
-    "ax[0].set_title(\"Normal distribution\", pad=10)\n",
-    "ax[0].xaxis.set_visible(False)\n",
-    "ax[0].yaxis.set_visible(False)\n",
-    "\n",
-    "ax[1].plot(x, triang_pdf)\n",
-    "ax[1].set_title(\"Triangular distribution\", pad=10)\n",
-    "ax[1].xaxis.set_visible(False)\n",
-    "ax[1].yaxis.set_visible(False)\n",
-    "\n",
-    "ax[2].plot(x, uni_pdf)\n",
-    "ax[2].set_title(\"Uniform distribution\", pad=10)\n",
-    "ax[2].xaxis.set_visible(False)\n",
-    "ax[2].yaxis.set_visible(False)\n",
-    "\n",
-    "plt.tight_layout()\n",
-    "plt.show()"
+    " This example demonstrates a uniform process noise distribution."
    ]
   },
   {
@@ -1643,7 +1614,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "In this example, we will be using `simulate_to_threshold` with vectorized states. The ThrownObject model will be used to simulate multiple thrown objects."
+    "In this example, we will be using `simulate_to_threshold` with vectorized states. Vectorized states are a representation of a system's current conditions. The ThrownObject model will be used to simulate multiple thrown objects. Let's start by getting the necessary imports."
    ]
   },
   {
@@ -1661,22 +1632,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "We will now set up the vectorized initial state. In this example, we will define 4 throws of varying positions (x) and strengths (v) in `first_state`. We will then simulate to the threshold using this state."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "first_state = {\n",
-    "    'x': array([1.75, 1.8, 1.85, 1.9]),\n",
-    "    'v': array([35, 39, 22, 47])\n",
-    "}\n",
-    "\n",
-    "m = ThrownObject()\n",
-    "simulated_results = m.simulate_to_threshold(x=first_state, events='impact', print = True, dt=0.1, save_freq=2)"
+    "We will also define a helper function to visualize the four throws."
    ]
   },
   {
@@ -1714,18 +1670,14 @@
     "    \n",
     "    plt.xlabel(\"time\")\n",
     "    plt.ylabel(\"state\") \n",
-    "    plt.legend(loc='upper left', bbox_to_anchor=(1, 1))\n",
-    "\n",
-    "print_vectorized_sim_plots(simulated_results)\n",
-    "plt.title(\"Vectorized simulation until any object hits the ground\", pad=10)\n",
-    "plt.show()"
+    "    plt.legend(loc='upper left', bbox_to_anchor=(1, 1))"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "Let's do the same thing but only stop when all objects hit the ground by defining a `thresholds_met_eqn`."
+    "We will now set up the vectorized initial state. In this example, we will define 4 throws of varying positions (x) and strengths (v) in `first_state`. We will then simulate to the threshold using this state. We should see the simulation stop once any one object hits the ground."
    ]
   },
   {
@@ -1734,10 +1686,24 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "def thresholds_met_eqn(thresholds_met):\n",
-    "    return all(thresholds_met['impact'])\n",
+    "first_state = {\n",
+    "    'x': array([1.75, 1.8, 1.85, 1.9]),\n",
+    "    'v': array([35, 39, 22, 47])\n",
+    "}\n",
     "\n",
-    "simulated_results = m.simulate_to_threshold(x = first_state, thresholds_met_eqn=thresholds_met_eqn, print = True, dt=0.1, save_freq=2)"
+    "m = ThrownObject()\n",
+    "simulated_results = m.simulate_to_threshold(x=first_state, events='impact', print=True, dt=0.1, save_freq=1)\n",
+    "\n",
+    "print_vectorized_sim_plots(simulated_results)\n",
+    "plt.title(\"Vectorized simulation until any object hits the ground\", pad=10)\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Let's do the same thing but only stop when all objects hit the ground by defining a `thresholds_met_eqn`."
    ]
   },
   {
@@ -1746,6 +1712,11 @@
    "metadata": {},
    "outputs": [],
    "source": [
+    "def thresholds_met_eqn(thresholds_met):\n",
+    "    return all(thresholds_met['impact'])\n",
+    "\n",
+    "simulated_results = m.simulate_to_threshold(x = first_state, thresholds_met_eqn=thresholds_met_eqn, print=True, dt=0.1, save_freq=1)\n",
+    "\n",
     "print_vectorized_sim_plots(simulated_results)\n",
     "plt.title(\"Vectorized simulation until all objects hit the ground\", pad=10)\n",
     "plt.show()"