From 0c03feb90593045f89a092b5af5d1897472db63b Mon Sep 17 00:00:00 2001
From: maximusron <aaronjomyjoseph@gmail.com>
Date: Sun, 17 Sep 2023 12:08:59 +0530
Subject: [PATCH] update rich text and remove matplotlib warning for kg plot

---
 notebooks/kalman_CUDA_demo/run_kf.ipynb | 41 ++++++++++++++++---------
 1 file changed, 27 insertions(+), 14 deletions(-)

diff --git a/notebooks/kalman_CUDA_demo/run_kf.ipynb b/notebooks/kalman_CUDA_demo/run_kf.ipynb
index 33f3b906..a31dab2c 100644
--- a/notebooks/kalman_CUDA_demo/run_kf.ipynb
+++ b/notebooks/kalman_CUDA_demo/run_kf.ipynb
@@ -146,7 +146,8 @@
    "id": "d8bb436d-238b-488f-a8a8-b8e1a4a0150d",
    "metadata": {},
    "source": [
-    "### User functions to run the CUDA routines on std::vectors"
+    "### Defining functions to run CUDA kernels and obtain the results:\n",
+    "This allows us to run calls to all matrix-matrix, matrix-vector and vector-vector CUDA operations without dealing with CUDA syntax"
    ]
   },
   {
@@ -781,6 +782,27 @@
     "}\n"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "id": "54fb13b2-51ca-4dda-8503-151aea8dbd68",
+   "metadata": {},
+   "source": [
+    "### Putting it all together:\n",
+    "We define the `run_kf` function that initialises the following:\n",
+    "- Number of states\n",
+    "- Dimensions of eacch measurement\n",
+    "- Time steps used $\\begin{aligned} & {dt}\\end{aligned}$\n",
+    "- Covariance matrices\n",
+    "- Passes the measurement data to $\\begin{aligned} & \\hat{x}_0^{-}\\end{aligned}$\n",
+    "\n",
+    "Then the measurements are fed into filter, and output estimated states\n",
+    "\n",
+    "The algorithm then runs by looping over the measurements:\n",
+    "\n",
+    "$\\begin{gathered} & for\\:y\\:in\\:measurements\\::\\end{gathered}$\n",
+    "$\\begin{gathered} & kf.update(y)\\end{gathered}$"
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": 24,
@@ -790,8 +812,8 @@
    "source": [
     "std::vector<std::vector<double>> run_kf(bool verbose) {\n",
     "    \n",
-    "    int n = 3; // Number of states\n",
-    "    int m = 1; // Number of measurements\n",
+    "    int n = 3; \n",
+    "    int m = 1; \n",
     "\n",
     "    double dt = 1.0 / 30; // Time step\n",
     "    \n",
@@ -850,7 +872,7 @@
     "    std::vector<std::vector<double>> gain;\n",
     "    kf.init(0, x0);\n",
     "\n",
-    "    // Feed measurements into filter, output estimated states\n",
+    "    \n",
     "    std::vector<double> y(m);\n",
     "    if(verbose) {\n",
     "        std::cout << \"t = \" << 0 << \", \" << \"x_hat[0]: \";\n",
@@ -1129,15 +1151,7 @@
    "execution_count": 29,
    "id": "f7bcd055-7470-42c9-aad8-238ff3d3566e",
    "metadata": {},
-   "outputs": [
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "No artists with labels found to put in legend.  Note that artists whose label start with an underscore are ignored when legend() is called with no argument.\n"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
     "%%python\n",
     "\n",
@@ -1146,7 +1160,6 @@
     "plt.xlabel('Time Steps')\n",
     "plt.ylabel('Kalman Gain')\n",
     "plt.title('Kalman Gain Plot')\n",
-    "plt.legend()\n",
     "plt.savefig(\"kalman_gain_plot.jpg\")\n",
     "    \n",
     "plt.yscale('symlog')\n",