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  {
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   "source": [
    "# Introduksjon til maskinlæring i praksis\n",
    "\n",
    "I forrige semester så vi på vektorer og matriser, og fant en matrise som kan gjøre om rette bokstaver til kursiv. \n",
    "\n",
    "Grunnen til at vi så på dette, er at matriser og vektorer spiller en stor rolle når vi jobber med maskinlæring, og spesielt når vi jobber med nevrale nett. Litt forenklet kan vi si at vi bruker vektorer til å representere data og matriser til å representere nevrale nettverk. Vi skal utvide og komplisere dette litt senere, men for nå kan vi tenke slik på det. \n",
    "\n",
    "Vi begynner med å repetere litt på matriser og vektorer. (Se eget notat på timeplanen). "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9369a71c",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "523ce754-8512-47e5-bb09-749ab03acc56",
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   "source": [
    "## Nå skal vi finne matrisen med maskinlæring i stedet\n",
    "\n",
    "Jeg har laget et datasett med punktbeskrivelser av bokstaver som er rette og i kursiv. Dataene kommer i par, slik at vi vet hvilken rett bokstav som hører til hvilken skjev bokstav. Dette skal vi bruke til å trene et nettverk for kursivbokstaver. Grunnen til at jeg bruker dette datasettet som eksempel er at dere allerede har gjort en oppgave der dere selv har prøvd å finne en matrise, og dermed har et visst forhold til hva som foregår. \n",
    "\n",
    "For dem som er interessert ligger scriptet som lager bokstavene i en fil som heter `create_letter_dataset.py`. \n",
    "\n",
    "Under lager vi en maskinlæringsalgoritme som trenes opp til å lage kursivbokstaver. \n",
    "\n",
    "## Treningsdata\n",
    "Vi begynner med å se på de dataene som vi skal trene kursiv-algoritmen vår med. "
   ]
  },
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    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x1320cabb0>"
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      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import json \n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "alphabet = \"ABCDEFGHIJKLMNOPQRSTUVWXYZÆØÅ\"\n",
    "\n",
    "straight_letters = json.load(open(\"../resources/straight_letters.json\", \"r\"))\n",
    "italic_letters = json.load(open(\"../resources/italic_letters.json\", \"r\"))\n",
    "\n",
    "for key in straight_letters.keys():\n",
    "    straight_letters[key] = np.asarray(straight_letters[key])\n",
    "    italic_letters[key] = np.asarray(italic_letters[key])\n",
    "\n",
    "letter = \"A\"\n",
    "plt.subplot(1, 2, 1)\n",
    "plt.scatter(straight_letters[letter][:,0], straight_letters[letter][:,1])\n",
    "plt.subplot(1, 2, 2)\n",
    "plt.scatter(italic_letters[letter][:,0], straight_letters[letter][:,1])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7f584b1a",
   "metadata": {},
   "source": [
    "Over ser vi et eksempel på bokstaven `A` representert som en punktsky både i rett og kursiv. Nå skal vi bruke maskinlæring til å finne den matrisen som kan transformere fra den rette til den skjeve versjonen av bokstaven. \n",
    "\n",
    "## Maskinlæringsmodell\n",
    "\n",
    "For å kunne gjøre backpropagation, altså finne ut hvordan vi skal justere vektene i nettverket for at det skal bli bedre på å gjøre prediksjoner som er i samsvar med treningsdataene, bruker vi et bibliotek som heter `jax`. Det finnes andre biblioteker vi kunne brukt, slik som PyTorch etter Tensorflow. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "8f97ad24-6f8c-48a3-8fbb-141c84566138",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/henriasv/.pyenv/versions/3.9.9/envs/hon1000/lib/python3.9/site-packages/jax/_src/lib/__init__.py:32: UserWarning: JAX on Mac ARM machines is experimental and minimally tested. Please see https://github.com/google/jax/issues/5501 in the event of problems.\n",
      "  warnings.warn(\"JAX on Mac ARM machines is experimental and minimally tested. \"\n"
     ]
    }
   ],
   "source": [
    "import jax.numpy as jnp\n",
    "from jax import grad\n",
    "from jax import random"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d681dc69",
   "metadata": {},
   "source": [
    "Vi kan implementere maskinlæringsalgoritmen i følgende rekkefølge. Koden under viser det endelige resultatet. \n",
    "\n",
    "1. Skrive opp funksjonene\n",
    "2. Fylle funksjonenen\n",
    "3. Initialisere matrisen, printe\n",
    "4. Treningsløkke med 3 epoker, printe matrise, visualisere punktsky\n",
    "5. Plotte loss. Kjøre flere epoker, plotte loss igjen. \n",
    "6. Visualisere punktsky\n",
    "7. Animere punktsky"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "16bf9c4d-ff9d-4edd-8485-0e24f1dfcc88",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1.0806346  0.20374385]\n",
      " [0.11557305 0.86203676]]\n"
     ]
    },
    {
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       "    /* MSIE used to detect old browsers and Trident used to newer ones*/\n",
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       "    this.img_id = img_id;\n",
       "    this.slider_id = slider_id;\n",
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       "\n",
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       "     this.frames[i] = new Image();\n",
       "     this.frames[i].src = frames[i];\n",
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       "    var slider = document.getElementById(this.slider_id);\n",
       "    slider.max = this.frames.length - 1;\n",
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       "        // like oninput. In contrast, Microsoft Edge behaves correctly.\n",
       "        slider.setAttribute('onchange', slider.getAttribute('oninput'));\n",
       "        slider.setAttribute('oninput', null);\n",
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       "        var button = button_group[i];\n",
       "        if (button.checked) {\n",
       "            return button.value;\n",
       "        }\n",
       "    }\n",
       "    return undefined;\n",
       "  }\n",
       "\n",
       "  Animation.prototype.set_frame = function(frame){\n",
       "    this.current_frame = frame;\n",
       "    document.getElementById(this.img_id).src =\n",
       "            this.frames[this.current_frame].src;\n",
       "    document.getElementById(this.slider_id).value = this.current_frame;\n",
       "  }\n",
       "\n",
       "  Animation.prototype.next_frame = function()\n",
       "  {\n",
       "    this.set_frame(Math.min(this.frames.length - 1, this.current_frame + 1));\n",
       "  }\n",
       "\n",
       "  Animation.prototype.previous_frame = function()\n",
       "  {\n",
       "    this.set_frame(Math.max(0, this.current_frame - 1));\n",
       "  }\n",
       "\n",
       "  Animation.prototype.first_frame = function()\n",
       "  {\n",
       "    this.set_frame(0);\n",
       "  }\n",
       "\n",
       "  Animation.prototype.last_frame = function()\n",
       "  {\n",
       "    this.set_frame(this.frames.length - 1);\n",
       "  }\n",
       "\n",
       "  Animation.prototype.slower = function()\n",
       "  {\n",
       "    this.interval /= 0.7;\n",
       "    if(this.direction > 0){this.play_animation();}\n",
       "    else if(this.direction < 0){this.reverse_animation();}\n",
       "  }\n",
       "\n",
       "  Animation.prototype.faster = function()\n",
       "  {\n",
       "    this.interval *= 0.7;\n",
       "    if(this.direction > 0){this.play_animation();}\n",
       "    else if(this.direction < 0){this.reverse_animation();}\n",
       "  }\n",
       "\n",
       "  Animation.prototype.anim_step_forward = function()\n",
       "  {\n",
       "    this.current_frame += 1;\n",
       "    if(this.current_frame < this.frames.length){\n",
       "      this.set_frame(this.current_frame);\n",
       "    }else{\n",
       "      var loop_state = this.get_loop_state();\n",
       "      if(loop_state == \"loop\"){\n",
       "        this.first_frame();\n",
       "      }else if(loop_state == \"reflect\"){\n",
       "        this.last_frame();\n",
       "        this.reverse_animation();\n",
       "      }else{\n",
       "        this.pause_animation();\n",
       "        this.last_frame();\n",
       "      }\n",
       "    }\n",
       "  }\n",
       "\n",
       "  Animation.prototype.anim_step_reverse = function()\n",
       "  {\n",
       "    this.current_frame -= 1;\n",
       "    if(this.current_frame >= 0){\n",
       "      this.set_frame(this.current_frame);\n",
       "    }else{\n",
       "      var loop_state = this.get_loop_state();\n",
       "      if(loop_state == \"loop\"){\n",
       "        this.last_frame();\n",
       "      }else if(loop_state == \"reflect\"){\n",
       "        this.first_frame();\n",
       "        this.play_animation();\n",
       "      }else{\n",
       "        this.pause_animation();\n",
       "        this.first_frame();\n",
       "      }\n",
       "    }\n",
       "  }\n",
       "\n",
       "  Animation.prototype.pause_animation = function()\n",
       "  {\n",
       "    this.direction = 0;\n",
       "    if (this.timer){\n",
       "      clearInterval(this.timer);\n",
       "      this.timer = null;\n",
       "    }\n",
       "  }\n",
       "\n",
       "  Animation.prototype.play_animation = function()\n",
       "  {\n",
       "    this.pause_animation();\n",
       "    this.direction = 1;\n",
       "    var t = this;\n",
       "    if (!this.timer) this.timer = setInterval(function() {\n",
       "        t.anim_step_forward();\n",
       "    }, this.interval);\n",
       "  }\n",
       "\n",
       "  Animation.prototype.reverse_animation = function()\n",
       "  {\n",
       "    this.pause_animation();\n",
       "    this.direction = -1;\n",
       "    var t = this;\n",
       "    if (!this.timer) this.timer = setInterval(function() {\n",
       "        t.anim_step_reverse();\n",
       "    }, this.interval);\n",
       "  }\n",
       "</script>\n",
       "\n",
       "<style>\n",
       ".animation {\n",
       "    display: inline-block;\n",
       "    text-align: center;\n",
       "}\n",
       "input[type=range].anim-slider {\n",
       "    width: 374px;\n",
       "    margin-left: auto;\n",
       "    margin-right: auto;\n",
       "}\n",
       ".anim-buttons {\n",
       "    margin: 8px 0px;\n",
       "}\n",
       ".anim-buttons button {\n",
       "    padding: 0;\n",
       "    width: 36px;\n",
       "}\n",
       ".anim-state label {\n",
       "    margin-right: 8px;\n",
       "}\n",
       ".anim-state input {\n",
       "    margin: 0;\n",
       "    vertical-align: middle;\n",
       "}\n",
       "</style>\n",
       "\n",
       "<div class=\"animation\">\n",
       "  <img id=\"_anim_imgd8365dbd68844d31b225853a109ee4a9\">\n",
       "  <div class=\"anim-controls\">\n",
       "    <input id=\"_anim_sliderd8365dbd68844d31b225853a109ee4a9\" type=\"range\" class=\"anim-slider\"\n",
       "           name=\"points\" min=\"0\" max=\"1\" step=\"1\" value=\"0\"\n",
       "           oninput=\"animd8365dbd68844d31b225853a109ee4a9.set_frame(parseInt(this.value));\"></input>\n",
       "    <div class=\"anim-buttons\">\n",
       "      <button title=\"Decrease speed\" aria-label=\"Decrease speed\" onclick=\"animd8365dbd68844d31b225853a109ee4a9.slower()\">\n",
       "          <i class=\"fa fa-minus\"></i></button>\n",
       "      <button title=\"First frame\" aria-label=\"First frame\" onclick=\"animd8365dbd68844d31b225853a109ee4a9.first_frame()\">\n",
       "        <i class=\"fa fa-fast-backward\"></i></button>\n",
       "      <button title=\"Previous frame\" aria-label=\"Previous frame\" onclick=\"animd8365dbd68844d31b225853a109ee4a9.previous_frame()\">\n",
       "          <i class=\"fa fa-step-backward\"></i></button>\n",
       "      <button title=\"Play backwards\" aria-label=\"Play backwards\" onclick=\"animd8365dbd68844d31b225853a109ee4a9.reverse_animation()\">\n",
       "          <i class=\"fa fa-play fa-flip-horizontal\"></i></button>\n",
       "      <button title=\"Pause\" aria-label=\"Pause\" onclick=\"animd8365dbd68844d31b225853a109ee4a9.pause_animation()\">\n",
       "          <i class=\"fa fa-pause\"></i></button>\n",
       "      <button title=\"Play\" aria-label=\"Play\" onclick=\"animd8365dbd68844d31b225853a109ee4a9.play_animation()\">\n",
       "          <i class=\"fa fa-play\"></i></button>\n",
       "      <button title=\"Next frame\" aria-label=\"Next frame\" onclick=\"animd8365dbd68844d31b225853a109ee4a9.next_frame()\">\n",
       "          <i class=\"fa fa-step-forward\"></i></button>\n",
       "      <button title=\"Last frame\" aria-label=\"Last frame\" onclick=\"animd8365dbd68844d31b225853a109ee4a9.last_frame()\">\n",
       "          <i class=\"fa fa-fast-forward\"></i></button>\n",
       "      <button title=\"Increase speed\" aria-label=\"Increase speed\" onclick=\"animd8365dbd68844d31b225853a109ee4a9.faster()\">\n",
       "          <i class=\"fa fa-plus\"></i></button>\n",
       "    </div>\n",
       "    <form title=\"Repetition mode\" aria-label=\"Repetition mode\" action=\"#n\" name=\"_anim_loop_selectd8365dbd68844d31b225853a109ee4a9\"\n",
       "          class=\"anim-state\">\n",
       "      <input type=\"radio\" name=\"state\" value=\"once\" id=\"_anim_radio1_d8365dbd68844d31b225853a109ee4a9\"\n",
       "             >\n",
       "      <label for=\"_anim_radio1_d8365dbd68844d31b225853a109ee4a9\">Once</label>\n",
       "      <input type=\"radio\" name=\"state\" value=\"loop\" id=\"_anim_radio2_d8365dbd68844d31b225853a109ee4a9\"\n",
       "             checked>\n",
       "      <label for=\"_anim_radio2_d8365dbd68844d31b225853a109ee4a9\">Loop</label>\n",
       "      <input type=\"radio\" name=\"state\" value=\"reflect\" id=\"_anim_radio3_d8365dbd68844d31b225853a109ee4a9\"\n",
       "             >\n",
       "      <label for=\"_anim_radio3_d8365dbd68844d31b225853a109ee4a9\">Reflect</label>\n",
       "    </form>\n",
       "  </div>\n",
       "</div>\n",
       "\n",
       "\n",
       "<script language=\"javascript\">\n",
       "  /* Instantiate the Animation class. */\n",
       "  /* The IDs given should match those used in the template above. */\n",
       "  (function() {\n",
       "    var img_id = \"_anim_imgd8365dbd68844d31b225853a109ee4a9\";\n",
       "    var slider_id = \"_anim_sliderd8365dbd68844d31b225853a109ee4a9\";\n",
       "    var loop_select_id = \"_anim_loop_selectd8365dbd68844d31b225853a109ee4a9\";\n",
       "    var frames = new Array(30);\n",
       "    \n",
       "  frames[0] = \"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAbAAAAEgCAYAAADVKCZpAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90\\\n",
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       "AAAASUVORK5CYII=\\\n",
       "\"\n",
       "\n",
       "\n",
       "    /* set a timeout to make sure all the above elements are created before\n",
       "       the object is initialized. */\n",
       "    setTimeout(function() {\n",
       "        animd8365dbd68844d31b225853a109ee4a9 = new Animation(frames, img_id, slider_id, 50.0,\n",
       "                                 loop_select_id);\n",
       "    }, 0);\n",
       "  })()\n",
       "</script>\n"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def init_random_weights(size):\n",
    "    return random.normal(random.PRNGKey(3), size)\n",
    "\n",
    "def predict(weights, inputs):\n",
    "    outputs = jnp.matmul(weights, inputs)\n",
    "    return outputs\n",
    "\n",
    "def loss(weights, inputs, targets):\n",
    "    predictions = predict(weights, inputs)\n",
    "    return jnp.mean((predictions-targets)**2)\n",
    "    \n",
    "def update(weights, x, y, step_size=0.003):\n",
    "    grads = grad(loss)(weights, x, y) # Backpropagation\n",
    "    return weights - step_size * grads\n",
    "\n",
    "# Vi trener nettet kun med punktene i bokstaven A     \n",
    "inputs  = jnp.array(straight_letters[\"A\"].T)\n",
    "targets = jnp.array(italic_letters[\"A\"].T)\n",
    "\n",
    "weights = init_random_weights((2,2))\n",
    "\n",
    "fig, ax = plt.subplots() # vent 2\n",
    "ims = [] # vent 2\n",
    "\n",
    "from IPython.display import HTML # vent 2\n",
    "import matplotlib.animation as animation # vent 2\n",
    "\n",
    "loss_list = [] # vent 1\n",
    "\n",
    "for i in range(30): # Prøv først med 3 epoker, print matrisen. Deretter med 100 og plott matrisen. \n",
    "    weights = update(weights, inputs, targets)\n",
    "    loss_list.append(loss(weights, inputs, targets)) # vent 1\n",
    "    out = predict(weights, inputs).T\n",
    "    im = ax.scatter(out[:,0], out[:,1], c=\"k\") # vent 2\n",
    "    ims.append([im]) # vent 2\n",
    "\n",
    "print(weights)\n",
    "\n",
    "ani = animation.ArtistAnimation(fig, ims, interval=50, blit=True,\n",
    "                    repeat_delay=1000) # vent 2\n",
    "plt.close()\n",
    "HTML(ani.to_jshtml())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d1fe24c6",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "5dbbdbf2",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Weights: \n",
      " [[1.0806346  0.20374385]\n",
      " [0.11557305 0.86203676]]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'loss')"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "print(\"Weights: \\n\", weights)\n",
    "plt.plot(loss_list)\n",
    "plt.xlabel(\"epoch\")\n",
    "plt.ylabel(\"loss\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "1368ce35-12b5-423b-81d1-0f969c89874d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def draw_letter(letter):\n",
    "    out = straight_letters[letter]\n",
    "    plt.scatter(out[:,0], out[:,1])\n",
    "    \n",
    "def draw_italic_letter(letter):\n",
    "    out = predict(weights, straight_letters[letter].T).T\n",
    "    plt.scatter(out[:,0], out[:,1])\n",
    "\n",
    "def draw_both(letter):\n",
    "    plt.subplot(1,2,1)\n",
    "    draw_letter(letter)\n",
    "    plt.subplot(1, 2, 2)\n",
    "    draw_italic_letter(letter)\n",
    "    \n",
    "draw_both(\"Å\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4d48f39c",
   "metadata": {},
   "source": [
    "Hva gjør denne modellen med en vanlig graf som vi er vant til å se på?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d24d8a67",
   "metadata": {},
   "source": [
    "## Funker algoritmen på alle bokstavene? "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "369bb205",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "<link rel=\"stylesheet\"\n",
       "href=\"https://maxcdn.bootstrapcdn.com/font-awesome/4.4.0/css/font-awesome.min.css\">\n",
       "<script language=\"javascript\">\n",
       "  function isInternetExplorer() {\n",
       "    ua = navigator.userAgent;\n",
       "    /* MSIE used to detect old browsers and Trident used to newer ones*/\n",
       "    return ua.indexOf(\"MSIE \") > -1 || ua.indexOf(\"Trident/\") > -1;\n",
       "  }\n",
       "\n",
       "  /* Define the Animation class */\n",
       "  function Animation(frames, img_id, slider_id, interval, loop_select_id){\n",
       "    this.img_id = img_id;\n",
       "    this.slider_id = slider_id;\n",
       "    this.loop_select_id = loop_select_id;\n",
       "    this.interval = interval;\n",
       "    this.current_frame = 0;\n",
       "    this.direction = 0;\n",
       "    this.timer = null;\n",
       "    this.frames = new Array(frames.length);\n",
       "\n",
       "    for (var i=0; i<frames.length; i++)\n",
       "    {\n",
       "     this.frames[i] = new Image();\n",
       "     this.frames[i].src = frames[i];\n",
       "    }\n",
       "    var slider = document.getElementById(this.slider_id);\n",
       "    slider.max = this.frames.length - 1;\n",
       "    if (isInternetExplorer()) {\n",
       "        // switch from oninput to onchange because IE <= 11 does not conform\n",
       "        // with W3C specification. It ignores oninput and onchange behaves\n",
       "        // like oninput. In contrast, Microsoft Edge behaves correctly.\n",
       "        slider.setAttribute('onchange', slider.getAttribute('oninput'));\n",
       "        slider.setAttribute('oninput', null);\n",
       "    }\n",
       "    this.set_frame(this.current_frame);\n",
       "  }\n",
       "\n",
       "  Animation.prototype.get_loop_state = function(){\n",
       "    var button_group = document[this.loop_select_id].state;\n",
       "    for (var i = 0; i < button_group.length; i++) {\n",
       "        var button = button_group[i];\n",
       "        if (button.checked) {\n",
       "            return button.value;\n",
       "        }\n",
       "    }\n",
       "    return undefined;\n",
       "  }\n",
       "\n",
       "  Animation.prototype.set_frame = function(frame){\n",
       "    this.current_frame = frame;\n",
       "    document.getElementById(this.img_id).src =\n",
       "            this.frames[this.current_frame].src;\n",
       "    document.getElementById(this.slider_id).value = this.current_frame;\n",
       "  }\n",
       "\n",
       "  Animation.prototype.next_frame = function()\n",
       "  {\n",
       "    this.set_frame(Math.min(this.frames.length - 1, this.current_frame + 1));\n",
       "  }\n",
       "\n",
       "  Animation.prototype.previous_frame = function()\n",
       "  {\n",
       "    this.set_frame(Math.max(0, this.current_frame - 1));\n",
       "  }\n",
       "\n",
       "  Animation.prototype.first_frame = function()\n",
       "  {\n",
       "    this.set_frame(0);\n",
       "  }\n",
       "\n",
       "  Animation.prototype.last_frame = function()\n",
       "  {\n",
       "    this.set_frame(this.frames.length - 1);\n",
       "  }\n",
       "\n",
       "  Animation.prototype.slower = function()\n",
       "  {\n",
       "    this.interval /= 0.7;\n",
       "    if(this.direction > 0){this.play_animation();}\n",
       "    else if(this.direction < 0){this.reverse_animation();}\n",
       "  }\n",
       "\n",
       "  Animation.prototype.faster = function()\n",
       "  {\n",
       "    this.interval *= 0.7;\n",
       "    if(this.direction > 0){this.play_animation();}\n",
       "    else if(this.direction < 0){this.reverse_animation();}\n",
       "  }\n",
       "\n",
       "  Animation.prototype.anim_step_forward = function()\n",
       "  {\n",
       "    this.current_frame += 1;\n",
       "    if(this.current_frame < this.frames.length){\n",
       "      this.set_frame(this.current_frame);\n",
       "    }else{\n",
       "      var loop_state = this.get_loop_state();\n",
       "      if(loop_state == \"loop\"){\n",
       "        this.first_frame();\n",
       "      }else if(loop_state == \"reflect\"){\n",
       "        this.last_frame();\n",
       "        this.reverse_animation();\n",
       "      }else{\n",
       "        this.pause_animation();\n",
       "        this.last_frame();\n",
       "      }\n",
       "    }\n",
       "  }\n",
       "\n",
       "  Animation.prototype.anim_step_reverse = function()\n",
       "  {\n",
       "    this.current_frame -= 1;\n",
       "    if(this.current_frame >= 0){\n",
       "      this.set_frame(this.current_frame);\n",
       "    }else{\n",
       "      var loop_state = this.get_loop_state();\n",
       "      if(loop_state == \"loop\"){\n",
       "        this.last_frame();\n",
       "      }else if(loop_state == \"reflect\"){\n",
       "        this.first_frame();\n",
       "        this.play_animation();\n",
       "      }else{\n",
       "        this.pause_animation();\n",
       "        this.first_frame();\n",
       "      }\n",
       "    }\n",
       "  }\n",
       "\n",
       "  Animation.prototype.pause_animation = function()\n",
       "  {\n",
       "    this.direction = 0;\n",
       "    if (this.timer){\n",
       "      clearInterval(this.timer);\n",
       "      this.timer = null;\n",
       "    }\n",
       "  }\n",
       "\n",
       "  Animation.prototype.play_animation = function()\n",
       "  {\n",
       "    this.pause_animation();\n",
       "    this.direction = 1;\n",
       "    var t = this;\n",
       "    if (!this.timer) this.timer = setInterval(function() {\n",
       "        t.anim_step_forward();\n",
       "    }, this.interval);\n",
       "  }\n",
       "\n",
       "  Animation.prototype.reverse_animation = function()\n",
       "  {\n",
       "    this.pause_animation();\n",
       "    this.direction = -1;\n",
       "    var t = this;\n",
       "    if (!this.timer) this.timer = setInterval(function() {\n",
       "        t.anim_step_reverse();\n",
       "    }, this.interval);\n",
       "  }\n",
       "</script>\n",
       "\n",
       "<style>\n",
       ".animation {\n",
       "    display: inline-block;\n",
       "    text-align: center;\n",
       "}\n",
       "input[type=range].anim-slider {\n",
       "    width: 374px;\n",
       "    margin-left: auto;\n",
       "    margin-right: auto;\n",
       "}\n",
       ".anim-buttons {\n",
       "    margin: 8px 0px;\n",
       "}\n",
       ".anim-buttons button {\n",
       "    padding: 0;\n",
       "    width: 36px;\n",
       "}\n",
       ".anim-state label {\n",
       "    margin-right: 8px;\n",
       "}\n",
       ".anim-state input {\n",
       "    margin: 0;\n",
       "    vertical-align: middle;\n",
       "}\n",
       "</style>\n",
       "\n",
       "<div class=\"animation\">\n",
       "  <img id=\"_anim_img03034ce80d4b475ea54cef4911940f39\">\n",
       "  <div class=\"anim-controls\">\n",
       "    <input id=\"_anim_slider03034ce80d4b475ea54cef4911940f39\" type=\"range\" class=\"anim-slider\"\n",
       "           name=\"points\" min=\"0\" max=\"1\" step=\"1\" value=\"0\"\n",
       "           oninput=\"anim03034ce80d4b475ea54cef4911940f39.set_frame(parseInt(this.value));\"></input>\n",
       "    <div class=\"anim-buttons\">\n",
       "      <button title=\"Decrease speed\" aria-label=\"Decrease speed\" onclick=\"anim03034ce80d4b475ea54cef4911940f39.slower()\">\n",
       "          <i class=\"fa fa-minus\"></i></button>\n",
       "      <button title=\"First frame\" aria-label=\"First frame\" onclick=\"anim03034ce80d4b475ea54cef4911940f39.first_frame()\">\n",
       "        <i class=\"fa fa-fast-backward\"></i></button>\n",
       "      <button title=\"Previous frame\" aria-label=\"Previous frame\" onclick=\"anim03034ce80d4b475ea54cef4911940f39.previous_frame()\">\n",
       "          <i class=\"fa fa-step-backward\"></i></button>\n",
       "      <button title=\"Play backwards\" aria-label=\"Play backwards\" onclick=\"anim03034ce80d4b475ea54cef4911940f39.reverse_animation()\">\n",
       "          <i class=\"fa fa-play fa-flip-horizontal\"></i></button>\n",
       "      <button title=\"Pause\" aria-label=\"Pause\" onclick=\"anim03034ce80d4b475ea54cef4911940f39.pause_animation()\">\n",
       "          <i class=\"fa fa-pause\"></i></button>\n",
       "      <button title=\"Play\" aria-label=\"Play\" onclick=\"anim03034ce80d4b475ea54cef4911940f39.play_animation()\">\n",
       "          <i class=\"fa fa-play\"></i></button>\n",
       "      <button title=\"Next frame\" aria-label=\"Next frame\" onclick=\"anim03034ce80d4b475ea54cef4911940f39.next_frame()\">\n",
       "          <i class=\"fa fa-step-forward\"></i></button>\n",
       "      <button title=\"Last frame\" aria-label=\"Last frame\" onclick=\"anim03034ce80d4b475ea54cef4911940f39.last_frame()\">\n",
       "          <i class=\"fa fa-fast-forward\"></i></button>\n",
       "      <button title=\"Increase speed\" aria-label=\"Increase speed\" onclick=\"anim03034ce80d4b475ea54cef4911940f39.faster()\">\n",
       "          <i class=\"fa fa-plus\"></i></button>\n",
       "    </div>\n",
       "    <form title=\"Repetition mode\" aria-label=\"Repetition mode\" action=\"#n\" name=\"_anim_loop_select03034ce80d4b475ea54cef4911940f39\"\n",
       "          class=\"anim-state\">\n",
       "      <input type=\"radio\" name=\"state\" value=\"once\" id=\"_anim_radio1_03034ce80d4b475ea54cef4911940f39\"\n",
       "             >\n",
       "      <label for=\"_anim_radio1_03034ce80d4b475ea54cef4911940f39\">Once</label>\n",
       "      <input type=\"radio\" name=\"state\" value=\"loop\" id=\"_anim_radio2_03034ce80d4b475ea54cef4911940f39\"\n",
       "             checked>\n",
       "      <label for=\"_anim_radio2_03034ce80d4b475ea54cef4911940f39\">Loop</label>\n",
       "      <input type=\"radio\" name=\"state\" value=\"reflect\" id=\"_anim_radio3_03034ce80d4b475ea54cef4911940f39\"\n",
       "             >\n",
       "      <label for=\"_anim_radio3_03034ce80d4b475ea54cef4911940f39\">Reflect</label>\n",
       "    </form>\n",
       "  </div>\n",
       "</div>\n",
       "\n",
       "\n",
       "<script language=\"javascript\">\n",
       "  /* Instantiate the Animation class. */\n",
       "  /* The IDs given should match those used in the template above. */\n",
       "  (function() {\n",
       "    var img_id = \"_anim_img03034ce80d4b475ea54cef4911940f39\";\n",
       "    var slider_id = \"_anim_slider03034ce80d4b475ea54cef4911940f39\";\n",
       "    var loop_select_id = \"_anim_loop_select03034ce80d4b475ea54cef4911940f39\";\n",
       "    var frames = new Array(29);\n",
       "    \n",
       "  frames[0] = \"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAbAAAAEgCAYAAADVKCZpAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90\\\n",
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       "JX1s0TmjZNi+UNKPJD0iaT4r/qwWzhMl//kN2L4r1YzP7y1aGKQxroWGybcj4gvZceabks6Q9N+S\\\n",
       "/ioi/q+6muaLAAMAJIkuRABAkggwAECSCDAAQJIIMABAkggwAECSCDAAQJIIMABAkggwAECSCDAA\\\n",
       "QJIIMABAkggwAECSCDAAQJIIMABAkggwAECSCDAAQJIIMABAkggwAECSCDAAQJIIMABAkggwAECS\\\n",
       "/h+tc7Eq5l8rXQAAAABJRU5ErkJggg==\\\n",
       "\"\n",
       "\n",
       "\n",
       "    /* set a timeout to make sure all the above elements are created before\n",
       "       the object is initialized. */\n",
       "    setTimeout(function() {\n",
       "        anim03034ce80d4b475ea54cef4911940f39 = new Animation(frames, img_id, slider_id, 50.0,\n",
       "                                 loop_select_id);\n",
       "    }, 0);\n",
       "  })()\n",
       "</script>\n"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Funker algoritmen på alle bokstavene? \n",
    "fig, ax = plt.subplots()\n",
    "ims = []\n",
    "\n",
    "from IPython.display import HTML\n",
    "import matplotlib.animation as animation\n",
    "\n",
    "for letter in alphabet:\n",
    "    inputs  = jnp.array(straight_letters[letter].T)\n",
    "    out = predict(weights, inputs).T\n",
    "    im = ax.scatter(out[:,0], out[:,1], c=\"k\")\n",
    "    ims.append([im])\n",
    "    \n",
    "ani = animation.ArtistAnimation(fig, ims, interval=50, blit=True,\n",
    "                    repeat_delay=1000)\n",
    "plt.close()\n",
    "HTML(ani.to_jshtml())\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "db970646",
   "metadata": {},
   "source": [
    "## Hva gjør algoritmen med en vanlig matematisk funksjon? "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "e8b87d22",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x2a43f9bb0>]"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def f(x): \n",
    "    return x**2\n",
    "\n",
    "x = np.linspace(-5, 5, 100)\n",
    "y = f(x)\n",
    "\n",
    "plt.figure()\n",
    "plt.plot(x, y)\n",
    "\n",
    "input=np.asarray([x, y])\n",
    "\n",
    "predictions = predict(weights, input).T\n",
    "plt.plot(predictions[:,0], predictions[:,1])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "105412be-8e18-40d0-bfa4-01a8b918fafc",
   "metadata": {},
   "source": [
    "# Teachablemachine \n",
    "\n",
    "Til slutt skal vi se på et ferdiglaget bildegjenkjenningsprogram som lar oss trene opp et nevralt nett til å skille mellom forskjellige objekter. \n",
    "\n",
    "1. Gå sammen 3–4 stykker i hver gruppe.\n",
    "2. Gå inn på https://teachablemachine.withgoogle.com/train/image\n",
    "3. Tren en modell som skal se forskjell på dere og sjekk at den fungerer \n",
    "4. Prøv så å manipulere modellen. Få den til å gjøre feil. Tren eventuelt på nytt for å gjøre den ustabil. \n",
    "\n",
    "\n",
    "\n",
    "*Tenk for eksempel tilbake til foredraget til Anders Hansen om ustabilitet og hva modellene egentlig lærer*"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}