Constant Velocity-Copy1.ipynb

Constant Velocity-Copy1.ipynb

{
  "cells": [
    {
      "metadata": {},
      "cell_type": "markdown",
      "source": "# Learning motion with constant velocity: teacher forcing\nIn this experiment, we are trying to construct a recurrent model that is able to predict the future positions of particle given first two positions. The ground truth is that particle moves with constant speed.\n\nOur setting is the following. We consider GRU network that is feeded with the sequence of coordinates and is learned to predict next item in a sequence (i.e. coordinates at the next timestep).\n\nThen we validate this network by creating new (test) sequence that is longer then initial ones. After some moment of time, we stop feeding network with actual data and feed it with its own outputs, to test for generalization."
    },
    {
      "metadata": {
        "trusted": true
      },
      "cell_type": "code",
      "source": "import matplotlib.pyplot as plt\n%matplotlib inline\nimport numpy as np",
      "execution_count": 45,
      "outputs": []
    },
    {
      "metadata": {
        "trusted": true
      },
      "cell_type": "code",
      "source": "def get_data(num_samples, timesteps, vnorm=0.03, x0=None, phi0=None, noise=0):\n    \"\"\"\n    Returns data that is needed to train the model\n    num_samples is number of samples\n    timesteps is number of timesteps to generate\n    vnorm is a velocity norm\n    x0 is a start position\n    phi0 is an angle\n    \n    returns \n        trajectories\n    \"\"\"\n    x0 = (np.random.uniform(0.33, 0.66, size=(num_samples, 2)) \n          if x0 is None else x0)\n    phi0 = (np.random.uniform(0, 2 * np.pi, size=(num_samples)) \n            if phi0 is None else phi0)\n    v = np.stack([np.cos(phi0), np.sin(phi0)], axis=1) * vnorm\n    t = np.arange(timesteps)\n        \n    trajectories = x0[:, np.newaxis, :] + np.einsum('t,sc->stc', t, v)\n    # motion with constant speed\n    \n    trajectories += np.random.uniform(low=-noise, high=noise,\n                                      size=trajectories.shape)\n    \n    return trajectories",
      "execution_count": 54,
      "outputs": []
    },
    {
      "metadata": {
        "trusted": true
      },
      "cell_type": "code",
      "source": "num_samples = 10000\ntimesteps = 10\ninput_data = get_data(num_samples, timesteps, noise=0.025)",
      "execution_count": 116,
      "outputs": []
    },
    {
      "metadata": {
        "trusted": true
      },
      "cell_type": "code",
      "source": "from keras.models import Model, Sequential\nfrom keras.layers import Input, SimpleRNNCell, SimpleRNN, GRU, Dense, Flatten\nfrom keras import backend as K",
      "execution_count": 117,
      "outputs": []
    },
    {
      "metadata": {
        "trusted": true
      },
      "cell_type": "code",
      "source": "sample = np.random.randint(len(input_data))\nplt.xlim(0, 1)\nplt.ylim(0, 1)\nplt.plot(input_data[sample][:, 0], input_data[sample][:, 1], 'o')",
      "execution_count": 126,
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 126,
          "data": {
            "text/plain": "[<matplotlib.lines.Line2D at 0x176eb71d0>]"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": "<matplotlib.figure.Figure at 0x176d7a128>",
            "image/png": 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67klyWVU9PtaqxmMH8MWq+ockf0zv/p/XVdUz4y7sxWDYZ/guyzCnS1+Q5K3Ah4FtVfXbEdU2akv1xfnA64DvJvk5vTHKmQmduO3ye3EEmKmqE1X1M+Cn9L4AJk2XvrgJuAugqr4PvITewmqt6ZQnCw078F2WYc6SfZFkK/B5emE/qeO0sERfVNUTVbW+qi6qqovozWdsq6plLxp1Fuvyf2QPvbN7kqynN8Tz4CiLHJEuffEQ8BaAJK+lF/jHRlrl2WEGeFf/ap0rgSeq6hdL/dBQh3RqeMsyvOh07ItdwMuAr/fnrR+qqm1jK3pIOvZFEzr2xT7gbUkOAk8Dt1TVxP0V3LEvPgh8Icnf0pvAffckniAm+Sq9L/n1/fmKjwFrAKrqc/TmL64DDgNPAu/p9L4T2FeSpEV4p60kNcLAl6RGGPiS1AgDX5IaYeBLUiMMfElqhIEvSY34fz/UtXt+QHq/AAAAAElFTkSuQmCC\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "metadata": {
        "trusted": true
      },
      "cell_type": "code",
      "source": "input_data.shape",
      "execution_count": 127,
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 127,
          "data": {
            "text/plain": "(10000, 10, 2)"
          },
          "metadata": {}
        }
      ]
    },
    {
      "metadata": {
        "trusted": true
      },
      "cell_type": "code",
      "source": "epochs = 10\nlatent_dim = 16\nbatch_size = 16\n\nprint('Number of samples:', len(input_data))\nprint('Sequence length:', (input_data.shape[1]))\n\n# Define an input sequence and process it.\ninputs = Input(shape=(None, 2))\n# two frames, env.n balls and 2 coordinates per ball\n\nrecurrent = GRU(latent_dim, return_sequences=True, return_state=True)\nrecurrent_dense = Dense(input_data.shape[2])\n\nrecurrent_outputs, _= recurrent(inputs)\nrecurrent_outputs = recurrent_dense(recurrent_outputs)\n\n# Define the model that will turn\nmodel = Model(inputs, recurrent_outputs)\n\n# Run training\nmodel.compile(optimizer='adam', loss='mse')\n\nmodel.fit(input_data[:, :-1,:], input_data[:, 1:, :],\n          batch_size=batch_size,\n          epochs=epochs, validation_split=0.2)\n# Save model\n# model.save('learning_motion.h5')",
      "execution_count": 128,
      "outputs": [
        {
          "output_type": "stream",
          "text": "Number of samples: 10000\nSequence length: 10\nTrain on 8000 samples, validate on 2000 samples\nEpoch 1/10\n8000/8000 [==============================] - 16s 2ms/step - loss: 0.0201 - val_loss: 0.0038\nEpoch 2/10\n8000/8000 [==============================] - 6s 754us/step - loss: 0.0023 - val_loss: 0.0013\nEpoch 3/10\n8000/8000 [==============================] - 6s 734us/step - loss: 0.0010 - val_loss: 8.9309e-04\nEpoch 4/10\n8000/8000 [==============================] - 7s 849us/step - loss: 8.3494e-04 - val_loss: 8.1289e-04\nEpoch 5/10\n8000/8000 [==============================] - 6s 727us/step - loss: 7.7412e-04 - val_loss: 7.5538e-04\nEpoch 6/10\n8000/8000 [==============================] - 7s 843us/step - loss: 7.4547e-04 - val_loss: 7.2933e-04\nEpoch 7/10\n8000/8000 [==============================] - 7s 824us/step - loss: 7.2485e-04 - val_loss: 7.2999e-04\nEpoch 8/10\n8000/8000 [==============================] - 6s 785us/step - loss: 7.1547e-04 - val_loss: 7.0301e-04\nEpoch 9/10\n8000/8000 [==============================] - 6s 768us/step - loss: 7.1046e-04 - val_loss: 6.9471e-04\nEpoch 10/10\n8000/8000 [==============================] - 7s 888us/step - loss: 6.9808e-04 - val_loss: 6.8332e-04\n",
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "execution_count": 128,
          "data": {
            "text/plain": "<keras.callbacks.History at 0x1772e9c50>"
          },
          "metadata": {}
        }
      ]
    },
    {
      "metadata": {
        "trusted": true
      },
      "cell_type": "code",
      "source": "def plot_traj(traj, mode='-', ax=None, label=None):\n    tr = traj.reshape(-1, 1, 2)\n    for i in range(1):\n        if ax is None:\n            plt.plot(tr[:, i, 0], tr[:, i, 1], mode, label=label)\n        else:\n            ax.plot(tr[:, i, 0], tr[:, i, 1], mode, label=label)",
      "execution_count": 129,
      "outputs": []
    },
    {
      "metadata": {
        "trusted": true
      },
      "cell_type": "code",
      "source": "def extended_predict(extended_input_data):\n    forcing_inputs = extended_input_data[:, :input_data.shape[1] - 1, :]\n    recurrent_outputs, state = recurrent(inputs)\n    recurrent_outputs = recurrent_dense(recurrent_outputs)\n\n    model_with_state = Model(inputs, [recurrent_outputs, state])\n    forcing_predictions, current_state = model_with_state.predict(\n        forcing_inputs)\n    \n    timestep_input = Input(shape=(1, 2))\n    state_input = Input(shape=(latent_dim,))\n    \n    recurrent_outputs, recurrent_state = recurrent(timestep_input, \n                                                   initial_state=state_input)\n    recurrent_outputs = recurrent_dense(recurrent_outputs)\n\n    next_timestep_model = Model([timestep_input, state_input],\n                                [recurrent_outputs, recurrent_state])\n\n   \n    extended_predictions = np.zeros(shape=(extended_input_data.shape[0],\n                                           extended_input_data.shape[1] - \n                                               input_data.shape[1],\n                                           extended_input_data.shape[2]))\n    prediction = extended_input_data[:, \n                                     input_data.shape[1] - 1:\n                                         input_data.shape[1], \n                                     :]\n    for i in range(extended_predictions.shape[1]):\n        prediction, current_state = next_timestep_model.predict(\n            [prediction, current_state])\n        extended_predictions[:, i, :] = prediction[:, 0, :]\n    return forcing_predictions, extended_predictions",
      "execution_count": 130,
      "outputs": []
    },
    {
      "metadata": {
        "trusted": true
      },
      "cell_type": "code",
      "source": "fig = plt.figure(figsize=(12, 12))\nax = fig.add_subplot(111)\ndef draw(theta, ax):\n    ax.set_xlim(-1, 2)\n    ax.set_ylim(-1, 2)\n    test_input_data = get_data(\n        1, timesteps * 2, x0=np.array([[0.5, 0.5]]), phi0 = np.array([theta]))\n    prediction, extended_predictions = extended_predict(test_input_data)\n    \n    plot_traj(test_input_data[0], mode='o-', label=\"Ground truth\", ax=ax)\n    plot_traj(prediction[0, :], mode='o-', label='Prediction', ax=ax)\n    plot_traj(extended_predictions[0, :], mode='o-', \n              label='Extended prediction', ax=ax)\n    \n    plt.legend()\ndraw(0, ax)",
      "execution_count": 131,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": "<matplotlib.figure.Figure at 0x177fb6a20>",
            "image/png": 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krrvuyt13351NN920V/t55ZVXcuyxx2bKlCnZe++989xzz2X99dfPBRdckGnTpuXiiy9OsijgX3XaaaflxBNPzIknnpjLL788p59+eq677rokyZw5c3Lrrbfm3nvvzaRJk3L00Ucv97XqC2IaAFgnLR3SK5q+sno6zePggw/Od77znXziE5/IL3/5y27X/dGPfpQ777wze++9d5JFYf76178+STJs2LAcccQRSZK99torP/zhD5Mkt912W6655pokyQc/+MH89V8viv0bb7wxN954Y/bcc88kyQsvvJAHHnggzz//fN797ndn/fXXT5Llnj5xzDHHZNCgQdlxxx2zww475N577+36WTbddNNe7+e+++7LqFGjun7ejTbaqMexvOq//uu/cu2113b9vGeddVbXvKOOOiqDBg3KLrvs0nXkfnUT0wDAa9KKjiAfcvUhmfPinGWmjxo5Kv9y2L/0+XgWLlyYGTNmZP3118/TTz+dbbbZZpllaq058cQT8/nPf36ZeUOHDk0pJcmiDzl2dHR0zXt1+tLbOuecc/KRj3xkien/8A//sNJjXnq7rz4fOXJkn+6nr6y33npdj2uta2SfzpkGANZJZ4w/I8MHD19i2vDBw3PG+DNWy/6+8IUvZOedd843vvGNnHzyyZk/f36SRZH86uODDjooV199dZ544okkyR/+8Ic88sgjy93u/vvvn29961tJkquuuqpr+qGHHprLL788L7zwQpJk9uzZeeKJJ3LAAQfkuuuuy7x58/L888/ne9/7Xo/b/s53vpOFCxfmoYceysMPP5wxY8Yss0xv9jNmzJjMmTMnd9xxR5Lk+eefT0dHRzbccMM8//zz3Y5pv/32W+Lnfetb37rcP5/VzZFpAGCd9OpVO/r6ah5LnzN92GGH5eSTT85ll12W22+/PRtuuGEOOOCAfOYzn8mnP/3pnHLKKRk7dmzGjx+fq666Kp/5zGdyyCGHZOHChRk6dGguueSSjB49usf9ffGLX8z73//+XHjhhTnyyCO7ph9yyCGZMWNG9t133ySLPsD49a9/PePHj8+xxx6bPfbYI69//eu7TrHoznbbbZeJEyfmueeey1e/+tUMHz58mWV6s59hw4ZlypQpOe200zJv3ryMGDEiN910U97xjndk8uTJGTduXM4555wl1vnHf/zHnHzyybnooouyxRZb5F/+pe//FWFVlDV1CHxVTZgwoU6bNq2/hwEADCAzZszIzjvv3N/DeE046aSTcsQRR6yRD/GtSd39HSml3FlrndCyPad5AABAI6d5AACwjMUvR0fPHJkGAF5T1tZTWOl/q+PvhpgGAF4zhg8fnqeeekpQs4xaa5566qluP0TZG07zAABeM7bZZpvMmjUrc+fO7e+hsBYaPnx4t9f37g0xDQC8ZgwdOjTbb799fw+DdYjTPAAAoJGYBgCARmIaAAAaiWkAAGgkpgEAoJGYBgCARmIaAAAaiWkAAGgkpgEAoJGYBgCARmIaAAAaiWkAAGgkpgEAoJGYBgCARmIaAAAaiWkAAGgkpgEAoJGYBgCARmIaAAAaiWkAAGgkpgEAoJGYBgCARmIaAAAaiWkAAGgkpgEAoJGYBgCARmIaAAAaiWkAAGgkpgEAoJGYBgCARmIaAAAaiWkAAGgkpgEAoJGYBgCARmIaAAAaiWkAAGgkpgEAoJGYBgCARmIaAAAaiWkAAGgkpgEAoJGYBgCARmIaAAAaiWkAAGgkpgEAoJGYBgCARmIaAAAaiWkAAGgkpgEAoJGYBgCARmIaAAAa9UlMl1IuL6U8UUr5dQ/z315KebaUMr3z69y+2C8AAPSnIX20nSuSXJzkX5ezzE9rrUf00f4AAKDf9cmR6VrrLUn+0BfbAgCAgWJNnjO9bynll6WU75dSdu1ugVLKKaWUaaWUaXPnzl2DQwMAgFW3pmL6riSja617JPnHJNd1t1Ct9dJa64Ra64QttthiDQ0NAADarJGYrrU+V2t9ofPxDUmGllI2XxP7BgCA1WWNxHQpZctSSul8PLFzv0+tiX0DAMDq0idX8yilfDPJ25NsXkqZleS8JEOTpNb61SRHJ/lYKaUjybwk76u11r7YNwAA9Jc+iela63ErmH9xFl06DwAAXjPcAREAABqJaQAAaCSmAQCgkZgGAIBGYhoAABqJaQAAaCSmAQCgkZgGAIBGYhoAABqJaQAAaCSmAQCgkZgGAIBGYhoAABqJaQAAaCSmAQCgkZgGAIBGYhoAABqJaQAAaCSmAQCgkZgGAIBGYhoAABqJaQAAaCSmAQCgkZgGAIBGYhoAABqJaQAAaCSmAQCgkZgGAIBGYhoAABqJaQAAaCSmAQCgkZgGAIBGYhoAABqJaQAAaCSmAQCgkZgGAIBGYhoAABqJaQAAaCSmAQCgkZgGAIBGYhoAABqJaQAAaCSmAQCgkZgGAIBGYhoAABqJaQAAaCSmAQCgkZgGAIBGYhoAABqJaQAAaCSmAQCgkZgGAIBGYhoAABqJaQAAaCSmAQCgkZgGAIBGYhoAABqJaQAAaCSmAQCgkZgGAIBGYhoAABqJaQAAaCSmAQCgkZgGAIBGYhoAABqJaQAAaCSmAQCgkZgGAIBGYhoAABqJaQAAaCSmAQCgkZgGAIBGYhoAABqJaQAAaCSmAQCgkZgGAIBGYhoAABqJaQAAaCSmAQCgkZgGAIBGYhoAABqJaQAAaCSmAQCgkZgGAIBGYhoAABqJaQAAaCSmAQCgkZgGAIBGYhoAABqJaQAAaCSmAQCgkZgGAIBGYhoAABqJaQAAaCSmAQCgkZgGAIBGYhoAABqJaQAAaCSmAQCgkZgGAIBGfRLTpZTLSylPlFJ+3cP8Ukr5UinlwVLK3aWU8X2xXwAA6E99dWT6iiSHLWf+O5Ps2Pl1SpKv9NF+AQCg3/RJTNdab0nyh+UscmSSf62L/DzJJqWUUX2xbwAA6C9r6pzprZM8utjzWZ3TllBKOaWUMq2UMm3u3LlraGgAANBmrfoAYq310lrrhFrrhC222KK/hwMAAMu1pmJ6dpJtF3u+Tec0AAAYsNZUTE9NckLnVT32SfJsrXXOGto3AACsFkP6YiOllG8meXuSzUsps5Kcl2RoktRav5rkhiTvSvJgkj8mObkv9gsAAP2pT2K61nrcCubXJJ/oi30BAMDaYq36ACIAAAwkYhoAABqJaQAAaCSmAQCgkZgGAIBGYhoAABqJaQAAaCSmAQCgkZgGAIBGYhoAABqJaQAAaCSmAQCgkZgGAIBGYhoAABqJaQAAaCSmAQCgkZgGAIBGYhoAABqJaQAAaCSmAQCgkZgGAIBGYhoAABqJaQAAaCSmAQCgkZgGAIBGYhoAABqJaQAAaCSmAQCgkZgGAIBGYhoAABqJaQAAaCSmAQCgkZgGAIBGYhoAABqJaQAAaCSmAQCgkZgGAIBGYhoAABqJaQAAaCSmAQCgkZgGAIBGYhoAABqJaQAAaCSmAQCgkZgGAIBGYhoAABqJaQAAaCSmAQCgkZgGAIBGYhoAABqJaQAAaCSmAQCgkZgGAIBGYhoAABqJaQAAaCSmAQCgkZgGAIBGYhoAABqJaQAAaCSmAQCgkZgGAIBGYhoAABqJaQAAaCSmAQCgkZgGAIBGYhoAABqJaQAAaCSmAQCgkZgGAIBGYhoAABqJaQAAaCSmAQCgkZgGAIBGYhoAABqJaQAAaCSmAQCgkZgGAIBGYhoAABqJaQAAaCSmAQCgkZgGAIBGYhoAABqJaQAAaCSmAQCgkZgGAIBGYhoAABqJaQAAaCSmAQCgkZgGAIBGYhoAABqJaQAAaCSmAQCgkZgGAIBGYhoAABqJaQAAaCSmAQCgkZgGAIBGYhoAABqJaQAAaNQnMV1KOayUcl8p5cFSytndzD+plDK3lDK98+tDfbFfAADoT0N6u4FSyuAklyQ5OMmsJHeUUqbWWu9ZatEptdZTe7s/AJZ1x9R/yrZ3XZTX17l5omyRR8efmb0nfSRJct0vZmf69ZfmQ698PVsNeiovjdgy67/zgmTsMT3Ou27B/rnoB/fl98/My1abjMiZh47JUXtu3bW9V+eduMHtOWvolKw/77Fk421yx5+clr+8Z8dl1lt8neVtry/m2d7/rAOsfqXW2rsNlLJvkvNrrYd2Pj8nSWqtn19smZOSTFiVmJ4wYUKdNm1ar8YGsC64Y+o/Zbc7P5UR5ZWuafPqsPx6r89k9jaH57+uuyTnl8uWmN8xeHh+sccFmTLtd7mgXJr1F5v3Slkvf7Pgw7n6lf2SJJMG3Zq/HvrtbFWeyrwRW+bcF/88V7+yXyYNujWTh162xLrz6rD89fwPZerCtyyx3u/rZrlw/jGZuvAtSZIRQwfnX/d+JLvO+EKG//Gx/L5ulr/tWDS/N/Mm7v7b3PncN5Ihz6TO3yQvzz00Q+dNyOffs3uS5Jxrf5V58xd0jXfE0MHLnffne22da+6cvUrrrC3bE9Sw8kopd9ZaJzSt2wcxfXSSw2qtH+p8/sEkf7p4OHfG9OeTzE1yf5L/XWt9dHnbFdMAK+ex89+ULTN3mekLa1JTMrh0/3v+5TokCzI465eXl5k3t26Uj77yv7PPoN/ktCH/luFlfte8l+rQ/GPHkTlxyA/z+vJsN+tunG90vCMfGXL9Mut9qeOo3LxwrxwwaHr+vyHXLDF/Xh2az81/fxZmUD419Kpl/ufgU/NPysIMyueGXr7EvD/WYTl7/odywwYjM3zUtSmD/mebdeHQvDTnPRkyqGTI5v+xRGR3PLdnkmTY4EVnPL6yYGG3f07dWd46a8P2tt5kRG47+8CVXh7WdQMhpjdL8kKt9eVSykeSHFtrXeZdXko5JckpSbLddtvt9cgjj/RqbADrgoXnbZxBZdnptSYXLzgqpw6+LqWH+Um6nTfQzFq4eQ7ddqsMGvbMMvMWdqyXMmhht5H9alC/1pQkv518eH8PAwaM3sR0X3wAcXaSbRd7vk3ntC611qdqra8e+rgsyV7dbajWemmtdUKtdcIWW2zRB0MDeO17onT/+/LxskW+tcGJmV0373F+T/Pm1o1z/CvnpKfjLbUmT9aNelh3oyxcznoffeUvl7vdlnlbladShi4b0kkyaMjLS4R0kpRB87PeFj9Ikmyx5W+y0Y4XZoOdzs7IP5mcIRv9omu5wT38n8bWm4zI1puMWOV5a2p7W/WwPND3+iKm70iyYyll+1LKsCTvSzJ18QVKKaMWezopyYw+2C8ASR4df2bm1WFLTJtXh+XR8WfmzEPH5B/yvvxxqfkdg4fn0fFndjvvlbJeLqwfzK0Ld+8xtmfXzXPB/OOXWXdeHZb/O//4/H456/3Hwon5fXqe3zLv93WzpGOTbuf1FOBl6DMZOWpqOjadkjrk6ZSSDBr2TIaPujZDNvpFRgwdnOP+dNuMGDp4ifVGDB2cMw8dkzMPHbPK89bk9oA1o9dX86i1dpRSTk3ygySDk1xea/1NKeWCJNNqrVOTnF5KmZSkI8kfkpzU2/0CsMjekz6SO5LOq3k8mSfK5nl0r0VX89g7SfLx/O31Q5a5YsfeY4/J7G1ndzvvLQv2z3/94L5c9NwxmTzsaxmR/zmvumPw8Fw25Ph875WJ2XTosCWu5vHrPzktd96zYy56LsusNy/r5aKOY7L1JiPy+13Oyta/Oi+ZP69r/h/rsFw27PgcPnarpnnv3eFN+ffffykvLXjpf/5wFg7NyKEj8scFzy3z51ZSUjb5WTqWiu0yaH7Wf8ON+fPtR+e2P/x9hrzpsWzUsUnmPX5IXj9ov2WulrG8K2l0N2/C6E1XeZ3ebA9YvXp9zvTq4gOIAGuJu7+d/OiC5NlZycbbJAedm4w9pvfrLW9+47zrH74+X7zri3nsxcey5cgtc8b4M5Ik5//s/CUie/jg4fk/+/yffPK2T/Y4/KGDhmb+wvlLrHP+fufn8B2ciwyvNf36AcTVRUwD0Fe6i+zDdzg8h1x9SOa8OGeltzNq5KjcePSNy90mMPCIaQBocP3D13d71HqJU0WW8t4kP+4jAAARDklEQVQ3vzfrD1k/U+6bssx6jlzDwNTfV/MAgAHp8B0Oz/n7nZ9RI0elpGTUyFFdz7szfPDwXP/w9bnyniuXCe6XFryUL971xTUxbGAt0usPIALAQHb4Dod3ezS5uyPW5+93fg4efXD2+nq3V3jNnBfn5OFnHs49T92TL/3iS04BgXWAmAaApbwavj2dEz1q5Kgez7U+8t+OTElJzaLTKOe8OCfn/+z8JbYLvHY4ZxoAVlFP51r/5V5/ma9M/0qefWXZ26y/br3X5cajb8zwIcO7tuEDjLB26M05045MA8AqWt6R6wtvv7DbdZ5++ekcMOWA7L/V/nnd8Ndl6kNT8/KCRdfhdvQaBi4xDQANejrXesuRW3Z7CsimwzfNwaMPzo9/9+M8Me+JZea/+gFGMQ0Di6t5AEAfOmP8GRk+ePgS04YPHp6z9j4rn9rnU/nhe3/Y47pzXpyT+5++P6+egnn9w9fnkKsPydgrx+aQqw/J9Q9fv1rHDqw6R6YBoA+t6MOLg8qg5X6A8c+n/nm22WCbvHGjN+b2x27PKwtfSeJUEFhb+QAiAKxhPX2A8a8m/FWGDBqSm393c346+6fdrrv4XRiBvuEDiAAwgKzo6PXRbz46Y68c23V5vcXNeXFOvvvAd/O2bd+WTYdv6qog0M8cmQaAtdAhVx/S7akgg8qgLKwLU1Ky3YbbZfYLs9NRO7rmu605rDq3EweA15iePsj42f0/m28f8e18dI+PZvaLS4Z04rbmsKaJaQBYCx2+w+E5f7/zM2rkqJSUjBo5Kufvd36O+JMjsvNmO+fj4z6eBQsXdLvunBfn5JO3fjI3zrwxL85/MYkrg8Dq4jQPABigejoVZMSQERk6aGiee+W5DBk0JNtvtH1++9xv07HQ6SDQHad5AMA6qKdTQc7b97z857H/mX859F9y/M7H5+FnH14ipBOng0BfcTUPABigVnRVkAlbTsiELSfkyt9c2e36j7342BobK7xWiWkAGMB6uq354nq6xfmWI7dcXcOCdYbTPADgNa6n00HOGH9GP40IXjscmQaA17gVnQ4CtBPTALAOWJnTQYBV5zQPAABoJKYBAKCRmAYAgEZiGgAAGolpAABoJKYBAKCRmAYAgEZiGgAAGolpAABoJKYBAKCRmAYAgEZiGgAAGolpAABoJKYBAKCRmAYAgEZiGgAAGolpAABoJKYBAKCRmAYAgEZiGgAAGolpAABoJKYBAKCRmAYAgEZiGgAAGolpAABoJKYBAKCRmAYAgEZiGgAAGolpAABoJKYBAKCRmAYAgEZiGgAAGolpAABoJKYBAKCRmAYAgEZiGgAAGolpAABoJKYBAKCRmAYAgEZiGgAAGolpAABoJKYBAKCRmAYAgEZiGgAAGolpAABoJKYBAKCRmAYAgEZiGgAAGolpAABoJKYBAKCRmAYAgEZiGgAAGolpAABoJKYBAKCRmAYAgEZiGgAAGolpAABoJKYBAKCRmAYAgEZiGgAAGolpAABoJKYBAKCRmAYAgEZiGgAAGolpAABoJKYBAKCRmAYAgEZiGgAAGolpAABoJKYBAKCRmAYAgEZiGgAAGolpAABoJKYBAKCRmAYAgEZiGgAAGolpAABoJKYBAKBRn8R0KeWwUsp9pZQHSylndzN/vVLKlM75/11KeWNf7BcAAPpTr2O6lDI4ySVJ3plklyTHlVJ2WWqxv0jydK31TUm+kOTC3u4XAAD6W18cmZ6Y5MFa68O11leSfCvJkUstc2SSKzsfX53koFJK6YN9AwBAv+mLmN46yaOLPZ/VOa3bZWqtHUmeTbLZ0hsqpZxSSplWSpk2d+7cPhgaAACsPmvVBxBrrZfWWifUWidsscUW/T0cAABYrr6I6dlJtl3s+Tad07pdppQyJMnGSZ7qg30DAEC/6YuYviPJjqWU7Uspw5K8L8nUpZaZmuTEzsdHJ7m51lr7YN8AANBvhvR2A7XWjlLKqUl+kGRwkstrrb8ppVyQZFqtdWqSryX5f6WUB5P8IYuCGwAABrRex3SS1FpvSHLDUtPOXezxS0ne2xf7AgCAtcVa9QFEAAAYSMQ0AAA0EtMAANBITAMAQCMxDQAAjcQ0AAA0EtMAANBITAMAQCMxDQAAjcQ0AAA0EtMAANBITAMAQCMxDQAAjcQ0AAA0EtMAANBITAMAQCMxDQAAjcQ0AAA0EtMAANBITAMAQCMxDQAAjcQ0AAA0EtMAANBITAMAQCMxDQAAjcQ0AAA0EtMAANBITAMAQCMxDQAAjcQ0AAA0EtMAANBITAMAQCMxDQAAjcQ0AAA0EtMAANBITAMAQCMxDQAAjcQ0AAA0EtMAANBITAMAQCMxDQAAjcQ0AAA0EtMAANBITAMAQCMxDQAAjcQ0AAA0EtMAANBITAMAQCMxDQAAjcQ0AAA0EtMAANBITAMAQCMxDQAAjcQ0AAA0EtMAANBITAMAQCMxDQAAjcQ0AAA0EtMAANBITAMAQCMxDQAAjcQ0AAA0EtMAANBITAMAQCMxDQAAjcQ0AAA0EtMAANBITAMAQCMxDQAAjcQ0AAA0EtMAANBITAMAQCMxDQAAjcQ0AAA0EtMAANBITAMAQCMxDQAAjcQ0AAA0EtMAANBITAMAQCMxDQAAjcQ0AAA0EtMAANBITAMAQCMxDQAAjcQ0AAA0EtMAANBITAMAQCMxDQAAjcQ0AAA0EtMAANBITAMAQCMxDQAAjcQ0AAA0EtMAANBITAMAQCMxDQAAjcQ0AAA0EtMAANBITAMAQKNexXQpZdNSyg9LKQ90fn9dD8stKKVM7/ya2pt9AgDA2qK3R6bPTvKjWuuOSX7U+bw782qt4zq/JvVynwAAsFbobUwfmeTKzsdXJjmql9sDAIABo7cx/YZa65zOx48leUMPyw0vpUwrpfy8lNJjcJdSTulcbtrcuXN7OTQAAFi9hqxogVLKTUm27GbWJxd/UmutpZTaw2ZG11pnl1J2SHJzKeVXtdaHll6o1nppkkuTZMKECT1tCwAA1gorjOla65/1NK+U8ngpZVStdU4pZVSSJ3rYxuzO7w+XUn6SZM8ky8Q0AAAMJL09zWNqkhM7H5+Y5N+WXqCU8rpSynqdjzdPsn+Se3q5XwAA6He9jenJSQ4upTyQ5M86n6eUMqGUclnnMjsnmVZK+WWSHyeZXGsV0wAADHgrPM1jeWqtTyU5qJvp05J8qPPxz5Ls3pv9AADA2sgdEAEAoJGYBgCARmIaAAAaiWkAAGgkpgEAoJGYBgCARmIaAAAaiWkAAGgkpgEAoJGYBgCARmIaAAAaiWkAAGgkpgEAoJGYBgCARmIaAAAaiWkAAGgkpgEAoJGYBgCARmIaAAAaiWkAAGgkpgEAoJGYBgCARmIaAAAaiWkAAGgkpgEAoJGYBgCARmIaAAAaiWkAAGgkpgEAoJGYBgCARmIaAAAaiWkAAGgkpgEAoJGYBgCARmIaAAAaiWkAAGgkpgEAoJGYBgCARmIaAAAaiWkAAGgkpgEAoJGYBgCARmIaAAAaiWkAAGgkpgEAoJGYBgCARmIaAAAaiWkAAGgkpgEAoJGYBgCARmIaAAAaiWkAAGgkpgEAoJGYBgCARmIaAAAaiWkAAGgkpgEAoJGYBgCARmIaAAAaiWkAAGgkpgEAoJGYBgCARmIaAAAaiWkAAGgkpgEAoJGYBgCARmIaAAAaiWkAAGgkpgEAoJGYBgCARmIaAAAaiWkAAGgkpgEAoJGYBgCARmIaAAAaiWkAAGgkpgEAoJGYBgCARmIaAAAaiWkAAGgkpgEAoJGYBgCARmIaAAAaiWkAAGgkpgEAoJGYBgCARmIaAAAaiWkAAGgkpgEAoJGYBgCARmIaAAAaiWkAAGgkpgEAoJGYBgCARmIaAAAaiWkAAGgkpgEAoJGYBgCARmIaAAAaiWkAAGjUq5gupby3lPKbUsrCUsqE5Sx3WCnlvlLKg6WUs3uzTwAAWFv09sj0r5O8J8ktPS1QShmc5JIk70yyS5LjSim79HK/AADQ74b0ZuVa64wkKaUsb7GJSR6stT7cuey3khyZ5J7e7BsAAPpbr2J6JW2d5NHFns9K8qfdLVhKOSXJKZ1PXy6l/Ho1j43VZ/MkT/b3IGjm9Ru4vHYDm9dv4PLaDWxjWldcYUyXUm5KsmU3sz5Za/231h13p9Z6aZJLO/c7rdba43nYrN28fgOb12/g8toNbF6/gctrN7CVUqa1rrvCmK61/lnrxjvNTrLtYs+36ZwGAAAD2pq4NN4dSXYspWxfShmW5H1Jpq6B/QIAwGrV20vjvbuUMivJvkmuL6X8oHP6VqWUG5Kk1tqR5NQkP0gyI8m3a62/WYnNX9qbsdHvvH4Dm9dv4PLaDWxev4HLazewNb9+pdbalwMBAIB1hjsgAgBAIzENAACN1pqYdmvyga2Usmkp5YellAc6v7+uh+UWlFKmd375IGo/WtF7qZSyXillSuf8/y6lvHHNj5KerMTrd1IpZe5i77cP9cc4WVYp5fJSyhM93UuhLPKlztf27lLK+DU9Rnq2Eq/f20spzy723jt3TY+R7pVSti2l/LiUck9nc57RzTKr/P5ba2I6bk0+0J2d5Ee11h2T/KjzeXfm1VrHdX5NWnPDY3Er+V76iyRP11rflOQLSS5cs6OkJ6vwu3DKYu+3y9boIFmeK5Ictpz570yyY+fXKUm+sgbGxMq7Ist//ZLkp4u99y5YA2Ni5XQk+ata6y5J9knyiW5+d67y+2+tiela64xa630rWKzr1uS11leSvHprcvrfkUmu7Hx8ZZKj+nEsrNjKvJcWf02vTnJQKaWswTHSM78LB7Ba6y1J/rCcRY5M8q91kZ8n2aSUMmrNjI4VWYnXj7VUrXVOrfWuzsfPZ9FV5rZearFVfv+tNTG9krq7NfnSfwj0jzfUWud0Pn4syRt6WG54KWVaKeXnpRTB3X9W5r3UtUznJS6fTbLZGhkdK7Kyvwv/vPOfKa8upWzbzXzWTv5bN/DtW0r5ZSnl+6WUXft7MCyr89TFPZP891KzVvn9t8I7IPalNXlrcvre8l6/xZ/UWmsppadrLo6utc4upeyQ5OZSyq9qrQ/19ViBfC/JN2utL5dSPpJF/8pwYD+PCdYFd2XRf+teKKW8K8l1WXTKAGuJUsoGSa5J8pe11ud6u701GtNuTT6wLe/1K6U8XkoZVWud0/nPIU/0sI3Znd8fLqX8JIv+r1BMr3kr8156dZlZpZQhSTZO8tSaGR4rsMLXr9a6+Gt1WZK/XQPjom/4b90Atnic1VpvKKV8uZSyea31yf4cF4uUUoZmUUhfVWu9tptFVvn9N9BO83Br8rXX1CQndj4+Mcky/9JQSnldKWW9zsebJ9k/yT1rbIQsbmXeS4u/pkcnubm6y9PaYoWv31Ln+E3KonMDGRimJjmh86oC+yR5drHT6FjLlVK2fPXzJaWUiVnUWg5ErAU6X5evJZlRa/37HhZb5fffGj0yvTyllHcn+cckW2TRrcmn11oPLaVsleSyWuu7aq0dpZRXb00+OMnlK3lrcla/yUm+XUr5iySPJDkmScqiyxx+tNb6oSQ7J/mnUsrCLPrlMrnWKqb7QU/vpVLKBUmm1VqnZtEvnP9XSnkwiz5s877+GzGLW8nX7/RSyqQs+vT6H5Kc1G8DZgmllG8meXuSzUsps5Kcl2RoktRav5rkhiTvSvJgkj8mObl/Rkp3VuL1OzrJx0opHUnmJXmfAxFrjf2TfDDJr0op0zun/U2S7ZL295/biQMAQKOBdpoHAACsNcQ0AAA0EtMAANBITAMAQCMxDQAAjcQ0AAA0EtMAANDo/we2MI8mM0VClwAAAABJRU5ErkJggg==\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "metadata": {
        "trusted": true
      },
      "cell_type": "code",
      "source": "import matplotlib.animation as animation\nfrom IPython.display import HTML\n\ndef show_ani():\n    \"\"\"\n    Shows an animation of trajectories for rotating angle\n    \"\"\"\n    frames = 30\n    \n    def ani_frame():\n        fig = plt.figure(figsize=(12, 12))\n        ax = fig.add_subplot(111)\n        draw(0, ax)\n\n        def update_img(n):\n            print(f\"{n} \", end=\"\")\n            ax.clear()\n            draw(np.linspace(0, 2 * np.pi, frames)[n], ax=ax)\n            return ax\n\n        ani = animation.FuncAnimation(fig, update_img, frames,\n                                      interval=100)\n        writer = animation.writers['ffmpeg'](fps=30)\n\n        return ani\n\n    ani = ani_frame()\n    return HTML(ani.to_html5_video())\nshow_ani()",
      "execution_count": 132,
      "outputs": [
        {
          "output_type": "stream",
          "text": "0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 ",
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "execution_count": 132,
          "data": {
            "text/plain": "<IPython.core.display.HTML object>",
            "text/html": "<video width=\"864\" height=\"864\" controls autoplay loop>\n  <source type=\"video/mp4\" 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AqNGDJ3ayF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\nkLk5sT6MjOG/MoTCKrmE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          "metadata": {}
        },
        {
          "output_type": "stream",
          "text": "0 ",
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": "<matplotlib.figure.Figure at 0x176fa0a90>",
            "image/png": 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\n"
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