jsl/demos/kalman_sampling_demo.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "kalman_sampling_demo.ipynb",
      "provenance": [],
      "authorship_tag": "ABX9TyOE8KcrgH4deVIsLeCZbWHr",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/probml/JSL/blob/main/jsl/demos/kalman_sampling_demo.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "UTJlEmKF1nzK",
        "outputId": "18593147-266f-44e5-cb62-75e318ce728f"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Collecting git+https://github.com/google/flax.git\n",
            "  Cloning https://github.com/google/flax.git to /tmp/pip-req-build-0hwmt6g7\n",
            "  Running command git clone -q https://github.com/google/flax.git /tmp/pip-req-build-0hwmt6g7\n",
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            "Collecting optax\n",
            "  Downloading optax-0.1.2-py3-none-any.whl (140 kB)\n",
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            "Collecting chex>=0.0.4\n",
            "  Downloading chex-0.1.3-py3-none-any.whl (72 kB)\n",
            "\u001b[K     |████████████████████████████████| 72 kB 652 kB/s \n",
            "\u001b[?25hRequirement already satisfied: jaxlib>=0.1.37 in /usr/local/lib/python3.7/dist-packages (from optax->flax==0.4.1) (0.3.2+cuda11.cudnn805)\n",
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            "Building wheels for collected packages: flax\n",
            "  Building wheel for flax (setup.py) ... \u001b[?25l\u001b[?25hdone\n",
            "  Created wheel for flax: filename=flax-0.4.1-py3-none-any.whl size=186136 sha256=d5342ce8fc05dd73f0d01481e21ff3a682569ac0590c7d85a087d7e2d9c4b1e0\n",
            "  Stored in directory: /tmp/pip-ephem-wheel-cache-wxzz5v1l/wheels/3e/9e/df/f792f5b2c0d0ccf00f3c1286bc060dab7cb2a4af5134d1c5b4\n",
            "Successfully built flax\n",
            "Installing collected packages: chex, optax, flax\n",
            "Successfully installed chex-0.1.3 flax-0.4.1 optax-0.1.2\n",
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            "Collecting git+https://github.com/blackjax-devs/blackjax.git\n",
            "  Cloning https://github.com/blackjax-devs/blackjax.git to /tmp/pip-req-build-oti4y44s\n",
            "  Running command git clone -q https://github.com/blackjax-devs/blackjax.git /tmp/pip-req-build-oti4y44s\n",
            "Requirement already satisfied: fastprogress>=0.2.0 in /usr/local/lib/python3.7/dist-packages (from blackjax==0.4.0) (1.0.2)\n",
            "Building wheels for collected packages: blackjax\n",
            "  Building wheel for blackjax (setup.py) ... \u001b[?25l\u001b[?25hdone\n",
            "  Created wheel for blackjax: filename=blackjax-0.4.0-py3-none-any.whl size=77597 sha256=4799295243baf5fd17b8c418402030f792e6fa602de320d7853a3c665ed35298\n",
            "  Stored in directory: /tmp/pip-ephem-wheel-cache-1o74sggy/wheels/8f/53/91/7460390e5f6442104728ae1c475ad03edb990afe2c5924eee7\n",
            "Successfully built blackjax\n",
            "Installing collected packages: blackjax\n",
            "Successfully installed blackjax-0.4.0\n",
            "Collecting git+https://github.com/deepmind/distrax.git\n",
            "  Cloning https://github.com/deepmind/distrax.git to /tmp/pip-req-build-rp8u5yfl\n",
            "  Running command git clone -q https://github.com/deepmind/distrax.git /tmp/pip-req-build-rp8u5yfl\n",
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            "Requirement already satisfied: numpy>=1.18.0 in /usr/local/lib/python3.7/dist-packages (from distrax==0.1.2) (1.21.6)\n",
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            "Requirement already satisfied: decorator in /usr/local/lib/python3.7/dist-packages (from tensorflow-probability>=0.15.0->distrax==0.1.2) (4.4.2)\n",
            "Building wheels for collected packages: distrax\n",
            "  Building wheel for distrax (setup.py) ... \u001b[?25l\u001b[?25hdone\n",
            "  Created wheel for distrax: filename=distrax-0.1.2-py3-none-any.whl size=285458 sha256=10254e80c4d8163b6ad3fdf771427dcc7a04cf41d822e9932a4f63bd6e1bbad3\n",
            "  Stored in directory: /tmp/pip-ephem-wheel-cache-ctz_o38h/wheels/34/f4/34/7d0bc13db0a98b0f2da8d8254a04d4d2ff1076bfe495cfb34e\n",
            "Successfully built distrax\n",
            "Installing collected packages: distrax\n",
            "Successfully installed distrax-0.1.2\n"
          ]
        }
      ],
      "source": [
        "!pip install --upgrade git+https://github.com/google/flax.git\n",
        "!pip install --upgrade tensorflow-probability\n",
        "!pip install git+https://github.com/blackjax-devs/blackjax.git\n",
        "!pip install git+https://github.com/deepmind/distrax.git\n",
        "\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "!git clone https://github.com/probml/JSL.git\n",
        "%cd JSL\n",
        "!pip install -e ."
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 735
        },
        "id": "y9apNUFE1zlT",
        "outputId": "c365b1c5-80f7-4425-f734-3cfb5066bbc9"
      },
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
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            "/content/JSL\n",
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            "Requirement already satisfied: decorator in /usr/local/lib/python3.7/dist-packages (from tensorflow_probability->jsl==0.0.0) (4.4.2)\n",
            "Requirement already satisfied: gast>=0.3.2 in /usr/local/lib/python3.7/dist-packages (from tensorflow_probability->jsl==0.0.0) (0.5.3)\n",
            "Requirement already satisfied: cloudpickle>=1.3 in /usr/local/lib/python3.7/dist-packages (from tensorflow_probability->jsl==0.0.0) (1.3.0)\n",
            "Installing collected packages: dataclasses, jsl\n",
            "  Running setup.py develop for jsl\n",
            "Successfully installed dataclasses-0.6 jsl-0.0.0\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "application/vnd.colab-display-data+json": {
              "pip_warning": {
                "packages": [
                  "dataclasses"
                ]
              }
            }
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "%run jsl/demos/lds_sampling_demo.py\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 283
        },
        "id": "Oi7mlTau1z4U",
        "outputId": "87ab4291-a0a2-4918-e5ff-681cb4cb57a0"
      },
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "WARNING:absl:No GPU/TPU found, falling back to CPU. (Set TF_CPP_MIN_LOG_LEVEL=0 and rerun for more info.)\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "\n",
        "import jax   \n",
        "from cProfile import label\n",
        "import jax.numpy as jnp\n",
        "from jax.random import  PRNGKey\n",
        "import tensorflow_probability as tfp\n",
        "import tensorflow as tf\n",
        "tfd = tfp.distributions\n",
        "import matplotlib.pyplot  as plt\n",
        "\n",
        "from jsl.lds.kalman_filter import LDS, kalman_filter\n",
        "from jsl.lds.kalman_sampler import smooth_sampler\n"
      ],
      "metadata": {
        "id": "fG-w-qflAvub"
      },
      "execution_count": 19,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# tensorflow_probability\n",
        "ndims = 1\n",
        "step_std = 1.0\n",
        "noise_std = 5.0\n",
        "model = tfd.LinearGaussianStateSpaceModel(\n",
        "  num_timesteps=100,\n",
        "  transition_matrix=tf.linalg.LinearOperatorDiag(jnp.array([1.01])),\n",
        "  transition_noise=tfd.MultivariateNormalDiag(\n",
        "   scale_diag=step_std * tf.ones([ndims])),\n",
        "  observation_matrix=tf.linalg.LinearOperatorIdentity(ndims),\n",
        "  observation_noise=tfd.MultivariateNormalDiag(\n",
        "   scale_diag=noise_std * tf.ones([ndims])),\n",
        "  initial_state_prior=tfd.MultivariateNormalDiag(loc=jnp.array([5.0]),\n",
        "   scale_diag=tf.ones([ndims])))\n",
        "\n",
        "# Sample 1 sequence from the prior of the LDS\n",
        "y = model.sample(seed=(1,2)) \n",
        "\n",
        "nsamples = 2000\n",
        "\n",
        "smps = model.posterior_sample(y, sample_shape=nsamples)\n",
        "s_tf = jnp.array(smps[:,:,0])\n",
        "\n",
        "mean_tf = jnp.mean(s_tf, axis=0)\n",
        "\n",
        "print(s_tf.shape)\n",
        "print(mean_tf.shape)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ek0l7w0WA1nO",
        "outputId": "30f68ae5-6661-4578-a40a-9a5ededd77fd"
      },
      "execution_count": 28,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "(2000, 100)\n",
            "(100,)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Define the same model as an LDS object defined in the kalman_filter file \n",
        "A = jnp.eye(1) * 1.01\n",
        "C = jnp.eye(1)\n",
        "Q = jnp.eye(1)\n",
        "R = jnp.eye(1) * 25.0\n",
        "mu0 = jnp.array([5.0])\n",
        "Sigma0 = jnp.eye(1)\n",
        "model_lds = LDS(A, C, Q, R, mu0, Sigma0)\n",
        "# Run the Kalman filter algorithm first\n",
        "mu_hist, Sigma_hist, mu_cond_hist, Sigma_cond_hist = kalman_filter(model_lds, jnp.array(y))\n",
        "# Sample backwards using the smoothing posterior\n",
        "smooth_sample = smooth_sampler(model_lds, PRNGKey(0), mu_hist, Sigma_hist, n_samples=nsamples)\n",
        "s_jax = smooth_sample[:,:,0]\n",
        "\n",
        "mean_jax = jnp.mean(s_jax, axis=0)\n",
        "\n",
        "print(s_jax.shape)\n",
        "print(mean_jax.shape)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "-MUd3UOABCxS",
        "outputId": "cb2e71ff-fc73-450a-9c22-8bb387f1f90f"
      },
      "execution_count": 29,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "(2000, 100)\n",
            "(100,)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "\n",
        "plt.figure()\n",
        "plt.plot(mean_tf, label='tf')\n",
        "plt.plot(mean_jax, label='jsl')\n",
        "plt.legend()\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "id": "5nTHzS4823NQ",
        "outputId": "25403f01-5252-46cf-a859-c6d9047afe3d"
      },
      "execution_count": 30,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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dPW12GiFEKyCF3IICe4+hq+0UO/fsMzuKEKIVkEJuQT7da5etK8+QfnIhhDFrdvoopTYrpXYqpdKUUk8ZEUxcQFQiFfYAOpzeSklFtdlphBAmM+KMvBIYp7XuDwwArlJKDTegXXE+NjtlUUMZqvaw5XCB2WmEECYzYs1OrbU+U/fQWfejm9quuLDA3mPoZsvmg5Vb5KxciDbOkD5ypZRdKbUDyAGWa603GdGuOD9n3CUA+GZv4vbXN5F/ptLkREIIsxhSyLXWLq31ACAGGKqUSvj+e5RS05VSKUqplNzcXCM227ZF9QO/MP7UbhGlpw4y+bUNnCgsNzuVEMIERi++XAh8DVx1jtdma62TtNZJERERRm62bbI74LYP8asu5MugPxJUfIBfzd9ldiohhAmMGLUSoZQKqfvdFxgPyADnltBpKNy1FC+b4kPnUxQd2MT+kyVmpxJCtDAjzsg7AF8rpXYBW6jtI//CgHZFfbSPh3u+wss3gKe93uGN9ZlmJxJCtDAjRq3s0loP1Fr301onaK3/YEQw0QDtYrEl/4z+6gD7t39DTkmF2YmEEC1I7uz0FP1vxW334WbbCt7bcMTsNEKIFiSF3FP4tsOWeCM3Or5l/oZ9MjOiEG2IFHJPknQ3PrqcMVWrmb8ty+w0QogWIoXck3QcjI5K5B6f1by66oCclQvRRkgh9yRKoZLuJs6VSWTxbmavlREsQrQFUsg9TeJk8ArgifB1zFp9kOwiudtTCE8nhdzTeAdC0l0MKVlJN32EPy+Ve7OE8HRSyD3RqEdQPkH8I/wzFu44IUvCCeHhpJB7Ir9QGPUIcYXfcJV/Bj//aAcZp+TWfSE8lRRyTzXsJxDUkb+2m09pRTXXv/INX6Zmm51KCNEMpJB7KqcvjH0S/7xdLB+fQ/f2gdz/3jZe+fqA2cmEEAaTQu7J+t8K7RNp9+UMFth+xcsdl/PBsm84kHPm4p8VQliGFHJPZrPDnZ/Blc9i8/JjUv5bfOz1B/6+bK/ZyYQQBpJC7un8w2DEDLhnGdz8LtEqj8o9i0k9XmR2MiGEQaSQtyW9JuIOjGaq1ypeWLbf7DRCCINIIW9L7A5sg6eSzE4Opqey5XCB2YmEEAYwYqm3Tkqpr5VSe5RSaUqpmUYEE81k0J1oZede3zX8flEaR/JLzU4khGgiI87Ia4BfaK3jgeHADKVUvAHtiuYQFI3qNYFbnWvJyivi8hfX8MfFeygqrzY7mRCikYxY6i1ba72t7vcSYC/QsantimY0+C68KwtYO+kMPxoYw5z1h7jsr2vkAqgQFmVoH7lSKhYYCGw6x2vTlVIpSqmU3NxcIzcrGqrbOAjpTPD21/jzxBg+f2gU3g4bt87eyLcH88xOJ4RoIMMKuVIqAJgPPKy1Lv7+61rr2VrrJK11UkREhFGbFY1hs8GYX0P2TvjnEBJylzD//hF0CPZh2ptb+DL1pNkJhRANYEghV0o5qS3i72utPzWiTdHMBtwGP1kDoV1h4f1ELZzMvB93IaFjEA+8v5V/rsrA7dZmpxRC1IMRo1YU8AawV2v9YtMjiRYTlQh3L4NrXoLj2wh+eywfjC3h2v7RvLAsnenvpshFUCEswIgz8mTgDmCcUmpH3c9EA9oVLcFmg6S7as/Og6Lx/ugWXgr9lGeu7sbq/blc/8o3FFdIMReiNTNi1Mp6rbXSWvfTWg+o+1liRDjRgsJ7wL0rYPBdqG//wZStk1l0+WkO5Z1h/tYss9MJIS5A7uwU/+P0hUkvwdTPwSuA+LUPMj/wReZtzEBr6S8XorWSQi5+qOto+Mk6uPwpBldvpW/BMrYcluXihGitpJCLc7M7IHkm7og+3OVczvsbD5udSAhxHlLIxfkphW3YdPpwmJNpaykorTI7kRDiHKSQiwtLvBmXVyC3qa+Yt/WY2WmEEOcghVxcmHcA9oFTuMa+maUbd8lNQqL5lBdC6qewe57ZSSzHYXYAYQFD7sWxaRbJRYvZfHg0w+PCzE4kPIjOXEPp8mfxy96CDRcAJTU2Agf+yORk1iFn5OLiwrvjih3DFMdKlqXKmHJhoKIsyt+7ncITB3jNdTV/CH+B3ToO26Kf4i44bHY6y5AzclEv9uHTiTp8OyW7v0RP6kftzAzCI5XmwernwFUFygY2J7SLhYheENkHgmOM2Y7bRd67d+HjqmFh4iymTBxDiJ8Xn63qQ+yam8h5awpRD38Ndud3P1dRBGX5EBpnTA4PIIVc1E/38VQ6gxhRsZa0E/eT0DHY7ESiuaz5CzrlTcqcodS43NhclQTyv5WkKsb9AZ/RTV8IrGTV3wjP28zLQQ/zwA2X47DXdhBcOzaZdw48xrQTfyDn/XuJ7NoPSk5B0TE4mQpFR2sb+PF86HF5k3N4AmXGHXtJSUk6JSWlxbcrmqbi0xnU7JzHG8OXMXNCf7PjiOZQfALXS/35uCqZJ2ruo3OoHz0iA6g+k4vX6QwmVy1ivH0rrsnv4uw7qXHb0Br3kQ24357ESj2YXg99SmxEwHfeUlpZw4oXpnBd9VIAquwBVPi1J4POrC1qz7WsoUOADb+Ht4CXf1P32jKUUlu11knff17OyEW9+fS/CXa9R+HuJSCF3CPVrPsbuF2siryDHfeOJ8TP6zuvL9h8NTu/uIW+8+5Fh3yJ6jiwfg273bB3Eez9HH3kG2wl2eTodhRf/vwPijiAv7eDgfe/ybPLN7DuWA1782ugFEL9vbhyQHtePzyQPxX/ipKvniZw0p+M2HVLkzNyUX+uGsr/3IOV5T2I/9mnxJ3jD1BYWPEJal7qzydVyXSaOodRPcLP+bbXFm/g6s1TCPGGgBlrIfgCKztqDQdWwMqn4ORuyrzCWV/di7VVPdG9r+aZKZfX63pLTkkFJworSIgOwmG3cSS/lM3/uIMb1dfo+1Zhr+//UCzufGfkMmpF1J/dgavPdVxm287KnYfMTiMMVr32RXC7+DZ6Ksndzz/EdPrE4bzf7QVslSWc/OQX52/w0Dp4awK8fxMlRad50jaTvsUv8e+Ov2PSPb/lj3eMr/dF88hAHwZ0CvlvP3qXMH+8rnqafB1I/gf3g6umQfvqaaSQiwYJGHQzvqqK4p2LzI4ijFR8ArX1HT6pGc3UiZdesMAqpfj57dcx3+dHRGUtpfrwxu++4dhmePsaeOcaKnIO8jfv+xl0+lkOtJ/AvAdG8d69wxhmwL0I1w6P57Poh4k8s48TC3/b5PasTAq5aJhOwznjFUm/wpVkF5WbnUYYpGLHPBy6im2dp5EUG3rR93s5bHS+9nFO6RBOL3istgsF4MAK9FsTqMjeyyve99G/8C8s9ZnIa9OG8+H04Qzu0s6wzEopJt/5U75wXEH07lfJ2dx27wg1as3ON5VSOUqpVCPaE62YzYYr/gYute3gV++to7zKZXYiYYBTaWs55o7gjolj6v2Z0fFdWBR6F5FFuyjdMR+ObcH94RQyVSeGFj3HZz6TeOG2YSydOZpxvds3y70Hwb5OEu/9F2l0w2/JTynO2mv4NqzAqDPyt4GrDGpLtHLBQ2/HS7m49uTLPPheCtUut9mRRFNoTXD+dtIcvUlswP0BSilG3vgz9rk7UbP0SWreu4njNcHc6/o1z94+ii9njmZS/2jstua9eaxLVBjVN75NtbZT9PYtVJUVN+v2WiNDCrnWei1QYERbwgKiB8CYJ7jJvpb4g3N49JOdMpmWlRVlEVKTR3HYwAafNfeNCWV17EyCq06SX6F4zPcp3pgxkWv6RWNr5gJ+tgGJ/Ugb+SIdq4+y87V70O62dXLRYn3kSqnpSqkUpVRKbm5uS21WNJdLfwX9buEx58e4ds3ns53HzU4kGil//3oAfLuNbNTnr/3RFB53z+CPkS8w66EfmTYsddSVN7O5y30MKVrGirkvmJLBLC1WyLXWs7XWSVrrpIiIiJbarGguSsG1L6M7j+CvXv9i345vzU4kGqlw/3rKtDdxCUMb9fnoEF8ef/z3/O2BG2nn73XxDzSjYVOfI90/iUsy/sLyr1eamqUlyagV0XgOb9Qt76OUja5H5uGS7hVL8s7eSird6R198dEq5xPi59XsfeH1oewOYqfPpdweSPfVD7Jg3fY20e0nhVw0jX8YeVGXMFZvYneWLNBsOdXlRJWncyo4sVUUYiN4BbfHeevbdFK5TFwxntXP38yR1A2U5R1j79Y1rF48l+xTp8yOaSijhh9+AGwAeimlspRS9xjRrrCGoEE30l4Vkr51ldlRRAOVZG7GgQvVaZjZUQwV0PNSbA9u4FiXGxhRvoYu867C758J9Pn8WsZseYCDcx81O6KhDJk0S2t9mxHtCGsKSLya6sUOfDMWAzeZHUc0wMnUtQQCHfpeYnYUw9kie9H97tcpyHuGdUvewGFThLXvhHPHO/QuXENFZRU+3ub26RtFZj8UTecTzLGQYQw8vZbi8iqCfD3jj6Mt0FmbydQd6NvDcxdpCA1vzxV3/vq/j/dRTfg3D7NxwzKGj7nGxGTGkT5yYYz4a4lReaSmrDU7iagvrWlfuJPDvn3xcdrNTtNiuiffQBUOynYuNDuKYaSQC0N0GnEjNdpG5W7P+ePwdJW5BwnWRVR2+MGsqB7N4RdCZuBQehasprzSM2ZNlEIuDOEMjCDDtz9xuava3F11VpW1czUAIT2SzQ1iAkffScSoXLZtXmN2FENIIReGKY6bQBd9nKz07WZHEfVQnvkNxdqXPv2GmB2lxcWOvAkXNoq3LzA7iiGkkAvDdBx+MwC5KZ+anETUR3DeNvY7exMS4Gt2lBbnCIrkSEB/uud/TVmV9btXpJALw8R07kq66krA8fVmRxEX4So7TceqIxSGDzY7imlU70n0UFls3rLJ7ChNJoVcGOp4u2F0LU9FV54xO4q4gKzda7EpjW9c4ybK8gSdk2u/QZ7ZYf0L9FLIhaFUt7E4qeHkbrnLszUr3L+OGm2j64BLzY5iGnu7TmR5xdE+X87IhfiOLgMvo1I7KExdbnYUcQE+2Slk2LrSMTLc7CimKo5IIt61j5wia3+DlEIuDBXbIZxdtj4EZ0s/eWula6roXL6HU8EDzI5iOt/uyfirSg7ssvZZuRRyYSilFCfChhFdmYkuOWl2HHEOp9JT8KUSWxfPmiirMaL7jQXgTIa1TzykkAvDObqPA6Bgt3SvtEan0mpvgolOHGNukFbAO6wLebZw/E6lmB2lSaSQC8N16zeS0zqAkr0rzI4izkFlbeIE4cTF9TQ7SquQEzKA7hWpVFZbdzy5FHJhuJ5RIaSoBEKyvwHt+auzWIrWRBfv5Kh/Yosujtyaqc7DiVIFpKfvNTtKoxm1sMRVSqn9SqkDSqnHjWhTWJfNpsgOH0FITS7kpZsdR5zl9IkDhOsCqqIbtz6nJ4pKqO0nz02z7sydTS7kSik78AowAYgHblNKxTe1XWFt3j1r+8mL05aZnESc7djOrwEI7T3a5CStR7uuAyjDB1uWdUeuGHFGPhQ4oLXO1FpXAR8C1xnQrrCwPvH9OOjuQGXq52ZHEWdxHVpPifale4Kckf+X3cEx/75EF+9AW7Qr0IhC3hE4dtbjrLrnvkMpNV0plaKUSsnNzTVgs6I1i+8QxErbCMLytsAZOd6tgtZ0zP+WPT4DPWaJM6NURg2huz7K8ZPWXJS5xS52aq1na62TtNZJERERLbVZYRKH3UZpt2uw4aY6bZHZcQRQlr2XSHcuRR2lW+X7gnuNxqY0R3dZc35yIwr5caDTWY9j6p4TbdzQ4aM55G5P4dZ5ZkcRQPbWxQAEJ1xlcpLWJybxElxaUZn5rdlRGsWIQr4F6KGU6qqU8gJuBeQUTDC8WzirHcmE5myE0nyz47R5toMraxda7ptodpRWx+4bxDGvOEIKdpgdpVGaXMi11jXAQ8BXwF7gY611WlPbFdZntymqe12LHTdluz4zO07bVl1BdOE20nyTCPB2mJ2mVSpql0DXqgwqLLjQhCF95FrrJVrrnlrrblrrPxrRpvAMw0aM4Yg7kqJt0r1ipqpD6/GmktKYtjtt7cU4YwYRokrJSLfeeajc2SmaVb9OIXzjnUxE7kYoKzA7TptVsHMpldpBROJlZkdptaJ6Dwcgd/9Gk5M0nBRy0e+R3QwAABOSSURBVKyUUug+1+PARfEO6V4xi/Pw16S4ezGoe4zZUVqt0LiBVOPAfdx6i4dLIRfNbljyZRx0d0Cv+ytUlZkdp+0pPkFY6UH2+CfRzl/Gj5+Xw5sTXl0JKZSuFSF+oHv7QN4Lf5jg8mNULv+D2XHaHFdG7SyUlV3GmBvEAkrDEujhOsDpM5VmR2kQKeSiRdx4422857oMry3/gmObzY7TphTvXUWuDqJzH1lI4mK8OycRrMrYv2+X2VEaRAq5aBEJHYPJ7P9LsnUolfMfgOoKsyO1GerENna4ezC0a5jZUVq9Dn1qL3jmZ1jrZEMGlIoW89MJg/h12v3MKvwjev2LqLG/NqZhtxsyvqIy7QtyyjRHSx2cqA4g8ZoZ9I79wbQ/bUt5ISFlRzjsk8z4YB+z07R6fjGJVOFAZVvrxiAp5KLFtPP3IvnKW1i1eDHDt7yH35gnQDVhcQNXDVUbZ1P17asElB6jUvsRgI1hlOFQbo68NZ+d18ym/5A2PHa6riBVRw00OYhFOLzJ8elGePEetNaopvz7bEHStSJa1G1DO7MzIBm/suOQ07QVWbJW/BOv5U+wv8SH/3P+gjdGrGD/1F3UPJlL3uSF+Nmq6f3Fjexe+GKbXamo+GDtHNvB3WTa2voqj0ikt84kq8A6I6ykkIsWZbcpIgfXTldfsL1pU/JU7FxIBp2onvYVv3/it/z8qr4MjwvDx8tBeN+xeM/4lj3e/Unc8RT7ls0xIr7llB3awmF3e/p2izU7imX4xSYRpMpIt9AFTynkosVdNqQ/O91xVKQtbnQbrjP5dC3bSWbYGIbHhZ1z/cmg8Cj6PPolB1UXfDf/A+12NSW2Jfnl7SSVbsR3CDI7imVE9qq94Fl4cIvJSepPCrlocVHBPuwPSiaqZDf6TE6j2jiy8VPsuPFNvPBiVD5eTvIHPEAX11G2r/y4UduyrJJTBFXlkBPUFy+H/KnXlzOqL9U4sFnogqccXWGKgP7XYkNzfHPjbtuvTvucbB3KwGEXv5A5aMLdnFQRODe+jNvddvrKa7JSALB1HGxyEotxeJHv34Po0jSKyqrNTlMvUsiFKUaMuJQTOozS3Y1Y07OqjC6nN5AaOIpA34vfcu7w8ian770kutLYuHZpI9JaU8H+jbi0IrLnELOjWE/XSxioMti477DZSepFCrkwRbsAb/YFjaTT6U24q8ob9NkT27/EhyrofXW9P9P3mhkUE4B7/d9xtZGz8upjKaTrGPrFRZsdxXIiBk7CS7k4teMrs6PUixRyYRrfhKvxo4KMzV826HNF2xdQrP1IGDmx3p+x+wRysvcdjKzexMtzF3C6tKqhca1Fa0IKU9lv70nHEF+z01iOPXYE5cqP4OOr0RYYutqkQq6UmqyUSlNKuZVSSUaFEm1Dv1GTKNXeFG5fWP8PuV1En1rNNu8hdAht2EiM7lf/ggpHINMyHuKJ5//Gm+sPUeNyNzC1RZw+jL+rmDNhiZa5qaVVsTvJjRzBkJqtHMw5Y3aai2rqGXkq8CNgrQFZRBvj7x/A/qCR9M5fTllpcb0+U7h/PcG6mNK4CQ3eni0wAr8Za/AN78yrPEfB0j/y5vqDDW7HCs4cqp0rxKuLnF81VkDfCUSrAnZtb/0LTTSpkGut92qt9xsVRrQ9viN/QjClpH31Vr3ef3rd65Rpb7oNv/Cww/MKjcP7J6tQ/SbzqPMTvLe/2bh2WrmC9I1Uaiede8uFzsYK7V/bdVe9r/X3k7dYH7lSarpSKkUplZKbm9tSmxWtXO9hV5Jp60JY2tsXvY1e52fS+cRilvpMoFeXDo3fqJcf6obZ5PjE0vX0tx7ZvWLL3s4e3YXEzuFmR7Gu4I6c9OlG7OlvqKxp3TeTXbSQK6VWKKVSz/HToFMirfVsrXWS1jopIiKi8YmFR1E2Gyd730mcK5MD21Ze8L2nljxLjbbjdcnMpvf7KkV5h2EMYD9pWaeb1lZr46ohomQvR3z64O8t8+I1RUXsOAaxn+3pR82OckEXLeRa68u11gnn+JEFGIUhEq66l2LtR8naWed/U+FRwg9+ykL75VwxvL8h2w3pPZogVc7BNGvNPX0xOicNb11BeaTMeNhU7QdPwqlcHN/WsJFVLU2GHwrTBQWFsCviGhIKv6Y499g533N62fO4NZQnzcDbYTdku8G9au8KrTy43pD2WovTGbUX53y7yoyHTeUbN5Iy5YfPkZWtehhiU4cf3qCUygJGAIuVUq3/qoBolSLHPYRTuTi49J8/fLH4BIF7P2CBHsN1lxq4XFlIJ0472xNWsLVV/5E2VGnmJgp0AHE9E8yOYn12J/kdRjOyagPrUjPNTnNeTR21skBrHaO19tZat9daX2lUMNG29Izvz2avYSRkziFv3VlTzhYdp/qDO9BuN1l9f2L4KvDFEUkMcO/lYE6Joe2ayfvUDnbp7vSSGQ8NETXxCdqpM+R/9bzZUc5LulZEqxHy4zmkEE/4yl9QsvBRSF+Ge9Yoak6m8fOaGdwwLtnwbfr3HE2kKmRPmnXmnr6gyhLCyzM54R9vWBdUW+eMGcCByCu5suRT9qanmx3nnKSQi1ajZ5fOBN6zkPeYSOCO12HuZA6UB/CjmmcZPule4iICDN9mWHxtP3lphmfc06ZPbMeGpkqWdjNU1A3P4KSGvMVPmx3lnGRskmhVEjqF4bpnFk/MeZ4uriNsiLmX1yYPpXOYX7NsT0X05owtiMAc6ywicCGn0zcQCgR1M/BagiCgQ0+2tr+BEac+JTszlQ5xrev6g5yRi1anf6cQ7rz/V3Sc/Bfemn5psxVxAJQiP2wQfavTOFHYsFkYW6OKw5s57G5Pr7hYs6N4nE7X/45KnBR+9gS4z3MTmdsFRVmQm96i68RKIRetUp8OQUzqH33OJdyM5hU3iq62U+zaZ/3ZJgLydrKbbvRsH2h2FI8TGd2Z1e2n0adoLUffvhtcNbUvuF3w7cvwUj94OgL+1hdeGQL/TIK1L9QW9mYmhVy0eZEJYwHI37PG5CRNVHyCoOpcTgUm4LTLn3ZzGHP3H/k4YAqdjy4ge87NkLOPijkTYNlv2FAQwDu263g14CE+av9zShyhsOrp2gK/aXaz5pI+ctHm2aP7U6F88DmxAZhpdpxGc2WlYAe0LO3WbPx9nFzzs7/z9j+DmJb9Krw6jCrtx+/1g9gH3EalS3OquILU40X8qmwIN8RW83/Od2m39DHI3QcT/gx2p+G5pJALYXeSFzqYfrm7OJpf1rx98s2oOGMD/tpOWHeZ8bA5+Xk5uOWhZ3j5XyHE5K4jPeFhHpk4ishAn/++p6yqhvc2HmH22kwGn5nGZ71jSEx5A/IPwM3vgG87QzPJ9y8hAN+eY+lhO86W1D1mR2k0fWgde3UXErpEmh3F4/l62XlgxmMk/3Iev7rl8u8Ucagt9tNHd2PdL8cxvm8HJu27gg2JT8PRjVC3KLaRpJALAYQmXg5A0Z4Lz8DYamVtJbRwN18wmm7NMN5e/JDDbvtBAf8+Xy87L982iHG9I7ltSzcWjVkKPcYbnkUKuRCAiupPmT2Q0FMbLLk4s944i1J8Se8wCXsLjPQR9eflsPHqjwdxSY9wZi45yYo9pwzfhhRyIQBsNgojh5Okd5OaVWh2moYpPoFOW8CHNWO4cWS82WnEOfg47bx+ZxL3JHdlaFyo4e1LIReiTlD8ZcSoPHal7jA7SoPoLW+AdrEi8DquTmzCykmiWfk47fzmmniCfIwftSKFXIg6Ab0vA6Bi/9cmJ2mA6nJqNr3BCtcgrh+XLN0qbZQUciH+I7wHJc4Iok9vpryqda/R+F+7PsZZdZrPfK7jhoExZqcRJmnqwhLPK6X2KaV2KaUWKKVCjAomRItTirKOyQxTaWzKtMAC4TWVlK/5G3vcXRhy6SS8HHJe1lY19cgvBxK01v2AdOCJpkcSwjztEi4nXBWzb6cF1vFc/xK+xYd41TGFW4Z2MTuNMFFTVwhaprWumzmGjYB8txOW5tWjdt6VM/tWUFHdirtX8g7gXvsCi1wjiB/9I3y9ZBGJtszI72J3A0sNbE+IlhccQ1lwd8a71rFwW/PPWtcoWsMXD1OBk7/Z7+KO4XI23tZdtJArpVYopVLP8XPdWe95EqgB3r9AO9OVUilKqZTcXAv0P4o2y/eSn9LflsnONQtaz6LM1eVQdBzyD8Km1+DwOp6pvJVJIwcQ2AzD2YS1qKb+Q1VKTQN+AlymtS6rz2eSkpJ0Sorx8w0IYYiaSspeSGR3WTuq71jMqB7h5mUpzoYN/4SUN6H6f39emb4JTCp9kvW/utzwBalF66WU2qq1Tvr+802a/VApdRXwS+DS+hZxIVo9hzdeox9m2LIneG7FQkb1uLfZNuV2a9Zk5HIot5T8gjwislcTWJmDn7uE0JocBpeuxaZdZEReiaNrMrFRYeRXOrjuMxs/vqSrFHEBNH0a238C3sBypRTARq31/U1OJYTJHEnTKPv6LySfeJuDubc2y0RUp4orePSTneQe2MaP7St40L4ef1UBgAsbxSqQL9QYXq25hvSjEXAUQvychAd4U2kv495RXQ3PJKypSYVca93dqCBCtCpefriHz2D0umf42Zw3UMGdaWcvJ8hejbcdfB0Q6OdDl+hIunWMIqxDLDh9z9+e1tQc/paqqiqqbL7sO55H2up5/F5vopv3CbTdG/peD0l3Q/u+2L0CaKcU1wPXA2cqa1ifkcdXaSdZtS+Hu5JjiQy68Mx7ou1och95Y0gfubCEimIqX4jHu6bkom/NtUUS9PMNeAeeuz99/weP02v/rO8858JGZcxI/BKvg8SbwM/4yZSEZ2mWPnIhPJpPEN5TPoLsHeATAr4htWfdyg42O+WVlRw7mcuxI5lcevB50t9/hPj7//2DZg7v2ULcvtl84zOKwvg78aUCfy8bA0ZNwO88hV+IhpBCLsSFxCbX/pyDL9CzF/QEvnrpCFee/JDcXcuJ6Pe/hQNKK6oonf8QpcqPnne9RkSU3DMnjCeTMwhhgIQpz3FEt8f9+czaMd+A1polbz1DX9c+ckf+Toq4aDZyRi6EATqGh7Ko/++4dteDHJv7U06FDSP1wGFuPP0GR9sNo8f45hvCKIQUciEMctW1t7F0z3wmHPqEToc+IQko82pHzB2vgZJ5wkXzkUIuhEG8HDai75zDrPWrGN4rhv7du+DnHwYOuWlHNC8p5EIYqH/nUPrffpPZMUQbIxc7hRDC4qSQCyGExUkhF0IIi5NCLoQQFieFXAghLE4KuRBCWJwUciGEsDgp5EIIYXGmzEeulMoFjjTy4+FAnoFxrKIt7ndb3Gdom/vdFvcZGr7fXbTWEd9/0pRC3hRKqZRzTazu6drifrfFfYa2ud9tcZ/BuP2WrhUhhLA4KeRCCGFxVizks80OYJK2uN9tcZ+hbe53W9xnMGi/LddHLoQQ4ruseEYuhBDiLFLIhRDC4ixVyJVSVyml9iulDiilHjc7T3NQSnVSSn2tlNqjlEpTSs2sez5UKbVcKZVR9992Zmc1mlLKrpTarpT6ou5xV6XUprrj/ZFSyuOW2lFKhSil5iml9iml9iqlRnj6sVZK/bzu33aqUuoDpZSPJx5rpdSbSqkcpVTqWc+d89iqWv+o2/9dSqlBDdmWZQq5UsoOvAJMAOKB25RS8eamahY1wC+01vHAcGBG3X4+DqzUWvcAVtY99jQzgb1nPf4z8DetdXfgNHCPKama19+BL7XWvYH+1O6/xx5rpVRH4GdAktY6AbADt+KZx/pt4KrvPXe+YzsB6FH3Mx2Y1ZANWaaQA0OBA1rrTK11FfAhcJ3JmQyntc7WWm+r+72E2j/sjtTu6zt1b3sHuN6chM1DKRUDXA3MqXusgHHAvLq3eOI+BwOjgTcAtNZVWutCPPxYU7vEpK9SygH4Adl44LHWWq8FCr739PmO7XXAv3WtjUCIUqpDfbdlpULeETh21uOsuuc8llIqFhgIbALaa62z6146CbQ3KVZzeQn4JeCuexwGFGqta+oee+Lx7grkAm/VdSnNUUr548HHWmt9HHgBOEptAS8CtuL5x/o/zndsm1TfrFTI2xSlVAAwH3hYa1189mu6dsyox4wbVUpdA+RorbeanaWFOYBBwCyt9UCglO91o3jgsW5H7dlnVyAa8OeH3Q9tgpHH1kqF/DjQ6azHMXXPeRyllJPaIv6+1vrTuqdP/eerVt1/c8zK1wySgWuVUoep7TIbR23fcUjd12/wzOOdBWRprTfVPZ5HbWH35GN9OXBIa52rta4GPqX2+Hv6sf6P8x3bJtU3KxXyLUCPuqvbXtReIFlkcibD1fUNvwHs1Vq/eNZLi4Cpdb9PBT5r6WzNRWv9hNY6RmsdS+1xXaW1/jHwNXBT3ds8ap8BtNYngWNKqV51T10G7MGDjzW1XSrDlVJ+df/W/7PPHn2sz3K+Y7sIuLNu9MpwoOisLpiL01pb5geYCKQDB4Enzc7TTPs4itqvW7uAHXU/E6ntM14JZAArgFCzszbT/o8Bvqj7PQ7YDBwAPgG8zc7XDPs7AEipO94LgXaefqyBp4B9QCrwLuDticca+IDa6wDV1H77uud8xxZQ1I7KOwjspnZUT723JbfoCyGExVmpa0UIIcQ5SCEXQgiLk0IuhBAWJ4VcCCEsTgq5EEJYnBRyIYSwOCnkQghhcf8PvsGsjUx4MJMAAAAASUVORK5CYII=\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "jnp.max(mean_tf - mean_jax)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "rR_MIcymAoLi",
        "outputId": "519325be-d962-403f-e6ab-04ae80e933ac"
      },
      "execution_count": 31,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "DeviceArray(0.27465248, dtype=float32)"
            ]
          },
          "metadata": {},
          "execution_count": 31
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "mean_tf - mean_jax"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "5kBAVZ0EDCFZ",
        "outputId": "6d44e8db-6863-4243-cb9c-1d070f45f630"
      },
      "execution_count": 32,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "DeviceArray([ 0.27465248,  0.1736412 ,  0.14441681,  0.0984354 ,\n",
              "              0.12129331,  0.10304689,  0.11484623,  0.17503166,\n",
              "              0.10844803,  0.06539965,  0.02367926,  0.02893591,\n",
              "              0.04644346,  0.04540443,  0.03775024,  0.05934906,\n",
              "              0.03860378,  0.08240652,  0.07577753,  0.08367157,\n",
              "              0.06808376,  0.05231547,  0.07461023,  0.0740571 ,\n",
              "              0.10213566,  0.11476636,  0.05582666,  0.12515938,\n",
              "              0.13173628,  0.11065626,  0.08664942,  0.07616603,\n",
              "              0.04648519,  0.05761021, -0.00808275, -0.05528012,\n",
              "             -0.03191137, -0.05396998,  0.00223547, -0.00743341,\n",
              "             -0.03241956, -0.04502571, -0.02139676, -0.01694328,\n",
              "             -0.02482587,  0.01200032, -0.00702184,  0.01766813,\n",
              "              0.04407704,  0.04392493,  0.05775714,  0.03118992,\n",
              "              0.01846123,  0.01203752, -0.00659704, -0.01738477,\n",
              "              0.0208261 , -0.01097298, -0.00208759,  0.0481286 ,\n",
              "              0.01110792,  0.00314498, -0.06618142, -0.1105237 ,\n",
              "             -0.05031073, -0.07602084, -0.04759371, -0.07517824,\n",
              "             -0.00685197, -0.02020764, -0.04692864, -0.05590868,\n",
              "             -0.02970982, -0.02623045, -0.02439976, -0.0263809 ,\n",
              "             -0.05619442, -0.05806541, -0.0561837 , -0.02605128,\n",
              "             -0.02249861, -0.01943481, -0.01511967, -0.05783796,\n",
              "             -0.03918278, -0.01716828, -0.00361395,  0.01762992,\n",
              "             -0.00581056,  0.00546557,  0.02476028,  0.01350318,\n",
              "              0.04631579,  0.03001642, -0.01019621, -0.01744175,\n",
              "             -0.03406513, -0.0619663 , -0.0772202 , -0.10103989],            dtype=float32)"
            ]
          },
          "metadata": {},
          "execution_count": 32
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        ""
      ],
      "metadata": {
        "id": "uuhD8A-DF6Hj"
      },
      "execution_count": null,
      "outputs": []
    }
  ]
}