How_to_autograd_by_TensorFlow_or_PyTorch.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "How to autograd by TensorFlow or PyTorch.ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "toc_visible": true,
      "authorship_tag": "ABX9TyPlI0q/BVRrm1RuiUNPEYhR",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/isshiki/MLnotebooks/blob/master/How_to_autograd_by_TensorFlow_or_PyTorch.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "RkxRy0WnwVGP",
        "colab_type": "text"
      },
      "source": [
        "##### Copyright 2020 Masahiko Isshiki - https://blog.masahiko.info/."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Q13TbBd0wjMV",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "#@title Licensed under the Apache License, Version 2.0 (the \"License\");\n",
        "# you may not use this file except in compliance with the License.\n",
        "# You may obtain a copy of the License at\n",
        "#\n",
        "# https://www.apache.org/licenses/LICENSE-2.0\n",
        "#\n",
        "# Unless required by applicable law or agreed to in writing, software\n",
        "# distributed under the License is distributed on an \"AS IS\" BASIS,\n",
        "# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
        "# See the License for the specific language governing permissions and\n",
        "# limitations under the License."
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "qmioFGhux6uZ",
        "colab_type": "text"
      },
      "source": [
        "# 「TensorFlowやPyTorchで自動微分して勾配を取得する方法」"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "obhOyKSewVCj",
        "colab_type": "text"
      },
      "source": [
        "## ■準備"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vyKG2UfDxRHg",
        "colab_type": "text"
      },
      "source": [
        "### ●Pythonバージョン：3.x"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "HmvkteB7wITi",
        "colab_type": "code",
        "outputId": "a2460184-bae7-41b1-f5da-06910c5b33c5",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 51
        }
      },
      "source": [
        "import sys\n",
        "print('Python', sys.version)\n",
        "# Python 3.6.9 (default, Nov  7 2019, 10:44:02)  …… などと表示される"
      ],
      "execution_count": 21,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Python 3.6.9 (default, Nov  7 2019, 10:44:02) \n",
            "[GCC 8.3.0]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "G4GUdDKHxbah",
        "colab_type": "text"
      },
      "source": [
        "### ●TensorFlowバージョン"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "mHg2OKuKxkVm",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Google Colabで最新の2.xを使う場合、2.xに切り替える（Colab専用）\n",
        "%tensorflow_version 2.x"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "HwkoyieUxfsw",
        "colab_type": "code",
        "outputId": "5c76891e-a22f-4bfb-b6f7-1b74574ff087",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "import tensorflow as tf\n",
        "print('TensorFlow', tf.__version__)\n",
        "# TensorFlow 2.1.0 ……などと表示される"
      ],
      "execution_count": 23,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "TensorFlow 2.1.0\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "s-6CaFtexsTA",
        "colab_type": "text"
      },
      "source": [
        "### ●PyTorchバージョン"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "-HX6bCruxvXs",
        "colab_type": "code",
        "outputId": "3925c121-526f-4d65-d6c0-4ff5ac70a8eb",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "import torch\n",
        "print('PyTorch', torch.__version__)\n",
        "# PyTorch 1.4.0 ……などと表示される"
      ],
      "execution_count": 24,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "PyTorch 1.4.0\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5mYpgfr0x_Hq",
        "colab_type": "text"
      },
      "source": [
        "## ■実装方法"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_sfMlmmSHxCf",
        "colab_type": "text"
      },
      "source": [
        "### ●例として使う計算式"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ar5FUyoDHpuQ",
        "colab_type": "text"
      },
      "source": [
        "  $$\n",
        "  y=2x^3+4x^2+5x+6\n",
        "  $$\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "YZVaf0jVJg9X",
        "colab_type": "text"
      },
      "source": [
        "#### ○これをPythonの式にすると..."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "kk08U7LDJgKn",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def calc(x):\n",
        "  return (2 * x ** 3) + (4 * x ** 2) + (5 * x) + 6"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "uBogAgIgH-VX",
        "colab_type": "text"
      },
      "source": [
        "### ●微分する導関数の式は..."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "eerYioXmIFaX",
        "colab_type": "text"
      },
      "source": [
        "$$\n",
        "\\frac{dy}{dx}=6x^2+8x+5\n",
        "$$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "z9-XU2MFIukF",
        "colab_type": "text"
      },
      "source": [
        "#### ○これをPythonの式にすると..."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "atMViT_QG_nr",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def der_calc(x):\n",
        "  return (6 * x ** 2) + (8 * x) + 5"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "VHiBU7inIflB",
        "colab_type": "text"
      },
      "source": [
        "### ●導関数に$x=0.5$を入力すると..."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "fQygP5uII9mf",
        "colab_type": "text"
      },
      "source": [
        "$$\n",
        "\\begin{align}\n",
        "\\frac{dy}{dx}&=6\\times(0.5)^2+8\\times(0.5)+5 \\\\\n",
        "&=(6\\times0.25)+(8\\times0.5)+5 \\\\\n",
        "&=1.5+4+5 \\\\\n",
        "&=10.5\n",
        "\\end{align}\n",
        "$$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "OULtbixOKEuc",
        "colab_type": "text"
      },
      "source": [
        "#### ○Pythonのコードで計算すると..."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "jPyYr8pjJ6Z-",
        "colab_type": "code",
        "outputId": "5080a890-dd81-4381-baed-a1d811b30adb",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "result = der_calc(0.5)\n",
        "result # 10.5"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "10.5"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 10
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "zdZBA7evLX56",
        "colab_type": "text"
      },
      "source": [
        "$10.5$が出力される。これと同じことをPyTorchとTensorFlowの自動微分機能を使って行う方法を紹介する。"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "llmh3xCK0T0d",
        "colab_type": "text"
      },
      "source": [
        "## ■PyTorch編"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6lDbGFAzLu_w",
        "colab_type": "text"
      },
      "source": [
        "- データをPyTorchテンソル化して、計算式を作る\n",
        "- `backward`メソッドで逆伝播する（自動微分）\n",
        "- データ（テンソル）の`grad`変数で微分係数（＝勾配）を取得できる\n",
        "\n",
        "という流れで書けばよい。具体的には以下の通り。"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "9W8Ghj-bzPDL",
        "colab_type": "code",
        "outputId": "eb39b50b-0686-4b91-a758-cdfcf4270dc4",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 51
        }
      },
      "source": [
        "import torch\n",
        "import torch.nn as nn  # 「ニューラルネットワーク」モジュールの別名定義\n",
        "\n",
        "x = torch.tensor(0.5, requires_grad=True)  # 変数に対して「勾配計算が必要」とマーク\n",
        "y = calc(x)    # 既存の計算式から計算グラフを動的に構築\n",
        "print(y)       # tensor(9.7500, grad_fn=<AddBackward0>) ……などと表示される\n",
        "\n",
        "y.backward()   # 逆伝播の処理として、上記式から微分係数（＝勾配）を計算（自動微分：Autograd）\n",
        "g = x.grad     # 与えられた入力（x）によって計算された勾配の値（grad）を取得\n",
        "print(g)       # tensor(10.5000)  ……などと表示される"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "tensor(9.7500, grad_fn=<AddBackward0>)\n",
            "tensor(10.5000)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "eX-9QA8g0d92",
        "colab_type": "text"
      },
      "source": [
        "### ●グラフを描画"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "YHFGGdxIMi45",
        "colab_type": "text"
      },
      "source": [
        "先ほどは単一のスカラーだったので、今度は複数のスカラー値で計算してみる。"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "tNgWOwD-0Nno",
        "colab_type": "code",
        "outputId": "c6e298b9-18de-4d1a-9e35-e733034b1d9b",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 269
        }
      },
      "source": [
        "# PyTorchの微分グラフ\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "x = torch.arange(-4.0, 4.0, 0.001, requires_grad=True)\n",
        "y = calc(x)\n",
        "y.backward(gradient=torch.ones_like(y)) # スカラーテンソルの場合は勾配を格納する場所が必要なのでテンソルを仮生成【重要】\n",
        "g = x.grad\n",
        "x_numpy = x.detach().numpy()  # デタッチして（＝追跡しないようにして）からndarray化する\n",
        "g_numpy = g.detach().numpy()\n",
        "plt.plot(x_numpy, g_numpy, label = \"Derivative\")\n",
        "plt.xlim(-4, 4)\n",
        "plt.ylim(-2.0, 30.0)\n",
        "plt.grid()\n",
        "plt.legend()\n",
        "plt.show()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXQAAAD8CAYAAABn919SAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nV0qpAKGFrpRSAeL/A3+xGmOwTpB2AAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "jS-FItpy0pIL",
        "colab_type": "text"
      },
      "source": [
        "## ■TensorFlow編"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "7N6Mago5NsjH",
        "colab_type": "text"
      },
      "source": [
        "- データをTensorテンソル化して、勾配テープ（GradientTape）内で計算式を作る\n",
        "- 勾配テープ（tape）の`gradient`メソッドで逆伝播する（自動微分）\n",
        "- 逆伝播により計算された微分係数（＝勾配）が取得される\n",
        "\n",
        "という流れで書けばよい。具体的には以下の通り。"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "co32NpCZyH-o",
        "colab_type": "code",
        "outputId": "00fb2db8-dbf0-46e9-ccf8-dba7e8dd2b85",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 51
        }
      },
      "source": [
        "import tensorflow as tf\n",
        "import tensorflow.keras.layers as layers  # 「レイヤー」モジュールの別名定義\n",
        "\n",
        "x = tf.Variable(0.5)\n",
        "with tf.GradientTape() as tape:  # 計算式に対して「勾配計算が必要」とマーク\n",
        "  y = calc(x)  # 既存の計算式から計算グラフを動的に構築\n",
        "print(y)       # tf.Tensor(9.75, shape=(), dtype=float32) ……などと表示される\n",
        "\n",
        "g = tape.gradient(y, x)   # 逆伝播の処理として、上記式から微分係数（＝勾配）を計算（自動微分：Autograd）\n",
        "print(g)       # tf.Tensor(10.5, shape=(), dtype=float32)  ……などと表示される"
      ],
      "execution_count": 26,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "tf.Tensor(9.75, shape=(), dtype=float32)\n",
            "tf.Tensor(10.5, shape=(), dtype=float32)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "KHvXUgIp0i-9",
        "colab_type": "text"
      },
      "source": [
        "### ●グラフを描画"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "yNmym0y8PpWe",
        "colab_type": "text"
      },
      "source": [
        "先ほどは単一のスカラーだったので、今度は複数のスカラー値で計算してみる。"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "bjkOGT1H0mdd",
        "colab_type": "code",
        "outputId": "b6ab2837-e84a-4215-bc9b-377f3c8b5ea9",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 269
        }
      },
      "source": [
        "# TensorFlowの微分グラフ\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "x = tf.Variable(tf.range(-4.0, 4.0, 0.001), trainable=True)\n",
        "with tf.GradientTape() as tape:\n",
        "  #tape.watch(x) # tf.constantなど「trainable=False」な状態であれば x を記録する（手動追跡）\n",
        "  # ↑tf.Variableであれば既に訓練可能な状態（自動追跡）なので不要\n",
        "  y = calc(x)\n",
        "g = tape.gradient(y, x)\n",
        "x_numpy = x.numpy()\n",
        "g_numpy = g.numpy()\n",
        "plt.plot(x_numpy, g_numpy, label = \"Derivative\")\n",
        "plt.xlim(-4, 4)\n",
        "plt.ylim(-2.0, 30.0)\n",
        "plt.grid()\n",
        "plt.legend()\n",
        "plt.show()"
      ],
      "execution_count": 29,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXQAAAD8CAYAAABn919SAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nChBa6EopFSC00JVSKkBooSulVID4P3pyGmtP/O7RAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "w0AcgUAw1og0",
        "colab_type": "text"
      },
      "source": [
        "# 簡単ですね。以上で終わりです。"
      ]
    }
  ]
}