code/34-多GPU训练实现.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "GPUs.ipynb",
      "provenance": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    },
    "accelerator": "GPU"
  },
  "cells": [
    {
      "cell_type": "markdown",
      "source": [
        "#调用GPU"
      ],
      "metadata": {
        "id": "Pue_m2w_1_KK"
      }
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {
        "id": "MSV3_ePh3l0j",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "6cd0080c-b389-4a43-d6f7-14469cefed59"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Found GPU at: /device:GPU:0\n"
          ]
        }
      ],
      "source": [
        "%tensorflow_version 2.x\n",
        "import tensorflow as tf\n",
        "device_name = tf.test.gpu_device_name()\n",
        "if device_name != '/device:GPU:0':\n",
        "  raise SystemError('GPU device not found')\n",
        "print('Found GPU at: {}'.format(device_name))"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#创建虚拟GPU（Tensorflow）"
      ],
      "metadata": {
        "id": "cSo7ULhY2IHY"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "gpus = tf.config.list_physical_devices('GPU')\n",
        "if gpus:\n",
        "  # Create 2 virtual GPUs with 1GB memory each\n",
        "  try:\n",
        "    tf.config.set_logical_device_configuration(\n",
        "        gpus[0],\n",
        "        [tf.config.LogicalDeviceConfiguration(memory_limit=1024),\n",
        "         tf.config.LogicalDeviceConfiguration(memory_limit=1024)])\n",
        "    logical_gpus = tf.config.list_logical_devices('GPU')\n",
        "    print(len(gpus), \"Physical GPU,\", len(logical_gpus), \"Logical GPUs\")\n",
        "  except RuntimeError as e:\n",
        "    # Virtual devices must be set before GPUs have been initialized\n",
        "    print(e)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "8R9y7tYXxzUB",
        "outputId": "c41fec70-b336-496b-a347-5e394d8f0b36"
      },
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "1 Physical GPU, 2 Logical GPUs\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "tf.debugging.set_log_device_placement(True)"
      ],
      "metadata": {
        "id": "LBIDvdFBz8Qd"
      },
      "execution_count": 4,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "#下载pytorch"
      ],
      "metadata": {
        "id": "77WgvREP3UVu"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "!pip3 install torch torchvision torchaudio"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "UzDofKvtUQCz",
        "outputId": "74a969c7-67ca-4380-9222-30d5e4b19356"
      },
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Requirement already satisfied: torch in /usr/local/lib/python3.7/dist-packages (1.10.0+cu111)\n",
            "Requirement already satisfied: torchvision in /usr/local/lib/python3.7/dist-packages (0.11.1+cu111)\n",
            "Requirement already satisfied: torchaudio in /usr/local/lib/python3.7/dist-packages (0.10.0+cu111)\n",
            "Requirement already satisfied: typing-extensions in /usr/local/lib/python3.7/dist-packages (from torch) (3.10.0.2)\n",
            "Requirement already satisfied: numpy in /usr/local/lib/python3.7/dist-packages (from torchvision) (1.19.5)\n",
            "Requirement already satisfied: pillow!=8.3.0,>=5.3.0 in /usr/local/lib/python3.7/dist-packages (from torchvision) (7.1.2)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "!pip install d2l==0.14"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Bd9GDWfyUUW2",
        "outputId": "da171369-c8d4-49d0-e1a2-4554a3e4b89f"
      },
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Collecting d2l==0.14\n",
            "  Downloading d2l-0.14.0-py3-none-any.whl (48 kB)\n",
            "\u001b[?25l\r\u001b[K     |██████▊                         | 10 kB 20.2 MB/s eta 0:00:01\r\u001b[K     |█████████████▍                  | 20 kB 18.8 MB/s eta 0:00:01\r\u001b[K     |████████████████████            | 30 kB 10.4 MB/s eta 0:00:01\r\u001b[K     |██████████████████████████▉     | 40 kB 8.3 MB/s eta 0:00:01\r\u001b[K     |████████████████████████████████| 48 kB 2.6 MB/s \n",
            "\u001b[?25hRequirement already satisfied: jupyter in /usr/local/lib/python3.7/dist-packages (from d2l==0.14) (1.0.0)\n",
            "Requirement already satisfied: numpy in /usr/local/lib/python3.7/dist-packages (from d2l==0.14) (1.19.5)\n",
            "Requirement already satisfied: matplotlib in /usr/local/lib/python3.7/dist-packages (from d2l==0.14) (3.2.2)\n",
            "Requirement already satisfied: pandas in /usr/local/lib/python3.7/dist-packages (from d2l==0.14) (1.1.5)\n",
            "Requirement already satisfied: jupyter-console in /usr/local/lib/python3.7/dist-packages (from jupyter->d2l==0.14) (5.2.0)\n",
            "Requirement already satisfied: ipywidgets in /usr/local/lib/python3.7/dist-packages (from jupyter->d2l==0.14) (7.6.5)\n",
            "Requirement already satisfied: nbconvert in /usr/local/lib/python3.7/dist-packages (from jupyter->d2l==0.14) (5.6.1)\n",
            "Requirement already satisfied: qtconsole in /usr/local/lib/python3.7/dist-packages (from jupyter->d2l==0.14) (5.2.2)\n",
            "Requirement already satisfied: notebook in /usr/local/lib/python3.7/dist-packages (from jupyter->d2l==0.14) (5.3.1)\n",
            "Requirement already satisfied: ipykernel in /usr/local/lib/python3.7/dist-packages (from jupyter->d2l==0.14) (4.10.1)\n",
            "Requirement already satisfied: tornado>=4.0 in /usr/local/lib/python3.7/dist-packages (from ipykernel->jupyter->d2l==0.14) (5.1.1)\n",
            "Requirement already satisfied: traitlets>=4.1.0 in /usr/local/lib/python3.7/dist-packages (from ipykernel->jupyter->d2l==0.14) (5.1.1)\n",
            "Requirement already satisfied: jupyter-client in /usr/local/lib/python3.7/dist-packages (from ipykernel->jupyter->d2l==0.14) (5.3.5)\n",
            "Requirement already satisfied: ipython>=4.0.0 in /usr/local/lib/python3.7/dist-packages (from ipykernel->jupyter->d2l==0.14) (5.5.0)\n",
            "Requirement already satisfied: setuptools>=18.5 in /usr/local/lib/python3.7/dist-packages (from ipython>=4.0.0->ipykernel->jupyter->d2l==0.14) (57.4.0)\n",
            "Requirement already satisfied: pickleshare in /usr/local/lib/python3.7/dist-packages (from ipython>=4.0.0->ipykernel->jupyter->d2l==0.14) (0.7.5)\n",
            "Requirement already satisfied: decorator in /usr/local/lib/python3.7/dist-packages (from ipython>=4.0.0->ipykernel->jupyter->d2l==0.14) (4.4.2)\n",
            "Requirement already satisfied: prompt-toolkit<2.0.0,>=1.0.4 in /usr/local/lib/python3.7/dist-packages (from ipython>=4.0.0->ipykernel->jupyter->d2l==0.14) (1.0.18)\n",
            "Requirement already satisfied: pygments in /usr/local/lib/python3.7/dist-packages (from ipython>=4.0.0->ipykernel->jupyter->d2l==0.14) (2.6.1)\n",
            "Requirement already satisfied: simplegeneric>0.8 in /usr/local/lib/python3.7/dist-packages (from ipython>=4.0.0->ipykernel->jupyter->d2l==0.14) (0.8.1)\n",
            "Requirement already satisfied: pexpect in /usr/local/lib/python3.7/dist-packages (from ipython>=4.0.0->ipykernel->jupyter->d2l==0.14) (4.8.0)\n",
            "Requirement already satisfied: wcwidth in /usr/local/lib/python3.7/dist-packages (from prompt-toolkit<2.0.0,>=1.0.4->ipython>=4.0.0->ipykernel->jupyter->d2l==0.14) (0.2.5)\n",
            "Requirement already satisfied: six>=1.9.0 in /usr/local/lib/python3.7/dist-packages (from prompt-toolkit<2.0.0,>=1.0.4->ipython>=4.0.0->ipykernel->jupyter->d2l==0.14) (1.15.0)\n",
            "Requirement already satisfied: jupyterlab-widgets>=1.0.0 in /usr/local/lib/python3.7/dist-packages (from ipywidgets->jupyter->d2l==0.14) (1.0.2)\n",
            "Requirement already satisfied: ipython-genutils~=0.2.0 in /usr/local/lib/python3.7/dist-packages (from ipywidgets->jupyter->d2l==0.14) (0.2.0)\n",
            "Requirement already satisfied: nbformat>=4.2.0 in /usr/local/lib/python3.7/dist-packages (from ipywidgets->jupyter->d2l==0.14) (5.1.3)\n",
            "Requirement already satisfied: widgetsnbextension~=3.5.0 in /usr/local/lib/python3.7/dist-packages (from ipywidgets->jupyter->d2l==0.14) (3.5.2)\n",
            "Requirement already satisfied: jsonschema!=2.5.0,>=2.4 in /usr/local/lib/python3.7/dist-packages (from nbformat>=4.2.0->ipywidgets->jupyter->d2l==0.14) (4.3.3)\n",
            "Requirement already satisfied: jupyter-core in /usr/local/lib/python3.7/dist-packages (from nbformat>=4.2.0->ipywidgets->jupyter->d2l==0.14) (4.9.1)\n",
            "Requirement already satisfied: attrs>=17.4.0 in /usr/local/lib/python3.7/dist-packages (from jsonschema!=2.5.0,>=2.4->nbformat>=4.2.0->ipywidgets->jupyter->d2l==0.14) (21.4.0)\n",
            "Requirement already satisfied: pyrsistent!=0.17.0,!=0.17.1,!=0.17.2,>=0.14.0 in /usr/local/lib/python3.7/dist-packages (from jsonschema!=2.5.0,>=2.4->nbformat>=4.2.0->ipywidgets->jupyter->d2l==0.14) (0.18.1)\n",
            "Requirement already satisfied: importlib-metadata in /usr/local/lib/python3.7/dist-packages (from jsonschema!=2.5.0,>=2.4->nbformat>=4.2.0->ipywidgets->jupyter->d2l==0.14) (4.10.1)\n",
            "Requirement already satisfied: typing-extensions in /usr/local/lib/python3.7/dist-packages (from jsonschema!=2.5.0,>=2.4->nbformat>=4.2.0->ipywidgets->jupyter->d2l==0.14) (3.10.0.2)\n",
            "Requirement already satisfied: importlib-resources>=1.4.0 in /usr/local/lib/python3.7/dist-packages (from jsonschema!=2.5.0,>=2.4->nbformat>=4.2.0->ipywidgets->jupyter->d2l==0.14) (5.4.0)\n",
            "Requirement already satisfied: zipp>=3.1.0 in /usr/local/lib/python3.7/dist-packages (from importlib-resources>=1.4.0->jsonschema!=2.5.0,>=2.4->nbformat>=4.2.0->ipywidgets->jupyter->d2l==0.14) (3.7.0)\n",
            "Requirement already satisfied: Send2Trash in /usr/local/lib/python3.7/dist-packages (from notebook->jupyter->d2l==0.14) (1.8.0)\n",
            "Requirement already satisfied: jinja2 in /usr/local/lib/python3.7/dist-packages (from notebook->jupyter->d2l==0.14) (2.11.3)\n",
            "Requirement already satisfied: terminado>=0.8.1 in /usr/local/lib/python3.7/dist-packages (from notebook->jupyter->d2l==0.14) (0.12.1)\n",
            "Requirement already satisfied: python-dateutil>=2.1 in /usr/local/lib/python3.7/dist-packages (from jupyter-client->ipykernel->jupyter->d2l==0.14) (2.8.2)\n",
            "Requirement already satisfied: pyzmq>=13 in /usr/local/lib/python3.7/dist-packages (from jupyter-client->ipykernel->jupyter->d2l==0.14) (22.3.0)\n",
            "Requirement already satisfied: ptyprocess in /usr/local/lib/python3.7/dist-packages (from terminado>=0.8.1->notebook->jupyter->d2l==0.14) (0.7.0)\n",
            "Requirement already satisfied: MarkupSafe>=0.23 in /usr/local/lib/python3.7/dist-packages (from jinja2->notebook->jupyter->d2l==0.14) (2.0.1)\n",
            "Requirement already satisfied: kiwisolver>=1.0.1 in /usr/local/lib/python3.7/dist-packages (from matplotlib->d2l==0.14) (1.3.2)\n",
            "Requirement already satisfied: pyparsing!=2.0.4,!=2.1.2,!=2.1.6,>=2.0.1 in /usr/local/lib/python3.7/dist-packages (from matplotlib->d2l==0.14) (3.0.7)\n",
            "Requirement already satisfied: cycler>=0.10 in /usr/local/lib/python3.7/dist-packages (from matplotlib->d2l==0.14) (0.11.0)\n",
            "Requirement already satisfied: mistune<2,>=0.8.1 in /usr/local/lib/python3.7/dist-packages (from nbconvert->jupyter->d2l==0.14) (0.8.4)\n",
            "Requirement already satisfied: pandocfilters>=1.4.1 in /usr/local/lib/python3.7/dist-packages (from nbconvert->jupyter->d2l==0.14) (1.5.0)\n",
            "Requirement already satisfied: testpath in /usr/local/lib/python3.7/dist-packages (from nbconvert->jupyter->d2l==0.14) (0.5.0)\n",
            "Requirement already satisfied: defusedxml in /usr/local/lib/python3.7/dist-packages (from nbconvert->jupyter->d2l==0.14) (0.7.1)\n",
            "Requirement already satisfied: entrypoints>=0.2.2 in /usr/local/lib/python3.7/dist-packages (from nbconvert->jupyter->d2l==0.14) (0.3)\n",
            "Requirement already satisfied: bleach in /usr/local/lib/python3.7/dist-packages (from nbconvert->jupyter->d2l==0.14) (4.1.0)\n",
            "Requirement already satisfied: packaging in /usr/local/lib/python3.7/dist-packages (from bleach->nbconvert->jupyter->d2l==0.14) (21.3)\n",
            "Requirement already satisfied: webencodings in /usr/local/lib/python3.7/dist-packages (from bleach->nbconvert->jupyter->d2l==0.14) (0.5.1)\n",
            "Requirement already satisfied: pytz>=2017.2 in /usr/local/lib/python3.7/dist-packages (from pandas->d2l==0.14) (2018.9)\n",
            "Requirement already satisfied: qtpy in /usr/local/lib/python3.7/dist-packages (from qtconsole->jupyter->d2l==0.14) (2.0.0)\n",
            "Installing collected packages: d2l\n",
            "Successfully installed d2l-0.14.0\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#多GPU数据并行的实现"
      ],
      "metadata": {
        "id": "6FNRNv863c9w"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "%matplotlib inline\n",
        "import torch\n",
        "from torch import nn\n",
        "from torch.nn import functional as F\n",
        "from d2l import torch as d2l"
      ],
      "metadata": {
        "id": "pGsmo-kEUU6g"
      },
      "execution_count": 7,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "#初始化模型参数\n",
        "scale = 0.01\n",
        "W1 = torch.randn(size=(20,1,3,3))*scale\n",
        "b1 = torch.zeros(20)\n",
        "W2 = torch.randn(size=(50,20,5,5))*scale\n",
        "b2 = torch.zeros(50)\n",
        "W3 = torch.randn(size=(800,128))*scale\n",
        "b3 = torch.zeros(128)\n",
        "W4 = torch.randn(size=(128,10))*scale\n",
        "b4 = torch.zeros(10)\n",
        "params = [W1,b1,W2,b2,W3,b3,W4,b4]\n",
        "\n",
        "#定义LeNet模型\n",
        "def lenet(X,params):\n",
        "    h1_conv = F.conv2d(input=X,weight=params[0],bias=params[1])\n",
        "    h1_activation = F.relu(h1_conv)\n",
        "    h1 = F.avg_pool2d(input=h1_activation,kernel_size=(2,2),stride=(2,2))\n",
        "    h2_conv = F.conv2d(input=h1,weight=params[2],bias=params[3])\n",
        "    h2_activation = F.relu(h2_conv)\n",
        "    h2 = F.avg_pool2d(input=h2_activation,kernel_size=(2,2),stride=(2,2))\n",
        "    h2 = h2.reshape(h2.shape[0],-1)\n",
        "    h3_linear = torch.mm(h2,params[4]) + params[5]\n",
        "    h3 = F.relu(h3_linear)\n",
        "    y_hat = torch.mm(h3,params[6])+params[7]\n",
        "    return y_hat\n",
        "\n",
        "#交叉熵损失函数\n",
        "loss = nn.CrossEntropyLoss(reduction='none')"
      ],
      "metadata": {
        "id": "b5lKSX7KbPUe"
      },
      "execution_count": 8,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "#确定CPU还是GPU训练，定义梯度下降\n",
        "def get_params(params,device):\n",
        "    new_params = [p.to(device) for p in params]\n",
        "    for p in new_params:\n",
        "        p.requires_grad_()\n",
        "    return new_params"
      ],
      "metadata": {
        "id": "U95GZMaduPFw"
      },
      "execution_count": 9,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "new_params = get_params(params,d2l.try_gpu(0))\n",
        "print('b1 weight:',new_params[1])\n",
        "print('b1 grad:',new_params[1].grad)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "tL2CN2Ggurok",
        "outputId": "0a823b10-001a-4f46-fd54-d9cdedb08042"
      },
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "b1 weight: tensor([0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.],\n",
            "       device='cuda:0', requires_grad=True)\n",
            "b1 grad: None\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#数据累积和数据复制\n",
        "def allreduce(data):\n",
        "    for i in range(1,len(data)):\n",
        "        data[0][:] += data[i].to(data[0].device)\n",
        "    for i in range(1,len(data)):\n",
        "        data[i][:] = data[0].to(data[i].device)"
      ],
      "metadata": {
        "id": "DCxTDrH0vAo9"
      },
      "execution_count": 11,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "data = [torch.ones((1,2),device=d2l.try_gpu(i))*(i+1) for i in range(2)]\n",
        "print('allreduce before: \\n',data[0],'\\n',data[1])\n",
        "allreduce(data)\n",
        "print('allreduce after: \\n',data[0],'\\n',data[1])"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "pX9BenRNvb7X",
        "outputId": "f3efd303-a61c-45e8-c08a-f88ae6abdd82"
      },
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "allreduce before: \n",
            " tensor([[1., 1.]], device='cuda:0') \n",
            " tensor([[2., 2.]])\n",
            "allreduce after: \n",
            " tensor([[3., 3.]], device='cuda:0') \n",
            " tensor([[3., 3.]])\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "data = torch.arange(20).reshape(4,5)\n",
        "devices = tf.config.list_logical_devices('GPU')\n",
        "split = nn.parallel.scatter(data,devices)\n",
        "print('input:',data)\n",
        "print('load into',devices)\n",
        "print('output:',split)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "cCZXamnIwV2j",
        "outputId": "2ef81fe7-d1b2-452c-9eab-198c5fe4b4ad"
      },
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "input: tensor([[ 0,  1,  2,  3,  4],\n",
            "        [ 5,  6,  7,  8,  9],\n",
            "        [10, 11, 12, 13, 14],\n",
            "        [15, 16, 17, 18, 19]])\n",
            "load into [LogicalDevice(name='/device:GPU:0', device_type='GPU'), LogicalDevice(name='/device:GPU:1', device_type='GPU')]\n",
            "output: (tensor([[0, 1, 2, 3, 4],\n",
            "        [5, 6, 7, 8, 9]], device='cuda:0'), tensor([[10, 11, 12, 13, 14],\n",
            "        [15, 16, 17, 18, 19]], device='cuda:0'))\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#将数据分配到各个GPU上\n",
        "def split_batch(X,y,devices):\n",
        "    \"\"\"将x和y拆分到多个设备上\"\"\"\n",
        "    assert X.shape[0] == y.shape[0]\n",
        "    return (nn.parallel.scatter(X,devices),\n",
        "            nn.parallel.scatter(y,devices))"
      ],
      "metadata": {
        "id": "vUV8uEEfysoN"
      },
      "execution_count": 14,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "#小批量训练\n",
        "def train_batch(X,y,device_params,devices,lr):\n",
        "    X_shards,y_shards = split_batch(X,y,devices)\n",
        "    #在每个GPU上分别计算损失\n",
        "    ls = [loss(lenet(X_shard,device_W),y_shard).sum() for X_shard,y_shard ,device_W in zip(X_shards,y_shards,device_params)]\n",
        "    for l in ls:  #反向传播在每个GPU上分别执行\n",
        "        l.backward()\n",
        "    #将每个GPU的所有梯度相加，并将其广播到所有GPU\n",
        "    with torch.no_grad():\n",
        "        for i in range(len(device_params[0])):\n",
        "            allreduce([device_params[c][i].grad for c in range(len(devices))])\n",
        "    #在每个GPU上分别更新模型参数\n",
        "    for param in device_params:\n",
        "        d2l.sgd(param,lr,X.shape[0]) # 使用全尺寸的小批量"
      ],
      "metadata": {
        "id": "FArYLHj20VST"
      },
      "execution_count": 15,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "#训练函数\n",
        "def train(num_gpus,batch_size,lr):\n",
        "    train_iter,test_iter = d2l.load_data_fashion_mnist(batch_size)\n",
        "    devices = [d2l.try_gpu(i) for i in range(num_gpus)]\n",
        "    #将模型参数复制到num_gpus个GPU\n",
        "    device_params = [get_params(params,d) for d in devices]\n",
        "    num_epochs = 10\n",
        "    animator = d2l.Animator('epoch','test acc',xlim=[1,num_epochs])\n",
        "    timer = d2l.Timer()\n",
        "    for epoch in range(num_epochs):\n",
        "        timer.start()\n",
        "        for X,y in train_iter:\n",
        "            #为单个小批量执行多GPU训练\n",
        "            train_batch(X,y,device_params,devices,lr)\n",
        "            torch.cuda.synchronize()\n",
        "        timer.stop()\n",
        "        #在GPU0上评估模型\n",
        "        animator.add(epoch+1,(d2l.evaluate_accuracy_gpu(lambda x: lenet(x,device_params[0]),test_iter,devices[0]),))\n",
        "    print(f'test acc:{animator.Y[0][-1]:.2f},{timer.avg():.1f}s/round,'\n",
        "          f'at{str(devices)}')"
      ],
      "metadata": {
        "id": "Jo9d0YR33Asa"
      },
      "execution_count": 18,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "train(num_gpus=1,batch_size=256,lr=0.2)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 279
        },
        "id": "Mb5BTgM-5jir",
        "outputId": "0ef5798e-ca4f-47d6-c6bf-d1c43acbf11f"
      },
      "execution_count": 19,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "test acc:0.83,9.5s/round,at[device(type='cuda', index=0)]\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 252x180 with 1 Axes>"
            ],
            "image/svg+xml": "<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>\n<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n  \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n<!-- Created with matplotlib (https://matplotlib.org/) -->\n<svg height=\"180.65625pt\" version=\"1.1\" viewBox=\"0 0 252.64375 180.65625\" width=\"252.64375pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n <defs>\n  <style type=\"text/css\">\n*{stroke-linecap:butt;stroke-linejoin:round;}\n  </style>\n </defs>\n <g id=\"figure_1\">\n  <g id=\"patch_1\">\n   <path d=\"M 0 180.65625 \nL 252.64375 180.65625 \nL 252.64375 0 \nL 0 0 \nz\n\" style=\"fill:none;\"/>\n  </g>\n  <g id=\"axes_1\">\n   <g id=\"patch_2\">\n    <path d=\"M 43.78125 143.1 \nL 239.08125 143.1 \nL 239.08125 7.2 \nL 43.78125 7.2 \nz\n\" style=\"fill:#ffffff;\"/>\n   </g>\n   <g id=\"matplotlib.axis_1\">\n    <g id=\"xtick_1\">\n     <g id=\"line2d_1\">\n      <path clip-path=\"url(#p0be343fa73)\" d=\"M 65.48125 143.1 \nL 65.48125 7.2 \n\" style=\"fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;\"/>\n     </g>\n     <g id=\"line2d_2\">\n      <defs>\n       <path d=\"M 0 0 \nL 0 3.5 \n\" id=\"m3d7542ac9c\" style=\"stroke:#000000;stroke-width:0.8;\"/>\n      </defs>\n      <g>\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"65.48125\" xlink:href=\"#m3d7542ac9c\" y=\"143.1\"/>\n      </g>\n     </g>\n     <g id=\"text_1\">\n      <!-- 2 -->\n      <defs>\n       <path d=\"M 19.1875 8.296875 \nL 53.609375 8.296875 \nL 53.609375 0 \nL 7.328125 0 \nL 7.328125 8.296875 \nQ 12.9375 14.109375 22.625 23.890625 \nQ 32.328125 33.6875 34.8125 36.53125 \nQ 39.546875 41.84375 41.421875 45.53125 \nQ 43.3125 49.21875 43.3125 52.78125 \nQ 43.3125 58.59375 39.234375 62.25 \nQ 35.15625 65.921875 28.609375 65.921875 \nQ 23.96875 65.921875 18.8125 64.3125 \nQ 13.671875 62.703125 7.8125 59.421875 \nL 7.8125 69.390625 \nQ 13.765625 71.78125 18.9375 73 \nQ 24.125 74.21875 28.421875 74.21875 \nQ 39.75 74.21875 46.484375 68.546875 \nQ 53.21875 62.890625 53.21875 53.421875 \nQ 53.21875 48.921875 51.53125 44.890625 \nQ 49.859375 40.875 45.40625 35.40625 \nQ 44.1875 33.984375 37.640625 27.21875 \nQ 31.109375 20.453125 19.1875 8.296875 \nz\n\" id=\"DejaVuSans-50\"/>\n      </defs>\n      <g transform=\"translate(62.3 157.698438)scale(0.1 -0.1)\">\n       <use xlink:href=\"#DejaVuSans-50\"/>\n      </g>\n     </g>\n    </g>\n    <g id=\"xtick_2\">\n     <g id=\"line2d_3\">\n      <path clip-path=\"url(#p0be343fa73)\" d=\"M 108.88125 143.1 \nL 108.88125 7.2 \n\" style=\"fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;\"/>\n     </g>\n     <g id=\"line2d_4\">\n      <g>\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"108.88125\" xlink:href=\"#m3d7542ac9c\" y=\"143.1\"/>\n      </g>\n     </g>\n     <g id=\"text_2\">\n      <!-- 4 -->\n      <defs>\n       <path d=\"M 37.796875 64.3125 \nL 12.890625 25.390625 \nL 37.796875 25.390625 \nz\nM 35.203125 72.90625 \nL 47.609375 72.90625 \nL 47.609375 25.390625 \nL 58.015625 25.390625 \nL 58.015625 17.1875 \nL 47.609375 17.1875 \nL 47.609375 0 \nL 37.796875 0 \nL 37.796875 17.1875 \nL 4.890625 17.1875 \nL 4.890625 26.703125 \nz\n\" id=\"DejaVuSans-52\"/>\n      </defs>\n      <g transform=\"translate(105.7 157.698438)scale(0.1 -0.1)\">\n       <use xlink:href=\"#DejaVuSans-52\"/>\n      </g>\n     </g>\n    </g>\n    <g id=\"xtick_3\">\n     <g id=\"line2d_5\">\n      <path clip-path=\"url(#p0be343fa73)\" d=\"M 152.28125 143.1 \nL 152.28125 7.2 \n\" style=\"fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;\"/>\n     </g>\n     <g id=\"line2d_6\">\n      <g>\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"152.28125\" xlink:href=\"#m3d7542ac9c\" y=\"143.1\"/>\n      </g>\n     </g>\n     <g id=\"text_3\">\n      <!-- 6 -->\n      <defs>\n       <path d=\"M 33.015625 40.375 \nQ 26.375 40.375 22.484375 35.828125 \nQ 18.609375 31.296875 18.609375 23.390625 \nQ 18.609375 15.53125 22.484375 10.953125 \nQ 26.375 6.390625 33.015625 6.390625 \nQ 39.65625 6.390625 43.53125 10.953125 \nQ 47.40625 15.53125 47.40625 23.390625 \nQ 47.40625 31.296875 43.53125 35.828125 \nQ 39.65625 40.375 33.015625 40.375 \nz\nM 52.59375 71.296875 \nL 52.59375 62.3125 \nQ 48.875 64.0625 45.09375 64.984375 \nQ 41.3125 65.921875 37.59375 65.921875 \nQ 27.828125 65.921875 22.671875 59.328125 \nQ 17.53125 52.734375 16.796875 39.40625 \nQ 19.671875 43.65625 24.015625 45.921875 \nQ 28.375 48.1875 33.59375 48.1875 \nQ 44.578125 48.1875 50.953125 41.515625 \nQ 57.328125 34.859375 57.328125 23.390625 \nQ 57.328125 12.15625 50.6875 5.359375 \nQ 44.046875 -1.421875 33.015625 -1.421875 \nQ 20.359375 -1.421875 13.671875 8.265625 \nQ 6.984375 17.96875 6.984375 36.375 \nQ 6.984375 53.65625 15.1875 63.9375 \nQ 23.390625 74.21875 37.203125 74.21875 \nQ 40.921875 74.21875 44.703125 73.484375 \nQ 48.484375 72.75 52.59375 71.296875 \nz\n\" id=\"DejaVuSans-54\"/>\n      </defs>\n      <g transform=\"translate(149.1 157.698438)scale(0.1 -0.1)\">\n       <use xlink:href=\"#DejaVuSans-54\"/>\n      </g>\n     </g>\n    </g>\n    <g id=\"xtick_4\">\n     <g id=\"line2d_7\">\n      <path clip-path=\"url(#p0be343fa73)\" d=\"M 195.68125 143.1 \nL 195.68125 7.2 \n\" style=\"fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;\"/>\n     </g>\n     <g id=\"line2d_8\">\n      <g>\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"195.68125\" xlink:href=\"#m3d7542ac9c\" y=\"143.1\"/>\n      </g>\n     </g>\n     <g id=\"text_4\">\n      <!-- 8 -->\n      <defs>\n       <path d=\"M 31.78125 34.625 \nQ 24.75 34.625 20.71875 30.859375 \nQ 16.703125 27.09375 16.703125 20.515625 \nQ 16.703125 13.921875 20.71875 10.15625 \nQ 24.75 6.390625 31.78125 6.390625 \nQ 38.8125 6.390625 42.859375 10.171875 \nQ 46.921875 13.96875 46.921875 20.515625 \nQ 46.921875 27.09375 42.890625 30.859375 \nQ 38.875 34.625 31.78125 34.625 \nz\nM 21.921875 38.8125 \nQ 15.578125 40.375 12.03125 44.71875 \nQ 8.5 49.078125 8.5 55.328125 \nQ 8.5 64.0625 14.71875 69.140625 \nQ 20.953125 74.21875 31.78125 74.21875 \nQ 42.671875 74.21875 48.875 69.140625 \nQ 55.078125 64.0625 55.078125 55.328125 \nQ 55.078125 49.078125 51.53125 44.71875 \nQ 48 40.375 41.703125 38.8125 \nQ 48.828125 37.15625 52.796875 32.3125 \nQ 56.78125 27.484375 56.78125 20.515625 \nQ 56.78125 9.90625 50.3125 4.234375 \nQ 43.84375 -1.421875 31.78125 -1.421875 \nQ 19.734375 -1.421875 13.25 4.234375 \nQ 6.78125 9.90625 6.78125 20.515625 \nQ 6.78125 27.484375 10.78125 32.3125 \nQ 14.796875 37.15625 21.921875 38.8125 \nz\nM 18.3125 54.390625 \nQ 18.3125 48.734375 21.84375 45.5625 \nQ 25.390625 42.390625 31.78125 42.390625 \nQ 38.140625 42.390625 41.71875 45.5625 \nQ 45.3125 48.734375 45.3125 54.390625 \nQ 45.3125 60.0625 41.71875 63.234375 \nQ 38.140625 66.40625 31.78125 66.40625 \nQ 25.390625 66.40625 21.84375 63.234375 \nQ 18.3125 60.0625 18.3125 54.390625 \nz\n\" id=\"DejaVuSans-56\"/>\n      </defs>\n      <g transform=\"translate(192.5 157.698438)scale(0.1 -0.1)\">\n       <use xlink:href=\"#DejaVuSans-56\"/>\n      </g>\n     </g>\n    </g>\n    <g id=\"xtick_5\">\n     <g id=\"line2d_9\">\n      <path clip-path=\"url(#p0be343fa73)\" d=\"M 239.08125 143.1 \nL 239.08125 7.2 \n\" style=\"fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;\"/>\n     </g>\n     <g id=\"line2d_10\">\n      <g>\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"239.08125\" xlink:href=\"#m3d7542ac9c\" y=\"143.1\"/>\n      </g>\n     </g>\n     <g id=\"text_5\">\n      <!-- 10 -->\n      <defs>\n       <path d=\"M 12.40625 8.296875 \nL 28.515625 8.296875 \nL 28.515625 63.921875 \nL 10.984375 60.40625 \nL 10.984375 69.390625 \nL 28.421875 72.90625 \nL 38.28125 72.90625 \nL 38.28125 8.296875 \nL 54.390625 8.296875 \nL 54.390625 0 \nL 12.40625 0 \nz\n\" id=\"DejaVuSans-49\"/>\n       <path d=\"M 31.78125 66.40625 \nQ 24.171875 66.40625 20.328125 58.90625 \nQ 16.5 51.421875 16.5 36.375 \nQ 16.5 21.390625 20.328125 13.890625 \nQ 24.171875 6.390625 31.78125 6.390625 \nQ 39.453125 6.390625 43.28125 13.890625 \nQ 47.125 21.390625 47.125 36.375 \nQ 47.125 51.421875 43.28125 58.90625 \nQ 39.453125 66.40625 31.78125 66.40625 \nz\nM 31.78125 74.21875 \nQ 44.046875 74.21875 50.515625 64.515625 \nQ 56.984375 54.828125 56.984375 36.375 \nQ 56.984375 17.96875 50.515625 8.265625 \nQ 44.046875 -1.421875 31.78125 -1.421875 \nQ 19.53125 -1.421875 13.0625 8.265625 \nQ 6.59375 17.96875 6.59375 36.375 \nQ 6.59375 54.828125 13.0625 64.515625 \nQ 19.53125 74.21875 31.78125 74.21875 \nz\n\" id=\"DejaVuSans-48\"/>\n      </defs>\n      <g transform=\"translate(232.71875 157.698438)scale(0.1 -0.1)\">\n       <use xlink:href=\"#DejaVuSans-49\"/>\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-48\"/>\n      </g>\n     </g>\n    </g>\n    <g id=\"text_6\">\n     <!-- epoch -->\n     <defs>\n      <path d=\"M 56.203125 29.59375 \nL 56.203125 25.203125 \nL 14.890625 25.203125 \nQ 15.484375 15.921875 20.484375 11.0625 \nQ 25.484375 6.203125 34.421875 6.203125 \nQ 39.59375 6.203125 44.453125 7.46875 \nQ 49.3125 8.734375 54.109375 11.28125 \nL 54.109375 2.78125 \nQ 49.265625 0.734375 44.1875 -0.34375 \nQ 39.109375 -1.421875 33.890625 -1.421875 \nQ 20.796875 -1.421875 13.15625 6.1875 \nQ 5.515625 13.8125 5.515625 26.8125 \nQ 5.515625 40.234375 12.765625 48.109375 \nQ 20.015625 56 32.328125 56 \nQ 43.359375 56 49.78125 48.890625 \nQ 56.203125 41.796875 56.203125 29.59375 \nz\nM 47.21875 32.234375 \nQ 47.125 39.59375 43.09375 43.984375 \nQ 39.0625 48.390625 32.421875 48.390625 \nQ 24.90625 48.390625 20.390625 44.140625 \nQ 15.875 39.890625 15.1875 32.171875 \nz\n\" id=\"DejaVuSans-101\"/>\n      <path d=\"M 18.109375 8.203125 \nL 18.109375 -20.796875 \nL 9.078125 -20.796875 \nL 9.078125 54.6875 \nL 18.109375 54.6875 \nL 18.109375 46.390625 \nQ 20.953125 51.265625 25.265625 53.625 \nQ 29.59375 56 35.59375 56 \nQ 45.5625 56 51.78125 48.09375 \nQ 58.015625 40.1875 58.015625 27.296875 \nQ 58.015625 14.40625 51.78125 6.484375 \nQ 45.5625 -1.421875 35.59375 -1.421875 \nQ 29.59375 -1.421875 25.265625 0.953125 \nQ 20.953125 3.328125 18.109375 8.203125 \nz\nM 48.6875 27.296875 \nQ 48.6875 37.203125 44.609375 42.84375 \nQ 40.53125 48.484375 33.40625 48.484375 \nQ 26.265625 48.484375 22.1875 42.84375 \nQ 18.109375 37.203125 18.109375 27.296875 \nQ 18.109375 17.390625 22.1875 11.75 \nQ 26.265625 6.109375 33.40625 6.109375 \nQ 40.53125 6.109375 44.609375 11.75 \nQ 48.6875 17.390625 48.6875 27.296875 \nz\n\" id=\"DejaVuSans-112\"/>\n      <path d=\"M 30.609375 48.390625 \nQ 23.390625 48.390625 19.1875 42.75 \nQ 14.984375 37.109375 14.984375 27.296875 \nQ 14.984375 17.484375 19.15625 11.84375 \nQ 23.34375 6.203125 30.609375 6.203125 \nQ 37.796875 6.203125 41.984375 11.859375 \nQ 46.1875 17.53125 46.1875 27.296875 \nQ 46.1875 37.015625 41.984375 42.703125 \nQ 37.796875 48.390625 30.609375 48.390625 \nz\nM 30.609375 56 \nQ 42.328125 56 49.015625 48.375 \nQ 55.71875 40.765625 55.71875 27.296875 \nQ 55.71875 13.875 49.015625 6.21875 \nQ 42.328125 -1.421875 30.609375 -1.421875 \nQ 18.84375 -1.421875 12.171875 6.21875 \nQ 5.515625 13.875 5.515625 27.296875 \nQ 5.515625 40.765625 12.171875 48.375 \nQ 18.84375 56 30.609375 56 \nz\n\" id=\"DejaVuSans-111\"/>\n      <path d=\"M 48.78125 52.59375 \nL 48.78125 44.1875 \nQ 44.96875 46.296875 41.140625 47.34375 \nQ 37.3125 48.390625 33.40625 48.390625 \nQ 24.65625 48.390625 19.8125 42.84375 \nQ 14.984375 37.3125 14.984375 27.296875 \nQ 14.984375 17.28125 19.8125 11.734375 \nQ 24.65625 6.203125 33.40625 6.203125 \nQ 37.3125 6.203125 41.140625 7.25 \nQ 44.96875 8.296875 48.78125 10.40625 \nL 48.78125 2.09375 \nQ 45.015625 0.34375 40.984375 -0.53125 \nQ 36.96875 -1.421875 32.421875 -1.421875 \nQ 20.0625 -1.421875 12.78125 6.34375 \nQ 5.515625 14.109375 5.515625 27.296875 \nQ 5.515625 40.671875 12.859375 48.328125 \nQ 20.21875 56 33.015625 56 \nQ 37.15625 56 41.109375 55.140625 \nQ 45.0625 54.296875 48.78125 52.59375 \nz\n\" id=\"DejaVuSans-99\"/>\n      <path d=\"M 54.890625 33.015625 \nL 54.890625 0 \nL 45.90625 0 \nL 45.90625 32.71875 \nQ 45.90625 40.484375 42.875 44.328125 \nQ 39.84375 48.1875 33.796875 48.1875 \nQ 26.515625 48.1875 22.3125 43.546875 \nQ 18.109375 38.921875 18.109375 30.90625 \nL 18.109375 0 \nL 9.078125 0 \nL 9.078125 75.984375 \nL 18.109375 75.984375 \nL 18.109375 46.1875 \nQ 21.34375 51.125 25.703125 53.5625 \nQ 30.078125 56 35.796875 56 \nQ 45.21875 56 50.046875 50.171875 \nQ 54.890625 44.34375 54.890625 33.015625 \nz\n\" id=\"DejaVuSans-104\"/>\n     </defs>\n     <g transform=\"translate(126.203125 171.376563)scale(0.1 -0.1)\">\n      <use xlink:href=\"#DejaVuSans-101\"/>\n      <use x=\"61.523438\" xlink:href=\"#DejaVuSans-112\"/>\n      <use x=\"125\" xlink:href=\"#DejaVuSans-111\"/>\n      <use x=\"186.181641\" xlink:href=\"#DejaVuSans-99\"/>\n      <use x=\"241.162109\" xlink:href=\"#DejaVuSans-104\"/>\n     </g>\n    </g>\n   </g>\n   <g id=\"matplotlib.axis_2\">\n    <g id=\"ytick_1\">\n     <g id=\"line2d_11\">\n      <path clip-path=\"url(#p0be343fa73)\" d=\"M 43.78125 119.940534 \nL 239.08125 119.940534 \n\" style=\"fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;\"/>\n     </g>\n     <g id=\"line2d_12\">\n      <defs>\n       <path d=\"M 0 0 \nL -3.5 0 \n\" id=\"md1d2e75660\" style=\"stroke:#000000;stroke-width:0.8;\"/>\n      </defs>\n      <g>\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"43.78125\" xlink:href=\"#md1d2e75660\" y=\"119.940534\"/>\n      </g>\n     </g>\n     <g id=\"text_7\">\n      <!-- 0.2 -->\n      <defs>\n       <path d=\"M 10.6875 12.40625 \nL 21 12.40625 \nL 21 0 \nL 10.6875 0 \nz\n\" id=\"DejaVuSans-46\"/>\n      </defs>\n      <g transform=\"translate(20.878125 123.739753)scale(0.1 -0.1)\">\n       <use xlink:href=\"#DejaVuSans-48\"/>\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-46\"/>\n       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-50\"/>\n      </g>\n     </g>\n    </g>\n    <g id=\"ytick_2\">\n     <g id=\"line2d_13\">\n      <path clip-path=\"url(#p0be343fa73)\" d=\"M 43.78125 85.976148 \nL 239.08125 85.976148 \n\" style=\"fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;\"/>\n     </g>\n     <g id=\"line2d_14\">\n      <g>\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"43.78125\" xlink:href=\"#md1d2e75660\" y=\"85.976148\"/>\n      </g>\n     </g>\n     <g id=\"text_8\">\n      <!-- 0.4 -->\n      <g transform=\"translate(20.878125 89.775367)scale(0.1 -0.1)\">\n       <use xlink:href=\"#DejaVuSans-48\"/>\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-46\"/>\n       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-52\"/>\n      </g>\n     </g>\n    </g>\n    <g id=\"ytick_3\">\n     <g id=\"line2d_15\">\n      <path clip-path=\"url(#p0be343fa73)\" d=\"M 43.78125 52.011762 \nL 239.08125 52.011762 \n\" style=\"fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;\"/>\n     </g>\n     <g id=\"line2d_16\">\n      <g>\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"43.78125\" xlink:href=\"#md1d2e75660\" y=\"52.011762\"/>\n      </g>\n     </g>\n     <g id=\"text_9\">\n      <!-- 0.6 -->\n      <g transform=\"translate(20.878125 55.810981)scale(0.1 -0.1)\">\n       <use xlink:href=\"#DejaVuSans-48\"/>\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-46\"/>\n       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-54\"/>\n      </g>\n     </g>\n    </g>\n    <g id=\"ytick_4\">\n     <g id=\"line2d_17\">\n      <path clip-path=\"url(#p0be343fa73)\" d=\"M 43.78125 18.047376 \nL 239.08125 18.047376 \n\" style=\"fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;\"/>\n     </g>\n     <g id=\"line2d_18\">\n      <g>\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"43.78125\" xlink:href=\"#md1d2e75660\" y=\"18.047376\"/>\n      </g>\n     </g>\n     <g id=\"text_10\">\n      <!-- 0.8 -->\n      <g transform=\"translate(20.878125 21.846595)scale(0.1 -0.1)\">\n       <use xlink:href=\"#DejaVuSans-48\"/>\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-46\"/>\n       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-56\"/>\n      </g>\n     </g>\n    </g>\n    <g id=\"text_11\">\n     <!-- test acc -->\n     <defs>\n      <path d=\"M 18.3125 70.21875 \nL 18.3125 54.6875 \nL 36.8125 54.6875 \nL 36.8125 47.703125 \nL 18.3125 47.703125 \nL 18.3125 18.015625 \nQ 18.3125 11.328125 20.140625 9.421875 \nQ 21.96875 7.515625 27.59375 7.515625 \nL 36.8125 7.515625 \nL 36.8125 0 \nL 27.59375 0 \nQ 17.1875 0 13.234375 3.875 \nQ 9.28125 7.765625 9.28125 18.015625 \nL 9.28125 47.703125 \nL 2.6875 47.703125 \nL 2.6875 54.6875 \nL 9.28125 54.6875 \nL 9.28125 70.21875 \nz\n\" id=\"DejaVuSans-116\"/>\n      <path d=\"M 44.28125 53.078125 \nL 44.28125 44.578125 \nQ 40.484375 46.53125 36.375 47.5 \nQ 32.28125 48.484375 27.875 48.484375 \nQ 21.1875 48.484375 17.84375 46.4375 \nQ 14.5 44.390625 14.5 40.28125 \nQ 14.5 37.15625 16.890625 35.375 \nQ 19.28125 33.59375 26.515625 31.984375 \nL 29.59375 31.296875 \nQ 39.15625 29.25 43.1875 25.515625 \nQ 47.21875 21.78125 47.21875 15.09375 \nQ 47.21875 7.46875 41.1875 3.015625 \nQ 35.15625 -1.421875 24.609375 -1.421875 \nQ 20.21875 -1.421875 15.453125 -0.5625 \nQ 10.6875 0.296875 5.421875 2 \nL 5.421875 11.28125 \nQ 10.40625 8.6875 15.234375 7.390625 \nQ 20.0625 6.109375 24.8125 6.109375 \nQ 31.15625 6.109375 34.5625 8.28125 \nQ 37.984375 10.453125 37.984375 14.40625 \nQ 37.984375 18.0625 35.515625 20.015625 \nQ 33.0625 21.96875 24.703125 23.78125 \nL 21.578125 24.515625 \nQ 13.234375 26.265625 9.515625 29.90625 \nQ 5.8125 33.546875 5.8125 39.890625 \nQ 5.8125 47.609375 11.28125 51.796875 \nQ 16.75 56 26.8125 56 \nQ 31.78125 56 36.171875 55.265625 \nQ 40.578125 54.546875 44.28125 53.078125 \nz\n\" id=\"DejaVuSans-115\"/>\n      <path id=\"DejaVuSans-32\"/>\n      <path d=\"M 34.28125 27.484375 \nQ 23.390625 27.484375 19.1875 25 \nQ 14.984375 22.515625 14.984375 16.5 \nQ 14.984375 11.71875 18.140625 8.90625 \nQ 21.296875 6.109375 26.703125 6.109375 \nQ 34.1875 6.109375 38.703125 11.40625 \nQ 43.21875 16.703125 43.21875 25.484375 \nL 43.21875 27.484375 \nz\nM 52.203125 31.203125 \nL 52.203125 0 \nL 43.21875 0 \nL 43.21875 8.296875 \nQ 40.140625 3.328125 35.546875 0.953125 \nQ 30.953125 -1.421875 24.3125 -1.421875 \nQ 15.921875 -1.421875 10.953125 3.296875 \nQ 6 8.015625 6 15.921875 \nQ 6 25.140625 12.171875 29.828125 \nQ 18.359375 34.515625 30.609375 34.515625 \nL 43.21875 34.515625 \nL 43.21875 35.40625 \nQ 43.21875 41.609375 39.140625 45 \nQ 35.0625 48.390625 27.6875 48.390625 \nQ 23 48.390625 18.546875 47.265625 \nQ 14.109375 46.140625 10.015625 43.890625 \nL 10.015625 52.203125 \nQ 14.9375 54.109375 19.578125 55.046875 \nQ 24.21875 56 28.609375 56 \nQ 40.484375 56 46.34375 49.84375 \nQ 52.203125 43.703125 52.203125 31.203125 \nz\n\" id=\"DejaVuSans-97\"/>\n     </defs>\n     <g transform=\"translate(14.798438 94.903125)rotate(-90)scale(0.1 -0.1)\">\n      <use xlink:href=\"#DejaVuSans-116\"/>\n      <use x=\"39.208984\" xlink:href=\"#DejaVuSans-101\"/>\n      <use x=\"100.732422\" xlink:href=\"#DejaVuSans-115\"/>\n      <use x=\"152.832031\" xlink:href=\"#DejaVuSans-116\"/>\n      <use x=\"192.041016\" xlink:href=\"#DejaVuSans-32\"/>\n      <use x=\"223.828125\" xlink:href=\"#DejaVuSans-97\"/>\n      <use x=\"285.107422\" xlink:href=\"#DejaVuSans-99\"/>\n      <use x=\"340.087891\" xlink:href=\"#DejaVuSans-99\"/>\n     </g>\n    </g>\n   </g>\n   <g id=\"line2d_19\">\n    <path clip-path=\"url(#p0be343fa73)\" d=\"M 43.78125 136.922727 \nL 65.48125 42.70552 \nL 87.18125 34.8088 \nL 108.88125 23.88925 \nL 130.58125 20.798491 \nL 152.28125 16.094424 \nL 173.98125 14.75283 \nL 195.68125 16.45105 \nL 217.38125 18.437966 \nL 239.08125 13.377273 \n\" style=\"fill:none;stroke:#1f77b4;stroke-linecap:square;stroke-width:1.5;\"/>\n   </g>\n   <g id=\"patch_3\">\n    <path d=\"M 43.78125 143.1 \nL 43.78125 7.2 \n\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n   </g>\n   <g id=\"patch_4\">\n    <path d=\"M 239.08125 143.1 \nL 239.08125 7.2 \n\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n   </g>\n   <g id=\"patch_5\">\n    <path d=\"M 43.78125 143.1 \nL 239.08125 143.1 \n\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n   </g>\n   <g id=\"patch_6\">\n    <path d=\"M 43.78125 7.2 \nL 239.08125 7.2 \n\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n   </g>\n  </g>\n </g>\n <defs>\n  <clipPath id=\"p0be343fa73\">\n   <rect height=\"135.9\" width=\"195.3\" x=\"43.78125\" y=\"7.2\"/>\n  </clipPath>\n </defs>\n</svg>\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#利用pytorch框架实现"
      ],
      "metadata": {
        "id": "31gYmNceH_fl"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import torch\n",
        "from torch import nn\n",
        "from d2l import torch as d2l"
      ],
      "metadata": {
        "id": "sUuKGN8n5o_h"
      },
      "execution_count": 21,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "#搭建ResNet18模型\n",
        "def resnet18(num_classes,in_channels=1):\n",
        "    \"\"\"经过修改的ResNet18模型\"\"\"\n",
        "    def resnet_block(in_channels,out_channels,num_residuals,first_block=False):\n",
        "        blk = []\n",
        "        for i in range(num_residuals):\n",
        "            if i == 0 and not first_block:\n",
        "                blk.append(d2l.Residual(in_channels,out_channels,use_1x1conv=True,strides=2))\n",
        "            else:\n",
        "                blk.append(d2l.Residual(out_channels,out_channels))\n",
        "        return nn.Sequential(*blk)\n",
        "\n",
        "    #该模型使用了更小的卷积核、步长和填充，而且删除了最大汇聚层\n",
        "    net = nn.Sequential(\n",
        "        nn.Conv2d(in_channels,64,kernel_size=3,stride=1,padding=1),\n",
        "        nn.BatchNorm2d(64),\n",
        "        nn.ReLU())\n",
        "    net.add_module(\"resnet_block1\",resnet_block(64,64,2,first_block=True))\n",
        "    net.add_module(\"resnet_block2\",resnet_block(64,128,2))\n",
        "    net.add_module(\"resnet_block3\",resnet_block(128,256,2))\n",
        "    net.add_module(\"resnet_block4\",resnet_block(256,512,2))\n",
        "    net.add_module(\"global_avg_pool\",nn.AdaptiveAvgPool2d((1,1)))\n",
        "    net.add_module(\"fc\",nn.Sequential(nn.Flatten(),nn.Linear(512,num_classes)))\n",
        "    return net"
      ],
      "metadata": {
        "id": "gq2zpt1PCu1V"
      },
      "execution_count": 26,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "net = resnet18(10)\n",
        "#获得GPU列表\n",
        "devices = d2l.try_all_gpus()"
      ],
      "metadata": {
        "id": "fMJrTQBVFaf5"
      },
      "execution_count": 27,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def train(net,num_gpus,batch_size,lr):\n",
        "    train_iter,test_iter = d2l.load_data_fashion_mnist(batch_size)\n",
        "    devices = [d2l.try_gpu(i) for i in range(num_gpus)]\n",
        "    #初始化网络\n",
        "    def init_weights(m):\n",
        "        if type(m) in [nn.Linear,nn.Conv2d]:\n",
        "            nn.init.normal_(m.weight,std=0.01)\n",
        "    net.apply(init_weights)\n",
        "    #在多个GPU上设置模型\n",
        "    net = nn.DataParallel(net,device_ids=devices)\n",
        "    trainer = torch.optim.SGD(net.parameters(),lr)\n",
        "    loss = nn.CrossEntropyLoss()\n",
        "    timer,num_epochs = d2l.Timer(),10\n",
        "    animator = d2l.Animator('epoch','test acc',xlim=[1,num_epochs])\n",
        "    for epoch in range(num_epochs):\n",
        "        net.train()\n",
        "        timer.start()\n",
        "        for X,y in train_iter:\n",
        "            trainer.zero_grad()\n",
        "            X,y = X.to(devices[0]),y.to(devices[0])\n",
        "            l = loss(net(X),y)\n",
        "            l.backward()\n",
        "            trainer.step()\n",
        "        timer.stop()\n",
        "        animator.add(epoch+1,(d2l.evaluate_accuracy_gpu(net,test_iter),))\n",
        "    print(f'test acc:{animator.Y[0][-1]:.2f},{timer.avg():.1f}s/round,'\n",
        "          f'at{str(devices)}')"
      ],
      "metadata": {
        "id": "xTRfsoXYFjEx"
      },
      "execution_count": 28,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "train(net,num_gpus=1,batch_size=256,lr=0.1)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 284
        },
        "id": "NlMNxz1fG3yc",
        "outputId": "94bc35e3-f58c-4eb9-98e8-297aee10ba7c"
      },
      "execution_count": 29,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "test acc:0.89,88.5s/round,at[device(type='cuda', index=0)]\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 252x180 with 1 Axes>"
            ],
            "image/svg+xml": "<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>\n<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n  \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n<!-- Created with matplotlib (https://matplotlib.org/) -->\n<svg height=\"184.285268pt\" version=\"1.1\" viewBox=\"0 0 259.00625 184.285268\" width=\"259.00625pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n <defs>\n  <style type=\"text/css\">\n*{stroke-linecap:butt;stroke-linejoin:round;}\n  </style>\n </defs>\n <g id=\"figure_1\">\n  <g id=\"patch_1\">\n   <path d=\"M 0 184.285268 \nL 259.00625 184.285268 \nL 259.00625 0 \nL 0 0 \nz\n\" style=\"fill:none;\"/>\n  </g>\n  <g id=\"axes_1\">\n   <g id=\"patch_2\">\n    <path d=\"M 50.14375 146.729018 \nL 245.44375 146.729018 \nL 245.44375 10.829018 \nL 50.14375 10.829018 \nz\n\" style=\"fill:#ffffff;\"/>\n   </g>\n   <g id=\"matplotlib.axis_1\">\n    <g id=\"xtick_1\">\n     <g id=\"line2d_1\">\n      <path clip-path=\"url(#pba2b5be525)\" d=\"M 71.84375 146.729018 \nL 71.84375 10.829018 \n\" style=\"fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;\"/>\n     </g>\n     <g id=\"line2d_2\">\n      <defs>\n       <path d=\"M 0 0 \nL 0 3.5 \n\" id=\"m7ac9f249ed\" style=\"stroke:#000000;stroke-width:0.8;\"/>\n      </defs>\n      <g>\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"71.84375\" xlink:href=\"#m7ac9f249ed\" y=\"146.729018\"/>\n      </g>\n     </g>\n     <g id=\"text_1\">\n      <!-- 2 -->\n      <defs>\n       <path d=\"M 19.1875 8.296875 \nL 53.609375 8.296875 \nL 53.609375 0 \nL 7.328125 0 \nL 7.328125 8.296875 \nQ 12.9375 14.109375 22.625 23.890625 \nQ 32.328125 33.6875 34.8125 36.53125 \nQ 39.546875 41.84375 41.421875 45.53125 \nQ 43.3125 49.21875 43.3125 52.78125 \nQ 43.3125 58.59375 39.234375 62.25 \nQ 35.15625 65.921875 28.609375 65.921875 \nQ 23.96875 65.921875 18.8125 64.3125 \nQ 13.671875 62.703125 7.8125 59.421875 \nL 7.8125 69.390625 \nQ 13.765625 71.78125 18.9375 73 \nQ 24.125 74.21875 28.421875 74.21875 \nQ 39.75 74.21875 46.484375 68.546875 \nQ 53.21875 62.890625 53.21875 53.421875 \nQ 53.21875 48.921875 51.53125 44.890625 \nQ 49.859375 40.875 45.40625 35.40625 \nQ 44.1875 33.984375 37.640625 27.21875 \nQ 31.109375 20.453125 19.1875 8.296875 \nz\n\" id=\"DejaVuSans-50\"/>\n      </defs>\n      <g transform=\"translate(68.6625 161.327456)scale(0.1 -0.1)\">\n       <use xlink:href=\"#DejaVuSans-50\"/>\n      </g>\n     </g>\n    </g>\n    <g id=\"xtick_2\">\n     <g id=\"line2d_3\">\n      <path clip-path=\"url(#pba2b5be525)\" d=\"M 115.24375 146.729018 \nL 115.24375 10.829018 \n\" style=\"fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;\"/>\n     </g>\n     <g id=\"line2d_4\">\n      <g>\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"115.24375\" xlink:href=\"#m7ac9f249ed\" y=\"146.729018\"/>\n      </g>\n     </g>\n     <g id=\"text_2\">\n      <!-- 4 -->\n      <defs>\n       <path d=\"M 37.796875 64.3125 \nL 12.890625 25.390625 \nL 37.796875 25.390625 \nz\nM 35.203125 72.90625 \nL 47.609375 72.90625 \nL 47.609375 25.390625 \nL 58.015625 25.390625 \nL 58.015625 17.1875 \nL 47.609375 17.1875 \nL 47.609375 0 \nL 37.796875 0 \nL 37.796875 17.1875 \nL 4.890625 17.1875 \nL 4.890625 26.703125 \nz\n\" id=\"DejaVuSans-52\"/>\n      </defs>\n      <g transform=\"translate(112.0625 161.327456)scale(0.1 -0.1)\">\n       <use xlink:href=\"#DejaVuSans-52\"/>\n      </g>\n     </g>\n    </g>\n    <g id=\"xtick_3\">\n     <g id=\"line2d_5\">\n      <path clip-path=\"url(#pba2b5be525)\" d=\"M 158.64375 146.729018 \nL 158.64375 10.829018 \n\" style=\"fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;\"/>\n     </g>\n     <g id=\"line2d_6\">\n      <g>\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"158.64375\" xlink:href=\"#m7ac9f249ed\" y=\"146.729018\"/>\n      </g>\n     </g>\n     <g id=\"text_3\">\n      <!-- 6 -->\n      <defs>\n       <path d=\"M 33.015625 40.375 \nQ 26.375 40.375 22.484375 35.828125 \nQ 18.609375 31.296875 18.609375 23.390625 \nQ 18.609375 15.53125 22.484375 10.953125 \nQ 26.375 6.390625 33.015625 6.390625 \nQ 39.65625 6.390625 43.53125 10.953125 \nQ 47.40625 15.53125 47.40625 23.390625 \nQ 47.40625 31.296875 43.53125 35.828125 \nQ 39.65625 40.375 33.015625 40.375 \nz\nM 52.59375 71.296875 \nL 52.59375 62.3125 \nQ 48.875 64.0625 45.09375 64.984375 \nQ 41.3125 65.921875 37.59375 65.921875 \nQ 27.828125 65.921875 22.671875 59.328125 \nQ 17.53125 52.734375 16.796875 39.40625 \nQ 19.671875 43.65625 24.015625 45.921875 \nQ 28.375 48.1875 33.59375 48.1875 \nQ 44.578125 48.1875 50.953125 41.515625 \nQ 57.328125 34.859375 57.328125 23.390625 \nQ 57.328125 12.15625 50.6875 5.359375 \nQ 44.046875 -1.421875 33.015625 -1.421875 \nQ 20.359375 -1.421875 13.671875 8.265625 \nQ 6.984375 17.96875 6.984375 36.375 \nQ 6.984375 53.65625 15.1875 63.9375 \nQ 23.390625 74.21875 37.203125 74.21875 \nQ 40.921875 74.21875 44.703125 73.484375 \nQ 48.484375 72.75 52.59375 71.296875 \nz\n\" id=\"DejaVuSans-54\"/>\n      </defs>\n      <g transform=\"translate(155.4625 161.327456)scale(0.1 -0.1)\">\n       <use xlink:href=\"#DejaVuSans-54\"/>\n      </g>\n     </g>\n    </g>\n    <g id=\"xtick_4\">\n     <g id=\"line2d_7\">\n      <path clip-path=\"url(#pba2b5be525)\" d=\"M 202.04375 146.729018 \nL 202.04375 10.829018 \n\" style=\"fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;\"/>\n     </g>\n     <g id=\"line2d_8\">\n      <g>\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"202.04375\" xlink:href=\"#m7ac9f249ed\" y=\"146.729018\"/>\n      </g>\n     </g>\n     <g id=\"text_4\">\n      <!-- 8 -->\n      <defs>\n       <path d=\"M 31.78125 34.625 \nQ 24.75 34.625 20.71875 30.859375 \nQ 16.703125 27.09375 16.703125 20.515625 \nQ 16.703125 13.921875 20.71875 10.15625 \nQ 24.75 6.390625 31.78125 6.390625 \nQ 38.8125 6.390625 42.859375 10.171875 \nQ 46.921875 13.96875 46.921875 20.515625 \nQ 46.921875 27.09375 42.890625 30.859375 \nQ 38.875 34.625 31.78125 34.625 \nz\nM 21.921875 38.8125 \nQ 15.578125 40.375 12.03125 44.71875 \nQ 8.5 49.078125 8.5 55.328125 \nQ 8.5 64.0625 14.71875 69.140625 \nQ 20.953125 74.21875 31.78125 74.21875 \nQ 42.671875 74.21875 48.875 69.140625 \nQ 55.078125 64.0625 55.078125 55.328125 \nQ 55.078125 49.078125 51.53125 44.71875 \nQ 48 40.375 41.703125 38.8125 \nQ 48.828125 37.15625 52.796875 32.3125 \nQ 56.78125 27.484375 56.78125 20.515625 \nQ 56.78125 9.90625 50.3125 4.234375 \nQ 43.84375 -1.421875 31.78125 -1.421875 \nQ 19.734375 -1.421875 13.25 4.234375 \nQ 6.78125 9.90625 6.78125 20.515625 \nQ 6.78125 27.484375 10.78125 32.3125 \nQ 14.796875 37.15625 21.921875 38.8125 \nz\nM 18.3125 54.390625 \nQ 18.3125 48.734375 21.84375 45.5625 \nQ 25.390625 42.390625 31.78125 42.390625 \nQ 38.140625 42.390625 41.71875 45.5625 \nQ 45.3125 48.734375 45.3125 54.390625 \nQ 45.3125 60.0625 41.71875 63.234375 \nQ 38.140625 66.40625 31.78125 66.40625 \nQ 25.390625 66.40625 21.84375 63.234375 \nQ 18.3125 60.0625 18.3125 54.390625 \nz\n\" id=\"DejaVuSans-56\"/>\n      </defs>\n      <g transform=\"translate(198.8625 161.327456)scale(0.1 -0.1)\">\n       <use xlink:href=\"#DejaVuSans-56\"/>\n      </g>\n     </g>\n    </g>\n    <g id=\"xtick_5\">\n     <g id=\"line2d_9\">\n      <path clip-path=\"url(#pba2b5be525)\" d=\"M 245.44375 146.729018 \nL 245.44375 10.829018 \n\" style=\"fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;\"/>\n     </g>\n     <g id=\"line2d_10\">\n      <g>\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"245.44375\" xlink:href=\"#m7ac9f249ed\" y=\"146.729018\"/>\n      </g>\n     </g>\n     <g id=\"text_5\">\n      <!-- 10 -->\n      <defs>\n       <path d=\"M 12.40625 8.296875 \nL 28.515625 8.296875 \nL 28.515625 63.921875 \nL 10.984375 60.40625 \nL 10.984375 69.390625 \nL 28.421875 72.90625 \nL 38.28125 72.90625 \nL 38.28125 8.296875 \nL 54.390625 8.296875 \nL 54.390625 0 \nL 12.40625 0 \nz\n\" id=\"DejaVuSans-49\"/>\n       <path d=\"M 31.78125 66.40625 \nQ 24.171875 66.40625 20.328125 58.90625 \nQ 16.5 51.421875 16.5 36.375 \nQ 16.5 21.390625 20.328125 13.890625 \nQ 24.171875 6.390625 31.78125 6.390625 \nQ 39.453125 6.390625 43.28125 13.890625 \nQ 47.125 21.390625 47.125 36.375 \nQ 47.125 51.421875 43.28125 58.90625 \nQ 39.453125 66.40625 31.78125 66.40625 \nz\nM 31.78125 74.21875 \nQ 44.046875 74.21875 50.515625 64.515625 \nQ 56.984375 54.828125 56.984375 36.375 \nQ 56.984375 17.96875 50.515625 8.265625 \nQ 44.046875 -1.421875 31.78125 -1.421875 \nQ 19.53125 -1.421875 13.0625 8.265625 \nQ 6.59375 17.96875 6.59375 36.375 \nQ 6.59375 54.828125 13.0625 64.515625 \nQ 19.53125 74.21875 31.78125 74.21875 \nz\n\" id=\"DejaVuSans-48\"/>\n      </defs>\n      <g transform=\"translate(239.08125 161.327456)scale(0.1 -0.1)\">\n       <use xlink:href=\"#DejaVuSans-49\"/>\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-48\"/>\n      </g>\n     </g>\n    </g>\n    <g id=\"text_6\">\n     <!-- epoch -->\n     <defs>\n      <path d=\"M 56.203125 29.59375 \nL 56.203125 25.203125 \nL 14.890625 25.203125 \nQ 15.484375 15.921875 20.484375 11.0625 \nQ 25.484375 6.203125 34.421875 6.203125 \nQ 39.59375 6.203125 44.453125 7.46875 \nQ 49.3125 8.734375 54.109375 11.28125 \nL 54.109375 2.78125 \nQ 49.265625 0.734375 44.1875 -0.34375 \nQ 39.109375 -1.421875 33.890625 -1.421875 \nQ 20.796875 -1.421875 13.15625 6.1875 \nQ 5.515625 13.8125 5.515625 26.8125 \nQ 5.515625 40.234375 12.765625 48.109375 \nQ 20.015625 56 32.328125 56 \nQ 43.359375 56 49.78125 48.890625 \nQ 56.203125 41.796875 56.203125 29.59375 \nz\nM 47.21875 32.234375 \nQ 47.125 39.59375 43.09375 43.984375 \nQ 39.0625 48.390625 32.421875 48.390625 \nQ 24.90625 48.390625 20.390625 44.140625 \nQ 15.875 39.890625 15.1875 32.171875 \nz\n\" id=\"DejaVuSans-101\"/>\n      <path d=\"M 18.109375 8.203125 \nL 18.109375 -20.796875 \nL 9.078125 -20.796875 \nL 9.078125 54.6875 \nL 18.109375 54.6875 \nL 18.109375 46.390625 \nQ 20.953125 51.265625 25.265625 53.625 \nQ 29.59375 56 35.59375 56 \nQ 45.5625 56 51.78125 48.09375 \nQ 58.015625 40.1875 58.015625 27.296875 \nQ 58.015625 14.40625 51.78125 6.484375 \nQ 45.5625 -1.421875 35.59375 -1.421875 \nQ 29.59375 -1.421875 25.265625 0.953125 \nQ 20.953125 3.328125 18.109375 8.203125 \nz\nM 48.6875 27.296875 \nQ 48.6875 37.203125 44.609375 42.84375 \nQ 40.53125 48.484375 33.40625 48.484375 \nQ 26.265625 48.484375 22.1875 42.84375 \nQ 18.109375 37.203125 18.109375 27.296875 \nQ 18.109375 17.390625 22.1875 11.75 \nQ 26.265625 6.109375 33.40625 6.109375 \nQ 40.53125 6.109375 44.609375 11.75 \nQ 48.6875 17.390625 48.6875 27.296875 \nz\n\" id=\"DejaVuSans-112\"/>\n      <path d=\"M 30.609375 48.390625 \nQ 23.390625 48.390625 19.1875 42.75 \nQ 14.984375 37.109375 14.984375 27.296875 \nQ 14.984375 17.484375 19.15625 11.84375 \nQ 23.34375 6.203125 30.609375 6.203125 \nQ 37.796875 6.203125 41.984375 11.859375 \nQ 46.1875 17.53125 46.1875 27.296875 \nQ 46.1875 37.015625 41.984375 42.703125 \nQ 37.796875 48.390625 30.609375 48.390625 \nz\nM 30.609375 56 \nQ 42.328125 56 49.015625 48.375 \nQ 55.71875 40.765625 55.71875 27.296875 \nQ 55.71875 13.875 49.015625 6.21875 \nQ 42.328125 -1.421875 30.609375 -1.421875 \nQ 18.84375 -1.421875 12.171875 6.21875 \nQ 5.515625 13.875 5.515625 27.296875 \nQ 5.515625 40.765625 12.171875 48.375 \nQ 18.84375 56 30.609375 56 \nz\n\" id=\"DejaVuSans-111\"/>\n      <path d=\"M 48.78125 52.59375 \nL 48.78125 44.1875 \nQ 44.96875 46.296875 41.140625 47.34375 \nQ 37.3125 48.390625 33.40625 48.390625 \nQ 24.65625 48.390625 19.8125 42.84375 \nQ 14.984375 37.3125 14.984375 27.296875 \nQ 14.984375 17.28125 19.8125 11.734375 \nQ 24.65625 6.203125 33.40625 6.203125 \nQ 37.3125 6.203125 41.140625 7.25 \nQ 44.96875 8.296875 48.78125 10.40625 \nL 48.78125 2.09375 \nQ 45.015625 0.34375 40.984375 -0.53125 \nQ 36.96875 -1.421875 32.421875 -1.421875 \nQ 20.0625 -1.421875 12.78125 6.34375 \nQ 5.515625 14.109375 5.515625 27.296875 \nQ 5.515625 40.671875 12.859375 48.328125 \nQ 20.21875 56 33.015625 56 \nQ 37.15625 56 41.109375 55.140625 \nQ 45.0625 54.296875 48.78125 52.59375 \nz\n\" id=\"DejaVuSans-99\"/>\n      <path d=\"M 54.890625 33.015625 \nL 54.890625 0 \nL 45.90625 0 \nL 45.90625 32.71875 \nQ 45.90625 40.484375 42.875 44.328125 \nQ 39.84375 48.1875 33.796875 48.1875 \nQ 26.515625 48.1875 22.3125 43.546875 \nQ 18.109375 38.921875 18.109375 30.90625 \nL 18.109375 0 \nL 9.078125 0 \nL 9.078125 75.984375 \nL 18.109375 75.984375 \nL 18.109375 46.1875 \nQ 21.34375 51.125 25.703125 53.5625 \nQ 30.078125 56 35.796875 56 \nQ 45.21875 56 50.046875 50.171875 \nQ 54.890625 44.34375 54.890625 33.015625 \nz\n\" id=\"DejaVuSans-104\"/>\n     </defs>\n     <g transform=\"translate(132.565625 175.005581)scale(0.1 -0.1)\">\n      <use xlink:href=\"#DejaVuSans-101\"/>\n      <use x=\"61.523438\" xlink:href=\"#DejaVuSans-112\"/>\n      <use x=\"125\" xlink:href=\"#DejaVuSans-111\"/>\n      <use x=\"186.181641\" xlink:href=\"#DejaVuSans-99\"/>\n      <use x=\"241.162109\" xlink:href=\"#DejaVuSans-104\"/>\n     </g>\n    </g>\n   </g>\n   <g id=\"matplotlib.axis_2\">\n    <g id=\"ytick_1\">\n     <g id=\"line2d_11\">\n      <path clip-path=\"url(#pba2b5be525)\" d=\"M 50.14375 131.140666 \nL 245.44375 131.140666 \n\" style=\"fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;\"/>\n     </g>\n     <g id=\"line2d_12\">\n      <defs>\n       <path d=\"M 0 0 \nL -3.5 0 \n\" id=\"mc7e0b0007a\" style=\"stroke:#000000;stroke-width:0.8;\"/>\n      </defs>\n      <g>\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"50.14375\" xlink:href=\"#mc7e0b0007a\" y=\"131.140666\"/>\n      </g>\n     </g>\n     <g id=\"text_7\">\n      <!-- 0.86 -->\n      <defs>\n       <path d=\"M 10.6875 12.40625 \nL 21 12.40625 \nL 21 0 \nL 10.6875 0 \nz\n\" id=\"DejaVuSans-46\"/>\n      </defs>\n      <g transform=\"translate(20.878125 134.939884)scale(0.1 -0.1)\">\n       <use xlink:href=\"#DejaVuSans-48\"/>\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-46\"/>\n       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-56\"/>\n       <use x=\"159.033203\" xlink:href=\"#DejaVuSans-54\"/>\n      </g>\n     </g>\n    </g>\n    <g id=\"ytick_2\">\n     <g id=\"line2d_13\">\n      <path clip-path=\"url(#pba2b5be525)\" d=\"M 50.14375 91.093517 \nL 245.44375 91.093517 \n\" style=\"fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;\"/>\n     </g>\n     <g id=\"line2d_14\">\n      <g>\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"50.14375\" xlink:href=\"#mc7e0b0007a\" y=\"91.093517\"/>\n      </g>\n     </g>\n     <g id=\"text_8\">\n      <!-- 0.88 -->\n      <g transform=\"translate(20.878125 94.892735)scale(0.1 -0.1)\">\n       <use xlink:href=\"#DejaVuSans-48\"/>\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-46\"/>\n       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-56\"/>\n       <use x=\"159.033203\" xlink:href=\"#DejaVuSans-56\"/>\n      </g>\n     </g>\n    </g>\n    <g id=\"ytick_3\">\n     <g id=\"line2d_15\">\n      <path clip-path=\"url(#pba2b5be525)\" d=\"M 50.14375 51.046368 \nL 245.44375 51.046368 \n\" style=\"fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;\"/>\n     </g>\n     <g id=\"line2d_16\">\n      <g>\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"50.14375\" xlink:href=\"#mc7e0b0007a\" y=\"51.046368\"/>\n      </g>\n     </g>\n     <g id=\"text_9\">\n      <!-- 0.90 -->\n      <defs>\n       <path d=\"M 10.984375 1.515625 \nL 10.984375 10.5 \nQ 14.703125 8.734375 18.5 7.8125 \nQ 22.3125 6.890625 25.984375 6.890625 \nQ 35.75 6.890625 40.890625 13.453125 \nQ 46.046875 20.015625 46.78125 33.40625 \nQ 43.953125 29.203125 39.59375 26.953125 \nQ 35.25 24.703125 29.984375 24.703125 \nQ 19.046875 24.703125 12.671875 31.3125 \nQ 6.296875 37.9375 6.296875 49.421875 \nQ 6.296875 60.640625 12.9375 67.421875 \nQ 19.578125 74.21875 30.609375 74.21875 \nQ 43.265625 74.21875 49.921875 64.515625 \nQ 56.59375 54.828125 56.59375 36.375 \nQ 56.59375 19.140625 48.40625 8.859375 \nQ 40.234375 -1.421875 26.421875 -1.421875 \nQ 22.703125 -1.421875 18.890625 -0.6875 \nQ 15.09375 0.046875 10.984375 1.515625 \nz\nM 30.609375 32.421875 \nQ 37.25 32.421875 41.125 36.953125 \nQ 45.015625 41.5 45.015625 49.421875 \nQ 45.015625 57.28125 41.125 61.84375 \nQ 37.25 66.40625 30.609375 66.40625 \nQ 23.96875 66.40625 20.09375 61.84375 \nQ 16.21875 57.28125 16.21875 49.421875 \nQ 16.21875 41.5 20.09375 36.953125 \nQ 23.96875 32.421875 30.609375 32.421875 \nz\n\" id=\"DejaVuSans-57\"/>\n      </defs>\n      <g transform=\"translate(20.878125 54.845586)scale(0.1 -0.1)\">\n       <use xlink:href=\"#DejaVuSans-48\"/>\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-46\"/>\n       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-57\"/>\n       <use x=\"159.033203\" xlink:href=\"#DejaVuSans-48\"/>\n      </g>\n     </g>\n    </g>\n    <g id=\"ytick_4\">\n     <g id=\"line2d_17\">\n      <path clip-path=\"url(#pba2b5be525)\" d=\"M 50.14375 10.999219 \nL 245.44375 10.999219 \n\" style=\"fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;\"/>\n     </g>\n     <g id=\"line2d_18\">\n      <g>\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"50.14375\" xlink:href=\"#mc7e0b0007a\" y=\"10.999219\"/>\n      </g>\n     </g>\n     <g id=\"text_10\">\n      <!-- 0.92 -->\n      <g transform=\"translate(20.878125 14.798437)scale(0.1 -0.1)\">\n       <use xlink:href=\"#DejaVuSans-48\"/>\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-46\"/>\n       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-57\"/>\n       <use x=\"159.033203\" xlink:href=\"#DejaVuSans-50\"/>\n      </g>\n     </g>\n    </g>\n    <g id=\"text_11\">\n     <!-- test acc -->\n     <defs>\n      <path d=\"M 18.3125 70.21875 \nL 18.3125 54.6875 \nL 36.8125 54.6875 \nL 36.8125 47.703125 \nL 18.3125 47.703125 \nL 18.3125 18.015625 \nQ 18.3125 11.328125 20.140625 9.421875 \nQ 21.96875 7.515625 27.59375 7.515625 \nL 36.8125 7.515625 \nL 36.8125 0 \nL 27.59375 0 \nQ 17.1875 0 13.234375 3.875 \nQ 9.28125 7.765625 9.28125 18.015625 \nL 9.28125 47.703125 \nL 2.6875 47.703125 \nL 2.6875 54.6875 \nL 9.28125 54.6875 \nL 9.28125 70.21875 \nz\n\" id=\"DejaVuSans-116\"/>\n      <path d=\"M 44.28125 53.078125 \nL 44.28125 44.578125 \nQ 40.484375 46.53125 36.375 47.5 \nQ 32.28125 48.484375 27.875 48.484375 \nQ 21.1875 48.484375 17.84375 46.4375 \nQ 14.5 44.390625 14.5 40.28125 \nQ 14.5 37.15625 16.890625 35.375 \nQ 19.28125 33.59375 26.515625 31.984375 \nL 29.59375 31.296875 \nQ 39.15625 29.25 43.1875 25.515625 \nQ 47.21875 21.78125 47.21875 15.09375 \nQ 47.21875 7.46875 41.1875 3.015625 \nQ 35.15625 -1.421875 24.609375 -1.421875 \nQ 20.21875 -1.421875 15.453125 -0.5625 \nQ 10.6875 0.296875 5.421875 2 \nL 5.421875 11.28125 \nQ 10.40625 8.6875 15.234375 7.390625 \nQ 20.0625 6.109375 24.8125 6.109375 \nQ 31.15625 6.109375 34.5625 8.28125 \nQ 37.984375 10.453125 37.984375 14.40625 \nQ 37.984375 18.0625 35.515625 20.015625 \nQ 33.0625 21.96875 24.703125 23.78125 \nL 21.578125 24.515625 \nQ 13.234375 26.265625 9.515625 29.90625 \nQ 5.8125 33.546875 5.8125 39.890625 \nQ 5.8125 47.609375 11.28125 51.796875 \nQ 16.75 56 26.8125 56 \nQ 31.78125 56 36.171875 55.265625 \nQ 40.578125 54.546875 44.28125 53.078125 \nz\n\" id=\"DejaVuSans-115\"/>\n      <path id=\"DejaVuSans-32\"/>\n      <path d=\"M 34.28125 27.484375 \nQ 23.390625 27.484375 19.1875 25 \nQ 14.984375 22.515625 14.984375 16.5 \nQ 14.984375 11.71875 18.140625 8.90625 \nQ 21.296875 6.109375 26.703125 6.109375 \nQ 34.1875 6.109375 38.703125 11.40625 \nQ 43.21875 16.703125 43.21875 25.484375 \nL 43.21875 27.484375 \nz\nM 52.203125 31.203125 \nL 52.203125 0 \nL 43.21875 0 \nL 43.21875 8.296875 \nQ 40.140625 3.328125 35.546875 0.953125 \nQ 30.953125 -1.421875 24.3125 -1.421875 \nQ 15.921875 -1.421875 10.953125 3.296875 \nQ 6 8.015625 6 15.921875 \nQ 6 25.140625 12.171875 29.828125 \nQ 18.359375 34.515625 30.609375 34.515625 \nL 43.21875 34.515625 \nL 43.21875 35.40625 \nQ 43.21875 41.609375 39.140625 45 \nQ 35.0625 48.390625 27.6875 48.390625 \nQ 23 48.390625 18.546875 47.265625 \nQ 14.109375 46.140625 10.015625 43.890625 \nL 10.015625 52.203125 \nQ 14.9375 54.109375 19.578125 55.046875 \nQ 24.21875 56 28.609375 56 \nQ 40.484375 56 46.34375 49.84375 \nQ 52.203125 43.703125 52.203125 31.203125 \nz\n\" id=\"DejaVuSans-97\"/>\n     </defs>\n     <g transform=\"translate(14.798437 98.532143)rotate(-90)scale(0.1 -0.1)\">\n      <use xlink:href=\"#DejaVuSans-116\"/>\n      <use x=\"39.208984\" xlink:href=\"#DejaVuSans-101\"/>\n      <use x=\"100.732422\" xlink:href=\"#DejaVuSans-115\"/>\n      <use x=\"152.832031\" xlink:href=\"#DejaVuSans-116\"/>\n      <use x=\"192.041016\" xlink:href=\"#DejaVuSans-32\"/>\n      <use x=\"223.828125\" xlink:href=\"#DejaVuSans-97\"/>\n      <use x=\"285.107422\" xlink:href=\"#DejaVuSans-99\"/>\n      <use x=\"340.087891\" xlink:href=\"#DejaVuSans-99\"/>\n     </g>\n    </g>\n   </g>\n   <g id=\"line2d_19\">\n    <path clip-path=\"url(#pba2b5be525)\" d=\"M 50.14375 116.323221 \nL 71.84375 140.551746 \nL 93.54375 48.843775 \nL 115.24375 30.021615 \nL 136.94375 22.012185 \nL 158.64375 39.63293 \nL 180.34375 21.611713 \nL 202.04375 17.006291 \nL 223.74375 48.643539 \nL 245.44375 74.874421 \n\" style=\"fill:none;stroke:#1f77b4;stroke-linecap:square;stroke-width:1.5;\"/>\n   </g>\n   <g id=\"patch_3\">\n    <path d=\"M 50.14375 146.729018 \nL 50.14375 10.829018 \n\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n   </g>\n   <g id=\"patch_4\">\n    <path d=\"M 245.44375 146.729018 \nL 245.44375 10.829018 \n\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n   </g>\n   <g id=\"patch_5\">\n    <path d=\"M 50.14375 146.729018 \nL 245.44375 146.729018 \n\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n   </g>\n   <g id=\"patch_6\">\n    <path d=\"M 50.14375 10.829018 \nL 245.44375 10.829018 \n\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n   </g>\n  </g>\n </g>\n <defs>\n  <clipPath id=\"pba2b5be525\">\n   <rect height=\"135.9\" width=\"195.3\" x=\"50.14375\" y=\"10.829018\"/>\n  </clipPath>\n </defs>\n</svg>\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    }
  ]
}