ASS3_Q1.ipynb

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  "metadata": {
    "colab": {
      "name": "ASS3_Q1.ipynb",
      "version": "0.3.2",
      "provenance": [],
      "collapsed_sections": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "metadata": {
        "id": "KQqHW_1cWHPG",
        "colab_type": "code",
        "outputId": "5bda04c5-d0d6-4302-b205-df5e251bebb2",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 200
        }
      },
      "cell_type": "code",
      "source": [
        "!wget https://raw.githubusercontent.com/CW-Huang/IFT6135H19_assignment/master/assignment3/samplers.py"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "--2019-04-22 20:54:32--  https://raw.githubusercontent.com/CW-Huang/IFT6135H19_assignment/master/assignment3/samplers.py\n",
            "Resolving raw.githubusercontent.com (raw.githubusercontent.com)... 151.101.0.133, 151.101.64.133, 151.101.128.133, ...\n",
            "Connecting to raw.githubusercontent.com (raw.githubusercontent.com)|151.101.0.133|:443... connected.\n",
            "HTTP request sent, awaiting response... 200 OK\n",
            "Length: 888 [text/plain]\n",
            "Saving to: ‘samplers.py.1’\n",
            "\n",
            "\rsamplers.py.1         0%[                    ]       0  --.-KB/s               \rsamplers.py.1       100%[===================>]     888  --.-KB/s    in 0s      \n",
            "\n",
            "2019-04-22 20:54:32 (163 MB/s) - ‘samplers.py.1’ saved [888/888]\n",
            "\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "id": "nHNkde0sWQVs",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "from samplers import distribution1,distribution2,distribution3,distribution4"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "u38TiKG7zJL0",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "import torch\n",
        "import torchvision\n",
        "import torch.nn as nn\n",
        "import torch.nn.functional as F"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "KomTIRPhzb-O",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "from torch.utils.data import DataLoader\n",
        "from torchvision import datasets\n",
        "from torchvision import transforms\n",
        "from torchvision.utils import save_image"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "FConpG0qzhpv",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import datetime\n",
        "import os, sys"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "L3XKSzL-znJg",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "import matplotlib.pyplot as plt\n",
        "from matplotlib.pyplot import imshow, imsave\n",
        "%matplotlib inline"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "0E-FhqdLv-Wo",
        "colab_type": "code",
        "outputId": "1c986c17-4eef-4a8a-870c-95ca1b1e81b4",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 33
        }
      },
      "cell_type": "code",
      "source": [
        "from google.colab import drive\n",
        "drive.mount('/content/drive')"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Drive already mounted at /content/drive; to attempt to forcibly remount, call drive.mount(\"/content/drive\", force_remount=True).\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "id": "Y3Hf9fvvzsl-",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "device = torch.device(\"cuda\" if torch.cuda.is_available() else \"cpu\")"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "5B_ttPwrYygX",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "class Discriminator_JS(nn.Module):\n",
        "    \"\"\"\n",
        "        Simple Discriminator w/ MLP\n",
        "    \"\"\"\n",
        "    def __init__(self, input_size=2, num_classes=1):\n",
        "        super(Discriminator_JS, self).__init__()\n",
        "        self.layer = nn.Sequential(\n",
        "            nn.Linear(input_size, 32),\n",
        "            nn.LeakyReLU(0.2),\n",
        "            #nn.Linear(32, 16),\n",
        "            #nn.LeakyReLU(0.2),\n",
        "            nn.Linear(32, 16),\n",
        "            nn.LeakyReLU(0.2),\n",
        "            nn.Linear(16, num_classes),\n",
        "            nn.Sigmoid(),\n",
        "        )\n",
        "    \n",
        "    def forward(self, x):\n",
        "        y_ = x.view(x.size(0), -1)\n",
        "        y_ = self.layer(y_)\n",
        "        return y_"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "4zpOtgQJ4eoP",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "#Loss function\n",
        "def JSD(Dx, Dy):\n",
        "  jsd = torch.log(torch.tensor(2.)) + (1/2)*torch.mean(torch.log(Dx)) + (1/2)*torch.mean(torch.log(1-Dy))\n",
        "  jsd=jsd.to(device)\n",
        "  return -jsd\n",
        "\n"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "Kue5PQI7q3m7",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "def init_weights_JS(m):\n",
        "    if type(m) == nn.Linear:\n",
        "        torch.nn.init.kaiming_normal_(m.weight)\n",
        "        m.bias.data.fill_(0.01)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "SArVguQimUxZ",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "**part 1.1**"
      ]
    },
    {
      "metadata": {
        "id": "tE46UvszamMj",
        "colab_type": "code",
        "outputId": "c6c66eaf-e87b-42f5-de43-7c46c5f9219d",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 367
        }
      },
      "cell_type": "code",
      "source": [
        "#Train loop\n",
        "batch_size = 512\n",
        "loss_JSD = []\n",
        "criterion=JSD\n",
        "\n",
        "#for epoch in range(10):\n",
        "for j in range(-10, 11):\n",
        "  D_JS = Discriminator_JS().to(device)\n",
        "  D_JS_opt= torch.optim.Adam(D_JS.parameters(), lr=0.001)\n",
        "\n",
        "  #D_JS_opt= torch.optim.SGD(D_JS.parameters(), lr=0.001)#torch.optim.Adam(D_JS.parameters(), lr=1e-3, betas=(0.5, 0.999))\n",
        "  D_JS.apply(init_weights_JS)\n",
        "  \n",
        "  for idx in range(5*1000):\n",
        "    #(x,y)=next(iter(zip(data1,data2)))  \n",
        "    x = next(iter(distribution1(0, batch_size=512)))\n",
        "    y = next(iter(distribution1(j/10, batch_size=512)))\n",
        "    \n",
        "    x=torch.from_numpy(x)\n",
        "    x=x.float()\n",
        "    x=x.to(device)\n",
        "    y=torch.from_numpy(y)\n",
        "    y=y.float()\n",
        "    y=y.to(device)\n",
        "\n",
        "\n",
        "    Dx = D_JS(x)\n",
        "    Dy = D_JS(y)\n",
        "    loss = criterion(Dx, Dy)\n",
        "    loss.to(device)\n",
        "\n",
        "    \n",
        "    loss.backward()\n",
        "    D_JS_opt.step()\n",
        "    D_JS_opt.zero_grad()\n",
        "  loss_JSD.append(-loss.item())\n",
        "  print('loss:',-loss.item())"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "loss: 0.6931391954421997\n",
            "loss: 0.6931424140930176\n",
            "loss: 0.6931426525115967\n",
            "loss: 0.6931368112564087\n",
            "loss: 0.6931414008140564\n",
            "loss: 0.6931409239768982\n",
            "loss: 0.6931359171867371\n",
            "loss: 0.6931366324424744\n",
            "loss: 0.6931369304656982\n",
            "loss: 0.693131685256958\n",
            "loss: -1.1086463928222656e-05\n",
            "loss: 0.6931231021881104\n",
            "loss: 0.69313645362854\n",
            "loss: 0.6931360960006714\n",
            "loss: 0.6931366920471191\n",
            "loss: 0.6931400895118713\n",
            "loss: 0.6931384205818176\n",
            "loss: 0.6931402683258057\n",
            "loss: 0.6931339502334595\n",
            "loss: 0.6931408047676086\n",
            "loss: 0.6931447982788086\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "id": "HEbaFiBBmbHD",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "**Part 1.2**"
      ]
    },
    {
      "metadata": {
        "id": "XNr90a0_megj",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "# loss function\n",
        "def WD(Dx, Dy, dz, lambda_=10):\n",
        "    wd = torch.mean(Dx) - torch.mean(Dy) - lambda_*torch.mean((torch.norm(dz, dim=1)-1)**2)\n",
        "    return -wd"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "Ej8edZhTqutx",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "def init_weights_WD(m):\n",
        "    if type(m) == nn.Linear:\n",
        "        torch.nn.init.kaiming_normal_(m.weight)\n",
        "        m.bias.data.fill_(0.01)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "SAYAK6WrnBrJ",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "class Discriminator_WD(nn.Module):\n",
        "    \"\"\"\n",
        "        Simple Discriminator w/ MLP\n",
        "    \"\"\"\n",
        "    def __init__(self, input_size=2, num_classes=1):\n",
        "        super(Discriminator_WD, self).__init__()\n",
        "        self.layer = nn.Sequential(\n",
        "            nn.Linear(input_size, 32),\n",
        "            nn.LeakyReLU(0.2),\n",
        "            #nn.Linear(512, 256),\n",
        "            #nn.LeakyReLU(0.2),\n",
        "            nn.Linear(32, 16),\n",
        "            nn.LeakyReLU(0.2),\n",
        "            nn.Linear(16, num_classes),\n",
        "            #nn.Sigmoid(),\n",
        "        )\n",
        "    \n",
        "    def forward(self, x):\n",
        "        y_ = x.view(x.size(0), -1)\n",
        "        y_ = self.layer(y_)\n",
        "        return y_"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "7W5jQ_r1n8VP",
        "colab_type": "code",
        "outputId": "25469a38-c089-40a2-be1c-1b4221e8882b",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 367
        }
      },
      "cell_type": "code",
      "source": [
        "#Train loop\n",
        "loss_WD = []\n",
        "criterion=WD\n",
        "#for epoch in range(10):\n",
        "for j in range(-10,11):\n",
        "  batch_size = 512\n",
        "  D_WD = Discriminator_WD().to(device)\n",
        "  D_WD_opt =torch.optim.Adam(D_WD.parameters(), lr=0.001)# torch.optim.RMSprop(D_WD.parameters(), lr=1e-5)\n",
        "  D_WD.apply(init_weights_WD)\n",
        "  \n",
        "  for idx in range(5*1000):\n",
        "    #(x,y)=next(iter(zip(data1,data2)))\n",
        "    x =next(iter(distribution1(0, batch_size=512)))\n",
        "    y =next(iter(distribution1(j/10, batch_size=512)))\n",
        "    a =next(iter(distribution2(batch_size=512)))\n",
        "    a.size \n",
        "        \n",
        "    x=torch.from_numpy(x)\n",
        "    x=x.float()\n",
        "    x=x.to(device)\n",
        "    y=torch.from_numpy(y)\n",
        "    y=y.float()\n",
        "    y=y.to(device)\n",
        "    a=torch.from_numpy(a)\n",
        "    a=a.float()\n",
        "    a=a.to(device)\n",
        "\n",
        "\n",
        "\n",
        "    Dx = D_WD(x)\n",
        "    Dy = D_WD(y)\n",
        "    \n",
        "    z = a*x + (1-a)*y\n",
        "    z.retain_grad()\n",
        "    z.requires_grad = True\n",
        "    Dz = D_WD(z)\n",
        "\n",
        "    \n",
        "    dz = torch.autograd.grad(Dz, z, grad_outputs=torch.ones_like(Dz), create_graph=True, retain_graph=True)[0]\n",
        "    loss = criterion(Dx, Dy, dz)\n",
        "    \n",
        "    #if idx % 1000 == 0:\n",
        "    #  print(loss.item())\n",
        "\n",
        "    loss.backward()\n",
        "    D_WD_opt.step()\n",
        "    #for ii in D_WD.parameters():\n",
        "    #  ii.data.clamp_(-0.01, 0.01)\n",
        "    D_WD_opt.zero_grad()\n",
        "  loss_WD.append(-loss.item()) \n",
        "  print('loss:',-loss.item())   "
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "loss: 1.0254312753677368\n",
            "loss: 0.9204578995704651\n",
            "loss: 0.8161530494689941\n",
            "loss: 0.7123019695281982\n",
            "loss: 0.6091760993003845\n",
            "loss: 0.5054112672805786\n",
            "loss: 0.4044192135334015\n",
            "loss: 0.3022436499595642\n",
            "loss: 0.20054258406162262\n",
            "loss: 0.10022018104791641\n",
            "loss: -0.005370713770389557\n",
            "loss: 0.10002093762159348\n",
            "loss: 0.20111893117427826\n",
            "loss: 0.3022443950176239\n",
            "loss: 0.4039749205112457\n",
            "loss: 0.5063872933387756\n",
            "loss: 0.6087861657142639\n",
            "loss: 0.7121270895004272\n",
            "loss: 0.8160949945449829\n",
            "loss: 0.9216030240058899\n",
            "loss: 1.024813175201416\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "id": "PZH-EX_ZrStD",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "**Part 1-3**\n",
        "\n"
      ]
    },
    {
      "metadata": {
        "id": "7V_5WXAc33c7",
        "colab_type": "code",
        "outputId": "bcb0d3fb-784b-4ded-bbcf-f0261d7791d5",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 33
        }
      },
      "cell_type": "code",
      "source": [
        "from google.colab import drive\n",
        "drive.mount('/content/drive')\n",
        "path = '/content/drive/My Drive/ift6135_A3/'"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Drive already mounted at /content/drive; to attempt to forcibly remount, call drive.mount(\"/content/drive\", force_remount=True).\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "id": "3463zlSS2VCA",
        "colab_type": "code",
        "outputId": "b9900781-2fbc-467c-d0cf-3e4bd8fdf3b8",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 295
        }
      },
      "cell_type": "code",
      "source": [
        "plt.figure()\n",
        "plt.plot([j/10 for j in range(-10,11)],loss_JSD,'ro',[j/10 for j in range(-10,11)],loss_WD, 'bo')\n",
        "plt.axis([-1.1, 1.1, -0.1, 1])\n",
        "plt.xlabel('phi')\n",
        "plt.ylabel('JSD and WD')\n",
        "plt.title('JSD and WD vs. phi')\n",
        "plt.legend(('JSD','WD'))\n",
        "plt.savefig(path+'jsd_gan_est.png')\n",
        "plt.show()\n"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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n7/uTks6vc1z/lInpN5I2Zcblub9ulLRe0q8rjJek69K4l0k6JjOutvsrIlrq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\nmVmJk4KZmZU4KZiZWcn/B/7BDHfCL5SsAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "metadata": {
        "id": "A3BmNR6HXC-p",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "**Part 1-4**"
      ]
    },
    {
      "metadata": {
        "id": "ji0OznjMXMlP",
        "colab_type": "code",
        "outputId": "902ff106-c2be-4c33-fb88-1db3d1ce6e24",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 50
        }
      },
      "cell_type": "code",
      "source": [
        "from __future__ import print_function\n",
        "import numpy as np\n",
        "import torch \n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "# plot p0 and p1\n",
        "plt.figure()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 0 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 34
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 0 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "metadata": {
        "id": "QWLEX5HCXT8j",
        "colab_type": "code",
        "outputId": "4ca15fa4-dcd3-4309-aa07-b6ef3051d482",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 285
        }
      },
      "cell_type": "code",
      "source": [
        "# empirical\n",
        "xx = torch.randn(10000)\n",
        "f = lambda x: torch.tanh(x*2+1) + x*0.75\n",
        "d = lambda x: (1-torch.tanh(x*2+1)**2)*2+0.75\n",
        "plt.hist(f(xx), 100, alpha=0.5, density=1)\n",
        "plt.hist(xx, 100, alpha=0.5, density=1)\n",
        "plt.xlim(-5,5)\n",
        "# exact\n",
        "xx = np.linspace(-5,5,1000)\n",
        "N = lambda x: np.exp(-x**2/2.)/((2*np.pi)**0.5)\n",
        "plt.plot(f(torch.from_numpy(xx)).numpy(), d(torch.from_numpy(xx)).numpy()**(-1)*N(xx))\n",
        "plt.plot(xx, N(xx))"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7f347a86ac50>]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 35
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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qufYJktyTSGp90kRC6tu2DaOnh/Sbbox3KKb7aeceFIp7YjhqPys0qQBXdwfL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\nXwzdUEbuW4HJSqlKpZQD+CT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            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "metadata": {
        "id": "RdeqhVYbDsZS",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "############### import the sampler ``samplers.distribution4'' \n",
        "############### train a discriminator on distribution4 and standard gaussian\n",
        "############### estimate the density of distribution4\n",
        "\n",
        "#######--- INSERT YOUR CODE BELOW ---#######\n",
        " \n",
        "#Train loop\n",
        "criterion=JSD\n",
        "\n",
        "\n",
        "D_JS = Discriminator_JS(input_size=1).to(device)\n",
        "D_JS_opt= torch.optim.Adam(D_JS.parameters(), lr=0.001)\n",
        "#D_JS_opt= torch.optim.SGD(D_JS.parameters(), lr=0.001)\n",
        "D_JS.apply(init_weights_JS)\n",
        "  \n",
        "for idx in range(7*1000):\n",
        "  #(x,y)=next(iter(zip(data1,data2)))  \n",
        "  x = next(iter(distribution4(batch_size=512)))\n",
        "  y = next(iter(distribution3(batch_size=512)))\n",
        "    \n",
        "  x=torch.from_numpy(x)\n",
        "  x=x.float()\n",
        "  x=x.to(device)\n",
        "  y=torch.from_numpy(y)\n",
        "  y=y.float()\n",
        "  y=y.to(device)\n",
        "\n",
        "\n",
        "  Dx = D_JS(x)\n",
        "  Dy = D_JS(y)\n",
        "  \n",
        "  loss = criterion(Dx, Dy)\n",
        "  loss.to(device)\n",
        "\n",
        "    \n",
        "\n",
        "  loss.backward()\n",
        "  D_JS_opt.step()\n",
        "  D_JS_opt.zero_grad()\n"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "eb8HWScMYTvH",
        "colab_type": "code",
        "outputId": "cd1bd9dd-950d-4b25-aa40-2dad8d4e8517",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        }
      },
      "cell_type": "code",
      "source": [
        "############### plotting things\n",
        "############### (1) plot the output of your trained discriminator \n",
        "############### (2) plot the estimated density contrasted with the true density\n",
        "\n",
        "r = D_JS(torch.from_numpy(xx).float().reshape((-1,1))).reshape(-1).detach().numpy() # evaluate xx using your discriminator; replace xx with the output\n",
        "plt.figure(figsize=(8,4))\n",
        "plt.subplot(1,2,1)\n",
        "plt.plot(xx,r)\n",
        "plt.title(r'$D(x)$')\n",
        "\n",
        "estimate = ((1/np.sqrt(2*np.pi)) * (np.e ** (-(xx**2)/2))) * r / (1 - r) # estimate the density of distribution4 (on xx) using the discriminator; \n",
        "                                # replace \"np.ones_like(xx)*0.\" with your estimate\n",
        "plt.subplot(1,2,2)\n",
        "plt.plot(xx,estimate)\n",
        "plt.plot(f(torch.from_numpy(xx)).numpy(), d(torch.from_numpy(xx)).numpy()**(-1)*N(xx))\n",
        "plt.legend(['Estimated','True'])\n",
        "plt.title('Estimated vs True')\n",
        "plt.savefig(path+'q14.png')"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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nEA5dTtKjXt9n46J73qS5e4A/XX0yX181X4exlfIy03aQBlKZkT65KYmD0Zkk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\n",
            "text/plain": [
              "<Figure size 576x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "metadata": {
        "id": "dOMK7quavLC_",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    }
  ]
}