5 - Inference and Validation.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Inference and Validation\n",
    "\n",
    "Now that you have a trained network, you can use it for making predictions. This is typically called **inference**, a term borrowed from statistics. However, neural networks have a tendency to perform *too well* on the training data and aren't able to generalize to data that hasn't been seen before. This is called **overfitting** and it impairs inference performance. To test for overfitting while training, we measure the performance on data not in the training set called the **validation** set. We avoid overfitting through regularization such as dropout while monitoring the validation performance during training. In this notebook, I'll show you how to do this in PyTorch. \n",
    "\n",
    "As usual, let's start by loading the dataset through torchvision. You'll learn more about torchvision and loading data in a later part. This time we'll be taking advantage of the test set which you can get by setting `train=False` here:\n",
    "\n",
    "```python\n",
    "testset = datasets.FashionMNIST('~/.pytorch/F_MNIST_data/', download=True, train=False, transform=transform)\n",
    "```\n",
    "\n",
    "The test set contains images just like the training set. Typically you'll see 10-20% of the original dataset held out for testing and validation with the rest being used for training."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Downloading http://fashion-mnist.s3-website.eu-central-1.amazonaws.com/train-images-idx3-ubyte.gz\n",
      "Downloading http://fashion-mnist.s3-website.eu-central-1.amazonaws.com/train-labels-idx1-ubyte.gz\n",
      "Downloading http://fashion-mnist.s3-website.eu-central-1.amazonaws.com/t10k-images-idx3-ubyte.gz\n",
      "Downloading http://fashion-mnist.s3-website.eu-central-1.amazonaws.com/t10k-labels-idx1-ubyte.gz\n",
      "Processing...\n",
      "Done!\n"
     ]
    }
   ],
   "source": [
    "import torch\n",
    "from torchvision import datasets, transforms\n",
    "\n",
    "# Define a transform to normalize the data\n",
    "transform = transforms.Compose([transforms.ToTensor(),\n",
    "                                transforms.Normalize((0.5, 0.5, 0.5), (0.5, 0.5, 0.5))])\n",
    "# Download and load the training data\n",
    "trainset = datasets.FashionMNIST('~/.pytorch/F_MNIST_data/', download=True, train=True, transform=transform)\n",
    "trainloader = torch.utils.data.DataLoader(trainset, batch_size=64, shuffle=True)\n",
    "\n",
    "# Download and load the test data\n",
    "testset = datasets.FashionMNIST('~/.pytorch/F_MNIST_data/', download=True, train=False, transform=transform)\n",
    "testloader = torch.utils.data.DataLoader(testset, batch_size=64, shuffle=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here I'll create a model like normal, using the same one from my solution for part 4."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "from torch import nn, optim\n",
    "import torch.nn.functional as F\n",
    "\n",
    "class Classifier(nn.Module):\n",
    "    def __init__(self):\n",
    "        super().__init__()\n",
    "        self.fc1 = nn.Linear(784, 256)\n",
    "        self.fc2 = nn.Linear(256, 128)\n",
    "        self.fc3 = nn.Linear(128, 64)\n",
    "        self.fc4 = nn.Linear(64, 10)\n",
    "        \n",
    "    def forward(self, x):\n",
    "        # make sure input tensor is flattened\n",
    "        x = x.view(x.shape[0], -1)\n",
    "        \n",
    "        x = F.relu(self.fc1(x))\n",
    "        x = F.relu(self.fc2(x))\n",
    "        x = F.relu(self.fc3(x))\n",
    "        x = F.log_softmax(self.fc4(x), dim=1)\n",
    "        \n",
    "        return x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The goal of validation is to measure the model's performance on data that isn't part of the training set. Performance here is up to the developer to define though. Typically this is just accuracy, the percentage of classes the network predicted correctly. Other options are [precision and recall](https://en.wikipedia.org/wiki/Precision_and_recall#Definition_(classification_context)) and top-5 error rate. We'll focus on accuracy here. First I'll do a forward pass with one batch from the test set."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "torch.Size([64, 10])\n"
     ]
    }
   ],
   "source": [
    "model = Classifier()\n",
    "\n",
    "images, labels = next(iter(testloader))\n",
    "# Get the class probabilities\n",
    "ps = torch.exp(model(images))\n",
    "# Make sure the shape is appropriate, we should get 10 class probabilities for 64 examples\n",
    "print(ps.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With the probabilities, we can get the most likely class using the `ps.topk` method. This returns the $k$ highest values. Since we just want the most likely class, we can use `ps.topk(1)`. This returns a tuple of the top-$k$ values and the top-$k$ indices. If the highest value is the fifth element, we'll get back 4 as the index."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([[ 6],\n",
      "        [ 6],\n",
      "        [ 6],\n",
      "        [ 6],\n",
      "        [ 6],\n",
      "        [ 6],\n",
      "        [ 6],\n",
      "        [ 6],\n",
      "        [ 6],\n",
      "        [ 6]])\n"
     ]
    }
   ],
   "source": [
    "top_p, top_class = ps.topk(1, dim=1)\n",
    "# Look at the most likely classes for the first 10 examples\n",
    "print(top_class[:10,:])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can check if the predicted classes match the labels. This is simple to do by equating `top_class` and `labels`, but we have to be careful of the shapes. Here `top_class` is a 2D tensor with shape `(64, 1)` while `labels` is 1D with shape `(64)`. To get the equality to work out the way we want, `top_class` and `labels` must have the same shape.\n",
    "\n",
    "If we do\n",
    "\n",
    "```python\n",
    "equals = top_class == labels\n",
    "```\n",
    "\n",
    "`equals` will have shape `(64, 64)`, try it yourself. What it's doing is comparing the one element in each row of `top_class` with each element in `labels` which returns 64 True/False boolean values for each row."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "equals = top_class == labels.view(*top_class.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we need to calculate the percentage of correct predictions. `equals` has binary values, either 0 or 1. This means that if we just sum up all the values and divide by the number of values, we get the percentage of correct predictions. This is the same operation as taking the mean, so we can get the accuracy with a call to `torch.mean`. If only it was that simple. If you try `torch.mean(equals)`, you'll get an error\n",
    "\n",
    "```\n",
    "RuntimeError: mean is not implemented for type torch.ByteTensor\n",
    "```\n",
    "\n",
    "This happens because `equals` has type `torch.ByteTensor` but `torch.mean` isn't implemented for tensors with that type. So we'll need to convert `equals` to a float tensor. Note that when we take `torch.mean` it returns a scalar tensor, to get the actual value as a float we'll need to do `accuracy.item()`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy: 9.375%\n"
     ]
    }
   ],
   "source": [
    "accuracy = torch.mean(equals.type(torch.FloatTensor))\n",
    "print(f'Accuracy: {accuracy.item()*100}%')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The network is untrained so it's making random guesses and we should see an accuracy around 10%. Now let's train our network and include our validation pass so we can measure how well the network is performing on the test set. Since we're not updating our parameters in the validation pass, we can speed up our code by turning off gradients using `torch.no_grad()`:\n",
    "\n",
    "```python\n",
    "# turn off gradients\n",
    "with torch.no_grad():\n",
    "    # validation pass here\n",
    "    for images, labels in testloader:\n",
    "        ...\n",
    "```\n",
    "\n",
    ">**Exercise:** Implement the validation loop below and print out the total accuracy after the loop. You can largely copy and paste the code from above, but I suggest typing it in because writing it out yourself is essential for building the skill. In general you'll always learn more by typing it rather than copy-pasting. You should be able to get an accuracy above 80%."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch: 1/30..  Training Loss: 0.518..  Test Loss: 0.452..  Test Accuracy: 0.842\n",
      "Epoch: 2/30..  Training Loss: 0.391..  Test Loss: 0.402..  Test Accuracy: 0.855\n",
      "Epoch: 3/30..  Training Loss: 0.353..  Test Loss: 0.391..  Test Accuracy: 0.858\n",
      "Epoch: 4/30..  Training Loss: 0.331..  Test Loss: 0.386..  Test Accuracy: 0.864\n",
      "Epoch: 5/30..  Training Loss: 0.318..  Test Loss: 0.384..  Test Accuracy: 0.863\n",
      "Epoch: 6/30..  Training Loss: 0.303..  Test Loss: 0.360..  Test Accuracy: 0.872\n",
      "Epoch: 7/30..  Training Loss: 0.290..  Test Loss: 0.403..  Test Accuracy: 0.862\n",
      "Epoch: 8/30..  Training Loss: 0.283..  Test Loss: 0.356..  Test Accuracy: 0.871\n",
      "Epoch: 9/30..  Training Loss: 0.278..  Test Loss: 0.356..  Test Accuracy: 0.876\n",
      "Epoch: 10/30..  Training Loss: 0.265..  Test Loss: 0.359..  Test Accuracy: 0.878\n",
      "Epoch: 11/30..  Training Loss: 0.261..  Test Loss: 0.385..  Test Accuracy: 0.874\n",
      "Epoch: 12/30..  Training Loss: 0.257..  Test Loss: 0.366..  Test Accuracy: 0.880\n",
      "Epoch: 13/30..  Training Loss: 0.248..  Test Loss: 0.381..  Test Accuracy: 0.872\n",
      "Epoch: 14/30..  Training Loss: 0.245..  Test Loss: 0.374..  Test Accuracy: 0.880\n",
      "Epoch: 15/30..  Training Loss: 0.236..  Test Loss: 0.372..  Test Accuracy: 0.883\n",
      "Epoch: 16/30..  Training Loss: 0.234..  Test Loss: 0.373..  Test Accuracy: 0.875\n",
      "Epoch: 17/30..  Training Loss: 0.230..  Test Loss: 0.383..  Test Accuracy: 0.874\n",
      "Epoch: 18/30..  Training Loss: 0.227..  Test Loss: 0.373..  Test Accuracy: 0.881\n",
      "Epoch: 19/30..  Training Loss: 0.222..  Test Loss: 0.373..  Test Accuracy: 0.883\n",
      "Epoch: 20/30..  Training Loss: 0.217..  Test Loss: 0.415..  Test Accuracy: 0.875\n",
      "Epoch: 21/30..  Training Loss: 0.217..  Test Loss: 0.362..  Test Accuracy: 0.886\n",
      "Epoch: 22/30..  Training Loss: 0.215..  Test Loss: 0.399..  Test Accuracy: 0.874\n",
      "Epoch: 23/30..  Training Loss: 0.207..  Test Loss: 0.373..  Test Accuracy: 0.881\n",
      "Epoch: 24/30..  Training Loss: 0.206..  Test Loss: 0.388..  Test Accuracy: 0.885\n",
      "Epoch: 25/30..  Training Loss: 0.201..  Test Loss: 0.373..  Test Accuracy: 0.885\n",
      "Epoch: 26/30..  Training Loss: 0.198..  Test Loss: 0.389..  Test Accuracy: 0.887\n",
      "Epoch: 27/30..  Training Loss: 0.195..  Test Loss: 0.403..  Test Accuracy: 0.881\n",
      "Epoch: 28/30..  Training Loss: 0.189..  Test Loss: 0.425..  Test Accuracy: 0.881\n",
      "Epoch: 29/30..  Training Loss: 0.188..  Test Loss: 0.418..  Test Accuracy: 0.883\n",
      "Epoch: 30/30..  Training Loss: 0.187..  Test Loss: 0.410..  Test Accuracy: 0.887\n"
     ]
    }
   ],
   "source": [
    "model = Classifier()\n",
    "criterion = nn.NLLLoss()\n",
    "optimizer = optim.Adam(model.parameters(), lr=0.003)\n",
    "\n",
    "epochs = 30\n",
    "steps = 0\n",
    "\n",
    "train_losses, test_losses = [], []\n",
    "for e in range(epochs):\n",
    "    running_loss = 0\n",
    "    for images, labels in trainloader:\n",
    "        \n",
    "        optimizer.zero_grad()\n",
    "        \n",
    "        log_ps = model(images)\n",
    "        loss = criterion(log_ps, labels)\n",
    "        loss.backward()\n",
    "        optimizer.step()\n",
    "        \n",
    "        running_loss += loss.item()\n",
    "        \n",
    "    else:\n",
    "        test_loss = 0\n",
    "        accuracy = 0\n",
    "        \n",
    "        # turn off gradients for validation, saves memory and computations\n",
    "        \n",
    "        with torch.no_grad():\n",
    "            for images, labels in testloader:\n",
    "                log_ps = model(images)\n",
    "                test_loss += criterion(log_ps,labels)\n",
    "                \n",
    "                ps = torch.exp(log_ps)\n",
    "                top_p, top_class = ps.topk(1, dim = 1)\n",
    "                equals = top_class == labels.view(*top_class.shape) \n",
    "                accuracy += torch.mean(equals.type(torch.FloatTensor))\n",
    "                \n",
    "                \n",
    "        train_losses.append(running_loss/len(trainloader))\n",
    "        test_losses.append(test_loss/len(testloader))\n",
    "        \n",
    "        print(\"Epoch: {}/{}.. \".format(e+1, epochs),\n",
    "              \"Training Loss: {:.3f}.. \".format(running_loss/len(trainloader)),\n",
    "              \"Test Loss: {:.3f}.. \".format(test_loss/len(testloader)),\n",
    "              \"Test Accuracy: {:.3f}\".format(accuracy/len(testloader)))\n",
    "                \n",
    "#         ## TODO: Implement the validation pass and print out the validation accuracy\n",
    "#         print(f'Accuracy: {accuracy.item()*100}%')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "%config InlineBackend.figure_format = 'retina'\n",
    "\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fe91c865f28>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fe91c8fe400>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 250,
       "width": 380
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(train_losses, label='Training loss')\n",
    "plt.plot(test_losses, label='Validation loss')\n",
    "plt.legend(frameon=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Overfitting\n",
    "\n",
    "If we look at the training and validation losses as we train the network, we can see a phenomenon known as overfitting.\n",
    "\n",
    "<img src='assets/overfitting.png' width=450px>\n",
    "\n",
    "The network learns the training set better and better, resulting in lower training losses. However, it starts having problems generalizing to data outside the training set leading to the validation loss increasing. The ultimate goal of any deep learning model is to make predictions on new data, so we should strive to get the lowest validation loss possible. One option is to use the version of the model with the lowest validation loss, here the one around 8-10 training epochs. This strategy is called *early-stopping*. In practice, you'd save the model frequently as you're training then later choose the model with the lowest validation loss.\n",
    "\n",
    "The most common method to reduce overfitting (outside of early-stopping) is *dropout*, where we randomly drop input units. This forces the network to share information between weights, increasing it's ability to generalize to new data. Adding dropout in PyTorch is straightforward using the [`nn.Dropout`](https://pytorch.org/docs/stable/nn.html#torch.nn.Dropout) module.\n",
    "\n",
    "```python\n",
    "class Classifier(nn.Module):\n",
    "    def __init__(self):\n",
    "        super().__init__()\n",
    "        self.fc1 = nn.Linear(784, 256)\n",
    "        self.fc2 = nn.Linear(256, 128)\n",
    "        self.fc3 = nn.Linear(128, 64)\n",
    "        self.fc4 = nn.Linear(64, 10)\n",
    "        \n",
    "        # Dropout module with 0.2 drop probability\n",
    "        self.dropout = nn.Dropout(p=0.2)\n",
    "        \n",
    "    def forward(self, x):\n",
    "        # make sure input tensor is flattened\n",
    "        x = x.view(x.shape[0], -1)\n",
    "        \n",
    "        # Now with dropout\n",
    "        x = self.dropout(F.relu(self.fc1(x)))\n",
    "        x = self.dropout(F.relu(self.fc2(x)))\n",
    "        x = self.dropout(F.relu(self.fc3(x)))\n",
    "        \n",
    "        # output so no dropout here\n",
    "        x = F.log_softmax(self.fc4(x), dim=1)\n",
    "        \n",
    "        return x\n",
    "```\n",
    "\n",
    "During training we want to use dropout to prevent overfitting, but during inference we want to use the entire network. So, we need to turn off dropout during validation, testing, and whenever we're using the network to make predictions. To do this, you use `model.eval()`. This sets the model to evaluation mode where the dropout probability is 0. You can turn dropout back on by setting the model to train mode with `model.train()`. In general, the pattern for the validation loop will look like this, where you turn off gradients, set the model to evaluation mode, calculate the validation loss and metric, then set the model back to train mode.\n",
    "\n",
    "```python\n",
    "# turn off gradients\n",
    "with torch.no_grad():\n",
    "    \n",
    "    # set model to evaluation mode\n",
    "    model.eval()\n",
    "    \n",
    "    # validation pass here\n",
    "    for images, labels in testloader:\n",
    "        ...\n",
    "\n",
    "# set model back to train mode\n",
    "model.train()\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> **Exercise:** Add dropout to your model and train it on Fashion-MNIST again. See if you can get a lower validation loss or higher accuracy."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "## TODO: Define your model with dropout added\n",
    "\n",
    "\n",
    "\n",
    "class Classifier(nn.Module):\n",
    "    def __init__(self):\n",
    "        super().__init__()\n",
    "        self.fc1 = nn.Linear(784,256)\n",
    "        self.fc2 = nn.Linear(256,128)\n",
    "        self.fc3 = nn.Linear(128,64)\n",
    "        self.fc4 = nn.Linear(64,10)\n",
    "        \n",
    "        # dropout module with 0.2 dropout probablity\n",
    "        self.dropout = nn.Dropout(p=0.2)\n",
    "        \n",
    "    def forward(self,x):\n",
    "        #make sure input tensor is flattened\n",
    "        \n",
    "        x = x.view(x.shape[0], -1)\n",
    "        \n",
    "        # Now with dropout\n",
    "        \n",
    "        x = self.dropout(F.relu(self.fc1(x)))\n",
    "        x = self.dropout(F.relu(self.fc2(x)))\n",
    "        x = self.dropout(F.relu(self.fc3(x)))\n",
    "        \n",
    "        \n",
    "        # output so no dropout here\n",
    "        \n",
    "        x = F.log_softmax(self.fc4(x), dim = 1)\n",
    "        \n",
    "        \n",
    "        \n",
    "        return x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch: 1/30..  Training Loss: 0.610..  Test Loss: 0.004..  Test Accuracy: 0.833\n",
      "Epoch: 2/30..  Training Loss: 0.482..  Test Loss: 0.004..  Test Accuracy: 0.835\n",
      "Epoch: 3/30..  Training Loss: 0.453..  Test Loss: 0.006..  Test Accuracy: 0.838\n",
      "Epoch: 4/30..  Training Loss: 0.434..  Test Loss: 0.002..  Test Accuracy: 0.857\n",
      "Epoch: 5/30..  Training Loss: 0.423..  Test Loss: 0.002..  Test Accuracy: 0.860\n",
      "Epoch: 6/30..  Training Loss: 0.415..  Test Loss: 0.002..  Test Accuracy: 0.840\n",
      "Epoch: 7/30..  Training Loss: 0.407..  Test Loss: 0.001..  Test Accuracy: 0.855\n",
      "Epoch: 8/30..  Training Loss: 0.399..  Test Loss: 0.003..  Test Accuracy: 0.854\n",
      "Epoch: 9/30..  Training Loss: 0.400..  Test Loss: 0.003..  Test Accuracy: 0.861\n",
      "Epoch: 10/30..  Training Loss: 0.389..  Test Loss: 0.002..  Test Accuracy: 0.858\n",
      "Epoch: 11/30..  Training Loss: 0.387..  Test Loss: 0.003..  Test Accuracy: 0.865\n",
      "Epoch: 12/30..  Training Loss: 0.382..  Test Loss: 0.003..  Test Accuracy: 0.863\n",
      "Epoch: 13/30..  Training Loss: 0.378..  Test Loss: 0.001..  Test Accuracy: 0.866\n",
      "Epoch: 14/30..  Training Loss: 0.374..  Test Loss: 0.003..  Test Accuracy: 0.869\n",
      "Epoch: 15/30..  Training Loss: 0.370..  Test Loss: 0.002..  Test Accuracy: 0.866\n",
      "Epoch: 16/30..  Training Loss: 0.372..  Test Loss: 0.002..  Test Accuracy: 0.867\n",
      "Epoch: 17/30..  Training Loss: 0.365..  Test Loss: 0.000..  Test Accuracy: 0.867\n",
      "Epoch: 18/30..  Training Loss: 0.367..  Test Loss: 0.001..  Test Accuracy: 0.868\n",
      "Epoch: 19/30..  Training Loss: 0.358..  Test Loss: 0.001..  Test Accuracy: 0.869\n",
      "Epoch: 20/30..  Training Loss: 0.361..  Test Loss: 0.003..  Test Accuracy: 0.874\n",
      "Epoch: 21/30..  Training Loss: 0.355..  Test Loss: 0.005..  Test Accuracy: 0.868\n",
      "Epoch: 22/30..  Training Loss: 0.350..  Test Loss: 0.003..  Test Accuracy: 0.863\n",
      "Epoch: 23/30..  Training Loss: 0.355..  Test Loss: 0.001..  Test Accuracy: 0.876\n",
      "Epoch: 24/30..  Training Loss: 0.348..  Test Loss: 0.003..  Test Accuracy: 0.868\n",
      "Epoch: 25/30..  Training Loss: 0.355..  Test Loss: 0.001..  Test Accuracy: 0.856\n",
      "Epoch: 26/30..  Training Loss: 0.341..  Test Loss: 0.001..  Test Accuracy: 0.873\n",
      "Epoch: 27/30..  Training Loss: 0.345..  Test Loss: 0.002..  Test Accuracy: 0.868\n",
      "Epoch: 28/30..  Training Loss: 0.340..  Test Loss: 0.001..  Test Accuracy: 0.868\n",
      "Epoch: 29/30..  Training Loss: 0.347..  Test Loss: 0.002..  Test Accuracy: 0.872\n",
      "Epoch: 30/30..  Training Loss: 0.348..  Test Loss: 0.002..  Test Accuracy: 0.877\n"
     ]
    }
   ],
   "source": [
    "## TODO: Train your model with dropout, and monitor the training progress with the validation loss and accuracy\n",
    "\n",
    "\n",
    "model = Classifier()\n",
    "criterion = nn.NLLLoss()\n",
    "optimizer = optim.Adam(model.parameters(), lr=0.003)\n",
    "\n",
    "epochs = 30\n",
    "steps = 0\n",
    "\n",
    "\n",
    "train_losses, test_losses = [], [] \n",
    "for e in range(epochs):\n",
    "    running_loss = 0\n",
    "    for images, labels  in trainloader:\n",
    "        \n",
    "        optimizer.zero_grad()\n",
    "        \n",
    "        log_ps = model(images)\n",
    "        loss = criterion(log_ps, labels)\n",
    "        loss.backward()\n",
    "        optimizer.step()\n",
    "        \n",
    "        \n",
    "        running_loss += loss.item()\n",
    "        \n",
    "        \n",
    "    else:\n",
    "        \n",
    "        test_loss = 0\n",
    "        accuracy = 0\n",
    "        \n",
    "        \n",
    "        # turn off gradients for validation, saves memory and computations\n",
    "        \n",
    "        with torch.no_grad():\n",
    "            model.eval()\n",
    "            for images, labels in testloader:\n",
    "                log_ps = model(images)\n",
    "                test_loss = criterion(log_ps, labels)\n",
    "                \n",
    "                \n",
    "                ps = torch.exp(log_ps)\n",
    "                top_p, top_class = ps.topk(1, dim=1)\n",
    "                equals = top_class == labels.view(*top_class.shape)\n",
    "                accuracy += torch.mean(equals.type(torch.FloatTensor))\n",
    "                \n",
    "        model.train()\n",
    "        \n",
    "        \n",
    "        train_losses.append(running_loss/len(trainloader))\n",
    "        test_losses.append(test_loss/len(testloader))\n",
    "        \n",
    "        \n",
    "        print(\"Epoch: {}/{}.. \".format(e+1, epochs),\n",
    "              \"Training Loss: {:.3f}.. \".format(running_loss/len(trainloader)),\n",
    "              \"Test Loss: {:.3f}.. \".format(test_loss/len(testloader)),\n",
    "              \"Test Accuracy: {:.3f}\".format(accuracy/len(testloader)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "%config InlineBackend.figure_format = 'retina'\n",
    "\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fe91c723470>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fe91c5c59b0>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 250,
       "width": 373
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(train_losses, label='Training loss')\n",
    "plt.plot(test_losses, label='Validation loss')\n",
    "plt.legend(frameon=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Inference\n",
    "\n",
    "Now that the model is trained, we can use it for inference. We've done this before, but now we need to remember to set the model in inference mode with `model.eval()`. You'll also want to turn off autograd with the `torch.no_grad()` context."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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iSWpDkjQkR5wkSRMuyQOA+wLfaXe9aAq7s7HWV9Vp7eunVXUs8HfA9oAPMZKkrYSFkyRpMowUSkcApwHPTTKvNyDJwnb62+uTvC7JRUluTPLzJA8Z1ECShye5OskJSRaME7ddkve3+VcnuTTJh8Y7ZwjXt9u1fW3tk+RbSa5NsjLJ2UleMEqf7pjkuCRXJlmV5Lz2M5jRHl8IXNWGv6VnquBRG9FnSdJGcKqeJGlCtQXSc4GfV9X5ST4LfBp4GvDFUU55JXA+8A/t+7cDJyW5U1VdP0o8SZ4FfAH4HPCqqlo3Rtx84MfAHYB3AecA9wLeBtw7yYFVVUNc08j/L0em6r0PuBY4qSfmHsCpwBXAq4BrgOcBxybZpare28bdro2bTTPl70/AwcD7gbsArwAuB54AnAx8FvhM28wlA/o51nTIvQZdoyRpfBZOkqSJ9gyaaWzHtO+/CnyIZhRqtMLpBuDgkeInyeXAL4AnAl/pD07yBuCdwD+NFCPjeDVwH+DBVfWrdt8PklwKHE9TnHx3QI4FwJq+fZcDT66qK3r2HUVTDB1QVSMFzklJdqAZNfpkWwi+FtgDeGBPn76XZCbwsiQfqqoLe4qgS6rqtAF9lCRNMqfqSZIm2ouA5TQFE1V1A/A1YP8kdx4l/sS+EaNz2u2efXFJ8kngrcChQxRN0IzknAucnWTWyAv4HlDA/kPkWAE8sH09mGbk7EKaouihPXGPBn7YUzSNOJZmoYeH9sT9tqdo6o0LNy9E0VlV7Tfai2ZET5K0ESycJEkTJsldgb+imcI2I8kO7YjL8TRFwWGjnLa0901VrWy/nNcXNwd4NvAbBo8SjdiFZsRpTd/rhrY/Ow+RY31V/ap9/bKqvgE8ieb+pn/tiduJZiSq32U9x7vESZI2I07VkyRNpBfSFCTPaF/9FiV5S1Wt34Dcq4ADaEaLTknyhKq6dsA5V9OMGL1wnOOdVdXyJH+gWTlwxFJg11HCd+9ra9g4SdJmxMJJkjQh2nt0XgD8AXjxKCFPoVkA4nE0ix50VlVnJXkUcAqwOMljq+rKcU45AfgnYGlVXbQhbY4myW1oFonobfsHwFOT7FZVvSNKf0szdfG0nrgjk+xbVWf2xRXwo/b9qnbbP/ImSZoCFk6SpInyRJpRkzdU1eL+g0l+Q7Ni3IvYwMIJoKrOS/JImuLpJ+3KeGOtNvch4Olt3Adp7p+aAdyRpoD7UFWdOqDJGT3Lo8+gWdjh1cBtaRaEGPFWmnuqFid5G82qen9D86ynI3pWCPwgTZF0YpJ/oVlV7yCaz+bjVXVhe503JLkYeHKS7wPXAZdN4gN3JUnjsHCSJE2UFwGruXk1vVuoqquSfINmVGaYe4vGVFV/7Cme/ifJY6rqj6PE3dTGvZHmobV3opm6dzHNyM8wo1DzgJ+PpKQZZToPeGpVfbOnrQuSPIxm2fN/b887DzisfWjuSNxVbdy729d2wB9pnnnVe88UNCN37wdOpLnH663csliTJG0iGeLxFVukx8545vS8MEkawvfX/2emug/afCQ5Y84ud9l3t0UfnvDcS44+aMJzStJE2W+//TjzzDPPbFcY3SiuqidJkiRJA1g4SZIkSdIAFk6SJEmSNICFkyRJkiQN4Kp6kiRtBfbZY3vOcCEHSdpgjjhJkiRJ0gAWTpIkSZI0gIWTJEmSJA1g4SRJkiRJA1g4SZIkSdIAFk6SJEmSNICFkyRJkiQNYOEkSZIkSQNYOEmSJEnSABZOkiRJkjSAhZMkSZIkDWDhJElSR0kWJam+15VJfpTkiVPdP0nSxLNwkiRpwx0GPBR4GPBSYD1wUpKDprRXkqQJN2uqOyBJ0hbs3Kr61cibJCcD1wKHAidOWa8kSRPOESdJkibOSmA1sHZkR5KjkvwyyTVJliU5M8mLkqT3xCRzk3wgyV+SLE/y0yQPSrIkybGb+DokSX0ccZIkacPNTDILCLAL8I/AAuDLPTF7Ap8ALm7fPwT4N2AP4G09cccAzwbeC/wQuCdwPLDdsJ1JcsYYh/YaNockaXQWTpIkbbjT+t6vAv6+qk4e2VFVh418nWQGsJim0Do8ydurqpLcE3gu8J6qOrIN/36SK7hlESZJmiIWTpIkbbi/Bc5rv94ZeCrw70lmVtVHAZI8Fngj8ABuPXp0e+AK4FHt+6/1HT8e+I9hO1NV+422vx2J2nfYPJKkW7NwkiRpw53XuzgEcHKSPYH3JjkOuAfwXZpRppcAl9DcA3UI8CZgXnveTu32it7kVbU2ydLJ674kaVgWTpIkTaxzgMcDdweeA6wBDq6qlSMBSQ7pO2ekONoFuLQnbhY3F1WSpCnkqnqSJE2s+7Xbq2ie67QWWDdyMMk84Pl95/yk3T6rb/8z8I+ckrRZ8B9jSZI23D7tqBA0I0NPAx4LfKOqLkpyIvBa4CtJPtHGvJ5mEYn/U1W/SfJl4PVJ1tOsqncv4HXA9TQFmCRpClk4SZK04Y7p+fp64CLgNcDHAarqh0leCLwB+A7NNLxPA1cCn+3LdRhwOfCiNsfZNCNQJwPXTd4lSJKGYeEkSVJHVXUscOyQscdwywJrxOf64lbRjDC9bmRfkocB2wO/QpI0pSycJEnaDCQ5EHgwcCbNVL770ixj/jvg61PYNUkSFk6SJG0ubgCeSDPitC1wNc1S5kf2rsgnSZoaFk6SJG0GquoXwCOmuh+SpNFZOEnDSoaPrZq0bqx/1P07xd+4+9yhY7f78mlduyNJkrRV8DlOkiRJkjSAhZMkSZIkDWDhJEmSJEkDWDhJkiRJ0gAWTpIkSZI0gIWTJEmSJA3gcuSSJG0Fzr30eha+8cSp7oakzciSow+a6i5sURxxkiRJkqQBLJwkSZIkaQALJ0mSJEkawHucpGGlw98Zal2n1LN23WXo2D/+/dpOuWH4+CufdP9Ome/6/LM69mXz8Lsv7Dt07KxL5nbKvW5eDR1719ed3ik367v9XEmSpInjiJMkSZIkDWDhJEmSJEkDWDhJkrYISR6c5JtJLk6yKskVSX6e5ANT3TeAJEuSnDDV/ZAkTQ4LJ0nSZi/JwcCpwLbAEcDjgMOBnwHPnsKuSZK2Ei4OIUnaEhwBLAEeX1W9K558JckRU9OlTStJgG2qasVU90WStkaOOEmStgQ7Alf1FU0AVNX6ka9HpssleWKSM5OsSHJ+khf2n5dk1ySfTHJJktVJLkryliSz+uKOSvLLJNckWdbmfVFbyIwrySuSrE3y1p59c5K8ue3XqiRXJTkmye36zh25lmclOQdYCbx0qE9LkjThHHGSJG0JTgVekuRDwH8A/ztaEdW6L/AB4N3AFcCLgc8m+X1V/QSaogn4JbAeeBvwB+ChwJuBhcBhPfn2BD4BXNy+fwjwb8Ae7bm30hZV7wNeDby4qo5t988AvgU8Enhve117Am8FFid5QN+I0n7APYC3A5cAS8f5jEhyxhiH9hrvPEnSYBZOkqQtwRuBu9Pc13Q4sDLJL4ATgI9V1fKe2J2Bh1fVxQBJfgIcCBwK/KSNOQq4LXCvkTjgB0lWAO9P8r6q+i1AVf1fEdUWPouBAIcneXtV3eLhXUnm0RR3BwJPrKof9Bx+FvAE4OlV9fWec/4XOB1YBHy871oeUVV/GPJzkiRNEgsnSdJmr6quAfZPcn/gMcCDgAOARwEvT/KgqhoZjTm7pxiiqlYmuZBmZGfEwcCPgMv6puZ9F3h/m/e3AEkeS1O4PQDYrq9rt6cZ1RqxE/BDmtGoR1TVuX3xBwPXAd/pa/ds4C/A/tyycPp1l6KpqvYbbX87EjX8k58lSbdi4SRJ2mJU1VnAWQBJZgNHA68F3kCzgASMPp1tJTCv5/0uwJOBNWM0tXPbxoNpiqnFwEtopsutBg4B3tSXE5pRsdsCnx6laBppd4c2x5jt9rh8jDhJ0iZm4SRJ2iJV1Zokb6MpnPbpePrVwDk0xc9oLmu3z6Eprg6uqpUjB5McMsZ5Pwf+k+aeKoCX9y5e0ba7lGa63mhu6Htfo0ZJkjY5CydpM7B24S5Dx6773YJOuRdcNnDhr/+z08F/6ZS7HnbfoWPXzu/2z836ucMv+jn/d9d0yj1vwaqhY5fftlu/Z2431gDGrc3abfjvO8DaSy8bHDRNJdmtqkYbfdm73Xb9cE4AngT8oaquHSduPbAWWNfTl3nA88c6oao+n+Qm4EvAgiQvqKqR80+gKcZmVtUvOvZZkjSFLJwkSVuCk5NcCnwHOJ/mcRr3A14H3Ah8uGO+fwEeC5ya5CPABcA2NCvqPQl4ZVX9CTiRZkTrK0k+QXMP0+uBcavvqjo+yXLgeGBekudW1WrgK8DfACcl+TDNyn5rgDvQ3LN1QlUd3/FaJEmbgIWTJGlL8E7gKcBrgN2AuTT3/5wCvLuqzuuSrKouT/IA4J+Bf6QpXG4ALgK+R3ufVFX9sH0G1BtoirZLgU8DVwKfHdDGSUme1J73rSRPq6oVSf6aZmXA5wNH0oxoXQL8mGb6oCRpM2ThJEna7FXV14CvDRG3cIz9+4+y72puXt58vJzHAMeMcuhzg9quqsXAtn371tI8Z+oDA9q9VT5J0tQZ/iYCSZIkSdpKWThJkiRJ0gAWTpIkSZI0gPc4SZK0Fdhnj+054+iDprobkrTFcsRJkiRJkgawcJIkSZKkASycJEmSJGkA73HS1i0ZPnb9uknrxkWHLBg6dpsrO/QZWDN8apbe0CEY2O7ci4aOXb/fXTvlnr101dCxWbW6U+7l19126Nj5f+72z+SKPYb//tS8uZ1yS5KkqeOIkyRJkiQNYOEkSZIkSQNYOEmSJEnSABZOkiRJkjSAhZMkSZIkDWDhJEmSJEkDWDhJkiRJ0gAWTpIkSZI0gIWTJEljSPLgJN9McnGSVUmuSPLzJB/oiVmS5IQhcu2fpJLsP2Tbr0iyaMN7L0maSBZOkiSNIsnBwKnAtsARwOOAw4GfAc/egJRnAg9tt8N4BbBoA9qRJE2CWVPdAUmSNlNHAEuAx1fV2p79X0lyRNdkVbUMOG1QXJJ5VbWia35J0uSycNLWrWpS0q553AM6xa/ddv3QsbOWdBsovnHh8LHrLlnQKXe2vc3QsTNWreuWu0N83WZ+p9xzt101dOy6bWZ3yr37Xa4aPveOw39+mhI7Alf1FU0AVNWt/qNN8kTgncDewJ+A91bV53qO7w/8CDigqha3+xYDOwOvAo4G7gN8MskhwJ5tzMg/VD+uqv0n5tIkSV1ZOEmSNLpTgZck+RDwH8D/jlZEte4LfAB4N3AF8GLgs0l+X1U/GdDO7sCxNIXT+cAK4PPA8cD1NFP2AJYN6nCSM8Y4tNegcyVJ47NwkiRpdG8E7k5zX9PhwMokvwBOAD5WVct7YncGHl5VFwMk+QlwIHAoMKhwui3w1Kr6ce/OJCuAZVU1cHqfJGnyWThJkjSKqroG2D/J/YHHAA8CDgAeBbw8yYOqamkbfvZI0dSeuzLJhbTT7Qa4tr9o2og+7zfa/nYkat+JaEOStlauqidJ0jiq6qyqen9VPYtmWt2/AncG3tATtnSUU1cC84Zo4vKN76UkabJZOEmSNKSqWgO8rX27z0SlnaA8kqRJZOEkSdIokuw2xqG92+1lk9yFVQw3YiVJ2gS8x0mSpNGdnORS4Ds0q93NAO4HvA64EfjwJLd/LvDsJM8ELgJuqKoLJrlNSdIYLJwkSRrdO4GnAK8BdgPm0tyPdArw7qo6b5LbfwuwB3AMsAD4MbD/JLcpSRqDhZMkSaOoqq8BXxsibuEY+/fve78YyHgxfceW0CxpLknaDHiPkyRJkiQN4IiTNKRZd144dOwfHz27U+55l2RwUGtdx1vF1+y8eujYBb+f0yl3rVo1dOy6bbr9c5O164cPHv4SAbj99jcOHbt0xbadcl+9bMHQsbnD/E655/+yU7gkSZpAjjhJkiRJ0gAWTpIkSZI0gIWTJEmSJA1g4SRJkiRJA1g4SZIkSdIAFk6SJEmSNICFkyRJkiQN4HOcJEnaCpx76fUsfOOJox5bcvRBm7g3krTlccRJkiRJkgawcJIkSZKkASycJEmSJGkA73GabEm3+KrJ6ccky9y5Q8fW6tXdcs+ZM3zuVas65Z51hz2Gjv3j83cfOnbfz6y9AAAgAElEQVSbpZ26wdoFw8duc2nHn5Gdbxo69Dbfm9ktdwfr5nX7O83cvwz/vVy/YPifP4DV69YNn7tbalYvH/7n9dLHdMt9t693i5ckSRPHESdJkiRJGsDCSZIkSZIGsHCSJE07SR6c5JtJLk6yKskVSX6e5ANT0JeFSSrJog04d//23P0nvmeSpC4snCRJ00qSg4FTgW2BI4DHAYcDPwOePYVdkyRtwVwcQpI03RwBLAEeX1Vre/Z/JckRU9MlSdKWzhEnSdJ0syNwVV/RBEBVrR/5Oslzknw/yeVJViQ5L8nRSW6xzmWSY5PcmORuSb7bfv3nJB9IMrcvdvckX0tyQ5Lrk3wV2LW/H0kekOQrSZa0bS9J8uUke07cxyBJmkiOOEmSpptTgZck+RDwH8D/jlZEAXcFTgQ+CNwE7AW8AXgQ8Oi+2NnAt4HPAO8H/gr4Z+B64G0ASeYBpwC7A0cCvwMOBr46StsLgQuArwDXALsBLwdOT3LPqrp6A66bJGeMcWivDcknSbqZhZMkabp5I3B3mvuaDgdWJvkFcALwsapaDlBV7xg5IUlo7oE6D/hxkvtU1Tk9OecA/1JV/9m+/0GSBwKH0hZOwAuAvYGnVNW3233fSzIfeGFvB6vqeOD4nvZntv27os35kY37CCRJE82pepKkaaWqrqmq/YF9gX8EvgPcC3gf8OskOwEkuWs7Pe4vwDpgDfDjNs3e/WlpCpte5wC9U+sOAG7oKZpGHNffxyTbJnlfkj8kWQusBW4EFozS9tCqar/RXsD5G5pTktRwxEmSNC1V1VnAWQBJZgNHA68F3pDk7cBPgOXAm4EL26//H/B1YF5fuuVVtaJv30pgm573O9GMGPW7fJR9X6YptN4OnA4soynOThqlbUnSZsDCabJVTXUPNkzSKbxWrZqkjnTLPWvhHTvl/uOiOwwdO3Pl8HmzrlM3ml+XhrRmweCYXnNnj3Zrx+i2u3BZp9y1++2Gjp1z7epuuWfPHDp23fxu/5TdefulQ8eevfb2nXKzbPi+7HyXa7rl7vjfpW5WVWuSvI2mcNqH5h6m3YD9q2pklIkkO2xEM0tp7o/qt1vvm7aNJwFvraqje/bPpVnYQpK0GXKqniRpWkmy2xiHRqbAXQaMrK7XX9G/dCOa/hGwbZK/7tv/vL7364GM0vaLgeH/YiBJ2qQccZIkTTcnJ7mU5t6m82n+SHg/4HU09xF9mKZ4uhb4ZJK30Nzf9DfAfTei3S8ArwG+kORN3Lyq3oG9QVW1LMlPgH9McjVwEfAo4EXAdRvRviRpEjniJEmabt5JUxS9hmYJ8e8Cr6ZZKvxBVfXrqloKHERTSB0HfK79+tkb2mi7Wt+j23aOplk1b3fgOaOEHwr8EHgPzT1VDwAeS7O8uSRpM+SIkyRpWqmqrwFfGyLu58DDRjmUvrhFwKJRzj8KOKpv36XAM4bIOVbcwr64xf3nSpKmhiNOkiRJkjSAhZMkSZIkDWDhJEmSJEkDWDhJkiRJ0gAuDiFJ0lZgnz2254yjD5rqbkjSFssRJ0mSJEkawBGnyZZJXEU2Heve9euGj63qlruDGfPnd4pfccC9ho695D6zO+Wee83wsdXhW7l+TqduMGNNt/gurl667dCx6x48t1PunT992tCxqw56YKfcCy7489Cxa3a/S6fc16wa/mdw9k2dUrNm5eT9PWrFX3f7DCVJ0sRxxEmSJEmSBrBwkiRJkqQBLJwkSZIkaQALJ0mSJEkawMJJkiRJkgawcJIkSZKkASycJEmSJGkACydJkiRJGsDCSZIkSZIGsHCSJGmAJPdOckySi5KsTHJjkjOTvCPJLpPU5sOSHJVkh8nIL0nqxsJJkqRxJDkMOAN4IPA+4AnAU4H/BA4FPjFJTT8MeAtg4SRJm4FZU92BSZNMXu6qyYnt3I91k5Y6c+d2il/z8H2Gjl22cE6n3Ku3H/57Oe+qbp/3qtsOn3v1DsPnnnVTt5+/ddsMn3vlTt1yz//NNkPH3un5F3bKfc2S/YaO3ebE0zvlXvfgew/fj5fe2Cn3yl/ecejY2fM6pWbGmuFjl900/PcGYPle0/ef7M1VkgcDnwa+DxxSVat6Dn8/yftpCilJ0jTniJMkSWN7E1DAS/qKJgCqak1VfQcgyYwkRyQ5P8mqJFcm+UKSO/Sek+SxSb6d5JJ22t/vk3wyyc49MUfRjG4BXJSk2tfCSbpOSdIA/vlSkqRRJJkJPAY4o6ouGeKUjwMvAf4NOAlYCLwd2D/JvlV1dRt3F+BUmpGs69u41wI/TXLvqloDfAbYEXgV8DTg8vbcke1YfT5jjEN7DdF/SdI4LJwkSRrdzsB84KJBgUn2Av4O+GhVHd6z/yzgF8BraEavqKpP9BwPTRG1GPgT8ETg21V1SZKL27CzqmrJBFyPJGkjOFVPkqSNd0C7/ULvzqr6JXAezcgVAEl2SfKpJJcAa4E1NEUTwN4b04mq2m+0F3D+xuSVJDniJEnSWK4GltNMpRtkp3Y72lS6y4A9obkPimahiV1ppvH9GriJ5g+ZpwEdlyORJG0qFk6SJI2iqtYlOQV4UpI9qurSccKXtttdgf77oXanKcIA7t2+FlXV50cCktx1grotSZokTtWTJGls7wICfDLJrZ6lkGR2kicDP2x3Pa/v+ANopt/9oN21vt2u7kv10lHaHlnFz1EoSdoMOOIkSdIYquoXSf4O+CTwqyQfB34LzAbuT7MgxLlV9dQknwJenaSA73Lzqnp/Bj7Ypjwf+ANwdDtt72rgycBjR2n+3Hb790mOo7kX6pyq6i+6JEmbgIWTJEnjqKrPJfkVzcp4bwB2oyliLgS+BHy0DX05TVH0IuCVNEuNnwwcWVVL21xr2hGqD9MsX74WOAU4EBhZRW/EYppnOT0feBnNLJE7AUsm4TIlSQNYOEmSNEBVnQMcNiBmPfDe9jVe3HnA40Y5lL64Ao5oX5KkKTZ9C6eqqe7BBpm5y+2Hjl1/x1065V55+22Gjr1+4exOuVdvP3zsrJs6pWbGmuFjl++WwUE9aubwsXOuGz73urmdusGsm4bPvWa7bj/bszvk/t3X794p9/avG/dZnLdw8aL7dso9f/6qwUGtGy/erlPu7S4b/jNZdtd1nXLPuW74W0f32PH6Trkvn71tp3hJkjRxXBxCkiRJkgawcJIkSZKkASycJEmSJGkACydJkiRJGsDCSZIkSZIGsHCSJEmSpAEsnCRJkiRpAAsnSZIkSRrAwkmSJEmSBrBwkiRJkqQBLJwkSZIkaYBZU92BzcGsOy/sFH/dA3YdOnbV9umUe8XOw8fPXNUpNbOW19Cxa+d1yz1jzfCx67bplnvNnA655wx/jV3VjA7fy27fdmrm8LFzruuWfNVth/9MZq7olnvpj3cbOnbdnh1+SIB1584fOnbB6k6pWTt8amYt7/b3pS7/7fzpyh075d7p4sn7+ZYkSeNzxEmSJEmSBrBwkiRJkqQBLJwkSZIkaQALJ0nSVinJoiTV81qZ5C9JfpTkyCS3n+o+SpI2HxZOkqSt3WHAQ4HHAq8EzgbeAJyX5MCp7JgkafPhqnqSpK3duVX1q573/5Xkg8D/AF9PcrequmK0E5PMr6rlm6SXkqQp5YiTJEl9qupi4HXAtsBLAZIcm+TGJPdN8sMkNwJfGjknyYFJfpBkWZLlSX6W5DG9eZPcLsmnkvw5yaokV7VxB/bE7JvkhCRXtjGXJTkxyR02zdVLkkbjiJMkSaM7CVgH/FXPvjnAN4GPAe8Y2ZnkecAXgG8BLwDW0BRc30vy+Kr6QRt6HHB/4E3AhcAOwL7ATm2e2wD/DSyhmTZ4BbArcABNETeuJGeMcWivQedKksZn4SRJ0iiqanmSq4Hde3bPBo6qqs+P7EgyH/gwcEJVPbVn/0nAmcC7gAe3ux8GfKaqPt2T81s9X9+Dpoh6UVX17v/aBFySJGkjWDhJkjS2jLLvG33vHwbsCHw+Sf//V08GjkiyoKpuAn4JLEqylGZk6ayqWtMT/3vgWuA9SXYFflxV5w/b2arab9SLaEai9h02jyTp1qZt4TRjwYKhYy89ePfBQb25V9fwses6pWb2TcPHrpvbLfeKXUb7///o1s8Z/hoBZqwZPndX62cP35ea2S33zJXD97tL7qzt1o8ZawbH3Jy8a+7hT5jV8Rb3tcP/Z8as6yfvn5s123X7ee2iy88IwNwbh4+dfY8VnXKvnzmvU7w2TpIFNKM/v+7ZvbyqlvWF7tJujx8n3Y7ATcCzgTcDLwbeDtyQ5OvAG6vqL1V1fZJH0Uzlezdw2ySXAZ8G3tlXZEmSNqFpWzhJkrSRDgJmAot79o1WpV/dbl8FnDZGrisAqupq4B+Af0iyB3AI8B6a+5ie0Mb8GngOQJJ9gBcBbwFWAkdv8NVIkjaKhZMkSX2S3BF4P7AM+NSA8J8B1wH3rKqPDttGVV0K/Hu7ot7Dx4g5F3hNkkU41U6SppSFkyRpa7dPe2/SLOD2wCNpHoq7Djikqq4c7+SqujHJq2jucdqRZsrelcDtgPsCu1TVS5NsD/yIZgnz84EbgAfSjDR9HSDJwcAraFbu+yPN5Nyn0ay+9/2JvGhJUjcWTpKkrd0x7XY1zcjReTTT5z5TVVcNk6CqjktyMXAE8EmapcOvBM6mWaYcmql2vwCeDyykWaHvTzTT797Xxvyu7cMRNKv5raYpshb1ruQnSdr0LJwkSVulqjoWOLZD/CJg0TjHfwL8ZJzjq4CXD2jjAuDQYfskSdp0Zkx1ByRJkiRpc2fhJEmSJEkDWDhJkiRJ0gAWTpIkSZI0gIWTJEmSJA1g4SRJkiRJA0zb5cgvfvV9h45dfvdVnXIvuGBu1+4MbZura/jYpcPHAmT98LGzVnXLvX5Who+d2Sk11aG8Xztv+H40uYe/zvVzhs+9cqdO3WDF3iuHjt12uxWdcu+8YPnQsc+9w+mdcq+p4b+Zt5u1rFPuK9bsMHTs7rOv7ZR7mxmrh469aX23/94//qf9h4790b2+1Sn3Pqe+olO8JEmaOI44SZIkSdIAFk6SJEmSNICFkyRJkiQNYOEkSZIkSQNYOEmSJEnSABZOkiRJkjSAhZMkSZIkDWDhJEmSJEkDWDhJkiRJ0gAWTpKkLUaSRUmq57UyyYVJPppklw3ItzjJ4p73C9u8iyay35KkLd+sqe7AZNn24vVDx67Yo9vHcNOd1wwdO2Pe2k6591r456Fjd93mhk65L1ux3dCxS67bsVPuubOHv85Va7p93kkNHXu3Ha/ulHvv2/xl6Nh95l0ydOxN6+d06sf5K3YfOvaUy+7RKfeffrvb0LH/fsIhnXLPWzr8f2fzr+z238Kcq1Z0iu9ixk0rh47N8uFjAeavHT7+Sds9vVPuO/zpjOGD39Up9ZboMOB8YB7wV8CRwJOS3LuqbprSnkmSpqVpWzhJkqa1c6vqV+3XP0oyE/hn4BDgi1PXrcmVZH5VLZ/qfkjS1sipepKk6eC0drtnkqMyylB1zzS/hV2TJ/nrJD9PsjzJDUm+n+ShPccPaXM/ZpRzX94eu1fPvgck+XaSa9rphmcledYY/X18ks8nWQpc2rXvkqSJ4YiTJGk6uEu7vQrYYyITJzmUZhTre8BzgbnAEcDiJI+pqp8CJ7ZtHwb8oC/FIuD0qvpNm+8A4GTgF8DLgOuB5wBfbUeUju07/7PAt4BDgdsM6OtY8zn3GnihkqRxWThJkrZEM5PMArYBHgm8GbgB+Dbw8olqJMkM4H3AOcCTqmp9u/8k4A/Ae4CHV9WaJMcBL0uyXVUta+PuCTwIeEVP2o8BvwEeXVUjN/99L8nOwLuSfGGkndb3q+qVE3VNkqQN41Q9SdKW6DRgDU2xdBJwBfDEqrpigtu5B7A7cFxvMVNVNwL/BTwkyfx29zE0i1U8u+f8w4CVwJcBktyVZvTni+37WSOv9jp2a9vs9Y1hO1tV+432ollIQ5K0ERxxkiRtif4WOA9YC1xRVZdPUjs7tdvR8l9G8wfI2wLLq+rX7VS5RcCn22Lo+cA3q+q69pyRJdPf375Gs3Pf+8m6NklSBxZOkqQt0Xk9q+r1WwmQZG5VrerZ31+QDGNpu911lGO7A+uBa3v2HQN8NMndaUaOdmn3jRh5ZsK7ga+P0eYFfe+HfyaDJGnSOFVPkjTdLGm39+nb/+QNyHUBzUp2f5MkIzuTLACeBvy8b3nwLwGraEadDgMuAU4ZOVhVFwC/A+5bVb8a49XtIX2SpE3CESdJ0nRzEnAN8Nkk/0IznW8R8P+6Jqqq9UmOoLkn6YQkn6RZVe8faabovbEv/tok3wJeCOwIvLdvoQeAlwLfTfI94FiawmxHYG/ggVX1tK79lCRNPkecJEnTSrui3RNoFo44DvgEcC7wzg3M9yWaB+vuBHyVZurdMuCAdinyfsfQTNGbTVMY9ef7Ec1Ke9cBH6IZkfo4cCDw/Q3poyRp8jniJEnaYrTPODp2iLjTgYePcuizfXH7971fAoQ+VfUtmmcpDdPHk0fL0RdzDrdcfW+0mGMZ4lolSZvGtC2ctv/iaYODWjscP7dT7hk7bD90bBbMHxzU48addhs69tzb36lT7tXbzhw6tnbqNhh5/W2Hj107v9t9zmsXDB9/5q93GhzU44JLh38m5I9/t3ro2G2WXDs4qNeVVw+Oae20+tJOqXdcd/HQsZk5/M8IQOZt0yF2XqfctaBD/MxuP681b87QsWtvt22n3F1cf5dun8lOs6ftP9mSJG32nKonSZIkSQNYOEmSJEnSABZOkiRJkjSAhZMkSZIkDWDhJEmSJEkDWDhJkiRJ0gAWTpIkSZI0gIWTJEmSJA1g4SRJkiRJA1g4SZIkSdIAs6a6A5uDWrWqU/y6K64cOjZz53bryx+XDB07N+mUe26Gr5O3rfWdcndS1S2+w3VmzpxOqWfM22b43NsMH8v8eZ36UbvvMnw/On7fmdkxvotVa4ePXdMhFsiq1cMHz+j2N6DctG741Nff1Ck3a4fPvfPls7ul7vDvgyRJmliOOEmSJEnSABZOkiRJkjSAhZMkSZIkDWDhJEmSJEkDWDhJkrYoSWrI1/5T3VdJ0vThqnqSpC3NQ/vevw54xij7f7tpuiNJ2hpYOEmStihVdVrv+yRXjLZ/LEnmASuruj4bYeolmVdVK6a6H5K0NXKqniRp2kryhHba3nOS/HtbZN0EzG2P3zfJCUmuS7IiyZlJDu3L8bI2x65j5H5Iz74HJflukquSrEpyaZLv9J6bZEaSw5Ock2RlkmuSfDXJnn35T0vyqySPS3J6kpXAWybhY5IkDcERJ0nS1uADwA+BRcBtgDVJ7g38DPgz8Arg+vb4F5PsXFUf6dJAkh2A/wbOA14GXAXsBjwaWNATeizwbOCDwOuB29EURD9Ncr+qWtoTuyfwaeCdwO9oir7x+nDGGIf26nItkqRbs3CSJG0Nzqmq5/fuSPK29sv9q+qK9usTk/wAeHuSz1bVuIVKn3sB2wNHVdX3evZ/tafN/YHnA6+sqo/17D8VOB94NbccVdoZeOiw0xAlSZPHwkmStDX4xij7Hg18r6doGvH59tgDgcUd2jgfWAZ8IMkdgR9X1YV9MQcD64AvJen9f/CfaRaz2L8v/vIuRVNV7Tfa/nYkat9h80iSbs3CaZLVqlWTmLzjfc21bnL6Mdk6XGfXz3tdp/jrO+WWtFm5vPdNkpnAdv37W5e12526NFBVS5M8CngT8F5ghySXAJ8E3l1V64BdgJnAtWOk6V8JcLT+SZKmgIWTJGlrcIu/wFTVuiTLgF1Hid293V7dble227l9cTvfqpGqs4FnJglwb+DvgLcDNwIfanOuBR5BM/LUr3/FvC1u5T9Jmq5cVU+StLX6AfD4JLfr2/+3NFPuftW+X9Ju79MX99djJa7GOVX19zTF0Mg0uRNo/mi5S1X9apTXbzbieiRJk8gRJ0nS1uotwOOAxUneCVwHvAB4DHB4z8IQPwMuAj7cPgPqBuCZwAN6kyV5Os2qfN9q42cCzwLmAd8HqKofJPkCzcp9HwV+CiynGeV6JHBmVX1qsi5YkrThLJwkSVulqvp1kkfQLPX9cZqpeL8FnldVX+yJW5PkIODfgM/QjCAdB7yWWy46cT7NcuFH0hRCK2mWJr9FPpri6mfAi2lW0YPmvqqfAadP7FVKkiaKhZMkaYvWTof7+zGOnQxknHPPBg4aoo3zgANHOZSemN8AzxkiVwGfal/jxT1kvOOSpE3Le5wkSZIkaQALJ0mSJEkawMJJkiRJkgawcJIkSZKkASycJEmSJGkACydJkiRJGsDCSZIkSZIGsHCSJEn6/+3dfZAlVXnH8e+P1yAqLypBRV2hlI2BQFjfQVxAFFMlULwkFbRKYqFWRSAVMAnyhy8RY7QM4ktVEBGJKKIYE40RFxExCKGUXZGAy5vIAoK8CggCgjz5o3uSW9eZ6Tsz9869M/X9VHX13u7T55w+c+ZuP3NOd0tSBwMnSZIkSepg4CRJkiRJHQycJEmSJKmDgZMkSZIkdTBwkiRJkqQOBk6SJEmS1MHASZIkSZI6GDhJkiRJUgcDJ0nSSCSpAZfVCyznpDafrQdIe2uS0wfMd68k703y1FnSHJfkziQbJ9mlTf/cudRfkrQ0bDLuCkiSlq1X9H0+Hjhsmu0/WZzqAPAG4P4B0+4FvAc4HXhghjSHAv9eVb9Nskub/gLg5oVWVJI0WQycJEkjUVWX9X5Ocsd02xdTVf2oK02SJ1XVrwdI9yyaIPDvh1E3SdJkc6qeJGlitVPg3p3k2iQPJ7kvyZVJjp4m+TOTfCnJA0l+keT0/ml2/VP1khzVTvPbP8lZSe4BNiQ5Cfhgm+yWnmmFO/RkdwjN6NWFSY4Cvthuv7gn/V4953FCex6PJrkjyb+0wVdv/b6f5Iok+yT5YZJHkmxI8jcLakhJ0oI54iRJmmQnAu+mGdX5PrAZsBLYZpq0XwXOAT4N7AZ8AHgCeNsA5Xy2Pf7PgScDP2jL+EvgQOCuNt2dPcccCny9qh5L8jVge+D9wNuBK9s0V7fr04C/AD4GnAfs2KbdO8mqqrq3J99nA2cBJwE3AYcDH06yeVWdNNtJJFk7w66Vsx0nSepm4CRJmmSvBH5UVb3T4b41Q9rTquqj7b8vSLIzcASDBU7nVdWxvRuS3NL+80dVdWvfvu2AV9GMOlFVdyW5od39k97piEn+EHgLcEpV/XXP9iuBS4C/ork3asrTgQOqas3U+SZ5BvCuJB+vqpnut5IkjZBT9SRJY5dkk74l7a4fAKuSfDLJa5I8ZZZsvt73+UpgyyRPG6AK/zbHKh8MPAycP0Dafdv153o3VtWlwPXAfn3pf9kTNE05G3gS8NLZCqqqVdMtwDUD1FOSNAsDJ0nSWCXZBHisb3lju/sk4G+BPYE1wD1Jzk/yx9NkdU/f50fa9RYDVOP2OVb7MOA/q+qRzpQwFbhNV8ZtPfun3DFNul/05SVJWmRO1ZMkjVVVPZ7kJX2bb2z3PQZ8BPhIkq2A/YF/BM5P8pwBA5eBqjFowiTbAPvQTAMcxFRAtz3/HwBNeRa/Gyj9/jR5bN+XlyRpkTniJEkau6q6vG+5d5o091fVV4B/prkPaNQvmn20XfePWB1EMyr2zQHTX9iu39S7McnLgRcA3+lLv02S1/VtOwL4Nc3URUnSGDjiJEmaWEm+CVwBrKV5st3zgWNoRqRuHHHxV7XrY5KcDTwO/Jhmmt6aqnqoL/3UE/TemuQh4DfANVV1dZIzgOPae7fWtOfxfmAD8PG+fO4GPtM+Ev1nwJ/SvLj3PT4YQpLGx8BJkjTJvkvzIIa3Ak+lmeq2Bnh/VT0+4rIvAE6mud/qHTSzNJ4HvAY4qj9xVV2X5O+Ao4GL2/SvonmM+tuAG2geSX4MzfufzgNOmGZ07efA8cCHgV1oHoH+LuBDwz09SdJcpGrgad1Lyv4bHb48T0ySBvDtJ85NdyrNVZIjaN75tF1V3T+C/L8PPLmqdh9yvmv32GOPPdaunek1T5K0PK1atYp169ata58wuiDe4yRJ0oCq6uyq2nwUQZMkabIZOEmSJElSB+9xkiRpQlTVXuOugyRpeo44SZIkSVIHAydJkiRJ6mDgJEmSJEkdDJwkSZIkqYOBkyRJkiR1MHCSJEmSpA4GTpIkSZLUwcBJkiRJkjoYOEmSJElSBwMnSZIkSepg4CRJkiRJHQycJEmSJKmDgZMkSZIkdTBwkiRJkqQOm4y7ApIkaeRWrF+/nlWrVo27HpK0qNavXw+wYhh5GThJkrT8Pfnhhx/+7bp163487opMsJXt+pqx1mKy2Uazs326jaONVgAPDCMjAydJkpa/qwCqyiGnGSRZC7bRbGyj2dk+3ZZ6G3mPkyRJkiR1MHCSJEmSpA7Ldqret584N+OugyRJkqTlwREnSZIkSepg4CRJkiRJHVJV466DJEmSJE00R5wkSZIkqYOBkyRJkiR1MHCSJEmSpA4GTpIkSZLUwcBJkiRJkjoYOEmSJElSBwMnSZIkSepg4CRJkiRJHQycJEmaUEl2SHJGktuSPJrkpiSnJNlmjvls2x53U5vPbW2+O4y67FFbaD2TbJnkjUnOTnJNkoeS/CrJ5UmOT7LZDMfVLMtlwz3LhRnGzzLJRR3n/HszHPeiJF9OcmeSR5Jcm+R9SbYY3hkuzBD60OqOtplantN33JLoQ0kOS/KJJBcneaCt3+fnmdec23qS+lCqarHLlCRJHZLsBFwKbAd8DbgGeCmwD3AtsGdV3TNAPk9r83khcCHwQ2AlcBBwJ/CKqrpxFGWP2jDqmeQA4DzgXuC7wA3AtsAbgO3b/Perqkf6jitgA3DmNNneWlWnz/vEhmiI/egi4NXA+2ZIclJVPd53zMto+tymwFeAW4B9gRcDl9C066NzP6vhGVIfWgEcOcPuXYFDgKuraq/0n2sAAAa/SURBVJe+45ZKH7oC2A14ELiV5vvjC1X1pjnmM+e2nrg+VFUuLi4uLi4uE7YAa4ACjunbfnK7/dQB8/lUm/7kvu3Httu/Naqyl0IbAbsDbwQ269v+FGBtm8/x0xxXwEXjboNF7EcXNZeNA5e7MfCTtowDe7ZvRHMBXMAJy6V9Zsn/i20+xy7hPrQP8AIgwOq23p8fdVtPYh9yxEmSpAmTZEfgp8BNwE5V9UTPvqcAt9NcxGxXVQ/Nks+WwF3AE8Azq+pXPfs2astY0ZZx4zDLHrXFqGeSI4AvAN+oqjf07Svge1W1el4nsAiG2UZTI05VlQHL3hf4DvBfVfXqGeq1AXh+jelidNR9qB3t/TnN79+zq+qXffsnvg/1S7KaZmR2TiNO82nrSexD3uMkSdLk2bddn997gQHQBj+XAE8CXt6RzyuALYBLeoOmNp8ngPPbj/uMoOxRW4x6PtauH59h/9ZJ3pLkxCTvSDLuNuk39DZK8mdJTkhyXJLXJ9m8o+xv9e9og/TrgOcBOw5a9giMug8dCWwOnNsfNPWY9D40LPNp64nrQwZOkiRNnp3b9XUz7L++Xb9wBPkMq+xRW4x6vqVd/86FW2s34DPAB4BPAv+d5Iokuy6gzGEaRRudA3wQ+Cfgm8DNSQ5bpLKHbdR1PKpdf2qWNJPeh4ZlWXwXGThJkjR5tmrX98+wf2r71iPIZ1hlj9pI65nkaOAA4ArgjGmSnAzsCTyD5n6ol9Dcd7EbcGGSZ8+n3CEbZht9jeaBGTvQjGKupAmgtga+lOT1Iyx7VEZWxySvpmmjq6vq0hmSLYU+NCzL4rvIwEmSpKVn6j6Thc7rn08+wyp71OZdzySHAKcAvwAOrarH+tNU1fFVdWlV3V1VD1bV5VV1OPCvwNOBdy6g7otl4Daqqo9W1Teq6udV9UhVXVtVJwLH01xP/sOoyh6jhdTxbe16xtGmZdKHhmVJfBcZOEmSNHmm/pK61Qz7n9qXbpj5DKvsURtJPZMcTDMd7U5gdfU9qn0Ap7brved43Cgsxs/ydJp7wHZvb/JfzLIXalR9aFvgUOBh4Kx51GuS+tCwLIvvIgMnSZImz7Xteqa5+y9o1zPN/V9IPsMqe9SGXs8khwPnAnfQPEHu2o5DpnNXu95yHscO28h/ltW832rqwSO957wU+tGo6vhmmodCfLmq7ptHvSapDw3LsvguMnCSJGnyfLddv7Z9bPj/af+qvyfNX7Mv68jnsjbdnn2jAVOPI39tX3nDLHvUhlrP9tHjXwRuowmaru84ZCZTTwWb60jVKIz8Z5lkZ2AbmuDp7p5dF7brA6Y5Zkeai+ENjLedRtU+b23Xp82zXpPUh4ZlPm09cX3IwEmSpAlTVT+leVT4CuAdfbvfR/OX6M/1vlsmycokK/vyeZBmqtCWwHv78jm6zX9N73S0+ZQ9DsNqo3b7m2na6WZg767peUn2aN+R1b/9j2iejgbw+cHPZjSG1UZJdpzuQQVJng58tv14TlX1Prb9e8B6YO8kB/YcsxHwofbjqeN6hxMMtw/17H8V8AfAVbM8FGLJ9KG5SrJp20Y79W6f5/fKxPUhX4ArSdIEai88LgW2o3mi2XrgZTTvXLoOeGVV3dOTvgD6X1DavoTzUpq/zl4I/IDmwu4gmvt4Xtle1My77HEZRhsl2Qe4gOaPyWcAt0xT1H1VdUrPMWcCh9C05y3AozRPUDsA2Bj4NPD2cQYFU4bURkfS3Mv0PZqXjt4LPBf4E5r7Ty4H9u+flpbkZTRttCnN0+JuBvYDXkzz3p79qurRYZ/zXAzr96xn/1nAm4Bjq+oTs5R7JkunDx0MHNx+3B54Hc0oz8Xttrur6p1t2hXAz4ANVbWiL585f69MXB+qKhcXFxcXF5cJXIDn0PxF/3bgNzTTUj4GbDtN2mr+W582n23b4za0+dxOEyTsMIyyl3Ib0byktDqWm/qOORj4KnAD8EBPm/4HcOC422QEbbQrcCbwP8A9NC8GvpfmwvkYYLNZyn4RzX1jd9MEB9fRjDBsMe52GVb79Ozbhma62a+BrTvKXDJ9iGa0eqDfD5oRpd/5nZlPW09iH3LESZIkSZI6eI+TJEmSJHUwcJIkSZKkDgZOkiRJktTBwEmSJEmSOhg4SZIkSVIHAydJkiRJ6mDgJEmSJEkdDJwkSZIkqYOBkyRJkiR1MHCSJEmSpA4GTpIkSZLUwcBJkiRJkjoYOEmSJElSBwMnSZIkSepg4CRJkiRJHQycJEmSJKmDgZMkSZIkdTBwkiRJkqQOBk6SJEmS1MHASZIkSZI6/C9acZoGZSCzwQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fe91c5054e0>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 204,
       "width": 423
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Import helper module (should be in the repo)\n",
    "import helper\n",
    "\n",
    "# Test out your network!\n",
    "\n",
    "model.eval()\n",
    "\n",
    "dataiter = iter(testloader)\n",
    "images, labels = dataiter.next()\n",
    "img = images[0]\n",
    "# Convert 2D image to 1D vector\n",
    "img = img.view(1, 784)\n",
    "\n",
    "# Calculate the class probabilities (softmax) for img\n",
    "with torch.no_grad():\n",
    "    output = model.forward(img)\n",
    "\n",
    "ps = torch.exp(output)\n",
    "\n",
    "# Plot the image and probabilities\n",
    "helper.view_classify(img.view(1, 28, 28), ps, version='Fashion')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Next Up!\n",
    "\n",
    "In the next part, I'll show you how to save your trained models. In general, you won't want to train a model everytime you need it. Instead, you'll train once, save it, then load the model when you want to train more or use if for inference."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}