Planar_data_classification_with_one_hidden_layer.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Planar data classification with one hidden layer\n",
    "\n",
    "Welcome to your week 3 programming assignment! It's time to build your first neural network, which will have one hidden layer. Now, you'll notice a big difference between this model and the one you implemented previously using logistic regression.\n",
    "\n",
    "By the end of this assignment, you'll be able to:\n",
    "\n",
    "- Implement a 2-class classification neural network with a single hidden layer\n",
    "- Use units with a non-linear activation function, such as tanh\n",
    "- Compute the cross entropy loss\n",
    "- Implement forward and backward propagation\n",
    "\n",
    "## Important Note on Submission to the AutoGrader\n",
    "\n",
    "Before submitting your assignment to the AutoGrader, please make sure you are not doing the following:\n",
    "\n",
    "1. You have not added any _extra_ `print` statement(s) in the assignment.\n",
    "2. You have not added any _extra_ code cell(s) in the assignment.\n",
    "3. You have not changed any of the function parameters.\n",
    "4. You are not using any global variables inside your graded exercises. Unless specifically instructed to do so, please refrain from it and use the local variables instead.\n",
    "5. You are not changing the assignment code where it is not required, like creating _extra_ variables.\n",
    "\n",
    "If you do any of the following, you will get something like, `Grader Error: Grader feedback not found` (or similarly unexpected) error upon submitting your assignment. Before asking for help/debugging the errors in your assignment, check for these first. If this is the case, and you don't remember the changes you have made, you can get a fresh copy of the assignment by following these [instructions](https://www.coursera.org/learn/neural-networks-deep-learning/supplement/iLwon/h-ow-to-refresh-your-workspace)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Table of Contents\n",
    "- [1 - Packages](#1)\n",
    "- [2 - Load the Dataset](#2)\n",
    "    - [Exercise 1](#ex-1)\n",
    "- [3 - Simple Logistic Regression](#3)\n",
    "- [4 - Neural Network model](#4)\n",
    "    - [4.1 - Defining the neural network structure](#4-1)\n",
    "        - [Exercise 2 - layer_sizes](#ex-2)\n",
    "    - [4.2 - Initialize the model's parameters](#4-2)\n",
    "        - [Exercise 3 - initialize_parameters](#ex-3)\n",
    "    - [4.3 - The Loop](#4-3)\n",
    "        - [Exercise 4 - forward_propagation](#ex-4)\n",
    "    - [4.4 - Compute the Cost](#4-4)\n",
    "        - [Exercise 5 - compute_cost](#ex-5)\n",
    "    - [4.5 - Implement Backpropagation](#4-5)\n",
    "        - [Exercise 6 - backward_propagation](#ex-6)\n",
    "    - [4.6 - Update Parameters](#4-6)\n",
    "        - [Exercise 7 - update_parameters](#ex-7)\n",
    "    - [4.7 - Integration](#4-7)\n",
    "        - [Exercise 8 - nn_model](#ex-8)\n",
    "- [5 - Test the Model](#5)\n",
    "    - [5.1 - Predict](#5-1)\n",
    "        - [Exercise 9 - predict](#ex-9)\n",
    "    - [5.2 - Test the Model on the Planar Dataset](#5-2)\n",
    "- [6 - Tuning hidden layer size (optional/ungraded exercise)](#6)\n",
    "- [7- Performance on other datasets](#7)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a name='1'></a>\n",
    "# 1 - Packages\n",
    "\n",
    "First import all the packages that you will need during this assignment.\n",
    "\n",
    "- [numpy](https://www.numpy.org/) is the fundamental package for scientific computing with Python.\n",
    "- [sklearn](http://scikit-learn.org/stable/) provides simple and efficient tools for data mining and data analysis. \n",
    "- [matplotlib](http://matplotlib.org) is a library for plotting graphs in Python.\n",
    "- testCases provides some test examples to assess the correctness of your functions\n",
    "- planar_utils provide various useful functions used in this assignment"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Package imports\n",
    "import numpy as np\n",
    "import copy\n",
    "import matplotlib.pyplot as plt\n",
    "from testCases_v2 import *\n",
    "from public_tests import *\n",
    "import sklearn\n",
    "import sklearn.datasets\n",
    "import sklearn.linear_model\n",
    "from planar_utils import plot_decision_boundary, sigmoid, load_planar_dataset, load_extra_datasets\n",
    "\n",
    "%matplotlib inline\n",
    "\n",
    "%load_ext autoreload\n",
    "%autoreload 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a name='2'></a>\n",
    "# 2 - Load the Dataset \n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "X, Y = load_planar_dataset()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Visualize the dataset using matplotlib. The data looks like a \"flower\" with some red (label y=0) and some blue (y=1) points. Your goal is to build a model to fit this data. In other words, we want the classifier to define regions as either red or blue."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Visualize the data:\n",
    "plt.scatter(X[0, :], X[1, :], c=Y, s=40, cmap=plt.cm.Spectral);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You have:\n",
    "    - a numpy-array (matrix) X that contains your features (x1, x2)\n",
    "    - a numpy-array (vector) Y that contains your labels (red:0, blue:1).\n",
    "\n",
    "First, get a better sense of what your data is like. \n",
    "\n",
    "<a name='ex-1'></a>\n",
    "### Exercise 1 \n",
    "\n",
    "How many training examples do you have? In addition, what is the `shape` of the variables `X` and `Y`? \n",
    "\n",
    "**Hint**: How do you get the shape of a numpy array? [(help)](https://docs.scipy.org/doc/numpy/reference/generated/numpy.ndarray.shape.html)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "cell_type": "code",
     "checksum": "d19673d5fa7f72081dde6ac5ebef8373",
     "grade": false,
     "grade_id": "cell-da23a484a9233d5c",
     "locked": false,
     "schema_version": 3,
     "solution": true,
     "task": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The shape of X is: (2, 400)\n",
      "The shape of Y is: (1, 400)\n",
      "I have m = 400 training examples!\n"
     ]
    }
   ],
   "source": [
    "# (≈ 3 lines of code)\n",
    "# shape_X = ...\n",
    "# shape_Y = ...\n",
    "# training set size\n",
    "# m = ...\n",
    "### START CODE HERE ### (≈ 3 lines of code)\n",
    "shape_X = X.shape\n",
    "shape_Y = Y.shape\n",
    "m = Y.shape[1]  # training set size\n",
    "### END CODE HERE ###\n",
    "\n",
    "print ('The shape of X is: ' + str(shape_X))\n",
    "print ('The shape of Y is: ' + str(shape_Y))\n",
    "print ('I have m = %d training examples!' % (m))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Expected Output**:\n",
    "       \n",
    "<table style=\"width:20%\">\n",
    "  <tr>\n",
    "    <td> shape of X </td>\n",
    "    <td> (2, 400) </td> \n",
    "  </tr>\n",
    "  <tr>\n",
    "    <td>shape of Y</td>\n",
    "    <td>(1, 400) </td> \n",
    "    </tr>\n",
    "    <tr>\n",
    "    <td>m</td>\n",
    "    <td> 400 </td> \n",
    "  </tr>\n",
    "</table>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a name='3'></a>\n",
    "## 3 - Simple Logistic Regression\n",
    "\n",
    "Before building a full neural network, let's check how logistic regression performs on this problem. You can use sklearn's built-in functions for this. Run the code below to train a logistic regression classifier on the dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Train the logistic regression classifier\n",
    "clf = sklearn.linear_model.LogisticRegressionCV();\n",
    "clf.fit(X.T, Y.T);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can now plot the decision boundary of these models! Run the code below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy of logistic regression: 47 % (percentage of correctly labelled datapoints)\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the decision boundary for logistic regression\n",
    "plot_decision_boundary(lambda x: clf.predict(x), X, Y)\n",
    "plt.title(\"Logistic Regression\")\n",
    "\n",
    "# Print accuracy\n",
    "LR_predictions = clf.predict(X.T)\n",
    "print ('Accuracy of logistic regression: %d ' % float((np.dot(Y,LR_predictions) + np.dot(1-Y,1-LR_predictions))/float(Y.size)*100) +\n",
    "       '% ' + \"(percentage of correctly labelled datapoints)\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Expected Output**:\n",
    "\n",
    "<table style=\"width:20%\">\n",
    "  <tr>\n",
    "    <td>Accuracy</td>\n",
    "    <td> 47% </td> \n",
    "  </tr>\n",
    "  \n",
    "</table>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Interpretation**: The dataset is not linearly separable, so logistic regression doesn't perform well. Hopefully a neural network will do better. Let's try this now! "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a name='4'></a>\n",
    "## 4 - Neural Network model\n",
    "\n",
    "Logistic regression didn't work well on the flower dataset. Next, you're going to train a Neural Network with a single hidden layer and see how that handles the same problem.\n",
    "\n",
    "**The model**:\n",
    "<img src=\"images/classification_kiank.png\" style=\"width:600px;height:300px;\">\n",
    "\n",
    "**Mathematically**:\n",
    "\n",
    "For one example $x^{(i)}$:\n",
    "$$z^{[1] (i)} =  W^{[1]} x^{(i)} + b^{[1]}\\tag{1}$$ \n",
    "$$a^{[1] (i)} = \\tanh(z^{[1] (i)})\\tag{2}$$\n",
    "$$z^{[2] (i)} = W^{[2]} a^{[1] (i)} + b^{[2]}\\tag{3}$$\n",
    "$$\\hat{y}^{(i)} = a^{[2] (i)} = \\sigma(z^{ [2] (i)})\\tag{4}$$\n",
    "$$y^{(i)}_{prediction} = \\begin{cases} 1 & \\mbox{if } a^{[2](i)} > 0.5 \\\\ 0 & \\mbox{otherwise } \\end{cases}\\tag{5}$$\n",
    "\n",
    "Given the predictions on all the examples, you can also compute the cost $J$ as follows: \n",
    "$$J = - \\frac{1}{m} \\sum\\limits_{i = 0}^{m} \\large\\left(\\small y^{(i)}\\log\\left(a^{[2] (i)}\\right) + (1-y^{(i)})\\log\\left(1- a^{[2] (i)}\\right)  \\large  \\right) \\small \\tag{6}$$\n",
    "\n",
    "**Reminder**: The general methodology to build a Neural Network is to:\n",
    "    1. Define the neural network structure ( # of input units,  # of hidden units, etc). \n",
    "    2. Initialize the model's parameters\n",
    "    3. Loop:\n",
    "        - Implement forward propagation\n",
    "        - Compute loss\n",
    "        - Implement backward propagation to get the gradients\n",
    "        - Update parameters (gradient descent)\n",
    "\n",
    "In practice, you'll often build helper functions to compute steps 1-3, then merge them into one function called `nn_model()`. Once you've built `nn_model()` and learned the right parameters, you can make predictions on new data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a name='4-1'></a>\n",
    "### 4.1 - Defining the neural network structure ####\n",
    "\n",
    "<a name='ex-2'></a>\n",
    "### Exercise 2 - layer_sizes \n",
    "\n",
    "Define three variables:\n",
    "    - n_x: the size of the input layer\n",
    "    - n_h: the size of the hidden layer (**set this to 4, only for this Exercise 2**) \n",
    "    - n_y: the size of the output layer\n",
    "\n",
    "**Hint**: Use shapes of X and Y to find n_x and n_y. Also, hard code the hidden layer size to be 4."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "cell_type": "code",
     "checksum": "40a4061cd6df43988d25ebea254e3a3b",
     "grade": false,
     "grade_id": "cell-bf6ef9d827b48201",
     "locked": false,
     "schema_version": 3,
     "solution": true,
     "task": false
    }
   },
   "outputs": [],
   "source": [
    "# GRADED FUNCTION: layer_sizes\n",
    "\n",
    "def layer_sizes(X, Y):\n",
    "    \"\"\"\n",
    "    Arguments:\n",
    "    X -- input dataset of shape (input size, number of examples)\n",
    "    Y -- labels of shape (output size, number of examples)\n",
    "    \n",
    "    Returns:\n",
    "    n_x -- the size of the input layer\n",
    "    n_h -- the size of the hidden layer\n",
    "    n_y -- the size of the output layer\n",
    "    \"\"\"\n",
    "    #(≈ 3 lines of code)\n",
    "    # n_x = ... \n",
    "    # n_h = ...\n",
    "    # n_y = ... \n",
    "    ### START CODE HERE ### (≈ 3 lines of code)\n",
    "    n_x = X.shape[0] # size of input layer\n",
    "    n_h = 4\n",
    "    n_y = Y.shape[0] # size of output layer\n",
    "    ### END CODE HERE ###\n",
    "    return (n_x, n_h, n_y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "cell_type": "code",
     "checksum": "314281d8cdb343ad6fc836d2f68ddc84",
     "grade": true,
     "grade_id": "cell-c98fce5b0806c953",
     "locked": true,
     "points": 10,
     "schema_version": 3,
     "solution": false,
     "task": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The size of the input layer is: n_x = 5\n",
      "The size of the hidden layer is: n_h = 4\n",
      "The size of the output layer is: n_y = 2\n",
      "\u001b[92mAll tests passed!\n"
     ]
    }
   ],
   "source": [
    "t_X, t_Y = layer_sizes_test_case()\n",
    "(n_x, n_h, n_y) = layer_sizes(t_X, t_Y)\n",
    "print(\"The size of the input layer is: n_x = \" + str(n_x))\n",
    "print(\"The size of the hidden layer is: n_h = \" + str(n_h))\n",
    "print(\"The size of the output layer is: n_y = \" + str(n_y))\n",
    "\n",
    "layer_sizes_test(layer_sizes)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***Expected output***\n",
    "```\n",
    "The size of the input layer is: n_x = 5\n",
    "The size of the hidden layer is: n_h = 4\n",
    "The size of the output layer is: n_y = 2\n",
    "All tests passed!\n",
    " All tests passed.\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a name='4-2'></a>\n",
    "### 4.2 - Initialize the model's parameters ####\n",
    "\n",
    "<a name='ex-3'></a>\n",
    "### Exercise 3 -  initialize_parameters\n",
    "\n",
    "Implement the function `initialize_parameters()`.\n",
    "\n",
    "**Instructions**:\n",
    "- Make sure your parameters' sizes are right. Refer to the neural network figure above if needed.\n",
    "- You will initialize the weights matrices with random values. \n",
    "    - Use: `np.random.randn(a,b) * 0.01` to randomly initialize a matrix of shape (a,b).\n",
    "- You will initialize the bias vectors as zeros. \n",
    "    - Use: `np.zeros((a,b))` to initialize a matrix of shape (a,b) with zeros."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "cell_type": "code",
     "checksum": "09cf806395560c43e4a130688bae9096",
     "grade": false,
     "grade_id": "cell-e701a137e4b826ea",
     "locked": false,
     "schema_version": 3,
     "solution": true,
     "task": false
    }
   },
   "outputs": [],
   "source": [
    "# GRADED FUNCTION: initialize_parameters\n",
    "\n",
    "def initialize_parameters(n_x, n_h, n_y):\n",
    "    \"\"\"\n",
    "    Argument:\n",
    "    n_x -- size of the input layer\n",
    "    n_h -- size of the hidden layer\n",
    "    n_y -- size of the output layer\n",
    "    \n",
    "    Returns:\n",
    "    params -- python dictionary containing your parameters:\n",
    "                    W1 -- weight matrix of shape (n_h, n_x)\n",
    "                    b1 -- bias vector of shape (n_h, 1)\n",
    "                    W2 -- weight matrix of shape (n_y, n_h)\n",
    "                    b2 -- bias vector of shape (n_y, 1)\n",
    "    \"\"\"    \n",
    "    #(≈ 4 lines of code)\n",
    "    # W1 = ...\n",
    "    # b1 = ...\n",
    "    # W2 = ...\n",
    "    # b2 = ...\n",
    "    ### START CODE HERE ### (≈ 4 lines of code)\n",
    "    W1 = np.random.randn(n_h, n_x) * 0.01\n",
    "    b1 = np.zeros(shape=(n_h, 1))\n",
    "    W2 = np.random.randn(n_y, n_h) * 0.01\n",
    "    b2 = np.zeros(shape=(n_y, 1))\n",
    "    ### END CODE HERE ###\n",
    "    parameters = {\"W1\": W1,\n",
    "                  \"b1\": b1,\n",
    "                  \"W2\": W2,\n",
    "                  \"b2\": b2}\n",
    "    \n",
    "    return parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "cell_type": "code",
     "checksum": "045cf9c8734315fb006b39700c252b85",
     "grade": true,
     "grade_id": "cell-7aa275067ab508e9",
     "locked": true,
     "points": 10,
     "schema_version": 3,
     "solution": false,
     "task": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "W1 = [[-0.00416758 -0.00056267]\n",
      " [-0.02136196  0.01640271]\n",
      " [-0.01793436 -0.00841747]\n",
      " [ 0.00502881 -0.01245288]]\n",
      "b1 = [[0.]\n",
      " [0.]\n",
      " [0.]\n",
      " [0.]]\n",
      "W2 = [[-0.01057952 -0.00909008  0.00551454  0.02292208]]\n",
      "b2 = [[0.]]\n",
      "\u001b[92mAll tests passed!\n"
     ]
    }
   ],
   "source": [
    "np.random.seed(2)\n",
    "n_x, n_h, n_y = initialize_parameters_test_case()\n",
    "parameters = initialize_parameters(n_x, n_h, n_y)\n",
    "\n",
    "print(\"W1 = \" + str(parameters[\"W1\"]))\n",
    "print(\"b1 = \" + str(parameters[\"b1\"]))\n",
    "print(\"W2 = \" + str(parameters[\"W2\"]))\n",
    "print(\"b2 = \" + str(parameters[\"b2\"]))\n",
    "\n",
    "initialize_parameters_test(initialize_parameters)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Expected output**\n",
    "```\n",
    "W1 = [[-0.00416758 -0.00056267]\n",
    " [-0.02136196  0.01640271]\n",
    " [-0.01793436 -0.00841747]\n",
    " [ 0.00502881 -0.01245288]]\n",
    "b1 = [[0.]\n",
    " [0.]\n",
    " [0.]\n",
    " [0.]]\n",
    "W2 = [[-0.01057952 -0.00909008  0.00551454  0.02292208]]\n",
    "b2 = [[0.]]\n",
    "All tests passed!\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a name='4-3'></a>\n",
    "### 4.3 - The Loop \n",
    "\n",
    "<a name='ex-4'></a>\n",
    "### Exercise 4 - forward_propagation\n",
    "\n",
    "Implement `forward_propagation()` using the following equations:\n",
    "\n",
    "$$Z^{[1]} =  W^{[1]} X + b^{[1]}\\tag{1}$$ \n",
    "$$A^{[1]} = \\tanh(Z^{[1]})\\tag{2}$$\n",
    "$$Z^{[2]} = W^{[2]} A^{[1]} + b^{[2]}\\tag{3}$$\n",
    "$$\\hat{Y} = A^{[2]} = \\sigma(Z^{[2]})\\tag{4}$$\n",
    "\n",
    "\n",
    "**Instructions**:\n",
    "\n",
    "- Check the mathematical representation of your classifier in the figure above.\n",
    "- Use the function `sigmoid()`. It's built into (imported) this notebook.\n",
    "- Use the function `np.tanh()`. It's part of the numpy library.\n",
    "- Implement using these steps:\n",
    "    1. Retrieve each parameter from the dictionary \"parameters\" (which is the output of `initialize_parameters()` by using `parameters[\"..\"]`.\n",
    "    2. Implement Forward Propagation. Compute $Z^{[1]}, A^{[1]}, Z^{[2]}$ and $A^{[2]}$ (the vector of all your predictions on all the examples in the training set).\n",
    "- Values needed in the backpropagation are stored in \"cache\". The cache will be given as an input to the backpropagation function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "cell_type": "code",
     "checksum": "f85c43256805578b8386a15d778dfd6a",
     "grade": false,
     "grade_id": "cell-b41d8713ffbb054c",
     "locked": false,
     "schema_version": 3,
     "solution": true,
     "task": false
    }
   },
   "outputs": [],
   "source": [
    "# GRADED FUNCTION:forward_propagation\n",
    "\n",
    "def forward_propagation(X, parameters):\n",
    "    \"\"\"\n",
    "    Argument:\n",
    "    X -- input data of size (n_x, m)\n",
    "    parameters -- python dictionary containing your parameters (output of initialization function)\n",
    "    \n",
    "    Returns:\n",
    "    A2 -- The sigmoid output of the second activation\n",
    "    cache -- a dictionary containing \"Z1\", \"A1\", \"Z2\" and \"A2\"\n",
    "    \"\"\"\n",
    "    # Retrieve each parameter from the dictionary \"parameters\"\n",
    "    #(≈ 4 lines of code)\n",
    "    # W1 = ...\n",
    "    # b1 = ...\n",
    "    # W2 = ...\n",
    "    # b2 = ...\n",
    "    ### START CODE HERE ### (≈ 4 lines of code)\n",
    "    W1 = parameters['W1']\n",
    "    b1 = parameters['b1']\n",
    "    W2 = parameters['W2']\n",
    "    b2 = parameters['b2']\n",
    "    ### END CODE HERE ###\n",
    "    \n",
    "    # Implement Forward Propagation to calculate A2 (probabilities)\n",
    "    ### START CODE HERE ### (≈ 4 lines of code)\n",
    "    Z1 = np.dot(W1, X) + b1\n",
    "    A1 = np.tanh(Z1)\n",
    "    Z2 = np.dot(W2, A1) + b2\n",
    "    A2 = sigmoid(Z2)\n",
    "    ### END CODE HERE ###\n",
    "    \n",
    "    assert(A2.shape == (1, X.shape[1]))\n",
    "    \n",
    "    cache = {\"Z1\": Z1,\n",
    "             \"A1\": A1,\n",
    "             \"Z2\": Z2,\n",
    "             \"A2\": A2}\n",
    "    \n",
    "    return A2, cache"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "cell_type": "code",
     "checksum": "8742f1f4bedcdb56dcc2a15bb794ff79",
     "grade": true,
     "grade_id": "cell-8c8104df1945b472",
     "locked": true,
     "points": 10,
     "schema_version": 3,
     "solution": false,
     "task": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "A2 = [[0.21292656 0.21274673 0.21295976]]\n",
      "\u001b[92mAll tests passed!\n"
     ]
    }
   ],
   "source": [
    "t_X, parameters = forward_propagation_test_case()\n",
    "A2, cache = forward_propagation(t_X, parameters)\n",
    "print(\"A2 = \" + str(A2))\n",
    "\n",
    "forward_propagation_test(forward_propagation)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***Expected output***\n",
    "```\n",
    "A2 = [[0.21292656 0.21274673 0.21295976]]\n",
    "All tests passed!\n",
    " All tests passed.\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a name='4-4'></a>\n",
    "### 4.4 - Compute the Cost\n",
    "\n",
    "Now that you've computed $A^{[2]}$ (in the Python variable \"`A2`\"), which contains $a^{[2](i)}$ for all examples, you can compute the cost function as follows:\n",
    "\n",
    "$$J = - \\frac{1}{m} \\sum\\limits_{i = 1}^{m} \\large{(} \\small y^{(i)}\\log\\left(a^{[2] (i)}\\right) + (1-y^{(i)})\\log\\left(1- a^{[2] (i)}\\right) \\large{)} \\small\\tag{13}$$\n",
    "\n",
    "<a name='ex-5'></a>\n",
    "### Exercise 5 - compute_cost \n",
    "\n",
    "Implement `compute_cost()` to compute the value of the cost $J$.\n",
    "\n",
    "**Instructions**:\n",
    "- There are many ways to implement the cross-entropy loss. This is one way to implement one part of the equation without for loops:\n",
    "$- \\sum\\limits_{i=1}^{m}  y^{(i)}\\log(a^{[2](i)})$:\n",
    "```python\n",
    "logprobs = np.multiply(np.log(A2),Y)\n",
    "cost = - np.sum(logprobs)          \n",
    "```\n",
    "\n",
    "- Use that to build the whole expression of the cost function.\n",
    "\n",
    "**Notes**: \n",
    "\n",
    "- You can use either `np.multiply()` and then `np.sum()` or directly `np.dot()`).  \n",
    "- If you use `np.multiply` followed by `np.sum` the end result will be a type `float`, whereas if you use `np.dot`, the result will be a 2D numpy array.  \n",
    "- You can use `np.squeeze()` to remove redundant dimensions (in the case of single float, this will be reduced to a zero-dimension array). \n",
    "- You can also cast the array as a type `float` using `float()`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "cell_type": "code",
     "checksum": "40359ee771bdf2b1c9306b2d03fc975f",
     "grade": false,
     "grade_id": "cell-3dba3a966f90c35a",
     "locked": false,
     "schema_version": 3,
     "solution": true,
     "task": false
    }
   },
   "outputs": [],
   "source": [
    "# GRADED FUNCTION: compute_cost\n",
    "\n",
    "def compute_cost(A2, Y):\n",
    "    \"\"\"\n",
    "    Computes the cross-entropy cost given in equation (13)\n",
    "    \n",
    "    Arguments:\n",
    "    A2 -- The sigmoid output of the second activation, of shape (1, number of examples)\n",
    "    Y -- \"true\" labels vector of shape (1, number of examples)\n",
    "\n",
    "    Returns:\n",
    "    cost -- cross-entropy cost given equation (13)\n",
    "    \n",
    "    \"\"\"\n",
    "    \n",
    "    m = Y.shape[1] # number of examples\n",
    "\n",
    "    # Compute the cross-entropy cost\n",
    "    # (≈ 2 lines of code)\n",
    "    # logprobs = ...\n",
    "    # cost = ...\n",
    "    ### START CODE HERE ### (≈ 2 lines of code)\n",
    "    W1 = parameters['W1']\n",
    "    W2 = parameters['W2']\n",
    "    ### END CODE HERE ###\n",
    "    \n",
    "    # Compute the cross-entropy cost\n",
    "    ### START CODE HERE ### (≈ 2 lines of code)\n",
    "    logprobs = np.multiply(np.log(A2), Y) + np.multiply((1 - Y), np.log(1 - A2))\n",
    "    cost = - np.sum(logprobs) / m\n",
    "    ### END CODE HERE ###\n",
    "    \n",
    "    cost = float(np.squeeze(cost))  # makes sure cost is the dimension we expect. \n",
    "                                    # E.g., turns [[17]] into 17 \n",
    "    \n",
    "    return cost"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "cell_type": "code",
     "checksum": "237213dfd4d9da35e08c7477d5fddd12",
     "grade": true,
     "grade_id": "cell-be9a6c2220f20d3a",
     "locked": true,
     "points": 10,
     "schema_version": 3,
     "solution": false,
     "task": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "cost = 0.6930587610394646\n",
      "\u001b[92mAll tests passed!\n"
     ]
    }
   ],
   "source": [
    "A2, t_Y = compute_cost_test_case()\n",
    "cost = compute_cost(A2, t_Y)\n",
    "print(\"cost = \" + str(compute_cost(A2, t_Y)))\n",
    "\n",
    "compute_cost_test(compute_cost)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***Expected output***\n",
    "```\n",
    "cost = 0.6930587610394646\n",
    "All tests passed!\n",
    " All tests passed.\n",
    "``` \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a name='4-5'></a>\n",
    "### 4.5 - Implement Backpropagation\n",
    "\n",
    "Using the cache computed during forward propagation, you can now implement backward propagation.\n",
    "\n",
    "<a name='ex-6'></a>\n",
    "### Exercise 6 -  backward_propagation\n",
    "\n",
    "Implement the function `backward_propagation()`.\n",
    "\n",
    "**Instructions**:\n",
    "Backpropagation is usually the hardest (most mathematical) part in deep learning. To help you, here again is the slide from the lecture on backpropagation. You'll want to use the six equations on the right of this slide, since you are building a vectorized implementation.  \n",
    "\n",
    "<img src=\"images/grad_summary.png\" style=\"width:600px;height:300px;\">\n",
    "<caption><center><font color='purple'><b>Figure 1</b>: Backpropagation. Use the six equations on the right.</font></center></caption>\n",
    "\n",
    "<!--\n",
    "$\\frac{\\partial \\mathcal{J} }{ \\partial z_{2}^{(i)} } = \\frac{1}{m} (a^{[2](i)} - y^{(i)})$\n",
    "\n",
    "$\\frac{\\partial \\mathcal{J} }{ \\partial W_2 } = \\frac{\\partial \\mathcal{J} }{ \\partial z_{2}^{(i)} } a^{[1] (i) T} $\n",
    "\n",
    "$\\frac{\\partial \\mathcal{J} }{ \\partial b_2 } = \\sum_i{\\frac{\\partial \\mathcal{J} }{ \\partial z_{2}^{(i)}}}$\n",
    "\n",
    "$\\frac{\\partial \\mathcal{J} }{ \\partial z_{1}^{(i)} } =  W_2^T \\frac{\\partial \\mathcal{J} }{ \\partial z_{2}^{(i)} } * ( 1 - a^{[1] (i) 2}) $\n",
    "\n",
    "$\\frac{\\partial \\mathcal{J} }{ \\partial W_1 } = \\frac{\\partial \\mathcal{J} }{ \\partial z_{1}^{(i)} }  X^T $\n",
    "\n",
    "$\\frac{\\partial \\mathcal{J} _i }{ \\partial b_1 } = \\sum_i{\\frac{\\partial \\mathcal{J} }{ \\partial z_{1}^{(i)}}}$\n",
    "\n",
    "- Note that $*$ denotes elementwise multiplication.\n",
    "- The notation you will use is common in deep learning coding:\n",
    "    - dW1 = $\\frac{\\partial \\mathcal{J} }{ \\partial W_1 }$\n",
    "    - db1 = $\\frac{\\partial \\mathcal{J} }{ \\partial b_1 }$\n",
    "    - dW2 = $\\frac{\\partial \\mathcal{J} }{ \\partial W_2 }$\n",
    "    - db2 = $\\frac{\\partial \\mathcal{J} }{ \\partial b_2 }$\n",
    "    \n",
    "!-->\n",
    "\n",
    "- Tips:\n",
    "    - To compute dZ1 you'll need to compute $g^{[1]'}(Z^{[1]})$. Since $g^{[1]}(.)$ is the tanh activation function, if $a = g^{[1]}(z)$ then $g^{[1]'}(z) = 1-a^2$. So you can compute \n",
    "    $g^{[1]'}(Z^{[1]})$ using `(1 - np.power(A1, 2))`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "cell_type": "code",
     "checksum": "b3e942b09120df109c1602281e11576b",
     "grade": false,
     "grade_id": "cell-0f8a26305f1ccef7",
     "locked": false,
     "schema_version": 3,
     "solution": true,
     "task": false
    }
   },
   "outputs": [],
   "source": [
    "# GRADED FUNCTION: backward_propagation\n",
    "\n",
    "def backward_propagation(parameters, cache, X, Y):\n",
    "    \"\"\"\n",
    "    Implement the backward propagation using the instructions above.\n",
    "    \n",
    "    Arguments:\n",
    "    parameters -- python dictionary containing our parameters \n",
    "    cache -- a dictionary containing \"Z1\", \"A1\", \"Z2\" and \"A2\".\n",
    "    X -- input data of shape (2, number of examples)\n",
    "    Y -- \"true\" labels vector of shape (1, number of examples)\n",
    "    \n",
    "    Returns:\n",
    "    grads -- python dictionary containing your gradients with respect to different parameters\n",
    "    \"\"\"\n",
    "    m = X.shape[1]\n",
    "    \n",
    "    # First, retrieve W1 and W2 from the dictionary \"parameters\".\n",
    "    #(≈ 2 lines of code)\n",
    "    # W1 = ...\n",
    "    # W2 = ...\n",
    "    # YOUR CODE STARTS HERE\n",
    "    \n",
    "    \n",
    "    # YOUR CODE ENDS HERE\n",
    "        \n",
    "    # Retrieve also A1 and A2 from dictionary \"cache\".\n",
    "    #(≈ 2 lines of code)\n",
    "    # A1 = ...\n",
    "    # A2 = ...\n",
    "    ### START CODE HERE ### (≈ 2 lines of code)\n",
    "    W1 = parameters['W1']\n",
    "    W2 = parameters['W2']\n",
    "    ### END CODE HERE ###\n",
    "        \n",
    "    # Retrieve also A1 and A2 from dictionary \"cache\".\n",
    "    ### START CODE HERE ### (≈ 2 lines of code)\n",
    "    A1 = cache['A1']\n",
    "    A2 = cache['A2']\n",
    "    ### END CODE HERE ###\n",
    "    \n",
    "    # Backward propagation: calculate dW1, db1, dW2, db2. \n",
    "    ### START CODE HERE ### (≈ 6 lines of code, corresponding to 6 equations on slide above)\n",
    "    dZ2= A2 - Y\n",
    "    dW2 = (1 / m) * np.dot(dZ2, A1.T)\n",
    "    db2 = (1 / m) * np.sum(dZ2, axis=1, keepdims=True)\n",
    "    dZ1 = np.multiply(np.dot(W2.T, dZ2), 1 - np.power(A1, 2))\n",
    "    dW1 = (1 / m) * np.dot(dZ1, X.T)\n",
    "    db1 = (1 / m) * np.sum(dZ1, axis=1, keepdims=True)\n",
    "    ### END CODE HERE ###\n",
    "    \n",
    "    grads = {\"dW1\": dW1,\n",
    "             \"db1\": db1,\n",
    "             \"dW2\": dW2,\n",
    "             \"db2\": db2}\n",
    "    \n",
    "    return grads"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "cell_type": "code",
     "checksum": "d7083c449c3dd88f91128e1c5d4d80c7",
     "grade": true,
     "grade_id": "cell-cbd08e4138b79fe9",
     "locked": true,
     "points": 10,
     "schema_version": 3,
     "solution": false,
     "task": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dW1 = [[ 0.00301023 -0.00747267]\n",
      " [ 0.00257968 -0.00641288]\n",
      " [-0.00156892  0.003893  ]\n",
      " [-0.00652037  0.01618243]]\n",
      "db1 = [[ 0.00176201]\n",
      " [ 0.00150995]\n",
      " [-0.00091736]\n",
      " [-0.00381422]]\n",
      "dW2 = [[ 0.00078841  0.01765429 -0.00084166 -0.01022527]]\n",
      "db2 = [[-0.16655712]]\n",
      "\u001b[92mAll tests passed!\n"
     ]
    }
   ],
   "source": [
    "parameters, cache, t_X, t_Y = backward_propagation_test_case()\n",
    "\n",
    "grads = backward_propagation(parameters, cache, t_X, t_Y)\n",
    "print (\"dW1 = \"+ str(grads[\"dW1\"]))\n",
    "print (\"db1 = \"+ str(grads[\"db1\"]))\n",
    "print (\"dW2 = \"+ str(grads[\"dW2\"]))\n",
    "print (\"db2 = \"+ str(grads[\"db2\"]))\n",
    "\n",
    "backward_propagation_test(backward_propagation)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***Expected output***\n",
    "```\n",
    "dW1 = [[ 0.00301023 -0.00747267]\n",
    " [ 0.00257968 -0.00641288]\n",
    " [-0.00156892  0.003893  ]\n",
    " [-0.00652037  0.01618243]]\n",
    "db1 = [[ 0.00176201]\n",
    " [ 0.00150995]\n",
    " [-0.00091736]\n",
    " [-0.00381422]]\n",
    "dW2 = [[ 0.00078841  0.01765429 -0.00084166 -0.01022527]]\n",
    "db2 = [[-0.16655712]]\n",
    "All tests passed!\n",
    " All tests passed.\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a name='4-6'></a>\n",
    "### 4.6 - Update Parameters \n",
    "\n",
    "<a name='ex-7'></a>\n",
    "### Exercise 7 - update_parameters\n",
    "\n",
    "Implement the update rule. Use gradient descent. You have to use (dW1, db1, dW2, db2) in order to update (W1, b1, W2, b2).\n",
    "\n",
    "**General gradient descent rule**: $\\theta = \\theta - \\alpha \\frac{\\partial J }{ \\partial \\theta }$ where $\\alpha$ is the learning rate and $\\theta$ represents a parameter.\n",
    "\n",
    "<img src=\"images/sgd.gif\" style=\"width:400;height:400;\"> <img src=\"images/sgd_bad.gif\" style=\"width:400;height:400;\">\n",
    "<caption><center><font color='purple'><b>Figure 2</b>: The gradient descent algorithm with a good learning rate (converging) and a bad learning rate (diverging). Images courtesy of Adam Harley.</font></center></caption>\n",
    "\n",
    "**Hint**\n",
    "\n",
    "- Use `copy.deepcopy(...)` when copying lists or dictionaries that are passed as parameters to functions. It avoids input parameters being modified within the function. In some scenarios, this could be inefficient, but it is required for grading purposes.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "cell_type": "code",
     "checksum": "63f89f94a280c8674c7ece8f915fb051",
     "grade": false,
     "grade_id": "cell-f0a3d6f05b55f29e",
     "locked": false,
     "schema_version": 3,
     "solution": true,
     "task": false
    }
   },
   "outputs": [],
   "source": [
    "# GRADED FUNCTION: update_parameters\n",
    "\n",
    "def update_parameters(parameters, grads, learning_rate = 1.2):\n",
    "    \"\"\"\n",
    "    Updates parameters using the gradient descent update rule given above\n",
    "    \n",
    "    Arguments:\n",
    "    parameters -- python dictionary containing your parameters \n",
    "    grads -- python dictionary containing your gradients \n",
    "    \n",
    "    Returns:\n",
    "    parameters -- python dictionary containing your updated parameters \n",
    "    \"\"\"\n",
    "    # Retrieve a copy of each parameter from the dictionary \"parameters\". Use copy.deepcopy(...) for W1 and W2\n",
    "    #(≈ 4 lines of code)\n",
    "    # W1 = ...\n",
    "    # b1 = ...\n",
    "    # W2 = ...\n",
    "    # b2 = ...\n",
    "    ### START CODE HERE ### (≈ 4 lines of code)\n",
    "    W1 = parameters['W1']\n",
    "    b1 = parameters['b1']\n",
    "    W2 = parameters['W2']\n",
    "    b2 = parameters['b2']\n",
    "    ### END CODE HERE ###\n",
    "    \n",
    "    # Retrieve each gradient from the dictionary \"grads\"\n",
    "    ### START CODE HERE ### (≈ 4 lines of code)\n",
    "    dW1 = grads['dW1']\n",
    "    db1 = grads['db1']\n",
    "    dW2 = grads['dW2']\n",
    "    db2 = grads['db2']\n",
    "    ## END CODE HERE ###\n",
    "    \n",
    "    # Update rule for each parameter\n",
    "    ### START CODE HERE ### (≈ 4 lines of code)\n",
    "    W1 = W1 - learning_rate * dW1\n",
    "    b1 = b1 - learning_rate * db1\n",
    "    W2 = W2 - learning_rate * dW2\n",
    "    b2 = b2 - learning_rate * db2\n",
    "    ### END CODE HERE ###\n",
    "    \n",
    "    parameters = {\"W1\": W1,\n",
    "                  \"b1\": b1,\n",
    "                  \"W2\": W2,\n",
    "                  \"b2\": b2}\n",
    "    \n",
    "    return parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "cell_type": "code",
     "checksum": "0979d8e5e535620971e081abfff45839",
     "grade": true,
     "grade_id": "cell-21bc2649c66c1c26",
     "locked": true,
     "points": 10,
     "schema_version": 3,
     "solution": false,
     "task": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "W1 = [[-0.00643025  0.01936718]\n",
      " [-0.02410458  0.03978052]\n",
      " [-0.01653973 -0.02096177]\n",
      " [ 0.01046864 -0.05990141]]\n",
      "b1 = [[-1.02420756e-06]\n",
      " [ 1.27373948e-05]\n",
      " [ 8.32996807e-07]\n",
      " [-3.20136836e-06]]\n",
      "W2 = [[-0.01041081 -0.04463285  0.01758031  0.04747113]]\n",
      "b2 = [[0.00010457]]\n",
      "\u001b[92mAll tests passed!\n"
     ]
    }
   ],
   "source": [
    "parameters, grads = update_parameters_test_case()\n",
    "parameters = update_parameters(parameters, grads)\n",
    "\n",
    "print(\"W1 = \" + str(parameters[\"W1\"]))\n",
    "print(\"b1 = \" + str(parameters[\"b1\"]))\n",
    "print(\"W2 = \" + str(parameters[\"W2\"]))\n",
    "print(\"b2 = \" + str(parameters[\"b2\"]))\n",
    "\n",
    "update_parameters_test(update_parameters)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***Expected output***\n",
    "```\n",
    "W1 = [[-0.00643025  0.01936718]\n",
    " [-0.02410458  0.03978052]\n",
    " [-0.01653973 -0.02096177]\n",
    " [ 0.01046864 -0.05990141]]\n",
    "b1 = [[-1.02420756e-06]\n",
    " [ 1.27373948e-05]\n",
    " [ 8.32996807e-07]\n",
    " [-3.20136836e-06]]\n",
    "W2 = [[-0.01041081 -0.04463285  0.01758031  0.04747113]]\n",
    "b2 = [[0.00010457]]\n",
    "All tests passed!\n",
    " All tests passed.\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a name='4-7'></a>\n",
    "### 4.7 - Integration\n",
    "\n",
    "Integrate your functions in `nn_model()` \n",
    "\n",
    "<a name='ex-8'></a>\n",
    "### Exercise 8 - nn_model\n",
    "\n",
    "Build your neural network model in `nn_model()`.\n",
    "\n",
    "**Instructions**: The neural network model has to use the previous functions in the right order."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "cell_type": "code",
     "checksum": "461c83f5d15193186d8b122d0a451895",
     "grade": false,
     "grade_id": "cell-25f5e3e9b4ef006f",
     "locked": false,
     "schema_version": 3,
     "solution": true,
     "task": false
    }
   },
   "outputs": [],
   "source": [
    "# GRADED FUNCTION: nn_model\n",
    "\n",
    "def nn_model(X, Y, n_h, num_iterations = 10000, print_cost=False):\n",
    "    \"\"\"\n",
    "    Arguments:\n",
    "    X -- dataset of shape (2, number of examples)\n",
    "    Y -- labels of shape (1, number of examples)\n",
    "    n_h -- size of the hidden layer\n",
    "    num_iterations -- Number of iterations in gradient descent loop\n",
    "    print_cost -- if True, print the cost every 1000 iterations\n",
    "    \n",
    "    Returns:\n",
    "    parameters -- parameters learnt by the model. They can then be used to predict.\n",
    "    \"\"\"\n",
    "    \n",
    "    np.random.seed(3)\n",
    "    n_x = layer_sizes(X, Y)[0]\n",
    "    n_y = layer_sizes(X, Y)[2]\n",
    "    \n",
    "    # Initialize parameters\n",
    "    #(≈ 1 line of code)\n",
    "    # parameters = ...\n",
    "    ### START CODE HERE ### (≈ 5 lines of code)\n",
    "    A2, cache = forward_propagation(X, parameters) \n",
    "    cost = compute_cost(A2, Y)\n",
    "    grads = backward_propagation(parameters, cache, X, Y)\n",
    "    parameters = update_parameters(parameters, grads)\n",
    "    ### END CODE HERE ###\n",
    "    \n",
    "    # Loop (gradient descent)\n",
    "\n",
    "    for i in range(0, num_iterations):\n",
    "         \n",
    "        ### START CODE HERE ### (≈ 4 lines of code)\n",
    "        # Forward propagation. Inputs: \"X, parameters\". Outputs: \"A2, cache\".\n",
    "        A2, cache = forward_propagation(X, parameters)\n",
    "        \n",
    "        # Cost function. Inputs: \"A2, Y, parameters\". Outputs: \"cost\".\n",
    "        cost = compute_cost(A2, Y, parameters)\n",
    " \n",
    "        # Backpropagation. Inputs: \"parameters, cache, X, Y\". Outputs: \"grads\".\n",
    "        grads = backward_propagation(parameters, cache, X, Y)\n",
    " \n",
    "        # Gradient descent parameter update. Inputs: \"parameters, grads\". Outputs: \"parameters\".\n",
    "        parameters = update_parameters(parameters, grads)\n",
    "        \n",
    "        ### END CODE HERE ###\n",
    "\n",
    "        \n",
    "        # Print the cost every 1000 iterations\n",
    "        if print_cost and i % 1000 == 0:\n",
    "            print (\"Cost after iteration %i: %f\" %(i, cost))\n",
    "\n",
    "    return parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "cell_type": "code",
     "checksum": "c5a88642effdc073e396131eecc242b2",
     "grade": true,
     "grade_id": "cell-3484cc5d41a6cff7",
     "locked": true,
     "points": 10,
     "schema_version": 3,
     "solution": false,
     "task": false
    }
   },
   "outputs": [
    {
     "ename": "UnboundLocalError",
     "evalue": "local variable 'parameters' referenced before assignment",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mUnboundLocalError\u001b[0m                         Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-45-1243cded3c7d>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mnn_model_test\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnn_model\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;32m~/work/release/W3A1/public_tests.py\u001b[0m in \u001b[0;36mnn_model_test\u001b[0;34m(target)\u001b[0m\n\u001b[1;32m    261\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    262\u001b[0m     \u001b[0mt_X\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mt_Y\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnn_model_test_case\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 263\u001b[0;31m     \u001b[0mparameters\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mtarget\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mt_X\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mt_Y\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mn_h\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnum_iterations\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m10000\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mprint_cost\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mTrue\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    264\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    265\u001b[0m     \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"W1 = \"\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mstr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mparameters\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m\"W1\"\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m<ipython-input-36-04034fa8f0a2>\u001b[0m in \u001b[0;36mnn_model\u001b[0;34m(X, Y, n_h, num_iterations, print_cost)\u001b[0m\n\u001b[1;32m     22\u001b[0m     \u001b[0;31m# parameters = ...\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     23\u001b[0m     \u001b[0;31m### START CODE HERE ### (≈ 5 lines of code)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 24\u001b[0;31m     \u001b[0mA2\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcache\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mforward_propagation\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mX\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mparameters\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     25\u001b[0m     \u001b[0mcost\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mcompute_cost\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mA2\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mY\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     26\u001b[0m     \u001b[0mgrads\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mbackward_propagation\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mparameters\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcache\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mX\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mY\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mUnboundLocalError\u001b[0m: local variable 'parameters' referenced before assignment"
     ]
    }
   ],
   "source": [
    "nn_model_test(nn_model)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***Expected output***\n",
    "```\n",
    "Cost after iteration 0: 0.693198\n",
    "Cost after iteration 1000: 0.000219\n",
    "Cost after iteration 2000: 0.000108\n",
    "...\n",
    "Cost after iteration 8000: 0.000027\n",
    "Cost after iteration 9000: 0.000024\n",
    "W1 = [[ 0.56305445 -1.03925886]\n",
    " [ 0.7345426  -1.36286875]\n",
    " [-0.72533346  1.33753027]\n",
    " [ 0.74757629 -1.38274074]]\n",
    "b1 = [[-0.22240654]\n",
    " [-0.34662093]\n",
    " [ 0.33663708]\n",
    " [-0.35296113]]\n",
    "W2 = [[ 1.82196893  3.09657075 -2.98193564  3.19946508]]\n",
    "b2 = [[0.21344644]]\n",
    "All tests passed!\n",
    " All tests passed.\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a name='5'></a>\n",
    "## 5 - Test the Model\n",
    "\n",
    "<a name='5-1'></a>\n",
    "### 5.1 - Predict\n",
    "\n",
    "<a name='ex-9'></a>\n",
    "### Exercise 9 - predict\n",
    "\n",
    "Predict with your model by building `predict()`.\n",
    "Use forward propagation to predict results.\n",
    "\n",
    "**Reminder**: predictions = $y_{prediction} = \\mathbb 1 \\text{{activation > 0.5}} = \\begin{cases}\n",
    "      1 & \\text{if}\\ activation > 0.5 \\\\\n",
    "      0 & \\text{otherwise}\n",
    "    \\end{cases}$  \n",
    "    \n",
    "As an example, if you would like to set the entries of a matrix X to 0 and 1 based on a threshold you would do: ```X_new = (X > threshold)```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "cell_type": "code",
     "checksum": "47f6c9deeb2c83107018f17aa987bfe2",
     "grade": false,
     "grade_id": "cell-54e92a8c3c22758b",
     "locked": false,
     "schema_version": 3,
     "solution": true,
     "task": false
    }
   },
   "outputs": [],
   "source": [
    "# GRADED FUNCTION: predict\n",
    "\n",
    "def predict(parameters, X):\n",
    "    \"\"\"\n",
    "    Using the learned parameters, predicts a class for each example in X\n",
    "    \n",
    "    Arguments:\n",
    "    parameters -- python dictionary containing your parameters \n",
    "    X -- input data of size (n_x, m)\n",
    "    \n",
    "    Returns\n",
    "    predictions -- vector of predictions of our model (red: 0 / blue: 1)\n",
    "    \"\"\"\n",
    "    \n",
    "    # Computes probabilities using forward propagation, and classifies to 0/1 using 0.5 as the threshold.\n",
    "    #(≈ 2 lines of code)\n",
    "    # A2, cache = ...\n",
    "    # predictions = ...\n",
    "     ### START CODE HERE ### (≈ 2 lines of code)\n",
    "    A2, cache = forward_propagation(X, parameters)\n",
    "    predictions = np.round(A2)\n",
    "    ### END CODE HERE ###\n",
    "    \n",
    "    return predictions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "cell_type": "code",
     "checksum": "930eb713dd8c9c0c38684deda0c4da0c",
     "grade": true,
     "grade_id": "cell-7d5ddc5f94da1d7a",
     "locked": true,
     "points": 10,
     "schema_version": 3,
     "solution": false,
     "task": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Predictions: [[1. 0. 1.]]\n",
      "\u001b[92mAll tests passed!\n"
     ]
    }
   ],
   "source": [
    "parameters, t_X = predict_test_case()\n",
    "\n",
    "predictions = predict(parameters, t_X)\n",
    "print(\"Predictions: \" + str(predictions))\n",
    "\n",
    "predict_test(predict)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***Expected output***\n",
    "```\n",
    "Predictions: [[ True False  True]]\n",
    "All tests passed!\n",
    " All tests passed.\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a name='5-2'></a>\n",
    "### 5.2 - Test the Model on the Planar Dataset\n",
    "\n",
    "It's time to run the model and see how it performs on a planar dataset. Run the following code to test your model with a single hidden layer of $n_h$ hidden units!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "ename": "UnboundLocalError",
     "evalue": "local variable 'parameters' referenced before assignment",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mUnboundLocalError\u001b[0m                         Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-41-936b4bb74d92>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0;31m# Build a model with a n_h-dimensional hidden layer\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 2\u001b[0;31m \u001b[0mparameters\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnn_model\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mX\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mY\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mn_h\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;36m4\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnum_iterations\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m10000\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mprint_cost\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mTrue\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      3\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      4\u001b[0m \u001b[0;31m# Plot the decision boundary\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      5\u001b[0m \u001b[0mplot_decision_boundary\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;32mlambda\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mpredict\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mparameters\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mT\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mX\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mY\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m<ipython-input-36-04034fa8f0a2>\u001b[0m in \u001b[0;36mnn_model\u001b[0;34m(X, Y, n_h, num_iterations, print_cost)\u001b[0m\n\u001b[1;32m     22\u001b[0m     \u001b[0;31m# parameters = ...\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     23\u001b[0m     \u001b[0;31m### START CODE HERE ### (≈ 5 lines of code)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 24\u001b[0;31m     \u001b[0mA2\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcache\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mforward_propagation\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mX\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mparameters\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     25\u001b[0m     \u001b[0mcost\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mcompute_cost\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mA2\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mY\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     26\u001b[0m     \u001b[0mgrads\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mbackward_propagation\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mparameters\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcache\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mX\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mY\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mUnboundLocalError\u001b[0m: local variable 'parameters' referenced before assignment"
     ]
    }
   ],
   "source": [
    "# Build a model with a n_h-dimensional hidden layer\n",
    "parameters = nn_model(X, Y, n_h = 4, num_iterations=10000, print_cost=True)\n",
    "\n",
    "# Plot the decision boundary\n",
    "plot_decision_boundary(lambda x: predict(parameters, x.T), X, Y)\n",
    "plt.title(\"Decision Boundary for hidden layer size \" + str(4))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy: 88%\n"
     ]
    }
   ],
   "source": [
    "# Print accuracy\n",
    "predictions = predict(parameters, X)\n",
    "print ('Accuracy: %d' % float((np.dot(Y, predictions.T) + np.dot(1 - Y, 1 - predictions.T)) / float(Y.size) * 100) + '%')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Expected Output**: \n",
    "\n",
    "<table style=\"width:30%\">\n",
    "  <tr>\n",
    "    <td><b>Accuracy</b></td>\n",
    "    <td> 90% </td> \n",
    "  </tr>\n",
    "</table>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Accuracy is really high compared to Logistic Regression. The model has learned the patterns of the flower's petals! Unlike logistic regression, neural networks are able to learn even highly non-linear decision boundaries. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Congrats on finishing this Programming Assignment! \n",
    "\n",
    "Here's a quick recap of all you just accomplished: \n",
    "\n",
    "- Built a complete 2-class classification neural network with a hidden layer\n",
    "- Made good use of a non-linear unit\n",
    "- Computed the cross entropy loss\n",
    "- Implemented forward and backward propagation\n",
    "- Seen the impact of varying the hidden layer size, including overfitting.\n",
    "\n",
    "You've created a neural network that can learn patterns! Excellent work. Below, there are some optional exercises to try out some other hidden layer sizes, and other datasets. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a name='6'></a>\n",
    "## 6 - Tuning hidden layer size (optional/ungraded exercise)\n",
    "\n",
    "Run the following code(it may take 1-2 minutes). Then, observe different behaviors of the model for various hidden layer sizes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "ename": "UnboundLocalError",
     "evalue": "local variable 'parameters' referenced before assignment",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mUnboundLocalError\u001b[0m                         Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-43-fb48d87d52d1>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      6\u001b[0m     \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msubplot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m5\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m2\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mi\u001b[0m\u001b[0;34m+\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      7\u001b[0m     \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtitle\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'Hidden Layer of size %d'\u001b[0m \u001b[0;34m%\u001b[0m \u001b[0mn_h\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 8\u001b[0;31m     \u001b[0mparameters\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnn_model\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mX\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mY\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mn_h\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnum_iterations\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;36m5000\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      9\u001b[0m     \u001b[0mplot_decision_boundary\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;32mlambda\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mpredict\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mparameters\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mT\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mX\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mY\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     10\u001b[0m     \u001b[0mpredictions\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mpredict\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mparameters\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mX\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m<ipython-input-36-04034fa8f0a2>\u001b[0m in \u001b[0;36mnn_model\u001b[0;34m(X, Y, n_h, num_iterations, print_cost)\u001b[0m\n\u001b[1;32m     22\u001b[0m     \u001b[0;31m# parameters = ...\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     23\u001b[0m     \u001b[0;31m### START CODE HERE ### (≈ 5 lines of code)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 24\u001b[0;31m     \u001b[0mA2\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcache\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mforward_propagation\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mX\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mparameters\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     25\u001b[0m     \u001b[0mcost\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mcompute_cost\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mA2\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mY\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     26\u001b[0m     \u001b[0mgrads\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mbackward_propagation\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mparameters\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcache\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mX\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mY\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mUnboundLocalError\u001b[0m: local variable 'parameters' referenced before assignment"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1152x2304 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# This may take about 2 minutes to run\n",
    "\n",
    "plt.figure(figsize=(16, 32))\n",
    "hidden_layer_sizes = [1, 2, 3, 4, 5, 20, 50]\n",
    "for i, n_h in enumerate(hidden_layer_sizes):\n",
    "    plt.subplot(5, 2, i+1)\n",
    "    plt.title('Hidden Layer of size %d' % n_h)\n",
    "    parameters = nn_model(X, Y, n_h, num_iterations = 5000)\n",
    "    plot_decision_boundary(lambda x: predict(parameters, x.T), X, Y)\n",
    "    predictions = predict(parameters, X)\n",
    "    accuracy = float((np.dot(Y,predictions.T) + np.dot(1 - Y, 1 - predictions.T)) / float(Y.size)*100)\n",
    "    print (\"Accuracy for {} hidden units: {} %\".format(n_h, accuracy))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Interpretation**:\n",
    "- The larger models (with more hidden units) are able to fit the training set better, until eventually the largest models overfit the data. \n",
    "- The best hidden layer size seems to be around n_h = 5. Indeed, a value around here seems to  fits the data well without also incurring noticeable overfitting.\n",
    "- Later, you'll become familiar with regularization, which lets you use very large models (such as n_h = 50) without much overfitting. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Note**: Remember to submit the assignment by clicking the blue \"Submit Assignment\" button at the upper-right. \n",
    "\n",
    "**Some optional/ungraded questions that you can explore if you wish**: \n",
    "- What happens when you change the tanh activation for a sigmoid activation or a ReLU activation?\n",
    "- Play with the learning_rate. What happens?\n",
    "- What if we change the dataset? (See part 7 below!)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a name='7'></a>\n",
    "## 7- Performance on other datasets"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If you want, you can rerun the whole notebook (minus the dataset part) for each of the following datasets."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Datasets\n",
    "noisy_circles, noisy_moons, blobs, gaussian_quantiles, no_structure = load_extra_datasets()\n",
    "\n",
    "datasets = {\"noisy_circles\": noisy_circles,\n",
    "            \"noisy_moons\": noisy_moons,\n",
    "            \"blobs\": blobs,\n",
    "            \"gaussian_quantiles\": gaussian_quantiles}\n",
    "\n",
    "### START CODE HERE ### (choose your dataset)\n",
    "dataset = \"noisy_moons\"\n",
    "### END CODE HERE ###\n",
    "\n",
    "X, Y = datasets[dataset]\n",
    "X, Y = X.T, Y.reshape(1, Y.shape[0])\n",
    "\n",
    "# make blobs binary\n",
    "if dataset == \"blobs\":\n",
    "    Y = Y%2\n",
    "\n",
    "# Visualize the data\n",
    "plt.scatter(X[0, :], X[1, :], c=Y, s=40, cmap=plt.cm.Spectral);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**References**:\n",
    "\n",
    "- http://scs.ryerson.ca/~aharley/neural-networks/\n",
    "- http://cs231n.github.io/neural-networks-case-study/"
   ]
  }
 ],
 "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": "3.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}