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": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The autoreload extension is already loaded. To reload it, use:\n",
      "  %reload_ext autoreload\n"
     ]
    }
   ],
   "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": 3,
   "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": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
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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": 6,
   "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",
    "# YOUR CODE STARTS HERE\n",
    "shape_X = np.shape(X)\n",
    "shape_Y = np.shape(Y)\n",
    "m = shape_X[1]\n",
    "# YOUR CODE ENDS 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": 7,
   "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": 8,
   "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, as `n_h = 4`, but 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": 9,
   "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",
    "    # YOUR CODE STARTS HERE\n",
    "    n_x = np.shape(X)[0]\n",
    "    n_h = 4\n",
    "    n_y = np.shape(Y)[0]\n",
    "    \n",
    "    # YOUR CODE ENDS HERE\n",
    "    return (n_x, n_h, n_y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "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",
    "```"
   ]
  },
  {
   "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": 13,
   "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",
    "    # YOUR CODE STARTS HERE\n",
    "    W1 = np.random.randn(n_h,n_x) * 0.01\n",
    "    b1 = np.zeros((n_h,1))\n",
    "    W2 = np.random.randn(n_y,n_h) * 0.01\n",
    "    b2 = np.zeros((n_y,1))\n",
    "    \n",
    "    # YOUR CODE ENDS HERE\n",
    "\n",
    "    parameters = {\"W1\": W1,\n",
    "                  \"b1\": b1,\n",
    "                  \"W2\": W2,\n",
    "                  \"b2\": b2}\n",
    "    \n",
    "    return parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "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": 17,
   "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",
    "    # YOUR CODE STARTS HERE\n",
    "    W1 = parameters[\"W1\"]\n",
    "    b1 = parameters[\"b1\"]\n",
    "    W2 = parameters[\"W2\"]\n",
    "    b2 = parameters[\"b2\"]\n",
    "    \n",
    "    # YOUR CODE ENDS HERE\n",
    "    \n",
    "    # Implement Forward Propagation to calculate A2 (probabilities)\n",
    "    # (≈ 4 lines of code)\n",
    "    # Z1 = ...\n",
    "    # A1 = ...\n",
    "    # Z2 = ...\n",
    "    # A2 = ...\n",
    "    # YOUR CODE STARTS HERE\n",
    "    Z1 = np.dot(W1,X) + b1\n",
    "    A1 = np.tanh(Z1)\n",
    "    Z2 = np.dot(W2,A1) + b2\n",
    "    A2 = sigmoid(Z2)\n",
    "    \n",
    "    # YOUR CODE ENDS 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": 18,
   "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",
    "```"
   ]
  },
  {
   "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": 29,
   "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",
    "    # YOUR CODE STARTS HERE\n",
    "    logprobs = np.multiply(np.log(A2),Y) + np.multiply(np.log(1-A2),1-Y)\n",
    "    cost = -np.sum(logprobs)/m\n",
    "    \n",
    "    # YOUR CODE ENDS 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": 30,
   "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",
    "``` \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": 33,
   "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",
    "    W1 = parameters[\"W1\"]\n",
    "    W2 = parameters[\"W2\"]\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",
    "    # YOUR CODE STARTS HERE\n",
    "    A1 = cache[\"A1\"]\n",
    "    A2 = cache[\"A2\"]\n",
    "    # YOUR CODE ENDS HERE\n",
    "    \n",
    "    # Backward propagation: calculate dW1, db1, dW2, db2. \n",
    "    #(≈ 6 lines of code, corresponding to 6 equations on slide above)\n",
    "    # dZ2 = ...\n",
    "    # dW2 = ...\n",
    "    # db2 = ...\n",
    "    # dZ1 = ...\n",
    "    # dW1 = ...\n",
    "    # db1 = ...\n",
    "    # YOUR CODE STARTS HERE\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.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",
    "    \n",
    "    # YOUR CODE ENDS HERE\n",
    "    \n",
    "    grads = {\"dW1\": dW1,\n",
    "             \"db1\": db1,\n",
    "             \"dW2\": dW2,\n",
    "             \"db2\": db2}\n",
    "    \n",
    "    return grads"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "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",
    "```"
   ]
  },
  {
   "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": 37,
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "cell_type": "code",
     "checksum": "63f89f94a280c8674c7ece8f915fb051",
     "grade": false,
     "grade_id": "cell-f0a3d6f05b55f29e",
     "locked": false,
     "schema_version": 3,
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   },
   "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",
    "    # YOUR CODE STARTS HERE\n",
    "    W1 = copy.deepcopy(parameters[\"W1\"])\n",
    "    b1 = parameters[\"b1\"]\n",
    "    W2 = copy.deepcopy(parameters[\"W2\"])\n",
    "    b2 = parameters[\"b2\"]\n",
    "    \n",
    "    # YOUR CODE ENDS HERE\n",
    "    \n",
    "    # Retrieve each gradient from the dictionary \"grads\"\n",
    "    #(≈ 4 lines of code)\n",
    "    # dW1 = ...\n",
    "    # db1 = ...\n",
    "    # dW2 = ...\n",
    "    # db2 = ...\n",
    "    # YOUR CODE STARTS HERE\n",
    "    dW1 = grads[\"dW1\"]\n",
    "    db1 = grads[\"db1\"]\n",
    "    dW2 = grads[\"dW2\"]\n",
    "    db2 = grads[\"db2\"]\n",
    "    \n",
    "    \n",
    "    # YOUR CODE ENDS HERE\n",
    "    \n",
    "    # Update rule for each parameter\n",
    "    #(≈ 4 lines of code)\n",
    "    # W1 = ...\n",
    "    # b1 = ...\n",
    "    # W2 = ...\n",
    "    # b2 = ...\n",
    "    # YOUR CODE STARTS HERE\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",
    "    \n",
    "    # YOUR CODE ENDS HERE\n",
    "    \n",
    "    parameters = {\"W1\": W1,\n",
    "                  \"b1\": b1,\n",
    "                  \"W2\": W2,\n",
    "                  \"b2\": b2}\n",
    "    \n",
    "    return parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "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",
    "```"
   ]
  },
  {
   "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": 39,
   "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",
    "    # YOUR CODE STARTS HERE\n",
    "    parameters = initialize_parameters(n_x, n_h, n_y)\n",
    "    \n",
    "    # YOUR CODE ENDS HERE\n",
    "    \n",
    "    # Loop (gradient descent)\n",
    "\n",
    "    for i in range(0, num_iterations):\n",
    "         \n",
    "        #(≈ 4 lines of code)\n",
    "        # Forward propagation. Inputs: \"X, parameters\". Outputs: \"A2, cache\".\n",
    "        # A2, cache = ...\n",
    "        \n",
    "        # Cost function. Inputs: \"A2, Y\". Outputs: \"cost\".\n",
    "        # cost = ...\n",
    " \n",
    "        # Backpropagation. Inputs: \"parameters, cache, X, Y\". Outputs: \"grads\".\n",
    "        # grads = ...\n",
    " \n",
    "        # Gradient descent parameter update. Inputs: \"parameters, grads\". Outputs: \"parameters\".\n",
    "        # parameters = ...\n",
    "        \n",
    "        # YOUR CODE STARTS HERE\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",
    "        \n",
    "        \n",
    "        # YOUR CODE ENDS HERE\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": 40,
   "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": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cost after iteration 0: 0.693086\n",
      "Cost after iteration 1000: 0.000220\n",
      "Cost after iteration 2000: 0.000108\n",
      "Cost after iteration 3000: 0.000072\n",
      "Cost after iteration 4000: 0.000054\n",
      "Cost after iteration 5000: 0.000043\n",
      "Cost after iteration 6000: 0.000036\n",
      "Cost after iteration 7000: 0.000030\n",
      "Cost after iteration 8000: 0.000027\n",
      "Cost after iteration 9000: 0.000024\n",
      "W1 = [[ 0.71392202  1.31281102]\n",
      " [-0.76411243 -1.41967065]\n",
      " [-0.75040545 -1.38857337]\n",
      " [ 0.56495575  1.04857776]]\n",
      "b1 = [[-0.0073536 ]\n",
      " [ 0.01534663]\n",
      " [ 0.01262938]\n",
      " [ 0.00218135]]\n",
      "W2 = [[ 2.82545815 -3.3063945  -3.16116615  1.8549574 ]]\n",
      "b2 = [[0.00393452]]\n",
      "\u001b[92mAll tests passed!\n"
     ]
    }
   ],
   "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 = [[ 0.71392202  1.31281102]\n",
    " [-0.76411243 -1.41967065]\n",
    " [-0.75040545 -1.38857337]\n",
    " [ 0.56495575  1.04857776]]\n",
    "b1 = [[-0.0073536 ]\n",
    " [ 0.01534663]\n",
    " [ 0.01262938]\n",
    " [ 0.00218135]]\n",
    "W2 = [[ 2.82545815 -3.3063945  -3.16116615  1.8549574 ]]\n",
    "b2 = [[0.00393452]]\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": 41,
   "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",
    "    # YOUR CODE STARTS HERE\n",
    "    A2, cache = forward_propagation(X, parameters)\n",
    "    predictions = (A2 > 0.5)\n",
    "    \n",
    "    # YOUR CODE ENDS HERE\n",
    "    \n",
    "    return predictions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "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: [[ True False  True]]\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",
    "```"
   ]
  },
  {
   "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": 51,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cost after iteration 0: 0.693157\n",
      "Cost after iteration 1000: 0.320255\n",
      "Cost after iteration 2000: 0.312043\n",
      "Cost after iteration 3000: 0.047968\n",
      "Cost after iteration 4000: 0.040920\n",
      "Cost after iteration 5000: 0.038086\n",
      "Cost after iteration 6000: 0.036551\n",
      "Cost after iteration 7000: 0.035552\n",
      "Cost after iteration 8000: 0.034818\n",
      "Cost after iteration 9000: 0.034234\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Decision Boundary for hidden layer size 4')"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "# 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": 52,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy: 99%\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": null,
   "metadata": {},
   "outputs": [],
   "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]\n",
    "\n",
    "# you can try with different hidden layer sizes\n",
    "# but make sure before you submit the assignment it is set as \"hidden_layer_sizes = [1, 2, 3, 4, 5]\"\n",
    "# hidden_layer_sizes = [1, 2, 3, 4, 5, 20, 50]\n",
    "\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": 45,
   "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/"
   ]
  }
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