01a-neuron-from-scratch-answers.ipynb

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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# The basic building blocks\n",
    "In this notebook we will take a closer look at elements used in computation in most machine learning systems, the **tensor**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A tensor is a generalization of vectors and matrices to an arbitrary number of **axes**. What does that mean? A scalar, or a single value, is a 0D tensor. A vector is a 1D tensor. A matrix is a 2D tensor and so on. When a new axis is added we increase the dimension of the tensor. The usage of the word **dimension** can be confusing as it is used to refer to the number of axes as well as the number of elements along an axis. We can eliminate this ambiguity by talking about the **rank** of a tensor as the number of axes it has. Similarly we also refer to the **shape** of the tensor as vector which describes the number of dimensions along each axis of a tensor. The picture below will show you how to think of tensors and their rank visually:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![Tensors](images/tensor.jpeg)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "R uses the internal data type `vector` to manipulate 0D and 1D tensors and the [`matrix`](https://www.rdocumentation.org/packages/base/versions/3.5.1/topics/matrix) data type to manipulate 2D tensors. For higher dimensional data the [`array`](https://www.rdocumentation.org/packages/base/versions/3.5.1/topics/array) data type is used. To better understand these concepts and how they relate to R, you will make the following excercise:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Excercise 1\n",
    "In the following cell complete the following tasks:\n",
    "1. Using R's [`c`](https://www.rdocumentation.org/packages/base/versions/3.5.1/topics/c) function, define a 0D tensor called 'x' with the value 4:\n",
    "$$\n",
    "x =\n",
    "\\left(\n",
    "\\begin{array}{c}\n",
    "4 \\\\\n",
    "\\end{array}\n",
    "\\right)\n",
    "$$\n",
    "2. Again using [`c`](https://www.rdocumentation.org/packages/base/versions/3.5.1/topics/c), define a 1D tensor called 'y':\n",
    "$$\n",
    "y =\n",
    "\\left(\n",
    "\\begin{array}{c}\n",
    "1\\\\\n",
    "2\\\\\n",
    "3\\\\\n",
    "4\\\\\n",
    "\\end{array}\n",
    "\\right)\n",
    "$$\n",
    "3. With the [`matrix`](https://www.rdocumentation.org/packages/base/versions/3.5.1/topics/matrix) function, define a 2D tensor called 'Z':\n",
    "$$\n",
    "Z =\n",
    "\\left(\n",
    "\\begin{array}{c}\n",
    "1 & 2 & 3 & 4\\\\\n",
    "5 & 6 & 7 & 8\\\\\n",
    "\\end{array}\n",
    "\\right)\n",
    "$$\n",
    "4. Print the dimensions of each tensor using [`dim`](https://www.rdocumentation.org/packages/base/versions/3.5.1/topics/dim) (use the `as.array()` function to get meaningful results for 1. and 2.)"
   ]
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       "<ol class=list-inline>\n",
       "\t<li>2</li>\n",
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       "\\begin{enumerate*}\n",
       "\\item 2\n",
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       "1. 2\n",
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   "source": [
    "x <- c(4)\n",
    "y <- c(1, 2, 3, 4)\n",
    "Z <- matrix(c(c(1, 5), c(2, 6), c(3, 7), c(4, 8)), nrow = 2)\n",
    "dim(as.array(x))\n",
    "dim(as.array(y))\n",
    "dim(Z)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In deep learning you will encounter data in various tensor dimensions\n",
    "- Vector data, 2D (samples, features)\n",
    "- Time-series, 3D (samples, timesteps, features)\n",
    "- Images, 4D (samples, height, width, channel) or (samples, channel, height, width)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Manipulating tensors\n",
    "Deep learning involves usually involves a lot of preprocessing of data to get it into the right shape for a model to train on. Often, you will need to manipulate a tensor's dimensions and axes, and it is crucial to understand how this works in R.\n",
    "\n",
    "During the course you will have plenty of opportunity to explore the different techniques with which R provides us. \n",
    "\n",
    "### Slicing\n",
    "The first technique we will discuss is **slicing**. With the bracket operators `[` and `]` we can slice data from a tensor by specifying the index or indices for axes we want to select:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
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       "<table>\n",
       "<tbody>\n",
       "\t<tr><td>1</td><td>4</td></tr>\n",
       "\t<tr><td>2</td><td>5</td></tr>\n",
       "\t<tr><td>3</td><td>6</td></tr>\n",
       "</tbody>\n",
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       "\\begin{tabular}{ll}\n",
       "\t 1 & 4\\\\\n",
       "\t 2 & 5\\\\\n",
       "\t 3 & 6\\\\\n",
       "\\end{tabular}\n"
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       "\n",
       "| 1 | 4 | \n",
       "| 2 | 5 | \n",
       "| 3 | 6 | \n",
       "\n",
       "\n"
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       "     [,1] [,2]\n",
       "[1,] 1    4   \n",
       "[2,] 2    5   \n",
       "[3,] 3    6   "
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       "\\begin{enumerate*}\n",
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       "1. 1\n",
       "2. 4\n",
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       "[1] 1 4"
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   "source": [
    "z <- matrix(c(1, 2, 3, 4, 5, 6),  ncol=2)\n",
    "z # This will show z\n",
    "\n",
    "slice <- z[1,] # This will slice the first row\n",
    "slice # This will show the slice"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<ol class=list-inline>\n",
       "\t<li>1</li>\n",
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       "\\begin{enumerate*}\n",
       "\\item 1\n",
       "\\item 2\n",
       "\\item 3\n",
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       "1. 1\n",
       "2. 2\n",
       "3. 3\n",
       "\n",
       "\n"
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       "[1] 1 2 3"
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   "source": [
    "z[,1] # This will slice the first column"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>1</li>\n",
       "\t<li>2</li>\n",
       "</ol>\n"
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       "\\begin{enumerate*}\n",
       "\\item 1\n",
       "\\item 2\n",
       "\\end{enumerate*}\n"
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       "1. 1\n",
       "2. 2\n",
       "\n",
       "\n"
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       "[1] 1 2"
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   "source": [
    "z[1:2, 1] # This will extract the first two elements of the first column"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise 2\n",
    "In the next cell we have defined a two-dimensional tensor called `Z`. It is a matrix of size 4 by 4. Extract the 'bottom right' section of the matrix, with size 2 by 2, pictured as the numbers in red in the following diagram:\n",
    "\n",
    "$$\n",
    "Z =\n",
    "\\left(\n",
    "\\begin{array}{cccc}\n",
    "1 & 2 & 3 & 4\\\\\n",
    "5 & 6 & 7 & 8\\\\\n",
    "9 & 10 & \\color{red}{11} & \\color{red}{12} \\\\\n",
    "13 & 14 & \\color{red}{15} & \\color{red}{16} \\\\\n",
    "\\end{array}\n",
    "\\right)\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<tbody>\n",
       "\t<tr><td>11</td><td>12</td></tr>\n",
       "\t<tr><td>15</td><td>16</td></tr>\n",
       "</tbody>\n",
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       "\\begin{tabular}{ll}\n",
       "\t 11 & 12\\\\\n",
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       "\n",
       "| 11 | 12 | \n",
       "| 15 | 16 | \n",
       "\n",
       "\n"
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       "     [,1] [,2]\n",
       "[1,] 11   12  \n",
       "[2,] 15   16  "
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   "source": [
    "Z <- matrix(c(1, 5, 9, 13, 2, 6, 10, 14, 3, 7, 11, 15, 4, 8, 12, 16), ncol = 4)\n",
    "Z[3:4, 3:4]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise 3\n",
    "In the next cell we have defined a three-dimensional tensor, also called `Z`. It is of size 4 by 4 by 4, and you can think of it as a cube. Extract the middle of the cube, with dimensions 2 by 2 by 2. The result (in R) should be:\n",
    "\n",
    "```\n",
    "22 23 26 27 38 39 42 43 \n",
    "```\n",
    "\n",
    "Please note that because we cannot easily visualise a three-dimensional tensor, R will give a list of numbers as its output."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
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       "<ol class=list-inline>\n",
       "\t<li>22</li>\n",
       "\t<li>23</li>\n",
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       "\t<li>27</li>\n",
       "\t<li>38</li>\n",
       "\t<li>39</li>\n",
       "\t<li>42</li>\n",
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       "\\begin{enumerate*}\n",
       "\\item 22\n",
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       "\\item 42\n",
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       "1. 22\n",
       "2. 23\n",
       "3. 26\n",
       "4. 27\n",
       "5. 38\n",
       "6. 39\n",
       "7. 42\n",
       "8. 43\n",
       "\n",
       "\n"
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       ", , 1\n",
       "\n",
       "     [,1] [,2]\n",
       "[1,]   22   26\n",
       "[2,]   23   27\n",
       "\n",
       ", , 2\n",
       "\n",
       "     [,1] [,2]\n",
       "[1,]   38   42\n",
       "[2,]   39   43\n"
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   "source": [
    "Z <- array(1:64, dim = c(4, 4, 4))  # 1:64 will generate a vector with elements 1, 2 ... 64\n",
    "Z[2:3, 2:3, 2:3]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Tensor arithmetic"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are a number of operations which can be performed on tensors, the first one is an **element-wise** operation, which applies a function to each element of the tensor independently. By default `+` and `*` in R are element-wise operations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
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       "<table>\n",
       "<tbody>\n",
       "\t<tr><td>1</td><td>3</td></tr>\n",
       "\t<tr><td>2</td><td>4</td></tr>\n",
       "</tbody>\n",
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       "\\begin{tabular}{ll}\n",
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       "\n",
       "| 1 | 3 | \n",
       "| 2 | 4 | \n",
       "\n",
       "\n"
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       "     [,1] [,2]\n",
       "[1,] 1    3   \n",
       "[2,] 2    4   "
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       "<table>\n",
       "<tbody>\n",
       "\t<tr><td>1 </td><td> 9</td></tr>\n",
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       "</tbody>\n",
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       "| 1  |  9 | \n",
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       "[2,] 4    16  "
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   "source": [
    "z <- matrix(c(1, 2, 3, 4), nrow=2, ncol=2) \n",
    "z\n",
    "a <- z * z\n",
    "a"
   ]
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  {
   "cell_type": "code",
   "execution_count": 8,
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       "<table>\n",
       "<tbody>\n",
       "\t<tr><td>2</td><td>6</td></tr>\n",
       "\t<tr><td>4</td><td>8</td></tr>\n",
       "</tbody>\n",
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       "\\begin{tabular}{ll}\n",
       "\t 2 & 6\\\\\n",
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       "\n",
       "| 2 | 6 | \n",
       "| 4 | 8 | \n",
       "\n",
       "\n"
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       "     [,1] [,2]\n",
       "[1,] 2    6   \n",
       "[2,] 4    8   "
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    "z + z"
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Multiplication\n",
    "The **multiplication** of two tensors returns a new tensor and is denoted by `%*%` in R. The multiplication will calculate the product for each row and column in the two tensors as follows:\n",
    "\n",
    "![Dot product](./images/Matrix_multiplication_diagram_2.svg)\n",
    "[[source]](https://en.wikipedia.org/wiki/Matrix_multiplication)\n",
    "\n",
    "In the following example the output tensor is of the same dimensions as the two input tensors."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
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       "<table>\n",
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       "\t<tr><td>1</td><td>3</td></tr>\n",
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       "<table>\n",
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       "\t<tr><td> 7</td><td>15</td></tr>\n",
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       "</tbody>\n",
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       "\n",
       "|  7 | 15 | \n",
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   "source": [
    "A <- matrix(c(1, 2, 3, 4), ncol = 2)\n",
    "A\n",
    "A %*% A"
   ]
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  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
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       "| 1 | 3 | \n",
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   "source": [
    "A <- matrix(1:4, ncol = 2)\n",
    "A\n",
    "B <- matrix(5:8, ncol = 2)\n",
    "B"
   ]
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  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
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       "\t<tr><td>23</td><td>31</td></tr>\n",
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       "\n",
       "| 23 | 31 | \n",
       "| 34 | 46 | \n",
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    "A %*% B"
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise 4\n",
    "Calculate the following matrix multiplication:\n",
    "\n",
    "$$\n",
    "\\left(\n",
    "\\begin{array}{cc}\n",
    "1 & 2 \\\\\n",
    "3 & 4 \\\\\n",
    "\\end{array}\n",
    "\\right)\n",
    "\\left(\n",
    "\\begin{array}{cc}\n",
    "5 & 6 \\\\\n",
    "7 & 8 \\\\\n",
    "\\end{array}\n",
    "\\right)\n",
    "=\n",
    "\\left(\n",
    "\\begin{array}{cc}\n",
    "19 & 22 \\\\\n",
    "43 & 50 \\\\\n",
    "\\end{array}\n",
    "\\right)\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<tbody>\n",
       "\t<tr><td>19</td><td>22</td></tr>\n",
       "\t<tr><td>43</td><td>50</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{ll}\n",
       "\t 19 & 22\\\\\n",
       "\t 43 & 50\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| 19 | 22 | \n",
       "| 43 | 50 | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "     [,1] [,2]\n",
       "[1,] 19   22  \n",
       "[2,] 43   50  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "matrix(c(1, 3, 2, 4), nrow = 2) %*% matrix(c(5, 7, 6, 8), nrow = 2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise 5\n",
    "Calculate the following multiplication of a matrix with a vector:\n",
    "\n",
    "$$\n",
    "\\left(\n",
    "\\begin{array}{cc}\n",
    "1 & 2 \\\\\n",
    "3 & 4 \\\\\n",
    "\\end{array}\n",
    "\\right)\n",
    "\\left(\n",
    "\\begin{array}{c}\n",
    "1\\\\\n",
    "2\\\\\n",
    "\\end{array}\n",
    "\\right)\n",
    "=\n",
    "\\left(\n",
    "\\begin{array}{c}\n",
    "5\\\\\n",
    "11\\\\\n",
    "\\end{array}\n",
    "\\right)\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<tbody>\n",
       "\t<tr><td> 5</td></tr>\n",
       "\t<tr><td>11</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{l}\n",
       "\t  5\\\\\n",
       "\t 11\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "|  5 | \n",
       "| 11 | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "     [,1]\n",
       "[1,]  5  \n",
       "[2,] 11  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "matrix(c(1, 3, 2, 4), nrow = 2) %*% c(1, 2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Transposition\n",
    "Transposition will flip a matrix over its main diagonal, like so:\n",
    "\n",
    "$$\n",
    "\\left(\n",
    "\\begin{array}{cc}\n",
    "1 & 2\\\\\n",
    "3 & 4\\\\\n",
    "\\end{array}\n",
    "\\right)^T\n",
    "=\n",
    "\\left(\n",
    "\\begin{array}{cc}\n",
    "1 & 3\\\\\n",
    "2 & 4\\\\\n",
    "\\end{array}\n",
    "\\right)\n",
    "$$\n",
    "\n",
    "R has a [`t`](https://www.rdocumentation.org/packages/base/versions/3.5.1/topics/t) function to do so:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<tbody>\n",
       "\t<tr><td>1</td><td>2</td></tr>\n",
       "\t<tr><td>3</td><td>4</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{ll}\n",
       "\t 1 & 2\\\\\n",
       "\t 3 & 4\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| 1 | 2 | \n",
       "| 3 | 4 | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "     [,1] [,2]\n",
       "[1,] 1    2   \n",
       "[2,] 3    4   "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<tbody>\n",
       "\t<tr><td>1</td><td>3</td></tr>\n",
       "\t<tr><td>2</td><td>4</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{ll}\n",
       "\t 1 & 3\\\\\n",
       "\t 2 & 4\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| 1 | 3 | \n",
       "| 2 | 4 | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "     [,1] [,2]\n",
       "[1,] 1    3   \n",
       "[2,] 2    4   "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "a <- matrix(c(1, 3, 2, 4), ncol = 2)\n",
    "a\n",
    "t(a)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise 6\n",
    "Create a matrix with 1 column and 1 row and transpose it. Inspect the dimensions with the [`dim`](https://www.rdocumentation.org/packages/base/versions/3.5.1/topics/dim) function. Try the same with a vector. What happens?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>1</li>\n",
       "\t<li>1</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 1\n",
       "\\item 1\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 1\n",
       "2. 1\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 1 1"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>1</li>\n",
       "\t<li>1</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 1\n",
       "\\item 1\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 1\n",
       "2. 1\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 1 1"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "NULL"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>1</li>\n",
       "\t<li>1</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 1\n",
       "\\item 1\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 1\n",
       "2. 1\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 1 1"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "M <- matrix(c(1), nrow = 1, ncol = 1)\n",
    "dim(M)\n",
    "dim(t(M)) # Dimensions stay the same when transposing matrices\n",
    "\n",
    "v <- c(1)\n",
    "dim(v) # A vector in R does not have a row or column dimension\n",
    "dim(t(v)) # Transposition will turn the vector into a matrix of 1 column and 1 row"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You will see that any vector that is transposed is automatically converted into a matrix. R has no concept of a row vector or column vector. Instead, it uses a matrix with one dimension set to 1, as you saw above."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Building a single dense layer\n",
    "In the remainder of this notebook you will solve the problem introduced in the slides. Let's load the data first:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "source(\"01-helpers.R\")  # this will load helper functions for this session\n",
    "\n",
    "data <- dataset_linear()\n",
    "X <- data$X\n",
    "y <- data$y"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We inspect the input variables `X` and the labels `y` using the [`head`](https://www.rdocumentation.org/packages/utils/versions/3.5.1/topics/head) function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col>x1</th><th scope=col>x2</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td>0.1996392</td><td>0.4562954</td></tr>\n",
       "\t<tr><td>0.1414231</td><td>0.2973767</td></tr>\n",
       "\t<tr><td>0.3190954</td><td>0.4629799</td></tr>\n",
       "\t<tr><td>0.3784599</td><td>0.4572429</td></tr>\n",
       "\t<tr><td>0.2453274</td><td>0.3714641</td></tr>\n",
       "\t<tr><td>0.2735707</td><td>0.1760050</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{ll}\n",
       " x1 & x2\\\\\n",
       "\\hline\n",
       "\t 0.1996392 & 0.4562954\\\\\n",
       "\t 0.1414231 & 0.2973767\\\\\n",
       "\t 0.3190954 & 0.4629799\\\\\n",
       "\t 0.3784599 & 0.4572429\\\\\n",
       "\t 0.2453274 & 0.3714641\\\\\n",
       "\t 0.2735707 & 0.1760050\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "x1 | x2 | \n",
       "|---|---|---|---|---|---|\n",
       "| 0.1996392 | 0.4562954 | \n",
       "| 0.1414231 | 0.2973767 | \n",
       "| 0.3190954 | 0.4629799 | \n",
       "| 0.3784599 | 0.4572429 | \n",
       "| 0.2453274 | 0.3714641 | \n",
       "| 0.2735707 | 0.1760050 | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "     x1        x2       \n",
       "[1,] 0.1996392 0.4562954\n",
       "[2,] 0.1414231 0.2973767\n",
       "[3,] 0.3190954 0.4629799\n",
       "[4,] 0.3784599 0.4572429\n",
       "[5,] 0.2453274 0.3714641\n",
       "[6,] 0.2735707 0.1760050"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "head(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>0</li>\n",
       "\t<li>0</li>\n",
       "\t<li>0</li>\n",
       "\t<li>0</li>\n",
       "\t<li>0</li>\n",
       "\t<li>0</li>\n",
       "</ol>\n",
       "\n",
       "<details>\n",
       "\t<summary style=display:list-item;cursor:pointer>\n",
       "\t\t<strong>Levels</strong>:\n",
       "\t</summary>\n",
       "\t<ol class=list-inline>\n",
       "\t\t<li>'0'</li>\n",
       "\t\t<li>'1'</li>\n",
       "\t</ol>\n",
       "</details>"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 0\n",
       "\\item 0\n",
       "\\item 0\n",
       "\\item 0\n",
       "\\item 0\n",
       "\\item 0\n",
       "\\end{enumerate*}\n",
       "\n",
       "\\emph{Levels}: \\begin{enumerate*}\n",
       "\\item '0'\n",
       "\\item '1'\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 0\n",
       "2. 0\n",
       "3. 0\n",
       "4. 0\n",
       "5. 0\n",
       "6. 0\n",
       "\n",
       "\n",
       "\n",
       "**Levels**: 1. '0'\n",
       "2. '1'\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 0 0 0 0 0 0\n",
       "Levels: 0 1"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "head(y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise 7\n",
    "Inspect the dimensions of `X` and `y`. How many instances do we have? How many input variables?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>50</li>\n",
       "\t<li>2</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 50\n",
       "\\item 2\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 50\n",
       "2. 2\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 50  2"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "50"
      ],
      "text/latex": [
       "50"
      ],
      "text/markdown": [
       "50"
      ],
      "text/plain": [
       "[1] 50"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dim(X)  # 50 instances, 2 input variables\n",
    "length(y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's plot the data set using one of the helper functions you just loaded:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {},
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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ETT7EwIYdXnxS2ftvOw+fn5U6dO9T6dOnVqQ0PDgQO+eySFro2X9Ha73fM3geO4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\nDRFFwvPC8FHCrbO48I8CBoAgkKDlw/UdQHz2JORIKPt28737kN7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ZYkUxOfqgc3JyCgoKvE8LCgp0Ol12dnaraoZ+EA8uZK2t3x5yBoq+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\nIUEDACjU/wfwkfZ/EXSTZAAAAABJRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_dataset(X, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Solving the problem - building a neuron\n",
    "During the remainder of this notebook you will build a single neuron that will perfectly classify all instances.\n",
    "\n",
    "Let's look at a diagram of this neuron you are going to build:\n",
    "\n",
    "![The neuron we are going to build](images/neuron.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You will build this neuron step by step, going from left to right through the diagram. Let's begin by defining the neuron's weights:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise 8\n",
    "The neuron will have two weights, one for each input, $w_1$ and $w_2$. Create a weight vector `w` with the values `0.5` and `0`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>0.5</li>\n",
       "\t<li>0</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 0.5\n",
       "\\item 0\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 0.5\n",
       "2. 0\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 0.5 0.0"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "w <- c(0.5, 0)\n",
    "w"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise 9\n",
    "Create the bias variable `b`. Set it to `0` for now. This means that we will ignore its effect in subsequent calculations. You will modify it later in order to solve the problem."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0"
      ],
      "text/latex": [
       "0"
      ],
      "text/markdown": [
       "0"
      ],
      "text/plain": [
       "[1] 0"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "b <- 0\n",
    "b"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise 10\n",
    "Create the sigmoid activation function `sigmoid`, which takes a vector or number `x` and returns as output the following:\n",
    "$$\n",
    "\\sigma(x) = sigmoid(x) = \\frac{1}{1 + e^{-x}}\n",
    "$$\n",
    "\n",
    "We have provided you with a skeleton below:\n",
    "\n",
    "**Hint**: you will need R's [`exp`](https://www.rdocumentation.org/packages/base/versions/3.5.1/topics/log) function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "sigmoid <- function(x) {\n",
    "    1 / (1 + exp(-x))\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise 11\n",
    "Perform the complete calculation of the neuron in R. You can either use the diagram as a reference above, or use the following equation:\n",
    "\n",
    "$$\n",
    "\\hat{y} = \\sigma(\\mathbf{w} \\mathbf{X}^\\top + b)\n",
    "$$\n",
    "\n",
    "The result should be a matrix with **1 row and 50 columns**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<tbody>\n",
       "\t<tr><td>0.0998196 </td><td>0.07071153</td><td>0.1595477 </td><td>0.18923   </td><td>0.1226637 </td><td>0.1367853 </td><td>0.1521444 </td><td>0.1466655 </td><td>0.1574736 </td><td>0.08866246</td><td>⋯         </td><td>0.3100344 </td><td>0.4186631 </td><td>0.3745815 </td><td>0.4190436 </td><td>0.345187  </td><td>0.3690141 </td><td>0.3891087 </td><td>0.3022006 </td><td>0.363549  </td><td>0.3251728 </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{llllllllllllllllllllllllllllllllllllllllllllllllll}\n",
       "\t 0.0998196  & 0.07071153 & 0.1595477  & 0.18923    & 0.1226637  & 0.1367853  & 0.1521444  & 0.1466655  & 0.1574736  & 0.08866246 & ⋯          & 0.3100344  & 0.4186631  & 0.3745815  & 0.4190436  & 0.345187   & 0.3690141  & 0.3891087  & 0.3022006  & 0.363549   & 0.3251728 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| 0.0998196  | 0.07071153 | 0.1595477  | 0.18923    | 0.1226637  | 0.1367853  | 0.1521444  | 0.1466655  | 0.1574736  | 0.08866246 | ⋯          | 0.3100344  | 0.4186631  | 0.3745815  | 0.4190436  | 0.345187   | 0.3690141  | 0.3891087  | 0.3022006  | 0.363549   | 0.3251728  | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "     [,1]      [,2]       [,3]      [,4]    [,5]      [,6]      [,7]     \n",
       "[1,] 0.0998196 0.07071153 0.1595477 0.18923 0.1226637 0.1367853 0.1521444\n",
       "     [,8]      [,9]      [,10]      [,11] [,12]     [,13]     [,14]    \n",
       "[1,] 0.1466655 0.1574736 0.08866246 ⋯     0.3100344 0.4186631 0.3745815\n",
       "     [,15]     [,16]    [,17]     [,18]     [,19]     [,20]    [,21]    \n",
       "[1,] 0.4190436 0.345187 0.3690141 0.3891087 0.3022006 0.363549 0.3251728"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "w %*% t(X) + b"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise 12\n",
    "Put the calculation above in an R function called `neuron` that takes as its input an input matrix `X` and returns the neuron's output. We will use this function for easily recalculating the neuron's output when modifying the weights and bias of the neuron.\n",
    "\n",
    "We have provided you with a skeleton to fill in below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [],
   "source": [
    "neuron <- function(X) {\n",
    "    sigmoid(w %*% t(X) + b)\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise 13\n",
    "Apply the function you defined above to the input matrix `X`.\n",
    "\n",
    "The results will be the probability of the instance belonging to the positive class (the blue one). For classification problems we usually threshold the this probability, with a value larger than $0.5$ meaning the instance is classified as positive (the 'blue' class in our case). Given the probabilities and the labels in `y`, how do you think your classifier is performing?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<tbody>\n",
       "\t<tr><td>0.5249342</td><td>0.5176705</td><td>0.5398025</td><td>0.5471668</td><td>0.5306275</td><td>0.5341431</td><td>0.5379629</td><td>0.5366008</td><td>0.5392872</td><td>0.5221511</td><td>⋯        </td><td>0.5768937</td><td>0.6031633</td><td>0.5925656</td><td>0.6032544</td><td>0.58545  </td><td>0.5912207</td><td>0.5960681</td><td>0.5749804</td><td>0.5898993</td><td>0.5805844</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{llllllllllllllllllllllllllllllllllllllllllllllllll}\n",
       "\t 0.5249342 & 0.5176705 & 0.5398025 & 0.5471668 & 0.5306275 & 0.5341431 & 0.5379629 & 0.5366008 & 0.5392872 & 0.5221511 & ⋯         & 0.5768937 & 0.6031633 & 0.5925656 & 0.6032544 & 0.58545   & 0.5912207 & 0.5960681 & 0.5749804 & 0.5898993 & 0.5805844\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| 0.5249342 | 0.5176705 | 0.5398025 | 0.5471668 | 0.5306275 | 0.5341431 | 0.5379629 | 0.5366008 | 0.5392872 | 0.5221511 | ⋯         | 0.5768937 | 0.6031633 | 0.5925656 | 0.6032544 | 0.58545   | 0.5912207 | 0.5960681 | 0.5749804 | 0.5898993 | 0.5805844 | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "     [,1]      [,2]      [,3]      [,4]      [,5]      [,6]      [,7]     \n",
       "[1,] 0.5249342 0.5176705 0.5398025 0.5471668 0.5306275 0.5341431 0.5379629\n",
       "     [,8]      [,9]      [,10]     [,11] [,12]     [,13]     [,14]    \n",
       "[1,] 0.5366008 0.5392872 0.5221511 ⋯     0.5768937 0.6031633 0.5925656\n",
       "     [,15]     [,16]   [,17]     [,18]     [,19]     [,20]     [,21]    \n",
       "[1,] 0.6032544 0.58545 0.5912207 0.5960681 0.5749804 0.5898993 0.5805844"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "neuron(X)  # All elements of the output are bigger than 0.5, so all instances are classified as class 1 (blue)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's plot the results of your prediction with a helper function that we have created for you, called `plot_predictions`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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5SUlISEhDwJtIaBafLpKs0nsEC66v+5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\nAAAJFNAAAACABApoAAAAQMJ/AdeFkE3TEw3AAAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_predictions(X, y, neuron)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As you can see, our accuracy is 50% simply because all instances are positive (blue). We need to tweak the decision boundary in order to get 100% accuracy."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise 14\n",
    "Modify the weights `w` and the bias variables `b` such that you classify the instances with 100% accuracy. Plot the probabilities and decision boundary based on your new weights and bias.\n",
    "\n",
    "How do the bias and weights affect the decision boundary?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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b29+/TpY5SYCCGEFFI5wB0XLxQouhDhXa2ShcIhhJAyqFoNKal49DC/JCYGz5+h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/l8MqeRrmpFswPwMs5XJQ9wohhJoB2+dy\nWHoHOiIiIiEhYd68eWKx+LfffktJSVmyZElUVJTpWosXL961a9f7779/69Yt3TR27u7uX375\npX5YmzZtunfvrm18+/btycnJ+o1PnDhx5cqVI0aMePHFF6uqqrZv367RUDyyZLoRs3Tq1Eko\nFH711Vd8Pt/Nzc3Hx2fgwIHaTdOnT3/33Xd/+eUXf3//0aNHM2gcIYQQQgg1C5YOoJcuXZqT\nk/Pdd989fPgwODh47dq1b7/9dpO1nJ2dz5w589FHH+3Zs2fHjh1ubm7jx4//6KOPDKaWW758\nuYnGly1bxuVyf/rpp/nz5/v6+k6cOPGtt94KCwsz2JfpRszi6ur622+/ffjhhwsXLpTJZP37\n99cNoF1dXSdPnvzTTz+9+uqrBlOOIIQQQgihloSgvGtLx65duyZNmrR3795x48ax26dmat68\neRs3bszJydFP47YBmUy2fPny5OTkrl27rlixwsvLS1sYExOjP6VJc1FRUaFQKDw9PYmS60/L\nnr5Fn71Xjb4x3kRRojYs0V8uglYLNEooNqkbDW7w08fSsTCszrRiI7XuVHqXy526etznkWpa\ntcDcM0Ynxpxu0z06q8UAi2fARAcar0VVsar71zKZzN3d3ZbTCrXUa5r8vQX27gtiLq3PIEFt\nbbsr5+zdEUSX8Rorij4J5eXlQqFQLBZb3j6muLGjrKxs27Ztw4YNs/HoGQDef//9Xbt2DRs2\n7ObNm926dbt79y4AaDSavLw8G/cEIZ22Lk96et3jkU1PiYOQAbymIQcUf/ZvHD0jfTiAtlRa\nWtrWrVsnTJhQU1OjW1jRlnbu3Lljx44VK1acOHFi1qxZAwcOfPDgge27gRBCrMBrGkLI8WG2\nrqW2bdu2du3aoKCgr7/+uk+fPrbvwJMnT3S54x988IFarR44cOCRI0ds3xOW6SYN1H3C/LRA\n/zPnRjdRlDz9c1FDdVuUVgs0SigafLpfQm0YTOjFm7ffxo+FcXVmFdmqBWaeMVox5naAztFZ\nLQZYPAMmOtB4rcZ6ZXMt9pqGELIh3YwcxrkcrGA+gJ44cSLj/OmW5PPPP//888/t2IE2bdpk\nZGT06tVL+3LFihVSqXTo0KHMWrt8+fLWrVsfPnzo6uo6ePDgKVOmNDb7Nf1IhBCiD69pCCHH\nhykczd6IESO2bNmiX7JmzZoRI0YwaCojI2P16tWxsbHr1q2bNm3anj17fv31VwsjEULILHhN\nQwg5PkzhaPYMJs/W+u9//7tq1Spzm9qzZ09gYODcuXMBICQk5NGjR/v37580aZLxYuz0Iy1A\nGPy/JedyMN8vS7kcYDrfgMZ+LaxFXdGGuRw0w6wXQx1mw1yOxnplcy33moYQsoNnq6v0SWCx\nWbwD3dLU1NQAAEEQbm5u5tZNT0/v0qWL7mWXLl3q6upyc3MtiUQIIUvgNQ0h5IDwDnSzNH78\n+M2bN7u7uxuU37x588UXX7x9+zaDNjUaTXl5uX6b2u+Nly6nH6mlVCrPnDljXB4bG2s8uWxm\nZqZMJjMo7Bgm8ZTwDQoz8msKSg0jQ30EYT6Gd4wKy5Xp+XUGhe7OnPg2PIPCWrkmJUduUEgS\n0D+G4iflbLZaoTIs7BYMEqFh4Y0CsrjaMJkyyksZ5GpY/345N6fEcF++YmWst+GRltdxUgud\nDAqFXHWvwAqDQo0GTj7wNO5/YkCJgGPYgSuPPSvlhqelg2ept7DWoDC70v2B1HAqzWDnikhJ\nKQDcKPctrnPq45PHI1WP68S3KnwNIl15dV3c7xsUytS8cyURxl0d4HXTuPB8ebs6lWFXu7hk\nunKkBoW3qsMfKzwMCiOE99sIHhkUPpT7Z9WFGhR6c0s6iAx/pqrUkss1XQwK+YS8t9NZ466e\nqhui1hi+AXoKTouIGoPCVHnPco3hP1Y7bqofaXiuclWxeeoYg8JAMjeavGpQWKIJuK42fL5Z\nDGXdicMGhQrgn4WGT9tcvgwA7du3J0nDuy2UP6pt27b19/cH8zWva5pGozl58qRxedu2bXk8\nw/dkTk6O9m8AGD5eVxiTdtGzMN8g8l7buILQSIPCgHvZoXduGBQW+wVmxvcwKBSXl3ZMOWVQ\nKBcKLz9Hkf3SK2mvcX73lf7DZCLDq0rchdOSshKDwqxO3Z/4BxkUhmTcCrybaVD4KCT8brtO\nBoUeRQVtUy8YFEpd3K4nDjAo5Mll3Y//adz/lKFj1UbvyS6njwprjH78e/St8PAyKIy6fsW7\nwPBn6n5U7MMIw58pvwd3w2+lAcCFoc8Lq6s7Jf8NAGU+/uldehpEOldVdEo+blCo4PEuDaJY\nnDjh6AGOyvDym9p3cK2zxKAw9lKyW8ljg8LsDl0eB4UYFAZn3wnOTjcofBwcmt2+s0GhW3FR\n7GXDKflqxJK0PoMNCjlKZcKxP4z7f3HQaKXRWz0++bhTleEvoPSuiWXehtf/iFtpvg/uGhQ+\niIh5EBVrUOidfz/qxhWDwgoP71s9DK9pwmpplzNHDQrVJCdl6PPPXj8dilAOP7Kzs2trG/ym\nEwgEiYmJ0AgcQDdLBw4c6Ny5844dOxISnn0esXHjxgULFjjmB45OToYXZQDg8XjGv5VFIhFJ\nkgRBcDTPBrJckgQgDD7+FvJJicjwB4DPJes/pdYL5nEJiYijt6gEAICTgDT+9JwkQSI0/LVC\nEoRxmwAgFoDSKG+Cw3naT730DBEPJIKGRQB8LgH6jyhpAAD4HJAIDBsVcjX1kXof33M5hESg\nbrgUC/A56oZJCfXBEr7SsBCAJIkGwQQJAE48lXESCpfQGJ8BAUcl4Rn+sSHgqJ4elO6/BJdU\nS3iGIy0RRw4EaTAHBUFoJFzDP3W0nX0a8yxLwZms4xGGx8UhKOZvEXHkErXBUFXDJ5XGHeCT\nSgmnWj8MAEQcmXFCEYdQS0hpg90A8Ail8RsVAMREpcbocTSS0ABBGEyC4UTWqDRcg0QgHqEw\nPgMCQiYhyg3aFEANAGmQy8EBhYQoe1pS37QIqp6+qZ79FBAESDSl+l1XioIAgMvlUv6oGv8G\n4vMN/9ClqcVc04xXohUIBBqNhiAIsrBAV8hVGP7sAAC/rlZcafhvyq8z/NsVAHhKhXGkSFpl\nHEmoNcaRjXGqquAZdYxUUVw9BDXVFF2VUfzw8uRy40hhTbVxJEetMo6kPFEA4FxZrjF6T5JU\nWXnC6iqV0T8K9fmX1VEcVI3hX7kAwFFQHVS14dgdAAgN9fmnfDrVqarSeFTNVSmMIwV1NTTf\nKlyq8y+iPv9q40jSqD9Pu1qu5hoOoCmDhTVScaXhjzBXbvgbAQAEMhnFWa2l6CpJ9f7n11L8\nS4GmwUGp/QK0s19wuVzjy5dQKDR4btj0BQ0H0M1SUlLStGnT+vbt++9//3vRokVSqXTOnDnb\nt29PSEjYvn07sza1n5CWlZXpSrTfe3gY3rqjH6nF5XL1fymaFh4eXr8SYdmt+qJGJnsJ8RaF\neAuNYiiCPcVcTzFXbwDdaLCAS3QL4xtubaQD8cEcOm0CQKS3BkDTZIMA4CdR+UmURmEU8WK+\nqltADdUqdIaRBAHd/CupGzQKbudRaXIdu2eCnauCnav0Yhqd+MxDUOshyKfuQEN8UtXNI49O\nPwGgo8u9JjupFS7KDxfR6oAPr9iHV0ynA05ETTenqw1jGj0DXYWXjGKoOxDDu0kdZhQeSOYG\nkrkNY6jbdCOKuxFPb8yY7AAXFN2IP/Wbqmr/pUwmc3V1Nf5l07mz4W0tSzSvaxpBEPSvaWFh\nYTRXIgy4lx1wL5tOm67FjzsWG96VpMSTyzqeO0EnEgDaXU2hGdkm63abLFofC3g9euj16CGd\nSJG0in5X44zutTcm4lYazUi/+7l+92kl7biUldDsKleppH9QMWkXaUYGZ98Jzr5DJ9KjqMCj\nqKDpOABBTTX9rna4SPFRG6Ww9OtNBwEAgM/Dez4P79GJlFSW0+wqqdHoR3I+XmdiJcL4+Hh6\nPa3HdACd/QNUGX5Sw4KOq4AjYr/ZFmfIkCFpaWlTp05dvHjxsWPHsrOzc3JyFi1a9Omnnxp/\ngEhfu3btrl69OmvWLO3Lq1evCoXC8PBwSyIRQqhJeE1DCDUvTAfQ9/8HhX+z2hMAAGi/DAfQ\nNPn7+x89evS5555LSkoCgP/+979vvvmmhW1OmDDh3Xff/f7774cPH56bm7t3795x48ZpPz9N\nTk4+cODAihUrtB9cmohkjzmzcFg4LwdYPp0Fsy7pfQRJaxIJOiWMDsR0C8wXZyEaZCmwMA2I\n1eblaKID1p+Xg25TVpuXg7KiDbWCaxpCqOXAFI7mqrKycs6cOWfPnu3SpcudO3c++OADf3//\niRMnWtJmTEzMsmXLtm3bduTIEVdX1/Hjx7/00kvaTSUlJenp6UqlsslIhBBiAK9pCKFmhGC4\nmuDxwVa5Az2xFPiGT2EjY1evXp08eXJOTs577723atWqjIyMF1988datW6+//vq6deua9V2T\nioqKpznQugS7xvOM6ZTQCtYvNE4StawDtLoEAOpG4xmWmHMgNFugvd8bZT7FdaI+vg94pIre\nOTF3d3ROlzmnlG4HrBZjdlMWngHTHajfWtX1C5lM5u7ubpwDza7WcE1rMgcaOTL9WThQM2U6\nB9pcjO9AN3x+H9lWYmKii4vL4cOHhw0bBgCxsbEXL1588803v/nmm3PnzqWmptq7g6ygmE2i\nHuu5HA0K7ZHLAeYmHtApMedAaLZAe7+x7iUajYZLqClnpaCbRWPLXA66HbBajNlNsZ3LQVnR\nVlrHNQ01Y11PHDbxpDJqhRhfJTkAPCt8IVoSEhLS0tK0v2m0nJycNm3a9Ouvv2Zn03qIGyGr\n4hDa0TNCtOA1DTk4rkLBVVLM6IdaLcYDaC4QPPa/aNzVPslVKeEAACAASURBVHToUHx8vFAo\nDA4OXrFihVrd6C/pioqKhQsXBgcHCwSC0NDQjz/+mOnBOpzjx48HBAQYl7/00ktXrhhOOY4Q\nQg4Or2kIoeaFaQoHwQHCDg8gpqSkjB07dt68eVu3bk1NTZ03b55KpVq9erVxZF1d3YABAxQK\nxaeffhoZGVlaWlpVRTHJfDNlIh8xOjralj2xIqPlMPQ2geEmC3M5qFuwYS4HME08YCuXw9wW\nmO3XKtOAsJTLYXYH2I5h3hRLuRyUjdtKq7imIYRaEMYDaC4Qdsi4WLNmTXR09IYNGwAgLi4u\nKytr/fr1S5cuNV4U6osvvrh//35mZmZjM+EjhBBCCCHEgCU50FwrfDVx3yM5OXn48OG6l8OH\nD6+urqZ8vmTXrl0DBw5ctmyZv79/VFTUnDlzSkpKmB4sQgghhBBC9ZjegZZEGqZwPD5nYiVb\nam6xIDDj9rBarS4qKvLz89OVaL8vKKBYpjInJ+fGjRvjx48/cOBAcXHxggULRo4cef78eZK0\n9dPliKnGF1IxCmFjEgwTLbSCXA7GLbBVi4XdWZbJwLwDLMWw0JTlZ8DkOwQhhNBTTAfQHCfg\nNxz7Etxnc47SxJMYNsIIQVDct1apVG5ubr/88gufzwcAoVA4cODA5OTkvn37Wr5HhJBp2RVu\n5TJevFcxzsWBEGoBbiT0E9TVRl+7ZO+OIEfBdABdkQWPzzUsIgDMnGm/OM2wpKupiTJIkvT1\n9S0sLNSVaL/39/c3Dg4ICPDy8tKOngGgQ4cOAHDv3j0cQCNkA7UqTpWCr9EQQPHnLUIINTM1\nrm5qLk62i55hms9AEECQ7H819cu2d+/eSUlJupdJSUnOzs6dO3c2juzXr19OTo5CodC+vH37\nNgCEhYUxPF5kewRR/wVPv4xLTGwyqzrdFvTfqGx0gKB5UGT9l4V7oXMgjFugOBAwo5bluzPv\ndBnFsNABy2LY3J3lZ0DXOEIIIQqMr48kAMcKX01YsmRJZmbm/Pnzb9y4sXXr1rVr1y5cuFA7\nBcfOnTv79OlTUVGhjXznnXcqKipmz55948aNkydP/vOf/0xISEhMTGR6vAghhBBCCAFYcAfa\nCrefadzt6Nmz5759+86ePdutW7f3339/8eLFH330kXZTfn5+cnKy7pZzTEzMsWPHcnJyevTo\nMXXq1J49ex48eBCfIEQIIYQQQhZivBgKaXbGM0tGjx49evRo4/KFCxcuXLhQvyQxMfHs2bO2\n6hdiHWHwf4aLpJhVnW4LbM/LYbpXzzZZbV4OYHwsjU8KoXtN8wRauDsL5+VoIsysDjCKscru\nLD4DCCGEqDBeSIWwSnqc4a9ehBBCCCGEHAvjO9AcIOxzBxoh5PjaSKS+omoOzmGHEGoRIq9d\n5qiU9u4FciCMB9CEBQ8gmm4WIS2jN4P1cjmYt8BSLofpMIo22c7lAMuPpUF1V74C+Jr6OHNz\nSOySy0EzzHq5HCw2xSyXgzIMIQQAAJ5FFEu2odaMcQoHznCEEEIIIYRaIwfLgUYIIYQQQsix\nOVoKB0JP6VZoZ5ZcYW6wpdkgluU/0A8z3MRSLgewdyzmJVfoN86oIlu5HDTDrJfLwWJTzHI5\nKMMQQghRsWAaO7wDjRBCCCGEWh9M4UAIIYQQQsgMliykggNoZFWNL6RiFGJpLoflLViY/9BE\nm3S6ZFkuB3UY81yOfKlIquBEukk5hIZWcoXp/dogl4NmmPVyOVhsilkuBzTy74IQArgb24kr\nlwVn37F3R5CjYLyUN2GXpbwRQs1CaR2/QCpSa3AghhBqCR4HhZT6Btq7F8iBONo0dvjrFiGE\nEEIIOTSchQM5KuNZOKyXy2F5CxbmP9Btk06XGOVyNBHGNC8FCACCojrjHBLr5XKA6TNm/VwO\nFptilssBjUzNgRBCyIgFA2iCaDoKIYQQQgihlgUfIkQIIYQQQsgMOI0dcng2yOUwHW+DXA5z\nO8B6Lgfd/dLP5SAAtBcKwvw5KGjsl/VcDqB5xqyWy0EzzHox0MjUHAghhIzgHWiEEPu8nWRO\nPAVJYC4tQqglCLibzZHL7N0L5EDwDjRCiH1+zjJ8Eg0h1GIEZ922dxeQY7FkAI0PESJaNBpN\nTU0NzWCVSgUA1dXVYuOPn62Xy0Ez3nq5HIw7wFYuh9n7Zb7GSqPV2Z9hw5xaYOYZYz2Xg2aY\n9WKA4uiUSiUA1NTUkCStOyZ8Pp/H49GJbO6qq6tpRmqvaTU1NYw/8EUIsaK2thYAFAoFzZ9f\nkiRFIlFjWx1tGjsclLdABEFwuXTfaXK5HAC4XC7IrdknhBANJEmqVCoul0tzAE0zrAUw95rG\n4XCs2R2EUNO0P4YkSdL8+SVM3im2IAcaUzgQbQKBgGZkXV2dSqUSCAQ4gEbI7rQDYj6fj+M/\nAwyuaXhJQ8i++Hx+TU0Nh8Oh//NrQvNbyvvQoUPx8fFCoTA4OHjFihVqNfXT4hs2bCAaOnbs\nGMODRXahTRMiiPrFOPQ/nTDeRBHc+CYTwTTjLdzdszc8ex2g1SWy/osymOF+Gz8Ws6rrt8Bs\nvxbWoq7Y+BkzL8bcDtA5OrZjqMMQQghRaGazcKSkpIwdO3bevHlbt25NTU2dN2+eSqVavXo1\nZbCnp6f+oDkyMtJW3UQIIYQQQi0W44cIwS43J9asWRMdHb1hwwYAiIuLy8rKWr9+/dKlS52c\nnIyDuVxufHy8zfuIEIIKGVemJLyc5CTexEQINX8lvgEcldKt+LG9O4IcBeMUDivkbxAkNPW7\nNjk5efjw4bqXw4cPr66uTk1NpQwuLS318/Pz8PBITEzctWsXwyNFdmMiOUEXwlJyBfNkDJZy\nOZinQLCUy2H5XhoeyP1K0a1isUrDMaOT9s3laKKi9XM5mB8dSzHUvUIIAQBkd+qWFxNn714g\nB8L0DrTAAyThDUqq8sye9lXkA1yKO8eNUavVRUVFfn5+uhLt9wUFBcbBsbGx33zzTYcOHWpr\na3/77bdJkyatX79+4cKF5vUQIYQQQgihhpgOoJ38QeDeoKT6IfXstiZIQsHJh2EH9FDOMzJw\n4MCBAwdqvx8wYEBFRcVnn32GA2iEEEIIIWQhpgPo8gwoM1qVx9ys6OIrhiUhI02EkyTp6+tb\nWFioK9F+7+/v3+SuEhMTd+7cKZfL+Xy+eZ1E9qJ7O5laNISlNVbMjadTYlZ1AOqFLSzpAK0u\n6SVx0VoQhE6JfmJYwzQAE9UpW2B9tRTTvaVV0WprrDTRAeuvsdJYrxBCCBlxtGnsmhiC9+7d\nOykpSfcyKSnJ2dm5c+fOTfY3OTnZ19cXR88IIYQQQshCjG8z6D0xw+ZXE5YsWZKZmTl//vwb\nN25s3bp17dq1Cxcu1E7BsXPnzj59+lRUVGgj58yZ88svvyQnJx87dmz27Nm7du1avHgx04NF\nCCGEEEKoHuNp7Owzx37Pnj337du3fPnyjRs3ent7L168eOXKldpN+fn5ycnJCoVC+1IkEq1a\ntSo/P18oFMbExGzfvn3y5Mm27zCyAGHwfyvmcpgbz3ouB5j8kN3CDtA9A2YlHjRRIuJpJHwV\nof2ois6BULdpw1wOsyuynctBtwNWi2msVwghAKeKckFdrb17gRwIodEwulJe/xLK77DdGYDE\ntWbNy4FanoqKCoVC4enpSVQ/fFr29C367L3aeIkOrWANw3g6wWZVp25BbRRmWQfongF1o/EM\nS+gciJktMNuvqVqMK9I5XXRizO0A6zEUYVUdlstkMnd3d1zKmzHdNU3+3gJ79wWhVo3z8bry\n8nKhUCgWiy1vjfFKhIRdViJECCGEEELIvppZCgdqTYzeYNbL5aDbuDnBlk8DYstcDmCaeMAs\np8J4p+a2wHouB/PdsZTLYXYH2I6hDEMIIUQF70AjhBBCCCFkBsZ3oEmcKBQhhBBCCLVCltyB\nxg/5kDUZ52A82wSGm5p7LkcTLbSCXA7GLbBVi4XdWZbLwbwDLMVQhiGEEKJiSQ60Ne5A46Ac\noZZAriJUahByNfisBEKoBZA5ORNqNR9nskNPMR4EW2EZQswJQailyCgWpDx0Vmpw+IwQagnS\n+gxK75po714gB8I4hQPwbjGyssYXUjEKsTSXg3nj5gRbnjpivVwOyl5ZkstB6L1oFrkcbO6O\nUS4HCx2wLIYyDCGEEBV8iBAhhBBCCCEzMB5AA84DjRBCCCGEWiHGKRwkzgONrMus2TMszOVg\noXFzgh0wl8N0r5jkcmiTNwgg6B0IMD4WlnI5rLI7c3I5mggzqwOMYijDEEIIUbFgGju8A40Q\nQgghhFofR5vGDiGEEEIIIYeGC6kgh9X4LBys53Kw2bg5wZZPA8JWLofpMIo2m0hOiPOTg0ZT\n/5puDomFx2JZLgfjimzlctAMs14uB2UYQggAABL+OmDvLiDH4mh3oPGyjRBCCCGEHJqDTWOH\n42eEEEIIIeTYMIUDOSyjN5j1cjnAGpN+mBlsaTaIZfkP9MMMN5m/xgplCbB3LMxyORhXZCuX\ng2aY9XI5KMMQQghRsWQWDnyIECGEEEIItToOlsKBEEIIIYSQY8OVCFEDly9f3rp168OHD11d\nXQcPHjxlyhSC6h/60KFD33//vX7JqlWrOnXqxGZXKJc7qd8EhptYSLdofJkVG+RysLg7ZvkP\nTbRJp0uW5XJQh9kwl4NxRbZyOWiGWS+XgzKs+XOgaxpCqAVpfisRHjp0aNmyZXfu3PH29n71\n1VdXrFhBkqZ6cu7cuf79+2s0GqVSabNONlMZGRmrV68eMWLEokWLcnJyvvnmG7VaPW3aNMpg\niUSyatUq3cuAgABbdRM1A3cec8prya6Bch7H3l1BrRhe0xBb0voMEtTWtrtyzt4dQY6imd2B\nTklJGTt27Lx587Zu3Zqamjpv3jyVSrV69erG4ouLi6dMmTJs2LCkpCRb9rOZ2rNnT2Bg4Ny5\ncwEgJCTk0aNH+/fvnzRpkkAgMA7mcDjh4eE27yNqHhQqslahfdQYV4VGdoPXNMQWmZMzgRcz\npMeCO9D2+IxvzZo10dHRGzZsAIC4uLisrKz169cvXbrUycnJOFitVk+dOnXmzJlisRgH0HSk\np6f3799f97JLly47duzIzc1t166dcXBVVdXLL7+sVCqDgoLGjh3bu3dva3XLBrkcDeLtkcth\neQsW5j/QbZNOl/SuDATRYAjNPIfE+rkcjCuylcsBpvM0rJ/LQRnWzDnoNQ0h1PxZMo2dHRZS\nSU5Ofumll3Qvhw8fvnr16tTUVMor3apVq+Ry+f/93/+tW7eO5W62RBqNpry83N3dXVei/b60\ntNQ4ODg4+J///GdISIhcLj916tRnn302e/bs559/vrGWS0pKzOpMSUmJl7NZNRBC7JPJZABQ\nVlZGM97Z2VkkElmzR2aw3jUNAIqLi83qTElJicSsCgghtpWXlwNAXV1dXV0dnXgOh6N/ATHA\ndADN4QFX2KBEJTO7EZJn1m1stVpdVFTk5+enK9F+X1BQYBx87Nix77777urVq6YzpFuz1NTU\nDz/8UPv9qFGjZs+eTb9ux44dO3bsqP0+Li6uurp69+7dJn7Z8Hg8mi0rlUqNRsPj8QDMf0ch\nhFhFkqRareZyuZQP3hnjcOyZ8+7w1zSEkD1xuVylUkmSJM0rlekBJNMBtDgYnAMblBSdB42Z\nH/u5RYOg0aE9fcZX9sLCwmnTpv3888/+/v6Wt99StWvXTpsMAwBisZggCDc3N/1bTdrvPTw8\n6DSVnJysVCq5XIp3FEEQrq6uNHtVUVGhUChcXFygTneDp/Gcimf7MIxlIYPClrkcpuNtkMth\nbgea7FJ9AAmgoZV1QHe/VsvlYFyRzWlA6ORpWC2XgyqMx+PJZDKJRGLfkTFNNrumAQCDa5qc\nZgWEkHWIxeLy8nI+ny8Wiy1vjekAuioPpA+NSs18rLDsjmGJRwcT4SRJ+vr6FhYW6kq03xuP\nktPS0oqKikaNGqV9qdFotDdRli1bprs/gYRCYVBQkH5Ju3btrl69OmvWLO3Lq1evCoVCOk/V\npKenu7m5NfabBiGEbACvaQghm2Ga3qBdSIX1r6b07t1b/3HApKQkZ2fnzp07G4T16dPnxo0b\naU+9/fbbHA4nLS3tjTfeYHi8rcOECRPy8/O///77vLy8EydO7N279/nnn9c+rp6cnPzuu+/W\n1NRoI7/++uvjx4+np6dfu3btq6++Sk5OHj9+vF37jhxLpJemW7CKS7aUh9FQ84TXNMSWDimn\no65dtHcvkAOxZClvO0xjt2TJkj59+syfP3/u3LlpaWlr165dtGiRdgqOnTt3fvnll4cOHXJ1\ndRWLxR06PLuZrU2V1i9BlGJiYpYtW7Zt27YjR464urqOHz9e98hmSUlJenq6bi5tPp+/Y8eO\nkpISPp8fGBi4ZMmSvn37stwbioQNq+VyNBFv/VwOmvHWy+Vg3IFGuiTiAfCebqaTdWD2ftnO\n5WBc0SrTgNgjl4MyrJlzrGsaas6cK8vt3QXkWAiNuYnLWvcOQnU+250BaDsDOBTTc+o7ePDg\n8uXL09PTtQuprFy5Upvl/cUXX7z99ttPnjzx8vIyqPL555+/9957uJBKs6DNF/T09CRkTyfu\nePYWNXqvUmzSNLrJRDDdeLOCzeqJmfEW7u7Z8Ii9DtDqkrrxYMb7NT4WZtUt3q+ltSgLGz9j\n5sWY24H6sKqYhTKZzN3dvVnkQDsm3TVN/t4Ce/cFoVaN8/G68vJyoVDISg400wF03p9WGUDH\nvNzkABq1bDiAxgE0DqBxAN2S4AAaIQfB7gDakick7JDCgVoTwuD/tHIqjGqzmUFhYr+Yy2HW\nGivGWQfM98tSLod+C3bJ5aCuaMNcDsowhBBCVBgv5W2flQgRQgghhBCyL8YDaMI6A2i8q40Q\nQgghhByaJUt542AXWZXRG6wF53KYG896LgcwToGgLrlfBlV1RIyPhqv/h7aJrANGe2lYYlku\nB2ULtszlaKKi9XM5KMMQQgAAkNmxq0AuD7lzw94dQY7CkmnsMIUDIUStohaKpRDtbe9+IIQQ\nG8r8AoXV1SH27gZyHIwH0CTzRVgQQgghhBBqtizJgcYUDmRNZmVlWJjLYW4867kc5saznssB\nlk9nYdymBggCCHrzcgDNxAM6JYwOxHQLNsjloFvRarkclB1ACCFExcEeIsSrNkIIIYQQcmyY\nwoEQQgghhJAZLFhIBVM4kHWZWEjFMMTSXA5z98J6Loe58azncoDJVAQmHdA8e0H3DJiVeECn\nxJwDodmC9XI5zK7Idi4HZQcQQghRwYVUEELs83MhXEVA4l/ZCKEWITjzNlepsHcvkANxsBxo\nTIJGqEXwluBcwgihliPgXra9u4AcCy6kghyVpfNamJPLwXgvbOVy0G3cnGDLpwFhfV4OumfA\nHrkc5rbAei4H892xlMtB2QGEEEJUHO0ONEIIIYQQQg7NkpUI8Q40QgghhBBqdXAaO+TwbJDL\nQVmxVeVyNNFCK8jlYNwCW7VY2J1luRyN9QohhJARxikcgHegEUIIIYRQK4TT2CGE2PekSlMr\n1wS6AQenskMINX8FoZFcpcLnYZ69O4IcBc7CgRyW0cfJLTiXg3nj5gRbnjpCO5ejsEJdLFX7\nu3E5BL0uUfaqVeVysLk7RrkclGEIIQAAeBAdK6yuxgE00sFZOBBCCCGEEDID40EwWZ/Fwe4X\njfsehw4dio+PFwqFwcHBK1asUKupl5zdsWNHr169PDw8hEJhZGTksmXLZDIZ04NF9kAQ9V+g\n+2p8E0WwiU1G7dCsaGmwiUOzbU9MVKfbgv7PLGX1+kM1owO0Doqs/2J2mCYOxNSxmHkqGJ9A\n9ndH53SRpsIQQghRYZzCAXa5tqakpIwdO3bevHlbt25NTU2dN2+eSqVavXq1cSSXy505c2Z0\ndLRQKLx8+fL7779fXFz8/fff277PCCGEEEKoJWlmDxGuWbMmOjp6w4YNABAXF5eVlbV+/fql\nS5c6OTkZRL7wwgu673v27Hnz5s3jx4/btK8IIYQQQqglYjoIJggzEjPMSOFoQnJy8vDhw3Uv\nhw8fXl1dnZqaaqKKSqVKTU09evTooEGDGB4ssg9GuRDMcjkom2KWAsEsl4PNxhmlNDBvobH8\nB70DNLcDdsnlMHUsNsnlsDwJxMJcDuowhBBCFCx5iNDW11a1Wl1UVOTn56cr0X5fUFBAGS+T\nyZydndVqtUajmT179ldffWWjjiLU6rmKSJIAAjQN/mBACKHmyb0wXyCX27sXyIEwHUALvUHo\n3aCkItfs1auc/IFnmHrBANHIUJ7P56elpdXV1V2+fHn58uXe3t6ffPKJ5btDCDWpjScHFytF\nCLUY0dev2LsLyLEwHUDXlYC8okEJAWbfaqothNqGJUIvE+EkSfr6+hYWFupKtN/7+/tTxhME\n0aFDBwDo1q0bh8OZO3fukiVL3N3dzeskshujt5OuwMLlsqk30Zgl2riiWXsx0X/K/VrauJnB\nFrZg4XLf9MMMN7E0RTSwdyzMpohmXJGtKaIpwxBCCFGxYBo7q3w1oXfv3klJSbqXSUlJzs7O\nnTt3brKiTCbTaDRy/PwFIYQQQghZppktpLJkyZI+ffrMnz9/7ty5aWlpa9euXbRokXYKjp07\nd3755ZeHDh1ydXUFgLfeeqtHjx5hYWFqtfrChQsfffTRyJEjfX19bd9nhBBCCCHUkjjYQ4RN\nNdmzZ899+/YtX75848aN3t7eixcvXrlypXZTfn5+cnKyQqHQvnR2dv7kk0/y8vI4HE5oaOj7\n77+/YMEC9juMaNBoNNXV1TSDVSoVAFRXV4uFug+mjYJYz+Wg2ZSJDrCQbsFSOgqzYBZ3xyz/\noYk26XTJslwO6jAb5nIwrshWLgdVmFKpBICamprGHjUxIBAIeDwencjmTiqV0ozUXdNaxXlB\nyIHV1NQAgEKhoPnzS5Kk8SzJOoRGY+aTf1rlmSCvYlLRNO94IDjsN4vsTfeHTZOqq6uVSqWL\niwufVNYXPXuLGn1DsQka3WSiHXObMtEmw2B6+7VeT6yxu2eDTvY6QKtL6kaDaf4TWHgsdKrT\nPQM0KlpaS38AbRhWETJDoVBIJBKSpPWRI4fDoRnZ3DG4pmk+WGzVLiGETNN8+B+pVMrn80Ui\nEc0qJu4IONgdaNRC0b8ppb3RxePxQKVsMhg5rFq5RqlSiwUkXieaNe1omMvlcjh4a6MBBtc0\nfASnWat2cSPUKiepFW4dIlvhcrkAQJIkKx+UMV7Km9YzfwixwKxUCmaJEOY2ZaKW5RkUdsnl\nsLyFhiXZRfLiKmWfGCceSS//gWYHrJfL0USY9XM5GFdkK5cDGpmaAyEEcLNnP2F1dafkv+3d\nEeQoGA+gAe9AI4QQQgihVgjvQCOEEEIIIWSGZjaNHWpNjD51bsG5HObul/VcDtPxjPNStK/p\n5D+Y2wHWczno7tdquRyMK7JVC6jOGEIIISr4ECFCCCGEEEJmsCCFA+9AI4QQQgih1ofxAJrA\nHGhkXRT5ElbL5bC8KRO1LM+gsEEuB8142rvjkASX8/SjKjr5D4w7wFYuh9n7ZTuXg3FFq0wD\ngpd3hBrgKBSkku7k36g1cLQUDkwLQagliA0SAgjs3QuEEGJHtxOH7d0F5FjwIUKEEEIIIYTM\nYEkKB94tRlZFGPzfirkc1PFMm2qsluUZFM0wl6OREsfL5WC+X5ZyOfRbsEsuB2VFhBBCVPAO\nNEII/X97dx8bRfUucPzMvpe2bFugApVgUC9Z87MWbiRekBASuEEhvGhKfiD6F01BIVYiehM0\ngnATNRGDgoEYSaSIVtIKJhiI8T0N3gS3JD+1grSGmxYELLulLd2d3Z29f+x1hb5sZ2Z3z759\nPyG6Ozuz85w9ndOnM8+eAQDAgCTOQDONHQAAAAoPdyJE1hr2F1r6ajmE2eKEvKnlMLp+yms5\nhOkSCHMhjXTHkCT3kmQtx4jvILOWY7SoAADDmC7hEJyBBgAAQAEynUBzIxUAo/rX/97880bo\nYU+p3cpf2gBy3v/853LXwMADrV9mOhBkC75EiGyVwhk2xtxqxA1l1nIYXT/ltRxG19dbOKEI\noZgvYEgyAEO1HGKkqTlk1nIkfgcJtRwjbggAGAnT2AEAAAAGJPElwrScgSYpBwAAQFajhANZ\nT0YtR8INJdRyGN1Lyms5jK4/dkmD8td/b9mH6QIGMwGY+ARGv82KhFoOne+QvlqOxAEDAG5h\nOglW0vNvbCdOnKipqXG5XNOmTXvllVc0beSB/uDBg4sWLaqsrCwpKZk1a9b7779vtqUAAADA\n37LsDPRYKfQPP/ywYsWKDRs2NDY2trW1bdiwIRKJ7Nq1a/iahw4dmj9//nPPPed2u5ubm9ev\nXx8KhTZs2JD6mAEAAFBIlGjU1Iz54ZtCC6c6GCEcpYmT6Mcff7y9vf2XX36JPX355Zffeuut\nq1evjhs3LvEbL1y40GKxfPklE9Bku97e3lAoNGHCBCUa+WvZsB/Rv39ohz0Y4SUdWxndUE4A\nhvaSbPxG33yMldWwFtE0l92qKDo3T/ye2tAlhqI1/wloo65vcsnoDTH9DqnaaqSFfdP+GQwG\ny8vLrVargCnxMU39r2czHQvMC44rVjTNERjMdCAwz/rfu/1+v8vlKikpSf7dkjmLnIESjtbW\n1iVLlsSfLlmyZGBgoK2tbcwNA4FAZWVlEo0FYIDDZilyWLnbEoD84Lw5QPaMWyUzC4epU9dJ\n0DTtypUrkydPji+JPb506VLiDQ8ePPjjjz++/fbb6Y0PAAAABcBsAm2xCcV+25KIaupNUlBI\nrSQ8zdXU1PTMM8988MEHDz74YPL7gjwjzGJhboILHVsZ3TDl83KMuGFG5uVIRyTJTwMic16O\n216VOC+H6XdI1VajLQQADGM2gY5qYuj0F8Yv1moRISK3LbE5E6xusVjuuOOOP/74I74k9njK\nlCmjbbJ///4tW7Z89NFHK1euNBweAAAAMIzZE8CKoZZUHgAADRZJREFUJS3/xsrC582bd/Lk\nyfjTkydPFhcXz5o1a8SVX3311a1bt3722WdkzwAAAEiVJKaxS+oLiCZt3br14Ycf3rRpU319\n/dmzZ998880tW7bEpuA4evTonj17Tpw44Xa7hRANDQ379u175513Jk6cePbsWSGE0+n0eDzy\nY4ZZypD/U8uRxloO829uZOXkS0fSV8sxYlQFVcsx4oYAgJGY/hKhkpER9qGHHjp27NhLL730\n3nvvTZo06fnnn9++fXvspe7u7tbW1lAoFHt6+PDhcDi8cePG+LZ33333hQsX5McMFKDfr9zs\nHQj9Y3qpzUouBiDntf/7fzgCgbt/HnvWLxSIJBLoDJ2jWLZs2bJly4Yvb2hoaGhoiD/9888/\nJQYF4Db9g2Fff4ivogHIDzcmTHINDGQ6CmSRZEo4kG/Onz/f3Nzc0dFx9erVxYsXb968OcHK\nZ86caWxs7OrqcrvdixYtWrNmTeLpUJKQ/loO0xumqpZD54bpq+VIwZvf/tL/70K57WpVNtdy\nJI5KQi2HMN2WFNVyjLhajsvWMQ1AzstAHTOyViAQmDJlypNPPplgYpOYc+fO7dq167777tu9\ne/e6detaWlo+/PBDOUECgE6MaQDSxHQJB/JQdXV1dXW1EKKlpSXxmi0tLVVVVfX19UKI6dOn\nX758+fjx47W1tU5nookIAUAmxjQAaUICDTPa29sXLFgQfzp79uympqbOzs7R5jmJRo1dEo5G\noyOVCQ2r5RjO+BVXVVVDoVBxcbHhLc3q6+tTVbWiokLaBeJQKBQMBktKSuTsTggRvnhWiGBk\n/L/ZZOUf8tvY398fDAbLy8stFkmX8sLhcCAQkNlG0d8vhIhGo/oP4Rwte5Awpjle25NUiLoF\ng8FIJBKbn0oOv9+vaVpFRYW0PQYCASGEy+WStsfod99plXdI60QhxMDAgN1udzgccnanaZrP\n53M4HKWlpXL2KITo6+srKiqy2STlouFwOPYgJQMaCTQMi0ajfr+/vLw8viT2+Pr166Ot39PT\nY2gXo71V+sSGY5nktzEYDErbl6ZpQoje3l6r1Sptp0JuG2N8Pp/kPcpvo9/v17lmcXFxUVFR\nWoNJB6NjmhAi+8e0wcFByXs0+pkkb0Dut/pM/C5LkvxfTKqqSm6jqhq/j3VyAoGAzg/WarXe\nOiwMQQJduNra2nbs2BF7vHTp0rq6uvTtS/9l0FAopGmazMummqZpmibtL2BRGG2srKwsKytz\nOp3SEmj5bQyHw5FIxOFwSDvnGo1GI5FINrdR8t9LQ2TnmKaqajQaze/jXX4bI5GIkPvzdued\nd9psNpltDIfDFotF2gWuaDSqqqrFYrHb7XL2KIQIhUI2m03mEKqqqtVq1Xl0JA6MBLpweTye\nvXv3xh4buiisKEpZWdmtJ95ij0e7fqcoiv5LQr29vZqmlZSUSDuiVFVVVVXmZfEbN27E9iiz\nhCMQCMi8MBcbp8aPHy9t9Jffxr6+vkgkUlJSIrOEY3BwUH4bi4uLM5sZ6yRtTBNCGBrTQqGQ\nzOM9GAyGw2GZZWk+n0/TNJk/mbHz6zIvd8QSL5lt7O/vdzgcMks4rl+/brPZZLbxxo0b48aN\nk1nCoaqq3W5PyW98ZuEoXC6X686/lJWVGdrW4/F4vd74U6/X63K5ZsyYkeoYAUAvxjQA0pBA\n42+qqnZ2dnZ2dqqq2t/f39nZ+fvvv8deam1tffHFF2/evBl7+thjj3V3dx84cODixYtff/31\np59+unz5cr6uDiCrMKYBSBNKOPC3rq6u+N0cu7u7T58+bbFYjh07JoTo6elpb2+Pf4N15syZ\n27ZtO3z48KlTp9xu96pVq9auXZuxuAFgJIxpANJEMToXD5BWsXrBCRMm5H0NtMw2yq8PjrWx\noqIiv2ugg8GgzDZmpAY6NlVfTtRAZyf5Y1qmaqAnTJggbY/ya6B7enqsVqvR0qBkZKQG2uFw\njB8/Xs4eRSZqoP1+v8vlogYaAAAAkI0SDgCp19PTMzAw4Ha7pZ2dBYD0uXLlis1mk3kGGlmO\n320AUs/v91+7di12OxUAyHXXrl2TfzccZDMSaAAAAMAAEmgAAADAABJoAAAAwAASaAAAAMAA\nEmgAAADAAKaxQ3ZxOBySb9lgtVrtdrvMPdrtdsmTu1ksFsltLC8vt9vtMrtSfhvtdruiKNLu\njiGEUBQlI21kLsJkZGRMk7k7IYTT6ZR8UzZpt96ImzRpUn7/plAUxeVySf5gHQ6HzDZaLBaX\ny5WqfuROhAAAAIABnFcAAAAADCCBBgAAAAwggQYAAAAMIIEGAAAADCCBBgAAAAwggQYAAAAM\nIIEGAAAADOBGKsiY8+fPNzc3d3R0XL16dfHixZs3b06w8pkzZxobG7u6utxu96JFi9asWSPz\nBhbJ0Bn5iRMnDhw4cOuSnTt3PvDAA7LCNEl/v9CDWatAjkQJCuSTzOMjggEtLhe7L0baYUgC\njYwJBAJTpkyZO3fukSNHEq957ty5Xbt2PfLII1u2bOno6Hj33Xc1TVu3bp2cOJNhKPLS0tKd\nO3fGn06dOlVWmCbpbx09mM0K4UiUoxA+yTw+IhjQhsit7ouTdhiSQCNjqqurq6urhRAtLS2J\n12xpaamqqqqvrxdCTJ8+/fLly8ePH6+trXU6nTICTYKhyK1W64wZM6THaJ7+1tGD2awQjkQ5\nCuGTzOMjggFtiNzqvjhphyE10MgB7e3ts2fPjj+dPXt2IBDo7OzMYEg6GYq8r6/vqaeeWrt2\n7QsvvNDa2iorRvP0t44ezA+524/ZJnc/yTw+IhjQhsit7jMhyX7kDDSyXTQa9fv95eXl8SWx\nx9evX89cULoYinzatGkbN26cPn26qqrffvvt66+/vn79+uXLl8sL1yD9raMH80Pu9mO2yd1P\nMo+PCAa0IXKr+0xIvh9JoCFJW1vbjh07Yo+XLl1aV1eX2XjSYUgb169fr3/b+FUnIcT9998/\nMDDQ3NycT6NV3qMHCw1jWmIcETmN7hsTCTQk8Xg8e/fujT0uKSnRv6GiKGVlZT6fL74k9rii\noiK1ESZvSBuTidzj8bS2tobDYZstSw9S/a3LoR4cIr970Kjc7cc0YUwTeXREMKAlluXdZ0Ly\n/UgNNCRxuVx3/qWsrMzQth6Px+v1xp96vV6Xy5WFX24Y3kbTkbe3t5eVlWX5UKW/dbnSg8Pl\ndw8albv9mA6MaSK/jggGtASyv/tMSLIfrdu3b09LXMBYVFW9ePGiz+f7/vvvi4qKqqqq4gVJ\nra2t+/btmzdvnt1uF0JUVla2tLT09vZOmjSpra3t0KFDK1asuLX2P2sliHxIG/ft29ff3x8I\nBC5dunT06NFvvvlmzZo1Ho8n0y1IRH/r6MFsVghHohyF8Enm8RHBgJbT3Rcn7TDMqz8mkFu6\nuroaGhpij7u7u0+fPm2xWI4dOyaE6OnpaW9vD4fDsVdnzpy5bdu2w4cPnzp1yu12r1q1au3a\ntRmL24gEkQ9po8PhaGpq6unpcTgcVVVVW7dunT9/fuYC10V/6+jBbFYIR6IchfBJ5vERwYCW\n090XJ+0wVKLRaMqjBwAAAPIVNdAAAACAASTQAAAAgAEk0AAAAIABJNAAAACAASTQAAAAgAEk\n0AAAAIABJNAAAACAASTQAAAAgAEk0ADMi0QiCxYscLlcXq83vvCLL76wWq0rV67MYGAAYBQD\nGvTjToQAknLp0qWamhq32+31ektLSy9fvlxTU1NUVNTW1lZeXp7p6ADAAAY06MQZaABJmTp1\namNjY0dHR11dnaZpTzzxhM/na2pq4pcNgJzDgAadrNu3b890DABy2z333BMMBvfv3//VV199\n9913b7zxRm1tbaaDAgAzGNCgByUcAFIgEonMmTPH6/UuWbLk888/VxQl0xEBgEkMaBgTJRwA\nUuDcuXO//vqrEOLChQv9/f23vnTo0KG5c+cWFxdPnjw5Q9EBgAEMaBgTCTSAZA0ODq5evdpm\ns+3Zs+fChQv19fW3vjpx4sSGhgaqxQDkBAY06GHLdAAAct6mTZt+/vnnTz75pLa29uLFi7t3\n7164cGFdXV3s1UcffVQI8fHHH2c0RgDQhQENenAGGkBSjhw5cvDgwaeffjr2PZvXXnttzpw5\nzz777E8//ZTp0ADAGAY06EQCDcC83377rb6+vqamZvfu3bEldru9qanJ6XSuXr365s2bmQ0P\nAPRjQIN+lHAAMO/ee+/t6+sbsvCuu+7y+XwZiQcATGNAg36cgQYAAAAM4Aw0gPSKRCKhUCgU\nCgkhAoGAoihOpzPTQQGAGQxoiOFGKgDSa//+/Rs3bow/tVqt4XA4g/EAgGkMaIghgQYAAAAM\noAYaAAAAMIAEGgAAADCABBoAAAAwgAQaAAAAMIAEGgAAADCABBoAAAAwgAQaAAAAMIAEGgAA\nADCABBoAAAAwgAQaAAAAMIAEGgAAADCABBoAAAAwgAQaAAAAMOD/ABLlJbzz8ffwAAAAAElF\nTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "w <- c(0.5, 0.5)\n",
    "b <- -0.5\n",
    "plot_predictions(X, y, neuron) # w controls the 'slope' of the decision boundary, b shifts it"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "R",
   "language": "R",
   "name": "ir"
  },
  "language_info": {
   "codemirror_mode": "r",
   "file_extension": ".r",
   "mimetype": "text/x-r-source",
   "name": "R",
   "pygments_lexer": "r",
   "version": "3.5.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}