NumPy/Lesson 5 - Universal Functions.ipynb

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   "source": [
    "# Universal Functions\n",
    "\n",
    "NumPy provides some useful out of the box functions to perform operations on matrices. These functions are divided into 2 different segments:\n",
    "1. Unary Functions\n",
    "2. Binary Functions\n",
    "\n",
    "A Unary function operates on a single matrix by itself, while a binary function requires 2 matrices. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Unary Functions\n",
    "\n",
    "## np.sqrt\n",
    "This function simply returns square root of all the elements in an array."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[2., 3., 4.],\n",
       "       [5., 6., 7.]])"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "a = np.array([[4,9,16],\n",
    "              [25,36,49]])\n",
    "\n",
    "np.sqrt(a)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## np.exp\n",
    "This function computes the exponent of each element in an array."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[5.45981500e+01, 8.10308393e+03, 8.88611052e+06],\n",
       "       [7.20048993e+10, 4.31123155e+15, 1.90734657e+21]])"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.exp(a)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## np.log\n",
    "This function will compute the natural logarithm (base e) of each element in an array. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.38629436, 2.19722458, 2.77258872],\n",
       "       [3.21887582, 3.58351894, 3.8918203 ]])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.log(a)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Similarly, we can also use **log10, log2, logp**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## np.rint\n",
    "This function rounds elements to their nearest integer. The function `rint` can be read as `Round to Integer`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1., 2., 3.],\n",
       "       [3., 4., 4.]])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.array([[1.38629436, 2.19722458, 2.77258872],\n",
    "       [3.21887582, 3.58351894, 3.8918203 ]])\n",
    "np.rint(a)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![](./images/ufuncs.JPG)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Binary Functions\n",
    "\n",
    "Lets start with 2 matrices and perform some basic arithmatic operations on them. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "a = np.array([[1,2,3],\n",
    "              [4,5,6]])\n",
    "\n",
    "b = np.array([[2,4,8],\n",
    "              [16,32,64]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Addition"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 3,  6, 11],\n",
       "       [20, 37, 70]])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a+b"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Subtraction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ -1,  -2,  -5],\n",
       "       [-12, -27, -58]])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a-b"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Multiplication"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  2,   8,  24],\n",
       "       [ 64, 160, 384]])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a*b"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Division"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.5    , 0.5    , 0.375  ],\n",
       "       [0.25   , 0.15625, 0.09375]])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a/b"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are several binary functions that one can choose from. The table below shows some of the binary function operations available.\n",
    "\n",
    "> Keep in mind that the matrices have to always be of appropriate size for the binary operation to work. We cannot add a (2,2) matrix to a (3x3) matrix. If you can perform the matrix operation mathematically, then the system can also perform it for you. But it will fail on attempting an invalid matrix operation.\n",
    "\n",
    "\n",
    "![](./images/binary_funcs.JPG)"
   ]
  }
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