Tut_Numpy.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Introduction\n",
    "\n",
    "NumPy is a Python package. It stands for 'Numerical Python'. It is a library consisting of multidimensional array objects and a collection of routines for processing of array.\n",
    "\n",
    "Numeric, the ancestor of NumPy, was developed by Jim Hugunin. Another package Numarray was also developed, having some additional functionalities. In 2005, Travis Oliphant created NumPy package by incorporating the features of Numarray into Numeric package. There are many contributors to this open source project.\n",
    "\n",
    "## Operations using NumPy\n",
    " Using NumPy, a developer can perform the following operations −\n",
    " \n",
    " <ul style=\"list-style-type:square\">\n",
    "  <li>Mathematical and logical operations on arrays.</li>\n",
    "  <li>Fourier transforms and routines for shape manipulation.</li>\n",
    "  <li>Operations related to linear algebra. NumPy has in-built functions for linear algebra and random number generation.</li>\n",
    "</ul>\n",
    "\n",
    "##  NumPy – A Replacement for MatLab\n",
    "\n",
    "NumPy is often used along with packages like SciPy (Scientific Python) and Mat−plotlib (plotting library). This combination is widely used as a replacement for MatLab, a popular platform for technical computing. However, Python alternative to MatLab is now seen as a more modern and complete programming language.\n",
    "\n",
    "It is open source, which is an added advantage of NumPy.\n",
    "\n",
    "## The Basics\n",
    "NumPy’s main object is the homogeneous multidimensional array. It is a table of elements (usually numbers), all of the same type, indexed by a tuple of positive integers. In NumPy dimensions are called axes. The number of axes is rank.\n",
    "\n",
    "For example, the coordinates of a point in 3D space [1, 2, 1] is an array of rank 1, because it has one axis. That axis has a length of 3. In the example pictured below, the array has rank 2 (it is 2-dimensional). The first dimension (axis) has a length of 2, the second dimension has a length of 3.\n",
    "\n",
    "[[ 1., 0., 0.],\n",
    " [ 0., 1., 2.]]\n",
    "NumPy’s array class is called ndarray. It is also known by the alias array. Note that numpy.array is not the same as the Standard Python Library class array.array, which only handles one-dimensional arrays and offers less functionality. The more important attributes of an ndarray object are:\n",
    "\n",
    "\n",
    "1. <b>ndarray.ndim:  </b>   \n",
    "the number of axes (dimensions) of the array. In the Python world, the number of dimensions is referred to as rank.\n",
    "    \n",
    "2. <b>ndarray.shape:</b>    \n",
    "the dimensions of the array. This is a tuple of integers indicating the size of the array in each dimension. For a matrix with n rows and m columns, shape will be (n,m). The length of the shape tuple is therefore the rank, or number of dimensions, ndim.\n",
    "    \n",
    "3. <b>ndarray.size:  </b>   \n",
    "the total number of elements of the array. This is equal to the product of the elements of shape.\n",
    "\n",
    "4. <b>ndarray.dtype:</b>\n",
    "an object describing the type of the elements in the array. One can create or specify dtype’s using standard Python types. Additionally NumPy provides types of its own. numpy.int32, numpy.int16, and numpy.float64 are some examples.\n",
    "    \n",
    "### Example\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "a =  [[ 0  1  2  3  4]\n",
      " [ 5  6  7  8  9]\n",
      " [10 11 12 13 14]]\n",
      "Number of axes (dimensions) of the array =  2\n",
      "Dimension of the array =  (3, 5)\n",
      "Total number of elements of the array =  15\n",
      "Type of the elements in the array =  int64\n"
     ]
    }
   ],
   "source": [
    "import numpy as np \n",
    "a = np.arange(15).reshape(3, 5)\n",
    "dim=a.ndim\n",
    "shape=a.shape\n",
    "size=a.size\n",
    "datatype=a.dtype.name\n",
    "print (\"a = \",a)\n",
    "print (\"Number of axes (dimensions) of the array = \", dim)\n",
    "print (\"Dimension of the array = \", shape)\n",
    "print (\"Total number of elements of the array = \", size)\n",
    "print (\"Type of the elements in the array = \", datatype)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Array Creation\n",
    "There are several ways to create arrays.\n",
    "\n",
    "For example, you can create an array from a regular Python list or tuple using the array function. The type of the resulting array is deduced from the type of the elements in the sequences.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2, 3, 4])"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.array([2,3,4])\n",
    "a\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A frequent error consists in calling array with multiple numeric arguments, rather than providing a single list of numbers as an argument.\n",
    "\n",
    "$a = np.array(1,2,3,4)$ <b style=\"color:Tomato;\">WRONG</b>\n",
    "\n",
    "$a = np.array([1,2,3,4])$ <b style=\"color:MediumSeaGreen;\">RIGHT</b>\n",
    "    \n",
    "Array transforms sequences of sequences into two-dimensional arrays, sequences of sequences of sequences into three-dimensional arrays, and so on.\n",
    "  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.5, 2. , 3. ],\n",
       "       [4. , 5. , 6. ]])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b = np.array([(1.5,2,3), (4,5,6)])\n",
    "b\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The type of the array can also be explicitly specified at creation time:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.+0.j, 2.+0.j],\n",
       "       [3.+0.j, 4.+0.j]])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c = np.array( [ [1,2], [3,4] ], dtype=complex )\n",
    "c"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Often, the elements of an array are originally unknown, but its size is known. Hence, NumPy offers several functions to create arrays with initial placeholder content. These minimize the necessity of growing arrays, an expensive operation.\n",
    "\n",
    "The function zeros creates an array full of zeros, the function ones creates an array full of ones, and the function empty creates an array whose initial content is random and depends on the state of the memory. By default, the dtype of the created array is float64."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0., 0., 0., 0.],\n",
       "       [0., 0., 0., 0.],\n",
       "       [0., 0., 0., 0.]])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.zeros( (3,4) )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[1, 1, 1, 1],\n",
       "        [1, 1, 1, 1],\n",
       "        [1, 1, 1, 1]],\n",
       "\n",
       "       [[1, 1, 1, 1],\n",
       "        [1, 1, 1, 1],\n",
       "        [1, 1, 1, 1]]], dtype=int16)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.ones( (2,3,4), dtype=np.int16 )                # dtype can also be specified"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.5, 2. , 3. ],\n",
       "       [4. , 5. , 6. ]])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.empty( (2,3) )                                 # uninitialized, output may vary"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To create sequences of numbers, NumPy provides a function analogous to range that returns arrays instead of lists."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([10, 15, 20, 25])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.arange( 10, 30, 5 )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0. , 0.3, 0.6, 0.9, 1.2, 1.5, 1.8])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.arange( 0, 2, 0.3 )                 # it accepts float arguments"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When arange is used with floating point arguments, it is generally not possible to predict the number of elements obtained, due to the finite floating point precision. For this reason, it is usually better to use the function linspace that receives as an argument the number of elements that we want, instead of the step:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.  , 0.25, 0.5 , 0.75, 1.  , 1.25, 1.5 , 1.75, 2.  ])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from numpy import pi\n",
    "np.linspace( 0, 2, 9 )                 # 9 numbers from 0 to 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.linspace( 0, 2*pi, 100 )        # useful to evaluate function at lots of points\n",
    "f = np.sin(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Printing Arrays\n",
    "When you print an array, NumPy displays it in a similar way to nested lists, but with the following layout:\n",
    "\n",
    "<ul style=\"list-style-type:square\">\n",
    "  <li>The last axis is printed from left to right</li>\n",
    "  <li>The second-to-last is printed from top to bottom</li>\n",
    "  <li>The rest are also printed from top to bottom, with each slice separated from the next by an empty line.</li>\n",
    "</ul>\n",
    "\n",
    "One-dimensional arrays are then printed as rows, bidimensionals as matrices and tridimensionals as lists of matrices."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "a = np.arange(6)                         # 1d array\n",
    "print(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "b = np.arange(12).reshape(4,3)           # 2d array\n",
    "print(b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "c = np.arange(24).reshape(2,3,4)         # 3d array\n",
    "print(c)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If an array is too large to be printed, NumPy automatically skips the central part of the array and only prints the corners:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "print(np.arange(10000))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "print(np.arange(10000).reshape(100,100))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To disable this behaviour and force NumPy to print the entire array, you can change the printing options using set_printoptions.\n",
    "\n",
    "np.set_printoptions(threshold='nan')   \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Basic Operations\n",
    "\n",
    "Arithmetic operators on arrays apply elementwise. A new array is created and filled with the result."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.array( [20,30,40,50] )\n",
    "b = np.arange( 4 )\n",
    "b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([20, 29, 38, 47])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c = a-b\n",
    "c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 4, 9])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 9.12945251, -9.88031624,  7.4511316 , -2.62374854])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "10*np.sin(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ True,  True, False, False])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a<35"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Unlike in many matrix languages, the product operator * operates elementwise in NumPy arrays. The matrix product can be performed using the dot function or method:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[2, 0],\n",
       "       [0, 4]])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = np.array( [[1,1],\n",
    "            [0,1]] )\n",
    "B = np.array( [[2,0],\n",
    "            [3,4]] )\n",
    "A*B                         # elementwise product\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[5, 4],\n",
       "       [3, 4]])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A.dot(B)                    # matrix product"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[5, 4],\n",
       "       [3, 4]])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.dot(A, B)                # another matrix product"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Some operations, such as += and *=, act in place to modify an existing array rather than create a new one"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[3., 3., 3.],\n",
       "       [3., 3., 3.]])"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.ones((2,3), dtype=int)\n",
    "b = np.random.random((2,3))\n",
    "a *= 3\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[3.18465326, 3.13212853, 3.34987092],\n",
       "       [3.64756347, 3.86280989, 3.02552218]])"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b += a\n",
    "b\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 9.36930652,  9.26425705,  9.69974184],\n",
       "       [10.29512694, 10.72561979,  9.05104435]])"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a += b                  # b is not automatically converted to integer type\n",
    "a"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When operating with arrays of different types, the type of the resulting array corresponds to the more general or precise one (a behavior known as upcasting)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'float64'"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.ones(3, dtype=np.int32)\n",
    "b = np.linspace(0,pi,3)\n",
    "b.dtype.name"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.        , 2.57079633, 4.14159265])"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c = a+b\n",
    "c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'float64'"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c.dtype.name"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.54030231+0.84147098j, -0.84147098+0.54030231j,\n",
       "       -0.54030231-0.84147098j])"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d = np.exp(c*1j)\n",
    "d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'complex128'"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d.dtype.name"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Many unary operations, such as computing the sum of all the elements in the array, are implemented as methods of the ndarray class."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.23763365, 0.47495911, 0.9222299 ],\n",
       "       [0.93911054, 0.35757632, 0.10409782]])"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.random.random((2,3))\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.0356073341888132"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a.sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.1040978223186173"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a.min()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9391105353501477"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a.max()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "By default, these operations apply to the array as though it were a list of numbers, regardless of its shape. However, by specifying the axis parameter you can apply an operation along the specified axis of an array:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0,  1,  2,  3],\n",
       "       [ 4,  5,  6,  7],\n",
       "       [ 8,  9, 10, 11]])"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b = np.arange(12).reshape(3,4)\n",
    "b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([12, 15, 18, 21])"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b.sum(axis=0)                            # sum of each column"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 4, 8])"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b.min(axis=1)                            # min of each row"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0  1  3  6]\n",
      " [ 4  9 15 22]\n",
      " [ 8 17 27 38]]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([[ 0,  1,  2,  3],\n",
       "       [ 4,  5,  6,  7],\n",
       "       [ 8,  9, 10, 11],\n",
       "       [ 0,  1,  3,  6],\n",
       "       [ 4,  9, 15, 22],\n",
       "       [ 8, 17, 27, 38]])"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x=b.cumsum(axis=1)      \n",
    "print(x)  # cumulative sum along each row\n",
    "np.concatenate((b,x),axis=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Universal Functions\n",
    "NumPy provides familiar mathematical functions such as sin, cos, and exp. In NumPy, these are called “universal functions”(ufunc). Within NumPy, these functions operate elementwise on an array, producing an array as output."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "B = np.arange(3)\n",
    "B"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.zeros(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.ones(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.exp(B)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.sqrt(B)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "C = np.array([2., -1., 4.])\n",
    "np.add(B, C)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Indexing Array Elements\n",
    "\n",
    "One-dimensional arrays can be indexed, sliced and iterated over, much like lists and other Python sequences."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  0,   1,   8,  27,  64, 125, 216, 343, 512, 729])"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.arange(10)**3\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 8, 27, 64])"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[2:5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-1000,     1, -1000,    27, -1000,   125,   216,   343,   512,\n",
       "         729])"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[:6:2] = -1000    # equivalent to a[0:6:2] = -1000; from start to position 6, exclusive, set every 2nd element to -1000\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  729,   512,   343,   216,   125, -1000,    27, -1000,     1,\n",
       "       -1000])"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[ : :-1]                                 # reversed a"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Multidimensional arrays can have one index per axis. These indices are given in a tuple separated by commas:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0,  1,  2,  3],\n",
       "       [10, 11, 12, 13],\n",
       "       [20, 21, 22, 23],\n",
       "       [30, 31, 32, 33],\n",
       "       [40, 41, 42, 43]])"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b =np.array([[ 0,  1,  2,  3],\n",
    "       [10, 11, 12, 13],\n",
    "       [20, 21, 22, 23],\n",
    "       [30, 31, 32, 33],\n",
    "       [40, 41, 42, 43]])\n",
    "b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "23"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b[2,3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "b[0:5, 1]                       # each row in the second column of b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "b[ : ,1]                        # equivalent to the previous example"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "b[1:3, : ]                      # each column in the second and third row of b"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Stacking together different arrays\n",
    "Several arrays can be stacked together along different axes:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "a= [[0 1]\n",
      " [2 3]]\n",
      "b= [[4 5]\n",
      " [6 7]]\n"
     ]
    }
   ],
   "source": [
    "a =np.array([[ 0, 1],\n",
    "       [2,3]])\n",
    "b=np.array([[ 4, 5],\n",
    "       [6,7]])\n",
    "print('a=',a)\n",
    "print('b=',b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 1],\n",
       "       [2, 3],\n",
       "       [4, 5],\n",
       "       [6, 7]])"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.vstack((a,b))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 1, 4, 5],\n",
       "       [2, 3, 6, 7]])"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.hstack((a,b))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Splitting one array into several smaller ones\n",
    "Using hsplit, you can split an array along its horizontal axis, either by specifying the number of equally shaped arrays to return, or by specifying the columns after which the division should occur. vsplit splits along the vertical axis, and array_split allows one to specify along which axis to split."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11],\n",
       "       [12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23]])"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b = np.arange(24).reshape(2,12)\n",
    "b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[array([[ 0,  1,  2,  3],\n",
       "        [12, 13, 14, 15]]), array([[ 4,  5,  6,  7],\n",
       "        [16, 17, 18, 19]]), array([[ 8,  9, 10, 11],\n",
       "        [20, 21, 22, 23]])]"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.hsplit(b,3)   # Split a into 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[array([[ 0,  1,  2],\n",
       "        [12, 13, 14]]), array([[ 3,  4,  5],\n",
       "        [15, 16, 17]]), array([[ 6,  7,  8,  9, 10, 11],\n",
       "        [18, 19, 20, 21, 22, 23]])]"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.hsplit(b,(3,6))   # Split a after the third and the fourth column"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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