Python/numpy&matplotlib.ipynb

{
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  {
   "cell_type": "markdown",
   "metadata": {
    "id": "_o_h0mrxtPqC"
   },
   "source": [
    "# Common Python Libraries"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "NLssLJ_ZtPqF"
   },
   "source": [
    "In this notebook we will be going through some essential python libraries, namely **Numpy** and **Matplotlib**\n",
    "\n",
    "As we've said earlier, this notebook is only meant to give you an idea of most of the major functionalities that exist in these libraries. You don't need to start learning the syntax, you'll get a hang of it with practice!!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "pTzsnGj8tPqH"
   },
   "source": [
    "## Introduction"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "1YO1t_hztPqJ"
   },
   "source": [
    "Python is a great general-purpose programming language on its own.\n",
    "Its computational capabilty, usability and convenience can be greatly enhanced with the help of the addition of a few libraries(such as numpy, matplotlib, scikit, pandas etc.)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "GfEieiwCtPqL"
   },
   "source": [
    "In this tutorial, we will cover the basics of these essential libraries:\n",
    "\n",
    "* Numpy: Arrays, Array indexing, Datatypes, Array math, Broadcasting\n",
    "* Matplotlib: Plotting, Subplots, Images "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "fUg8sTe6tPqN"
   },
   "source": [
    "## Numpy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "QqKVQX83tPqO"
   },
   "source": [
    "Numpy is the core library for scientific computing in Python. It provides a high-performance multidimensional array object, and tools for computation and manipulation of these arrays."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "-9ZPTbwatPqS"
   },
   "source": [
    "To use Numpy, we first need to import the `numpy` package:"
   ]
  },
  {
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   "execution_count": 1,
   "metadata": {
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   },
   "outputs": [],
   "source": [
    "import numpy as np  # Importing it as np allows us to use \"np\" instead of \"numpy\" whenever we need to use one of it's functions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "GKvol477tPqc"
   },
   "source": [
    "### Arrays"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "UmjYm_iXtPqd"
   },
   "source": [
    "A numpy array is a grid of values, all of the same type, and is indexed by a tuple of nonnegative integers. The number of dimensions is the rank of the array; the shape of an array is a tuple of integers giving the size of the array along each dimension."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Xwfz4oUWtPqf"
   },
   "source": [
    "Numpy arrays can be initialized from nested Python lists, and elements can be accessed by using square brackets:"
   ]
  },
  {
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   "execution_count": null,
   "metadata": {
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    "outputId": "14a4b15f-68de-45d5-c078-34da1d1731c9"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(<type 'numpy.ndarray'>, '\\n', (3,), 1, 2, 3)\n",
      "[5 2 3]\n"
     ]
    }
   ],
   "source": [
    "a = np.array([1, 2, 3])  # Create a rank 1 array\n",
    "print(type(a),\"\\n\", a.shape, a[0], a[1], a[2])\n",
    "a[0] = 5                 # Change an element of the array\n",
    "print(a)                  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "-xmmwt3ktPqn",
    "outputId": "c58e7fcb-cbf0-43d6-bde1-2762b616f116"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1 2 3]\n",
      " [4 5 6]]\n"
     ]
    }
   ],
   "source": [
    "b = np.array([[1,2,3],[4,5,6]])   # Create a rank 2 array\n",
    "print(b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "IAGXd9GKtPqu",
    "outputId": "be3e5327-0c4b-4fb8-f550-829d80e9bb70"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(2, 3)\n",
      "1 2 4\n"
     ]
    }
   ],
   "source": [
    "print (b.shape) # Prints the shape of the array               \n",
    "print (b[0, 0], b[0, 1], b[1, 0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "D_YzIgWZtPq0"
   },
   "source": [
    "**Note** : the shapes (2, ) and (2,1) are NOT the same. In both cases, only two elements are present but in the first example you only require one index to access both elements, whereas in the second case you need two sets of indices but the second would always be 0. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "KY2rFpIutPq6"
   },
   "source": [
    "Numpy also provides many functions to create arrays:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "sV-esO1DtPq7",
    "outputId": "38b71c6e-c686-4d8f-9670-953ef41419a3"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0. 0.]\n",
      " [0. 0.]]\n"
     ]
    }
   ],
   "source": [
    "a = np.zeros((2,2))  # Create an array of all zeros\n",
    "print (a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "GFhxpGE6tPrA",
    "outputId": "a4496390-0fa6-44f6-b231-00ede2cedaf5"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1. 1.]]\n"
     ]
    }
   ],
   "source": [
    "b = np.ones((1,2))   # Create an array of all ones\n",
    "print (b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "HJVD9s5ItPrG",
    "outputId": "f2f1a892-783d-4750-d633-da0c71e88f16"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[7 7]\n",
      " [7 7]]\n"
     ]
    }
   ],
   "source": [
    "c = np.full((2,2), 7) # Create a constant array\n",
    "print (c) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "0ni6kDajtPrK",
    "outputId": "aca711d8-c983-46a1-9b7a-ccfe6afce65f"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1. 0.]\n",
      " [0. 1.]]\n"
     ]
    }
   ],
   "source": [
    "d = np.eye(2)        # Create a 2x2 identity matrix\n",
    "print (d)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "_A66GHWctPrP",
    "outputId": "716c4617-049a-42d7-9631-7f8c0a103352"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.04522778 0.19508671]\n",
      " [0.00598023 0.39154546]]\n"
     ]
    }
   ],
   "source": [
    "e = np.random.random((2,2)) # Create an array filled with random values\n",
    "print (e)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "HbHPnDtxtPrV"
   },
   "source": [
    "### Array indexing"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "-DBzsxQDtPrW"
   },
   "source": [
    "Numpy offers several ways to index into arrays."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "mCRotdf_tPrW"
   },
   "source": [
    "**Slicing** : Similar to Python lists, numpy arrays can be sliced. Since arrays may be multidimensional, you must specify a slice for each dimension of the array:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "Bj22zSBxtPrY",
    "outputId": "f67d3633-970f-4924-a82a-fc4ee30b22fe"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[2 3]\n",
      " [6 7]]\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "a = np.array([[1,2,3,4], [5,6,7,8], [9,10,11,12]])\n",
    "b = a[:2, 1:3]\n",
    "print (b)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "inlS8YxhtPrc"
   },
   "source": [
    "A slice of an array is a view into the same data, so modifying it will modify the original array."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "_sCwfXritPrd",
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   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2\n",
      "77\n"
     ]
    }
   ],
   "source": [
    "print (a[0, 1])\n",
    "b[0, 0] = 77    # b[0, 0] is the same piece of data as a[0, 1]\n",
    "print (a[0, 1]) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "dWxPRfJ6tPrh"
   },
   "source": [
    "You can also mix integer indexing with slice indexing. However, doing so will yield an array of lower rank than the original array. Note that this is quite different from the way that MATLAB handles array slicing:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
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    "id": "u-Y_fYkftPri",
    "outputId": "7a5a9d8c-6776-4c30-d1d7-b3d9a136d536"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 1  2  3  4]\n",
      " [ 5  6  7  8]\n",
      " [ 9 10 11 12]]\n"
     ]
    }
   ],
   "source": [
    "# Create the following rank 2 array with shape (3, 4)\n",
    "a = np.array([[1,2,3,4], [5,6,7,8], [9,10,11,12]])\n",
    "print (a)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Pz6sxe6vtPrm"
   },
   "source": [
    "Two ways of accessing the data in the middle row of the array.\n",
    "Mixing integer indexing with slices yields an array of lower rank,\n",
    "while using only slices yields an array of the same rank as the\n",
    "original array:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "5SiJ8GXetPrn",
    "outputId": "b0b01d8d-5a1e-4859-c5e5-56f6693c6533"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[5 6 7 8] (4,)\n",
      "[[5 6 7 8]] (1, 4)\n",
      "[[5 6 7 8]] (1, 4)\n"
     ]
    }
   ],
   "source": [
    "row_r1 = a[1, :]    # Rank 1 view of the second row of a  \n",
    "row_r2 = a[1:2, :]  # Rank 2 view of the second row of a\n",
    "row_r3 = a[[1], :]  # Rank 2 view of the second row of a\n",
    "print (row_r1, row_r1.shape) \n",
    "print (row_r2, row_r2.shape)\n",
    "print (row_r3, row_r3.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "V7DoPbyJtPrr"
   },
   "source": [
    "Integer array indexing: When you index into numpy arrays using slicing, the resulting array view will always be a subarray of the original array. In contrast, integer array indexing allows you to construct arbitrary arrays using the data from another array. Here is an example:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "40qp01DMtPrt",
    "outputId": "e5dbc1dd-240f-4379-c001-0bd07d5fe90e"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1 4 5]\n",
      "[1 4 5]\n"
     ]
    }
   ],
   "source": [
    "a = np.array([[1,2], [3, 4], [5, 6]])\n",
    "\n",
    "# An example of integer array indexing.\n",
    "# The returned array will have shape (3,) and \n",
    "print (a[[0, 1, 2], [0, 1, 0]])\n",
    "\n",
    "# The above example of integer array indexing is equivalent to this:\n",
    "print (np.array([a[0, 0], a[1, 1], a[2, 0]]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "2xgsWSzYtPrx"
   },
   "source": [
    "One useful trick with integer array indexing is selecting or mutating one element from each row of a matrix:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "TS3lkttTtPrz",
    "outputId": "f31e14aa-1677-4290-ef11-ea21626cf146"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 1  2  3]\n",
      " [ 4  5  6]\n",
      " [ 7  8  9]\n",
      " [10 11 12]]\n"
     ]
    }
   ],
   "source": [
    "# Create a new array from which we will select elements\n",
    "a = np.array([[1,2,3], [4,5,6], [7,8,9], [10, 11, 12]])\n",
    "print (a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "Jr168ZS9tPr3",
    "outputId": "d120bb3f-a6d4-4cd7-b2f9-4806c42b5d31"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 1  6  7 11]\n"
     ]
    }
   ],
   "source": [
    "# Create an array of indices\n",
    "b = np.array([0, 2, 0, 1])\n",
    "\n",
    "# Select one element from each row of a using the indices in b\n",
    "print (a[np.arange(4), b])  # Prints \"[ 1  6  7 11]\"\n",
    "# np.arange essentially gives you evenly spaced values given a certain interval"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "YMOV_aCItPr7",
    "outputId": "1e1b4ae6-1653-4f21-b064-cd906879bbd5"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[11  2  3]\n",
      " [ 4  5 16]\n",
      " [17  8  9]\n",
      " [10 21 12]]\n"
     ]
    }
   ],
   "source": [
    "# Mutate one element from each row of a using the indices in b\n",
    "a[np.arange(4), b] += 10\n",
    "print (a)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "LQft2DUJtPr_"
   },
   "source": [
    "**Boolean array indexing** : Boolean array indexing lets you pick out arbitrary elements of an array. Frequently this type of indexing is used to select the elements of an array that satisfy some condition. Here is an example:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "X-LYmRwPtPr_",
    "outputId": "f28d3040-9b1b-4151-ecfa-bda88acef4e4"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[3 4 5 6]\n",
      "[3 4 5 6]\n"
     ]
    }
   ],
   "source": [
    "# We use boolean array indexing to construct a rank 1 array\n",
    "# consisting of the elements of a corresponding to the True values\n",
    "# of bool_idx\n",
    "print (a[bool_idx])\n",
    "\n",
    "# We can do all of the above in a single concise statement:\n",
    "print (a[a > 2])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "cq4kMvX0tPsD"
   },
   "source": [
    "### Datatypes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Z3_nhEDntPsE"
   },
   "source": [
    "Every numpy array is a grid of elements of the same type. Numpy provides a large set of numeric datatypes that you can use to construct arrays. Numpy tries to guess a datatype when you create an array, but functions that construct arrays usually also include an optional argument to explicitly specify the datatype. Here is an example:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "VUeU3CtntPsF",
    "outputId": "08ef68f4-c9a4-4c52-c197-ede8a15c16c2"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "int32 float64 int64\n"
     ]
    }
   ],
   "source": [
    "x = np.array([1, 2])  # Let numpy choose the datatype\n",
    "y = np.array([1.0, 2.0])  # Let numpy choose the datatype\n",
    "z = np.array([1, 2], dtype=np.int64)  # Force a particular datatype\n",
    "\n",
    "print (x.dtype, y.dtype, z.dtype)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "z74NDkiPtPsK"
   },
   "source": [
    "You can read all about numpy datatypes in the [documentation](http://docs.scipy.org/doc/numpy/reference/arrays.dtypes.html)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "91-JpxARtPsK"
   },
   "source": [
    "### Array math"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "gmTLjziytPsL"
   },
   "source": [
    "Basic mathematical functions operate elementwise on arrays, and are available both as operator overloads and as functions in the numpy module:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "_dhNenkOtPsL",
    "outputId": "57c89cca-aa16-4635-b2c1-d90b85320027"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1. 2.]\n",
      " [3. 4.]] \n",
      "\n",
      "[[5. 6.]\n",
      " [7. 8.]] \n",
      "\n",
      "[[ 6.  8.]\n",
      " [10. 12.]]\n",
      "[[ 6.  8.]\n",
      " [10. 12.]]\n"
     ]
    }
   ],
   "source": [
    "x = np.array([[1,2],[3,4]], dtype=np.float64)\n",
    "y = np.array([[5,6],[7,8]], dtype=np.float64)\n",
    "print(x,\"\\n\")\n",
    "print(y,\"\\n\")\n",
    "\n",
    "# Elementwise sum; both produce the array\n",
    "print (x + y)\n",
    "print (np.add(x, y))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "yCUCQg2ttPsQ",
    "outputId": "2087c2e1-1373-422e-a495-545c082e769a"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[-4. -4.]\n",
      " [-4. -4.]]\n",
      "[[-4. -4.]\n",
      " [-4. -4.]]\n"
     ]
    }
   ],
   "source": [
    "# Elementwise difference; both produce the array\n",
    "print (x - y)\n",
    "print (np.subtract(x, y))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "AGuU2RNmtPsU",
    "outputId": "ad105c95-d2ff-4080-ce2e-9c1386b057c2"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 5. 12.]\n",
      " [21. 32.]]\n",
      "[[ 5. 12.]\n",
      " [21. 32.]]\n"
     ]
    }
   ],
   "source": [
    "# Elementwise product; both produce the array\n",
    "print (x * y)\n",
    "print (np.multiply(x, y))"
   ]
  },
  {
   "cell_type": "code",
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    "id": "XYEd0h_HtPsY",
    "outputId": "f1c37baf-0c4c-45c2-8805-3b7f1f690e0f"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.2        0.33333333]\n",
      " [0.42857143 0.5       ]]\n",
      "[[0.2        0.33333333]\n",
      " [0.42857143 0.5       ]]\n"
     ]
    }
   ],
   "source": [
    "# Elementwise division; both produce the array\n",
    "print (x / y)\n",
    "print (np.divide(x, y))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "I2vve_4gtPsc",
    "outputId": "631c9052-1811-4bfb-c16a-b5dceaeb4c45"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1.         1.41421356]\n",
      " [1.73205081 2.        ]]\n"
     ]
    }
   ],
   "source": [
    "# Elementwise square root; produces the array\n",
    "print (np.sqrt(x))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Zv8-0voatPsf"
   },
   "source": [
    "Note that unlike MATLAB, `*` is elementwise multiplication, not matrix multiplication. We instead use the dot function to compute inner products of vectors, to multiply a vector by a matrix, and to multiply matrices. dot is available both as a function in the numpy module and as an instance method of array objects:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "o_1oofbdtPsf",
    "outputId": "6e01c86d-b435-495b-a78d-397b6cbcff61"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "219\n",
      "219\n"
     ]
    }
   ],
   "source": [
    "x = np.array([[1,2],[3,4]])\n",
    "y = np.array([[5,6],[7,8]])\n",
    "\n",
    "v = np.array([9,10])\n",
    "w = np.array([11, 12])\n",
    "\n",
    "\n",
    "# Inner product of vectors; both produce 219 (9x11 + 10x12)\n",
    "print (v.dot(w))\n",
    "print (np.dot(v, w))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "w1CXIkkhtPsj",
    "outputId": "d13f5c2e-afbf-4f2b-d1d2-ea748679c5ab"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[29 67]\n",
      "[29 67]\n"
     ]
    }
   ],
   "source": [
    "# Matrix / vector product; both produce the rank 1 array [29 67]\n",
    "print (x.dot(v))\n",
    "print (np.dot(x, v))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "BeMUaCYwtPsl",
    "outputId": "3f2edc09-2314-479b-ae90-9ec9cafd8dd6"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[19 22]\n",
      " [43 50]]\n",
      "[[19 22]\n",
      " [43 50]]\n"
     ]
    }
   ],
   "source": [
    "# Matrix / matrix product; both produce the rank 2 array\n",
    "print (x.dot(y))\n",
    "print (np.dot(x, y))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "5Ie6NZ8xtPsp"
   },
   "source": [
    "Numpy provides many useful functions for performing computations on arrays; one of the most useful is `sum`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "zXs4SebetPsp",
    "outputId": "50233bfb-14c1-44ba-cbce-a80c29dcba22"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1 2]\n",
      " [3 4]] \n",
      "\n",
      "10\n",
      "[4 6]\n",
      "[3 7]\n"
     ]
    }
   ],
   "source": [
    "x = np.array([[1,2],[3,4]])\n",
    "\n",
    "print(x,\"\\n\")\n",
    "print (np.sum(x))  # Compute sum of all elements; prints \"10\"\n",
    "print (np.sum(x, axis=0))  # Compute sum of each column; prints \"[4 6]\"\n",
    "print (np.sum(x, axis=1))  # Compute sum of each row; prints \"[3 7]\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "kgMjOFVZtPsu"
   },
   "source": [
    "You can find the full list of mathematical functions provided by numpy in the [documentation](http://docs.scipy.org/doc/numpy/reference/routines.math.html).\n",
    "\n",
    "Apart from computing mathematical functions using arrays, we frequently need to reshape or otherwise manipulate data in arrays. The simplest example of this type of operation is transposing a matrix; to transpose a matrix, simply use the T attribute of an array object:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "iBDwx_zRtPsv",
    "outputId": "d3f89e3f-2256-4275-be4c-64a9310a4573"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1 2]\n",
      " [3 4]]\n",
      "[[1 3]\n",
      " [2 4]]\n"
     ]
    }
   ],
   "source": [
    "print (x)\n",
    "print (x.T)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "QtIRAUZRtPsy"
   },
   "source": [
    "### Broadcasting"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "eA90u4fttPsy"
   },
   "source": [
    "Broadcasting is a powerful mechanism that allows numpy to work with arrays of different shapes when performing arithmetic operations. Frequently we have a smaller array and a larger array, and we want to use the smaller array multiple times to perform some operation on the larger array.\n",
    "\n",
    "For example, suppose that we want to add a constant vector to each row of a matrix. We could do it like this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "PFlf7jFItPsz",
    "outputId": "103619dc-6229-4609-eb54-6efc41397165"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 2  2  4]\n",
      " [ 5  5  7]\n",
      " [ 8  8 10]\n",
      " [11 11 13]]\n"
     ]
    }
   ],
   "source": [
    "# We will add the vector v to each row of the matrix x,\n",
    "# storing the result in the matrix y\n",
    "x = np.array([[1,2,3], [4,5,6], [7,8,9], [10, 11, 12]])\n",
    "v = np.array([1, 0, 1])\n",
    "y = np.empty_like(x)   # Create an empty matrix with the same shape as x\n",
    "\n",
    "# Add the vector v to each row of the matrix x with an explicit loop\n",
    "for i in range(4):\n",
    "    y[i, :] = x[i, :] + v\n",
    "\n",
    "print (y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "xUhhNTKPtPs2"
   },
   "source": [
    "This works; however when the matrix `x` is very large, computing an explicit loop in Python could be slow. Note that adding the vector v to each row of the matrix `x` is equivalent to forming a matrix `vv` by stacking multiple copies of `v` vertically, then performing elementwise summation of `x` and `vv`. We could implement this approach like this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "3y7dTPDutPs2",
    "outputId": "7370b4ed-c3d5-4554-9613-9464200f911f"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1 0 1]\n",
      " [1 0 1]\n",
      " [1 0 1]\n",
      " [1 0 1]]\n"
     ]
    }
   ],
   "source": [
    "vv = np.tile(v, (4, 1))  # Stack 4 copies of v on top of each other\n",
    "print (vv)               # Prints \"[[1 0 1]\n",
    "                         #          [1 0 1]\n",
    "                         #          [1 0 1]\n",
    "                         #          [1 0 1]]\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "D_3C07WVtPs5",
    "outputId": "20dcdbdc-c442-4891-f606-516d6f864c64"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 2  2  4]\n",
      " [ 5  5  7]\n",
      " [ 8  8 10]\n",
      " [11 11 13]]\n"
     ]
    }
   ],
   "source": [
    "y = x + vv  # Add x and vv elementwise\n",
    "print (y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "BG2CTA82tPs8"
   },
   "source": [
    "Numpy broadcasting allows us to perform this computation without actually creating multiple copies of v. Consider this version, using broadcasting:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "bIYzeG51tPs8",
    "outputId": "4f1e8635-6883-41ee-992b-f0ec053d3e5f"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 2  2  4]\n",
      " [ 5  5  7]\n",
      " [ 8  8 10]\n",
      " [11 11 13]]\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "# We will add the vector v to each row of the matrix x,\n",
    "# storing the result in the matrix y\n",
    "x = np.array([[1,2,3], [4,5,6], [7,8,9], [10, 11, 12]])\n",
    "v = np.array([1, 0, 1])\n",
    "y = x + v  # Add v to each row of x using broadcasting\n",
    "print (y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "IfsH4cIptPs_"
   },
   "source": [
    "The line `y = x + v` works even though `x` has shape `(4, 3)` and `v` has shape `(3,)` due to broadcasting; this line works as if v actually had shape `(4, 3)`, where each row was a copy of `v`, and the sum was performed elementwise.\n",
    "\n",
    "Rules of Broadcasting can be found in the [documentation](https://numpy.org/doc/stable/user/basics.broadcasting.html).\n",
    "\n",
    "\n",
    "Functions that support broadcasting are known as universal functions. You can find the list of all universal functions in the [documentation](http://docs.scipy.org/doc/numpy/reference/ufuncs.html#available-ufuncs).\n",
    "\n",
    "Here are some applications of broadcasting:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "ak7-mNQrtPs_",
    "outputId": "65e74d3c-5131-4967-a273-4f9b6d620452"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 4  5]\n",
      " [ 8 10]\n",
      " [12 15]]\n"
     ]
    }
   ],
   "source": [
    "# Compute outer product of vectors\n",
    "## which is the same as v.wT\n",
    "v = np.array([1,2,3])  # v has shape (3,)\n",
    "w = np.array([4,5])    # w has shape (2,)\n",
    "# To compute an outer product, we first reshape v to be a column\n",
    "# vector of shape (3, 1); we can then broadcast it against w to yield\n",
    "# an output of shape (3, 2), which is the outer product of v and w:\n",
    "\n",
    "print (np.reshape(v, (3, 1)) * w)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "Y4edVu1itPtC",
    "outputId": "ae53f1ed-11b4-4a4b-e3c1-370175174ffa"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[2 4 6]\n",
      " [5 7 9]]\n"
     ]
    }
   ],
   "source": [
    "# Add a vector to each row of a matrix\n",
    "x = np.array([[1,2,3], [4,5,6]])\n",
    "# x has shape (2, 3) and v has shape (3,) so they broadcast to (2, 3),\n",
    "# giving the following matrix:\n",
    "\n",
    "print (x + v)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "yw_D3iq8tPtF",
    "outputId": "15914029-d761-455c-befc-eec89d13db5e"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 5  6  7]\n",
      " [ 9 10 11]]\n"
     ]
    }
   ],
   "source": [
    "# Add a vector to each column of a matrix\n",
    "# x has shape (2, 3) and w has shape (2,).\n",
    "# If we transpose x then it has shape (3, 2) and can be broadcast\n",
    "# against w to yield a result of shape (3, 2); transposing this result\n",
    "# yields the final result of shape (2, 3) which is the matrix x with\n",
    "# the vector w added to each column. Gives the following matrix:\n",
    "\n",
    "print ((x.T + w).T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "RURXVsM-tPtH",
    "outputId": "190452c2-bac9-4b70-d78e-0277a33c482a"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 5  6  7]\n",
      " [ 9 10 11]]\n"
     ]
    }
   ],
   "source": [
    "# Another solution is to reshape w to be a row vector of shape (2, 1);\n",
    "# we can then broadcast it directly against x to produce the same\n",
    "# output.\n",
    "print (x + np.reshape(w, (2, 1)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "oqy8t7BztPtL",
    "outputId": "58005c4c-0fcf-4c33-95c9-2c30ffeec43d"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 2  4  6]\n",
      " [ 8 10 12]]\n"
     ]
    }
   ],
   "source": [
    "# Multiply a matrix by a constant:\n",
    "# x has shape (2, 3). Numpy treats scalars as arrays of shape ();\n",
    "# these can be broadcast together to shape (2, 3), producing the\n",
    "# following array:\n",
    "print( x * 2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "BJFgYE8GtPtN"
   },
   "source": [
    "Broadcasting typically makes your code more concise and faster, so you should strive to use it where possible."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "8dLPlwA6tPtP"
   },
   "source": [
    "This brief overview has touched on many of the important things that you need to know about numpy, but is far from complete. Check out the [numpy reference](http://docs.scipy.org/doc/numpy/reference/) to find out much more about numpy."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "WHgE5F1mbyz3"
   },
   "source": [
    "Now lets go back to one of the code snippets we wrote earlier"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 52
    },
    "id": "B1yTN4nmb6M6",
    "outputId": "5442d298-8b93-4ca3-802e-1047a55a1f8c"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Time taken by Lists : 0.5566177368164062 seconds\n",
      "Time taken by NumPy Arrays : 0.015178918838500977 seconds\n"
     ]
    }
   ],
   "source": [
    "import time\n",
    "import numpy as np\n",
    "\n",
    "n = 1000000\n",
    "\n",
    "a = np.arange(n)   \n",
    "b = np.arange(n)\n",
    "\n",
    "c = range(n)\n",
    "d = range(n)\n",
    "res = []\n",
    "\n",
    "init_time = time.time() \n",
    "for i in range(0,n):\n",
    "  res.append(int (c[i] * d[i]))  \n",
    "  \n",
    "\n",
    "print(\"Time taken by Lists :\",  \n",
    "      (time.time() - init_time), \n",
    "      \"seconds\") \n",
    "  \n",
    " \n",
    "init_time = time.time() \n",
    "res = a * b \n",
    "  \n",
    "  \n",
    "print(\"Time taken by NumPy Arrays :\", \n",
    "      (time.time() - init_time), \n",
    "      \"seconds\") "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice that NumPy arrays take roughly 3.5 times lesser time to do that same computation(in this case) when compared to Python Lists!!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "k-2fTMOctPtP"
   },
   "source": [
    "## Matplotlib"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "squEVccRtPtP"
   },
   "source": [
    "Matplotlib is a plotting library that can help you with interpretation of data and its supposed distribution. In this section give a brief introduction to the `matplotlib.pyplot` module, which provides a plotting system similar to that of MATLAB."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "id": "-HsdFOsOtPtQ"
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "etTOyxNLtPtS"
   },
   "source": [
    "By running this special iPython command, we will be displaying plots inline:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "hsqpImPUtPtS"
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "8v5zsQGLtPtV"
   },
   "source": [
    "### Plotting"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "6CpMaF0JtPtX"
   },
   "source": [
    "The most important function in `matplotlib` is plot, which allows you to plot 2D data. Here is a simple example:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "ZWiMUYsutPtX",
    "outputId": "b47d456d-10ae-4c66-e341-44193c62dfbc",
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1b57fb58898>]"
      ]
     },
     "execution_count": 45,
     "metadata": {
      "tags": []
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light",
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Compute the x and y coordinates for points on a sine curve\n",
    "x = np.arange(0, 3 * np.pi, 0.1)\n",
    "y = np.sin(x)\n",
    "\n",
    "# Plot the points using matplotlib\n",
    "plt.plot(x, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "PSLvJ09YtPtb"
   },
   "source": [
    "With just a little bit of extra work we can easily plot multiple lines at once, and add a title, legend, and axis labels:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "TphPSBXytPto",
    "outputId": "064aab50-535c-4655-d709-ae93ffda0aec"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1b57fc057b8>"
      ]
     },
     "execution_count": 46,
     "metadata": {
      "tags": []
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light",
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "y_sin = np.sin(x)\n",
    "y_cos = np.cos(x)\n",
    "\n",
    "# Plot the points using matplotlib\n",
    "plt.plot(x, y_sin)\n",
    "plt.plot(x, y_cos)\n",
    "plt.xlabel('x axis label')\n",
    "plt.ylabel('y axis label')\n",
    "plt.title('Sine and Cosine')\n",
    "plt.legend(['Sine', 'Cosine'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "x7It0VVOtPtt"
   },
   "source": [
    "You can also create **scatter plots** to know the overall distribution of data as a function of two variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "sGUIpAAWtPtt",
    "outputId": "eb73c2ac-7924-44f2-8b0f-1bc0ddc1b7ee"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<function matplotlib.pyplot.show>"
      ]
     },
     "execution_count": 6,
     "metadata": {
      "tags": []
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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       "      </defs>\n",
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       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_6\">\n",
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       "     <g id=\"text_15\">\n",
       "      <!-- 10 -->\n",
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       "    </g>\n",
       "   </g>\n",
       "   <g id=\"patch_3\">\n",
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       "   <g id=\"patch_4\">\n",
       "    <path d=\"M 361.725 228.14 \n",
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       "   </g>\n",
       "   <g id=\"patch_5\">\n",
       "    <path d=\"M 26.925 228.14 \n",
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       "   <g id=\"patch_6\">\n",
       "    <path d=\"M 26.925 10.7 \n",
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       "   </g>\n",
       "  </g>\n",
       " </g>\n",
       " <defs>\n",
       "  <clipPath id=\"p8bc4885b32\">\n",
       "   <rect height=\"217.44\" width=\"334.8\" x=\"26.925\" y=\"10.7\"/>\n",
       "  </clipPath>\n",
       " </defs>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light",
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_scatter = np.random.rand(40,) * 20\n",
    "y_scatter = np.random.rand(40,) * 15\n",
    "\n",
    "plt.scatter(x_scatter,y_scatter)\n",
    "plt.show"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "PoyLG2pntPtw"
   },
   "source": [
    "You can even create contour plots to visualise 3D data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "USI2ebwMtPtw"
   },
   "outputs": [],
   "source": [
    "def func(x,y):\n",
    "    return np.sin(x * y) ** 2 + np.cos(10 + x) * np.cos(10 + y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "v3depjvFtPtz",
    "outputId": "639b8646-d2f1-4b87-8888-106b5d7475a8"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x7f4768c6f510>"
      ]
     },
     "execution_count": 11,
     "metadata": {
      "tags": []
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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       "L 314.683125 216.995008 \n",
       "L 314.683125 22.443429 \n",
       "L 314.683125 10.999219 \n",
       "L 325.555125 10.999219 \n",
       "L 325.555125 22.443429 \n",
       "L 325.555125 216.995008 \n",
       "L 325.555125 228.439219 \n",
       "z\n",
       "\" style=\"fill:none;stroke:#000000;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "  </g>\n",
       " </g>\n",
       " <defs>\n",
       "  <clipPath id=\"p24e62a577f\">\n",
       "   <rect height=\"217.44\" width=\"267.84\" x=\"30.103125\" y=\"10.999219\"/>\n",
       "  </clipPath>\n",
       "  <clipPath id=\"p2f6087b68a\">\n",
       "   <rect height=\"217.44\" width=\"10.872\" x=\"314.683125\" y=\"10.999219\"/>\n",
       "  </clipPath>\n",
       " </defs>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light",
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(0,4,30)\n",
    "y = np.linspace(0,4,25)\n",
    "\n",
    "X,Y = np.meshgrid(x,y)\n",
    "Z = func(X,Y)\n",
    "\n",
    "plt.contourf(X, Y, Z, 20, cmap = 'hsv')\n",
    "plt.colorbar()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "PQtKKkIUtPt2"
   },
   "source": [
    "**Note** : the functions np.arange and np.linspace are very similar in purpose in picking evenly spaced values in the given interval. But the key difference between them is that in the former case you can control the increments/steps of the evenly spaced values whereas in the later case you only control the start and the stop values(both being inclusive)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Bl5UnWFPtPt2"
   },
   "source": [
    "### Subplots "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "sU6nvCBytPt2"
   },
   "source": [
    "You can plot different things in the same figure using the subplot function. Here is an example:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "TXjPhH-qtPt3",
    "outputId": "bc80277d-dc70-4b84-afe8-c2a5231ac01d"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light",
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Compute the x and y coordinates for points on sine and cosine curves\n",
    "x = np.arange(0, 3 * np.pi, 0.1)\n",
    "y_sin = np.sin(x)\n",
    "y_cos = np.cos(x)\n",
    "\n",
    "# Set up a subplot grid that has height 2 and width 1,\n",
    "# and set the first such subplot as active.\n",
    "plt.subplot(2, 1, 1)\n",
    "\n",
    "# Make the first plot\n",
    "plt.plot(x, y_sin)\n",
    "plt.title('Sine')\n",
    "\n",
    "# Set the second subplot as active, and make the second plot.\n",
    "plt.subplot(2, 1, 2)\n",
    "plt.plot(x, y_cos)\n",
    "plt.title('Cosine')\n",
    "\n",
    "# Show the figure.\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "sF0jxCHAtPt6"
   },
   "source": [
    "You can read much more about the `subplot` function in the [documentation](http://matplotlib.org/api/pyplot_api.html#matplotlib.pyplot.subplot)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "J-rcEUyDtPt7"
   },
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "dMQoa80qwopR"
   },
   "source": [
    "### Animation using Matplotlib"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "LoiyMpfF5AUc"
   },
   "source": [
    "A really dope thing we can do with this library is to create animations.\n",
    "The code below shows the animation of a sine wave"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 269
    },
    "id": "ytuSZnip5Z_A",
    "outputId": "02dc9287-b140-4b10-90f6-738743a24a68"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light",
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib import animation\n",
    "\n",
    "# Setting up of the figure, axes and the object to be animated\n",
    "fig = plt.figure()\n",
    "ax = plt.axes(xlim=(0, 2), ylim=(-2, 2))\n",
    "line, = ax.plot([], [], lw=2)\n",
    "\n",
    "# Function to plot the background for each frame\n",
    "def init():\n",
    "    line.set_data([], [])\n",
    "    return line,\n",
    "\n",
    "# Animation Function \n",
    "def update(i):                      # i denotes the frame number for which the curve shifts\n",
    "    x = np.linspace(0, 2, 1000)\n",
    "    y = np.sin(2 * np.pi * (x - 0.01 * i))\n",
    "    line.set_data(x, y)\n",
    "    return line,\n",
    "\n",
    "# Animation Object Creation \n",
    "anim = animation.FuncAnimation(fig, update, init_func=init, frames=200, interval=20, blit=True)\n",
    "\n",
    "anim.save('sin_anim.mp4', fps=30, extra_args=['-vcodec', 'libx264'])\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "colab": {
   "name": "numpy&matplotlib.ipynb",
   "provenance": [],
   "toc_visible": true
  },
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}