{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "# numpy: Introduction"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Let's import the `numpy` module."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "import numpy as np"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "metadata": {
        "collapsed": false
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]\n",
            "[0 1 2 3 4 5 6 7 8 9]\n"
          ]
        }
      ],
      "source": [
        "n = 10  # CHANGE ME\n",
        "a1 = list(range(n))\n",
        "a2 = np.arange(n)\n",
        "\n",
        "if n <= 10:\n",
        "    print(a1)\n",
        "    print(a2)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "metadata": {
        "collapsed": false
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "100000 loops, best of 3: 2.36 \u00b5s per loop\n"
          ]
        }
      ],
      "source": [
        "%timeit [i**2 for i in a1]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 5,
      "metadata": {
        "collapsed": false
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "1000000 loops, best of 3: 1.06 \u00b5s per loop\n"
          ]
        }
      ],
      "source": [
        "%timeit a2**2"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Numpy Arrays: much less flexible, but:\n",
        "\n",
        "* much faster\n",
        "* less memory"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "---\n",
        "\n",
        "Ways to create a numpy array:\n",
        "\n",
        "* Casting from a list"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 6,
      "metadata": {
        "collapsed": false
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([1, 2, 3])"
            ]
          },
          "execution_count": 6,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "np.array([1,2,3])"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "* `linspace`"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 7,
      "metadata": {
        "collapsed": false
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([-1.        , -0.77777778, -0.55555556, -0.33333333, -0.11111111,\n",
              "        0.11111111,  0.33333333,  0.55555556,  0.77777778,  1.        ])"
            ]
          },
          "execution_count": 7,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "np.linspace(-1, 1, 10)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "* `zeros`"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 8,
      "metadata": {
        "collapsed": false
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([[ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.],\n",
              "       [ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.],\n",
              "       [ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.],\n",
              "       [ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.],\n",
              "       [ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.],\n",
              "       [ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.],\n",
              "       [ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.],\n",
              "       [ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.],\n",
              "       [ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.],\n",
              "       [ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.]])"
            ]
          },
          "execution_count": 8,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "np.zeros((10,10), np.float64)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "---\n",
        "\n",
        "Operations on arrays propagate to all elements:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 9,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "\n",
        "a = np.array([1.2, 3, 4])\n",
        "b = np.array([0.5, 0, 1])"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Addition, multiplication, power, .. are all elementwise:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 10,
      "metadata": {
        "collapsed": false
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([ 1.7,  3. ,  5. ])"
            ]
          },
          "execution_count": 10,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "a+b"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 11,
      "metadata": {
        "collapsed": false
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([ 0.6,  0. ,  4. ])"
            ]
          },
          "execution_count": 11,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "a*b"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 12,
      "metadata": {
        "collapsed": false
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([ 1.09544512,  1.        ,  4.        ])"
            ]
          },
          "execution_count": 12,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "a**b"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Matrix multiplication is `np.dot(A, B)` for two 2D arrays."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "---\n",
        "\n",
        "Numpy arrays have two (most) important attributes:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 13,
      "metadata": {
        "collapsed": false
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "(5, 4, 3)"
            ]
          },
          "execution_count": 13,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "a = np.random.rand(5, 4, 3)\n",
        "a.shape"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "The `.shape` attribute contains the dimensionality array as a tuple. So the tuple `(5,4,3)` means that we're dealing with a three-dimensional array of size $5 \\times 4 \\times 3$.\n",
        "\n",
        "(`numpy.random.rand` just generates an array of random numbers of the given shape.)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 14,
      "metadata": {
        "collapsed": false
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "dtype('float64')"
            ]
          },
          "execution_count": 14,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "a.dtype"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Other `dtype`s include `np.complex64`, `np.int32`, ..."
      ]
    }
  ],
  "metadata": {},
  "nbformat": 4,
  "nbformat_minor": 0
}