ch09-numpy.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Numpy: Thinking In Arrays\n",
    "\n",
    "At the core of most computational physics problems lives an array.\n",
    "\n",
    "## Arrays\n",
    "The basic type that NumPy provides is the N-dimensional array class ndarray. Rather\n",
    "than being created directly, ndarrays are often instantiated via the array() function\n",
    "that NumPy also provides. To create an array, import numpy and call array() on a\n",
    "sequence:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# A common abbreviation for numpy is np\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Creating Arrays\n",
    "\n",
    "Here are some examples of how to create new arrays.\n",
    "The most basic way is with the array() function.\n",
    "Other methods include using the arange(), zeros(), ones(), and empty() functions:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([   6,   28,  496, 8128])"
      ]
     },
     "execution_count": 102,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.array([6, 28, 496, 8128])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3, 4, 5])"
      ]
     },
     "execution_count": 103,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.arange(6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.,  0.,  0.,  0.])"
      ]
     },
     "execution_count": 104,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.zeros(4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.,  1.,  1.],\n",
       "       [ 1.,  1.,  1.]])"
      ]
     },
     "execution_count": 105,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.ones((2, 3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.,  0.,  0.,  0.])"
      ]
     },
     "execution_count": 106,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.empty(4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The linspace() and logspace() functions are also important to know. These create\n",
    "an even linearly or logarithmically spaced grid of points between a lower and upper\n",
    "bound that is inclusive on both ends. Note that logspace() may also take a base keyword\n",
    "argument, which defaults to 10. The lower and upper bounds are then interpreted\n",
    "as the base to these powers."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.  ,  1.25,  1.5 ,  1.75,  2.  ])"
      ]
     },
     "execution_count": 107,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linspace(1, 2, 5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 10. ,   1. ,   0.1])"
      ]
     },
     "execution_count": 108,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.logspace(1, -1, 3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Make a scatter plot of the various arrays above:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1092b4ed0>"
      ]
     },
     "execution_count": 109,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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kMZAZr0rsDfwpFsl6PYlxi0KlpaJSaRncOnESohesk1q4ndIPc5sis4aZvZrc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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x108155f90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "x = np.linspace(1, 10, 10)\n",
    "y_lin = np.linspace(1, 2, 10)\n",
    "y_cust = np.array([3, 1, 8, 7, 2, 3, 2, 3, 4, 5])\n",
    "y_log = np.logspace(1, -1, 10)\n",
    "y_ones = np.ones(10)\n",
    "y_range = np.arange(10)\n",
    "y_zeros = np.zeros(10)\n",
    "\n",
    "\n",
    "plt.plot(x, y_lin, color='g', label='lin')\n",
    "plt.plot(x, y_log, color='b', label='log')\n",
    "plt.plot(x, y_ones, color='r', label='ones')\n",
    "plt.plot(x, y_cust, color='k', label='cust')\n",
    "plt.plot(x, y_zeros, color='y', label='zeros')\n",
    "plt.plot(x, y_range, color='c', label='arange')\n",
    "plt.legend()\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Attributes of Arrays\n",
    "\n",
    "A common method of reshaping an existing array is to assign a new tuple of integers\n",
    "to the shape attribute. This will change the shape in-place. For example:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise: Explore Array Attributes\n",
    "\n",
    "1. Create an array"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "a = np.array([1,2,3,42,4,5,24])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "2. Using the dot and tab functionality in the ipython notebook, determine the meaning of arange, shape, and dtype."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(7,)"
      ]
     },
     "execution_count": 111,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3])"
      ]
     },
     "execution_count": 112,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.arange(4)\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 1],\n",
       "       [2, 3]])"
      ]
     },
     "execution_count": 113,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a.shape = (2, 2)\n",
    "a"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The dtype or data type is the most important ndarray attribute."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dtype('int64')"
      ]
     },
     "execution_count": 114,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.array([6, 28, 496, 8128])\n",
    "a.dtype"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dtype('float64')"
      ]
     },
     "execution_count": 115,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b = np.array([6, 28.0, 496, 8128])\n",
    "b.dtype"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When you are creating an array, the dtype that is automatically selected will always be\n",
    "that of the least precise element. Say you have a list that is entirely integers with the\n",
    "exception of a single float. An array created from this list will have the dtype\n",
    "np.float64, because floats are less precise than integers. The order of data types sorted\n",
    "from greatest to least precision is Boolean, unsigned integer, integer, float, complex,\n",
    "string, and object. An example of this downcasting follows, where 28 is an\n",
    "integer in the a array and a float in the b array:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  6,  28, -16, -64], dtype=int8)"
      ]
     },
     "execution_count": 116,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.array([6, 28.0, 496, 8128],\n",
    "             dtype=np.int8)\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  6.00000000e+00,   2.80000000e+01,   4.96000000e+02,\n",
       "         8.12800000e+03], dtype=float32)"
      ]
     },
     "execution_count": 117,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b = np.array([6, 28.0, 496, 8128],\n",
    "             dtype='f')\n",
    "b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([b'I will', b'and so'], \n",
       "      dtype='|S6')"
      ]
     },
     "execution_count": 118,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.array(['I will have length six', 'and so will I!'], dtype='S6')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Slicing and Views\n",
    "\n",
    "What is different about slicing in NumPy is that because NumPy arrays are N-dimensional,\n",
    "you may slice along any and all axes!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "a = np.arange(8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([7, 6, 5, 4, 3, 2, 1, 0])"
      ]
     },
     "execution_count": 120,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[::-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2, 3, 4, 5])"
      ]
     },
     "execution_count": 121,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[2:6]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 4, 7])"
      ]
     },
     "execution_count": 122,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[1::3]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise:  Reshaping and Slicing\n",
    "\n",
    "1) Create a 1D array that is 16 elements long and reshape it to be 4x4."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0,  1,  2,  3],\n",
       "       [ 4,  5,  6,  7],\n",
       "       [ 8,  9, 10, 11],\n",
       "       [12, 13, 14, 15]])"
      ]
     },
     "execution_count": 123,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.arange(16)\n",
    "a.shape = (4, 4)\n",
    "a"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "2) Slice the even rows and the odd columns."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1,  3],\n",
       "       [ 9, 11]])"
      ]
     },
     "execution_count": 124,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[::2, 1::2]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "3) Slice the inner 2x2 array."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 5,  6],\n",
       "       [ 9, 10]])"
      ]
     },
     "execution_count": 125,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[1:3, 1:3]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "4) Reverse the first 3 rows, taking the first 3 columns."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 8,  9, 10],\n",
       "       [ 4,  5,  6],\n",
       "       [ 0,  1,  2]])"
      ]
     },
     "execution_count": 126,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[2::-1, :3]     "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since slices are views, this means that modifications to their elements are reflected\n",
    "back in the original arrays. This makes sense, as there is only one block of memory\n",
    "between them. As a demonstration,\n",
    "\n",
    "**If you have two arrays a and b, where b is a slice of a,**\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0,  1,  2, 42,  4,  5])"
      ]
     },
     "execution_count": 127,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.arange(6)\n",
    "b = a[1::2]\n",
    "b[1] = 42\n",
    "a"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**then you can tell that b is a view whose base is a**\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 128,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b.base is a"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "Furthermore, changes to the contents of either a or b will also affect the other array. \n",
    "Can you show this by changing an element of b?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If you truly want a copy of a slice of an array, you can always create a new array from\n",
    "the slice:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "a = np.arange(16)\n",
    "b = np.array(a[1::11])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Arithmetic and Broadcasting\n",
    "\n",
    "*broadcasting* : one element of a goes into all elements of b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3, 4, 5])"
      ]
     },
     "execution_count": 130,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.arange(6, dtype=np.int64)\n",
    "a"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Slices are not the only way to create a view. The ndarray class has a view() method\n",
    "on it that will give you a view into the whole array."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 0, 1, 0, 2, 0, 3, 0, 4, 0, 5, 0], dtype=int32)"
      ]
     },
     "execution_count": 131,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a.view('i4')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3, 4, 5])"
      ]
     },
     "execution_count": 132,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.arange(6)\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-1,  0,  1,  2,  3,  4])"
      ]
     },
     "execution_count": 133,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a - 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0,  2,  4,  6,  8, 10])"
      ]
     },
     "execution_count": 134,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a + a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1,  6, 15, 28, 45, 66])"
      ]
     },
     "execution_count": 135,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "2*a**2 + 3*a + 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 136,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 1],\n",
       "       [2, 3]])"
      ]
     },
     "execution_count": 136,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.arange(4)\n",
    "a.shape = (2, 2)\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[42],\n",
       "       [43]])"
      ]
     },
     "execution_count": 137,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b = np.array([[42], [43]])\n",
    "b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 138,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  0,  42],\n",
       "       [ 86, 129]])"
      ]
     },
     "execution_count": 138,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a * b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 139,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 43],\n",
       "       [213]])"
      ]
     },
     "execution_count": 139,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.dot(a, b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 140,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 43],\n",
       "       [213]])"
      ]
     },
     "execution_count": 140,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.array([[ 43],\n",
    "      [213]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 141,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0,  1,  2],\n",
       "       [ 3,  4,  5],\n",
       "       [ 6,  7,  8],\n",
       "       [ 9, 10, 11]])"
      ]
     },
     "execution_count": 141,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.arange(12)\n",
    "a.shape = (4, 3)\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 142,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([16, 17, 18])"
      ]
     },
     "execution_count": 142,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b = np.array([16, 17, 18])\n",
    "b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 143,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[16, 18, 20],\n",
       "       [19, 21, 23],\n",
       "       [22, 24, 26],\n",
       "       [25, 27, 29]])"
      ]
     },
     "execution_count": 143,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a + b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 144,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0,  1,  2,  3],\n",
       "       [ 4,  5,  6,  7],\n",
       "       [ 8,  9, 10, 11]])"
      ]
     },
     "execution_count": 144,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a.shape = (3, 4)\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 145,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "ename": "ValueError",
     "evalue": "operands could not be broadcast together with shapes (3,4) (3,) ",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-145-f96fb8f649b6>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0ma\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mb\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m: operands could not be broadcast together with shapes (3,4) (3,) "
     ]
    }
   ],
   "source": [
    "a + b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 146,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[16],\n",
       "       [17],\n",
       "       [18]])"
      ]
     },
     "execution_count": 146,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b.shape = (3, 1)\n",
    "b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 147,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[16, 17, 18, 19],\n",
       "       [21, 22, 23, 24],\n",
       "       [26, 27, 28, 29]])"
      ]
     },
     "execution_count": 147,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a + b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 148,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 1, 2],\n",
       "       [3, 4, 5]])"
      ]
     },
     "execution_count": 148,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.arange(6)\n",
    "a.shape = (2, 3)\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 149,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2, 3])"
      ]
     },
     "execution_count": 149,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b = np.array([2, 3])\n",
    "b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 150,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "ename": "ValueError",
     "evalue": "operands could not be broadcast together with shapes (2,3) (2,) ",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-150-a5f966a4b1f4>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0ma\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0mb\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m: operands could not be broadcast together with shapes (2,3) (2,) "
     ]
    }
   ],
   "source": [
    "a - b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 151,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 2,  1,  0],\n",
       "       [ 0, -1, -2]])"
      ]
     },
     "execution_count": 151,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b[:, np.newaxis] - a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 152,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[ 2,  1,  0],\n",
       "                                     [-1, -2, -3]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]],\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "       [[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[ 3,  2,  1],\n",
       "                                     [ 0, -1, -2]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]])"
      ]
     },
     "execution_count": 152,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b[(slice(None),) + 31* (np.newaxis,)] - a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 153,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[ 2,  1,  0],\n",
       "                                    [-1, -2, -3]]]]]]]]]]]]]]]]]]]]]]]]]]]]]],\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "       [[[[[[[[[[[[[[[[[[[[[[[[[[[[[[ 3,  2,  1],\n",
       "                                    [ 0, -1, -2]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]])"
      ]
     },
     "execution_count": 153,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b[(slice(None),) + 30 * (np.newaxis,)] - a"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Fancy Indexing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 154,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1,  3,  9, 19, 33, 51, 73, 99])"
      ]
     },
     "execution_count": 154,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = 2*np.arange(8)**2 + 1\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 155,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([19, 99,  3])"
      ]
     },
     "execution_count": 155,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# pull out the fourth, last, and\n",
    "# second indices\n",
    "a[[3, -1, 1]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 156,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1,  3,  3,  9, 19, 51])"
      ]
     },
     "execution_count": 156,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# pull out the Fibonacci sequence\n",
    "fib = np.array([0, 1, 1, 2, 3, 5])\n",
    "a[fib]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 157,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 9, 99],\n",
       "       [33,  9]])"
      ]
     },
     "execution_count": 157,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# pull out a 2x2 array\n",
    "a[[[[2, 7], [4, 2]]]] "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 158,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-8, -7, -6, -5],\n",
       "       [-4, -3, -2, -1],\n",
       "       [ 0,  1,  2,  3],\n",
       "       [ 4,  5,  6,  7]])"
      ]
     },
     "execution_count": 158,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.arange(16) - 8\n",
    "a.shape = (4, 4)\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 159,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-6, -5, -8],\n",
       "       [-2, -1, -4],\n",
       "       [ 2,  3,  0],\n",
       "       [ 6,  7,  4]])"
      ]
     },
     "execution_count": 159,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# pull out the third, last, and\n",
    "# first columns\n",
    "a[:, [2, -1, 0]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 160,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-5, -7],\n",
       "       [-1, -3],\n",
       "       [-1, -3],\n",
       "       [ 3,  1],\n",
       "       [ 7,  5]])"
      ]
     },
     "execution_count": 160,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# pull out a Fibonacci sequence of\n",
    "# rows for every other column, starting\n",
    "# from the back\n",
    "fib = np.array([0, 1, 1, 2, 3])\n",
    "a[fib, ::-2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 161,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-8, -3,  2,  7])"
      ]
     },
     "execution_count": 161,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# get the diagonal with a range\n",
    "i = np.arange(4)\n",
    "a[i, i]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 162,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-4,  1,  6])"
      ]
     },
     "execution_count": 162,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# lower diagonal by subtracting one to \n",
    "# part of the range\n",
    "a[i[1:], i[1:] - 1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 163,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-7, -2,  3])"
      ]
     },
     "execution_count": 163,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# upper diagonal by adding one to part \n",
    "# of the range\n",
    "a[i[:3], i[:3] + 1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 164,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-5, -2,  1,  4])"
      ]
     },
     "execution_count": 164,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# anti-diagonal by reversal\n",
    "a[i, i[::-1]]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Masking"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 165,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 1, 2],\n",
       "       [3, 4, 5],\n",
       "       [6, 7, 8]])"
      ]
     },
     "execution_count": 165,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# create an array\n",
    "a = np.arange(9)\n",
    "a.shape = (3,3)\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 166,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ True,  True,  True], dtype=bool)"
      ]
     },
     "execution_count": 166,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# create an all True mask\n",
    "m = np.ones(3, dtype=bool)\n",
    "m"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 167,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 4, 8])"
      ]
     },
     "execution_count": 167,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# take the diagonal\n",
    "a[m, m]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 168,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 2, 4, 8])"
      ]
     },
     "execution_count": 168,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# create a mask\n",
    "m = np.array([[1, 0, 1], \n",
    "              [False, True, False], \n",
    "              [0, 0, 1]], dtype=bool)\n",
    "\n",
    "a[m]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 169,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ True,  True,  True],\n",
       "       [ True,  True, False],\n",
       "       [False, False, False]], dtype=bool)"
      ]
     },
     "execution_count": 169,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a < 5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 170,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "m = (a >= 7)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 171,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([7, 8])"
      ]
     },
     "execution_count": 171,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[m]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 172,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3, 4])"
      ]
     },
     "execution_count": 172,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[a < 5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 173,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3, 4])"
      ]
     },
     "execution_count": 173,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.array([0, 1, 2, 3, 4])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 174,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3, 4, 7, 8])"
      ]
     },
     "execution_count": 174,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[(a < 5) | (a >= 7)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 175,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3, 4, 7, 8])"
      ]
     },
     "execution_count": 175,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.array([0, 1, 2, 3, 4, 7, 8])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 176,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([0, 0, 0, 1, 1]), array([0, 1, 2, 0, 1]))"
      ]
     },
     "execution_count": 176,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.where(a < 5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 177,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([7, 8])"
      ]
     },
     "execution_count": 177,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[np.where(a >= 7)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 178,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 1],\n",
       "       [3, 4],\n",
       "       [6, 7]])"
      ]
     },
     "execution_count": 178,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[:, np.where(a < 2)[1]]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Structured Arrays"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 179,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# a simple flat dtype\n",
    "fluid = np.dtype([\n",
    "    ('x', int),\n",
    "    ('y', np.int64),\n",
    "    ('rho', 'f8'),\n",
    "    ('vel', 'f8'),\n",
    "    ])\n",
    "\n",
    "# a dtype with a nested dtype\n",
    "# and a subarray\n",
    "particles = np.dtype([\n",
    "    ('pos', [('x', int), \n",
    "             ('y', int), \n",
    "             ('z', int)]),\n",
    "    ('mass', float), \n",
    "    ('vel', 'f4', 3)\n",
    "    ])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 180,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "('pos', 'mass', 'vel')"
      ]
     },
     "execution_count": 180,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "particles.names"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 181,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "mappingproxy({'vel': (dtype('float64'), 24), 'y': (dtype('int64'), 8), 'x': (dtype('int64'), 0), 'rho': (dtype('float64'), 16)})"
      ]
     },
     "execution_count": 181,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fluid.fields"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 182,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([((0, 0, 0), 0.0, [0.0, 0.0, 0.0]),\n",
       "       ((0, 0, 0), 0.0, [0.0, 0.0, 0.0]),\n",
       "       ((0, 0, 0), 0.0, [0.0, 0.0, 0.0]), ((0, 0, 0), 0.0, [0.0, 0.0, 0.0])], \n",
       "      dtype=[('pos', [('x', '<i8'), ('y', '<i8'), ('z', '<i8')]), ('mass', '<f8'), ('vel', '<f4', (3,))])"
      ]
     },
     "execution_count": 182,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.zeros(4, dtype=particles)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 183,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([(42, 43, 6.0, 2.1), (65, 66, 128.0, 3.7), (127, 128, 3.0, 1.5)], \n",
       "      dtype=[('x', '<i8'), ('y', '<i8'), ('rho', '<f8'), ('vel', '<f8')])"
      ]
     },
     "execution_count": 183,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# note that the rows are tuples\n",
    "f = np.array([(42, 43, 6.0, 2.1), \n",
    "              (65, 66, 128.0, 3.7), \n",
    "              (127, 128, 3.0, 1.5)],\n",
    "             dtype=fluid)\n",
    "f"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 184,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(65, 66, 128.0, 3.7)"
      ]
     },
     "execution_count": 184,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 185,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([(42, 43, 6.0, 2.1), (127, 128, 3.0, 1.5)], \n",
       "      dtype=[('x', '<i8'), ('y', '<i8'), ('rho', '<f8'), ('vel', '<f8')])"
      ]
     },
     "execution_count": 185,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f[::2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 186,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([   6.,  128.,    3.])"
      ]
     },
     "execution_count": 186,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f['rho']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 187,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([(2.1, 42, 6.0), (3.7, 65, 128.0), (1.5, 127, 3.0)], \n",
       "      dtype=[('vel', '<f8'), ('x', '<i8'), ('rho', '<f8')])"
      ]
     },
     "execution_count": 187,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f[['vel', 'x', 'rho']]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Universal Functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 188,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "x = np.linspace(0.0, np.pi, 5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 189,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  0.00000000e+00,   7.07106781e-01,   1.00000000e+00,\n",
       "         7.07106781e-01,   1.22464680e-16])"
      ]
     },
     "execution_count": 189,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sin(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 190,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 1, 2],\n",
       "       [3, 4, 5],\n",
       "       [6, 7, 8]])"
      ]
     },
     "execution_count": 190,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.arange(9)\n",
    "a.shape = (3, 3)\n",
    "a"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Other Valuable Functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 191,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "36"
      ]
     },
     "execution_count": 191,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sum(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 192,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 9, 12, 15])"
      ]
     },
     "execution_count": 192,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sum(a, axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 193,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 3, 12, 21])"
      ]
     },
     "execution_count": 193,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sum(a, axis=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Numpy Wrap-up\n",
    "\n",
    "\n",
    "Congratulations! You now have a breadth of understanding about NumPy. More\n",
    "importantly, you now have the basic skills required to approach any array data language.\n",
    "They all share common themes on how to think about and manipulate arrays\n",
    "of data. Though the particulars of the syntax may vary between languages, the underlying\n",
    "concepts are the same. For NumPy in particular, though, you should now be\n",
    "comfortable with the following ideas:\n",
    "\n",
    "- Arrays have an associated data type or dtype.\n",
    "- Arrays are fixed-length, though their contents are mutable.\n",
    "- Manipulating array attributes changes how you view the array, not the data itself.\n",
    "- Slices are views and do not copy data.\n",
    "- Fancy indexes are more general than slices but do copy data.\n",
    "- Comparison operators return masks.\n",
    "- Broadcasting stretches an array along applicable dimensions.\n",
    "- Structured arrays use compound dtypes to represent tables.\n",
    "- Universal and other functions are helpful for day-to-day NumPy use.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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       "\n",
       "/* #52575c <-grey\n",
       " * #f5f7fa <-nearly white\n",
       " * #62676c <-grey\n",
       " * #42474c <- also grey\n",
       " * #c2c7cc <-light grey\n",
       " * #f35858 <- salmon\n",
       " * #B73F98 <- o'reilly pink\n",
       " */\n",
       "\n",
       "@font-face {\n",
       "    font-family: \"Slabo 27px\", \"Helvetica Neue\", Helvetica, Arial, sans-serif;\n",
       "}\n",
       "\n",
       "\n",
       "#notebook_panel { /* main background */\n",
       "    background: rgb(245,245,245);\n",
       "}\n",
       "\n",
       "div.cell { /* set cell width */\n",
       "    width: 750px;\n",
       "}\n",
       "\n",
       "div #notebook { /* centre the content */\n",
       "    background: #fff; /* white background for content */\n",
       "    width: 1000px;\n",
       "    margin: auto;\n",
       "    padding-left: 0em;\n",
       "}\n",
       "\n",
       "#notebook li { /* More space between bullet points */\n",
       "margin-top:0.8em;\n",
       "}\n",
       "\n",
       "/* draw border around running cells */\n",
       "div.cell.border-box-sizing.code_cell.running { \n",
       "    border: 1px solid #111;\n",
       "}\n",
       "\n",
       "/* Put a solid color box around each cell and its output, visually linking them*/\n",
       "div.cell.code_cell {\n",
       "    background-color: rgb(256,256,256); \n",
       "    border-radius: 0px; \n",
       "    padding: 0.5em;\n",
       "    margin-left:1em;\n",
       "    margin-top: 1em;\n",
       "}\n",
       "\n",
       "\n",
       "div.text_cell_render{\n",
       "    font-family: \"Slabo 27px\", \"Helvetica Neue\", Helvetica, Arial, sans-serif;\n",
       "    line-height: 140%;\n",
       "    font-size: 125%;\n",
       "    font-weight: 400;\n",
       "    width:600px;\n",
       "    color:#42474c;\n",
       "    margin-left:auto;\n",
       "    margin-right:auto;\n",
       "}\n",
       "\n",
       "/* Formatting for header cells */\n",
       ".text_cell_render h1 {\n",
       "    font-family: \"Slabo 27px\", \"Helvetica Neue\", Helvetica, Arial, sans-serif;\n",
       "    font-style:regular;\n",
       "    font-weight: 200;    \n",
       "    font-size: 50pt;\n",
       "    line-height: 100%;\n",
       "    color:#B73F98;\n",
       "    margin-bottom: 0.5em;\n",
       "    margin-top: 0.5em;\n",
       "    display: block;\n",
       "}       \n",
       ".text_cell_render h2 {\n",
       "    font-family: 'Fenix', serif;\n",
       "    font-size: 22pt;\n",
       "    line-height: 100%;\n",
       "    margin-bottom: 0.1em;\n",
       "    margin-top: 0.3em;\n",
       "    display: block;\n",
       "}       \n",
       "\n",
       ".text_cell_render h3 {\n",
       "    font-family: 'Fenix', serif;\n",
       "    margin-top:12px;\n",
       "        font-size: 16pt;\n",
       "    margin-bottom: 3px;\n",
       "    font-style: regular;\n",
       "}\n",
       "\n",
       ".text_cell_render h4 {    /*Use this for captions*/\n",
       "    font-family: 'Fenix', serif;\n",
       "    font-size: 2pt;\n",
       "    text-align: center;\n",
       "    margin-top: 0em;\n",
       "    margin-bottom: 2em;\n",
       "    font-style: regular;\n",
       "}\n",
       "\n",
       ".text_cell_render h5 {  /*Use this for small titles*/\n",
       "    font-family: \"Slabo 27px\", \"Helvetica Neue\", Helvetica, Arial, sans-serif;\n",
       "    font-weight: 300;\n",
       "    font-size: 16pt;\n",
       "    color: #B73F98;\n",
       "    font-style: italic;\n",
       "    margin-bottom: .5em;\n",
       "    margin-top: 0.5em;\n",
       "    display: block;\n",
       "}\n",
       "\n",
       ".text_cell_render h6 { /*use this for copyright note*/\n",
       "    font-family: 'Source Code Pro', sans-serif;\n",
       "    font-weight: 300;\n",
       "    font-size: 9pt;\n",
       "    line-height: 100%;\n",
       "    color: grey;\n",
       "    margin-bottom: 1px;\n",
       "    margin-top: 1px;\n",
       "}\n",
       "\n",
       "    .CodeMirror{\n",
       "            font-family: \"Source Code Pro\";\n",
       "                        font-size: 90%;\n",
       "    }\n",
       "/*    .prompt{\n",
       "        display: None;\n",
       "    }*/\n",
       "        \n",
       "    \n",
       "    .warning{\n",
       "        color: rgb( 240, 20, 20 )\n",
       "        }  \n",
       "</style>\n",
       "<script>\n",
       "    MathJax.Hub.Config({\n",
       "                        TeX: {\n",
       "                           extensions: [\"AMSmath.js\"], \n",
       "                           equationNumbers: { autoNumber: \"AMS\", useLabelIds: true}\n",
       "                           },\n",
       "                tex2jax: {\n",
       "                    inlineMath: [ ['$','$'], [\"\\\\(\",\"\\\\)\"] ],\n",
       "                    displayMath: [ ['$$','$$'], [\"\\\\[\",\"\\\\]\"] ]\n",
       "                },\n",
       "                displayAlign: 'center', // Change this to 'center' to center equations.\n",
       "                \"HTML-CSS\": {\n",
       "                    styles: {'.MathJax_Display': {\"margin\": 4}}\n",
       "                }\n",
       "        });\n",
       "</script>\n"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython.core.display import HTML\n",
    "def css_styling():\n",
    "    styles = open(\"styles/custom.css\", \"r\").read()\n",
    "    return HTML(styles)\n",
    "css_styling()"
   ]
  }
 ],
 "metadata": {
  "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": "3.4.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}