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   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Introduction to NumPy\n",
      "\n",
      "- *Jake VanderPlas*\n",
      "- *Presented at PyData @ Strata, New York City*\n",
      "- *October 15, 2014*\n",
      "\n",
      "*The source for this notebook can be found at http://github.com/jakevdp/PyData2014 *\n",
      "\n",
      "NumPy is a **huge** project, and there's no way to give a complete picture of it in ~40 minutes.\n",
      "So the goal today is to give a motivation for NumPy and a quick intro to what you'll need to get started.\n",
      "\n",
      "Note that this tutorial is written for **Python 3.3 or newer**. In order to be compatible with Python 2.x, we'll do some ``__future__`` imports to start off:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import print_function, division"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Outline\n",
      "\n",
      "1. Motivating NumPy: it increases both *coding efficiency* and *computational efficiency*\n",
      "2. Why is NumPy Faster than Python?\n",
      "3. The core of it all: the ndarray\n",
      "4. Universal Functions\n",
      "5. Aggregates"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Motivating NumPy: Efficient Numerical Computing\n",
      "\n",
      "We'll start by attempting to motivate *why* you might want to use NumPy for numerical code.\n",
      "Suppose you'd like to use a plotting tool to graph $y = \\sin(x)$ for $0 \\le x \\le 2\\pi$.\n",
      "Let's think about how you might do this in Python.\n",
      "\n",
      "We'll briefly preview ``matplotlib`` for plotting here; more on this later!"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%matplotlib inline\n",
      "import matplotlib.pyplot as plt\n",
      "\n",
      "# Setup ggplot style, if using matplotlib 1.4 or newer\n",
      "try:\n",
      "    plt.style.use('ggplot')\n",
      "    print(\"Setting Matplotlib style to ggplot\")\n",
      "except AttributeError:\n",
      "    print(\"Update matplotlib to enable styles\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Setting Matplotlib style to ggplot\n"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### First Try: A C-like Approach\n",
      "\n",
      "A new Python user with a background in a low-level language like C or Fortran might approach the problem this way:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "xmin = 0\n",
      "xmax = 2 * math.pi\n",
      "N = 1000"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# build the arrays\n",
      "x = []\n",
      "y = []\n",
      "for i in range(N):\n",
      "    xval = xmin + i * (xmax - xmin) / N\n",
      "    x.append(xval)\n",
      "    y.append(math.sin(xval))\n",
      "\n",
      "# Plot the result with matplotlib\n",
      "plt.plot(x, y);"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
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GBz9RNZG+w6Abvy+9MQhVCS08Dp33Cayht5tOcRQOfqJqIrXCIQNuhP3pe6ZT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\nAsz/Aksw1UUGf9+/AAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x106c05950>"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The C/Fortran approach is very prodecural, low-level, and \"hands-on\".\n",
      "Our program individually creates and modifies every value in each list."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Second Try: A \"Pythonic\" Approach\n",
      "\n",
      "A more \"Pythonic\" approach would be to avoid the loops in favor of constructs like list or generator comprehensions. A Python expert without too much numerical background might proceed like this:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x = [xmin + i * (xmax - xmin) / N for i in range(N)]\n",
      "y = [math.sin(xi) for xi in x]\n",
      "\n",
      "plt.plot(x, y);"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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GBz9RNZG+w6Abvy+9MQhVCS08Dp33Cayht5tOcRQOfqJqIrXCIQNuhP3pe6ZT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\nAsz/Aksw1UUGf9+/AAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x106d40c90>"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The Pythonic approach is beautiful, in that the lists are created in terse yet easy to grok one-line statements."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Third Try: a NumPy Approach"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np\n",
      "\n",
      "x = np.linspace(xmin, xmax, N)\n",
      "y = np.sin(x)\n",
      "\n",
      "plt.plot(x, y);"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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fvWk6JeDo6iVAg8aQdommU1yDg5+ohkj/YdAvN0C/3206JWBo0XHox+/CGnaL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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x106d40ed0>"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The NumPy version is perhaps the simplest of all: instead of setting each element of each array \"by hand\", as it were, we instead use simple functions which will create arrays and operate on them element-wise.\n",
      "\n",
      "Let's look at all these side-by-side:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#---------------------------------------------------\n",
      "# 1. C/Fortran style\n",
      "x = []\n",
      "y = []\n",
      "for i in range(N):\n",
      "    xval = xmin + i * (xmax - xmin) / N\n",
      "    x.append(xval)\n",
      "    y.append(math.sin(xval))\n",
      "\n",
      "#---------------------------------------------------\n",
      "# 2. Pythonic approach\n",
      "x = [xmin + i * (xmax - xmin) / N for i in range(N)]\n",
      "y = [math.sin(xi) for xi in x]\n",
      "\n",
      "#---------------------------------------------------\n",
      "# 3. NumPy approach\n",
      "x = np.linspace(xmin, xmax, N)\n",
      "y = np.sin(x)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "It's clear that NumPy is the most efficient to type; how does it compare when it comes to computation time? Let's use IPython's ``%%timeit`` cell magic to check. To make things more interesting, let's increase *N* to 100,000:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "N = 100000"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%timeit\n",
      "# 1. C/Fortran style\n",
      "x = []\n",
      "y = []\n",
      "for i in range(N):\n",
      "    xval = xmin + i * (xmax - xmin) / N\n",
      "    x.append(xval)\n",
      "    y.append(math.sin(xval))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "10 loops, best of 3: 61.2 ms per loop\n"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%timeit\n",
      "# 2. Pythonic style\n",
      "x = [xmin + i * (xmax - xmin) / N for i in range(N)]\n",
      "y = [math.sin(xi) for xi in x]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "10 loops, best of 3: 45.3 ms per loop\n"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%timeit\n",
      "# 3. NumPy approach\n",
      "x = np.linspace(xmin, xmax, N)\n",
      "y = np.sin(x)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "1000 loops, best of 3: 1.74 ms per loop\n"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We see that for this operation, NumPy is **30-40x faster** than either of the pure Python approaches!\n",
      "\n",
      "What we've seen above, in a nutshell, is why NumPy is useful for numerical computing:\n",
      "\n",
      "1. Numerical operations across arrays are **faster and more natural to type.**\n",
      "2. Numerical operations across arrays are **more clear to read.**\n",
      "3. Numerical operations across arrays are **more computationally efficient.**"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## So Why is NumPy So Much Faster?\n",
      "\n",
      "The reasons that these operations are so much faster in NumPy than in Python boils down to the fact that **Python is not a compiled language**, while NumPy pushes certain operations down into compiled code. We'll talk about three main components of this below:"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### 1. Python is Dynamically rather than Statically Typed\n",
      "\n",
      "Python is a dynamically-typed language, where just about anything goes.\n",
      "This means you can do things that would seem downright silly in C or Fortran, like replace an integer in an array with a string:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "L = list(range(5))\n",
      "L"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 12,
       "text": [
        "[0, 1, 2, 3, 4]"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "L[3] = \"three\"\n",
      "L"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 13,
       "text": [
        "[0, 1, 2, 'three', 4]"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The reason that Python can be so flexible is that, fundamentally **all objects are of the same type**: they are ``PyObject`` instances. Each ``PyObject`` does have an indicator of what type it is, but this information is *accessed at run-time*, rather than at some compile phase.\n",
      "\n",
      "Functionally, the difference between a C integer and a Python integer looks like this:\n",
      "\n",
      "<img src=\"images/cint_vs_pyint.png\" width=45%>\n",
      "\n",
      "That ``PyObject_HEAD`` block is what contains all of Python's dynamic goodies, like the type, reference count, etc.\n",
      "\n",
      "*Yes, there are modern JIT-compiled languages which bridge this gap, but Python doesn't yet do this, and the projects that do (PyPy, Pyston, etc.) aren't yet mature enough to use for numerical computing in practice.*"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### 2. Python is Interpreted rather than Compiled\n",
      "\n",
      "This dynamic type-checking means that Python's code cannot be pre-compiled, as with C/Fortran/etc.\n",
      "So, for example, when we multiply each of our list elements by two, we get the following:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "[2 * Li for Li in L]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 14,
       "text": [
        "[0, 2, 4, 'threethree', 8]"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Notice that the ``*`` operator does fundamentally different things with integer vs. string objects!\n",
      "Here the ``*`` cannot be mapped onto some machine-code function until the program is actually run: this leads to type-checking overhead each time the function is called, even if you have an array of all integers! There's no way for Python to know ahead of time that the same ``*`` needs to be used each time: this is the sense in which it's interpreted rather than compiled.\n",
      "\n",
      "*Yes, Python is compiled to a sort of bytecode (i.e. ``.pyc`` files), but no deep optimization takes place: this bytecode is basically a 1-to-1 mapping to the Python code that generates it.*"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### 3. Python's flexible object model can lead to inefficiencies\n",
      "\n",
      "When it comes to creating lists or arrays of objects, the fact that Python is dynamically typed can make a **huge** difference: consider the memory layout of a NumPy array vs that of a Python list.\n",
      "Consider the following two objects:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "L = list(range(1, 9))\n",
      "L"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 15,
       "text": [
        "[1, 2, 3, 4, 5, 6, 7, 8]"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "A = np.arange(1, 9)\n",
      "A"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 16,
       "text": [
        "array([1, 2, 3, 4, 5, 6, 7, 8])"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "They may look superfically similar, but under the hood they are anything but. Here's a schematic of their memory configuration under-the-hood:\n",
      "\n",
      "<img src=\"images/array_vs_list.png\" width=80%>\n",
      "\n",
      "NumPy arrays are simply pointers to buffers containing data of a uniform type; Python lists are *pointers to pointers*, each of which in turn points to a ``PyObject`` instance existing in memory.\n",
      "\n",
      "*Yes, Python has built-in ``array`` objects that provide mono-typed storage buffers, but they are nowhere near as useful as NumPy's arrays.*"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Exploring NumPy's ``ndarray`` object\n",
      "\n",
      "NumPy's ``ndarray`` object is essentially a pointer to a data buffer, with metadata telling us how to interpret it.\n",
      "\n",
      "<center>\n",
      "<img src=\"files/images/dtype.png\" width=60%>\n",
      "</center>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "For example, we can create the following one-dimensional array:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x = np.arange(10)\n",
      "x"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 17,
       "text": [
        "array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Let's look at some of the important attributes of this object:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# data type\n",
      "x.dtype"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 18,
       "text": [
        "dtype('int64')"
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# array shape\n",
      "x.shape"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 19,
       "text": [
        "(10,)"
       ]
      }
     ],
     "prompt_number": 19
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# number of dimensions\n",
      "x.ndim"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 20,
       "text": [
        "1"
       ]
      }
     ],
     "prompt_number": 20
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# size of the array\n",
      "x.size"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 21,
       "text": [
        "10"
       ]
      }
     ],
     "prompt_number": 21
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# number of bytes to step for each dimension\n",
      "x.strides"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 22,
       "text": [
        "(8,)"
       ]
      }
     ],
     "prompt_number": 22
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# flags specifying array properties\n",
      "x.flags"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 23,
       "text": [
        "  C_CONTIGUOUS : True\n",
        "  F_CONTIGUOUS : True\n",
        "  OWNDATA : True\n",
        "  WRITEABLE : True\n",
        "  ALIGNED : True\n",
        "  UPDATEIFCOPY : False"
       ]
      }
     ],
     "prompt_number": 23
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Arrays as Views"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Let's focus on this ``OWNDATA`` property of the ``x`` array above.\n",
      "Here we see that the array ``x`` owns its data, but if we create some derived array from ``x``, this will change.\n",
      "Let's use Python's standard slicing syntax to create a new array containing every other item in ``x``:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "y = x[::2]\n",
      "y"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 24,
       "text": [
        "array([0, 2, 4, 6, 8])"
       ]
      }
     ],
     "prompt_number": 24
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Checking ``y``'s flags, we see now that ``OWNDATA`` is False:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "y.flags"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 25,
       "text": [
        "  C_CONTIGUOUS : False\n",
        "  F_CONTIGUOUS : False\n",
        "  OWNDATA : False\n",
        "  WRITEABLE : True\n",
        "  ALIGNED : True\n",
        "  UPDATEIFCOPY : False"
       ]
      }
     ],
     "prompt_number": 25
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "``x`` still owns the data; ``y`` simply has a pointer to it!\n",
      "Let's demonstrate this by changing one of the values in ``y``, and observing that the corresponding ``x`` value changes as well:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "y[2] = 100\n",
      "x"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 26,
       "text": [
        "array([  0,   1,   2,   3, 100,   5,   6,   7,   8,   9])"
       ]
      }
     ],
     "prompt_number": 26
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "So how does this work?\n",
      "It turns out that ``x`` and ``y`` point to the *same memory buffer*, but view it in different ways:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import ctypes\n",
      "print(x.data, x.itemsize, x.strides)\n",
      "print(y.data, y.itemsize, y.strides)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "<memory at 0x106b72c80> 8 (8,)\n",
        "<memory at 0x106b72c80> 8 (16,)\n"
       ]
      }
     ],
     "prompt_number": 27
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The ``strides`` attribute shows you the number of bytes for each step in the array; ``y`` essentially takes two 8-byte steps each time it accesses the next array element."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print(x)\n",
      "print(y)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[  0   1   2   3 100   5   6   7   8   9]\n",
        "[  0   2 100   6   8]\n"
       ]
      }
     ],
     "prompt_number": 28
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Thus we see that when constructing arrays, we generally will end up with **views** rather than **copies** of source arrays. This is one extremely powerful aspect of NumPy, but also something you should certainly be aware of!"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Side note: if you actually want a copy, you can do, e.g.\n",
      "y = x[::2].copy()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 29
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Such views can be even more powerful: for example, we can reshape ``x`` into a two-dimensional array:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x2 = x.reshape(2, 5)\n",
      "x2"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 30,
       "text": [
        "array([[  0,   1,   2,   3, 100],\n",
        "       [  5,   6,   7,   8,   9]])"
       ]
      }
     ],
     "prompt_number": 30
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Again, this is simply a view of ``x``:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x2[1, 4] = 42\n",
      "x2"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 31,
       "text": [
        "array([[  0,   1,   2,   3, 100],\n",
        "       [  5,   6,   7,   8,  42]])"
       ]
      }
     ],
     "prompt_number": 31
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 32,
       "text": [
        "array([  0,   1,   2,   3, 100,   5,   6,   7,   8,  42])"
       ]
      }
     ],
     "prompt_number": 32
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Let's see some of the attributes of ``x2``:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# number of dimensions\n",
      "x2.ndim"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 33,
       "text": [
        "2"
       ]
      }
     ],
     "prompt_number": 33
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# shape of the array\n",
      "x2.shape"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 34,
       "text": [
        "(2, 5)"
       ]
      }
     ],
     "prompt_number": 34
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# size of the array\n",
      "x2.size"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 35,
       "text": [
        "10"
       ]
      }
     ],
     "prompt_number": 35
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# number of bytes to step for each dimension\n",
      "x2.strides"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 36,
       "text": [
        "(40, 8)"
       ]
      }
     ],
     "prompt_number": 36
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x2.flags"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 37,
       "text": [
        "  C_CONTIGUOUS : True\n",
        "  F_CONTIGUOUS : False\n",
        "  OWNDATA : False\n",
        "  WRITEABLE : True\n",
        "  ALIGNED : True\n",
        "  UPDATEIFCOPY : False"
       ]
      }
     ],
     "prompt_number": 37
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "So as you use NumPy arrays, keep this in mind! What you are using is a *Python object* which views a *raw data buffer* as a flexible array:\n",
      "\n",
      "<center>\n",
      "<img src=\"files/images/dtype.png\" width=60%>\n",
      "</center>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Creating NumPy Arrays\n",
      "\n",
      "Here we'll demonstrate some functions to create NumPy arrays from scratch:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Array of zeros\n",
      "np.zeros((2, 3))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 38,
       "text": [
        "array([[ 0.,  0.,  0.],\n",
        "       [ 0.,  0.,  0.]])"
       ]
      }
     ],
     "prompt_number": 38
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Array of ones\n",
      "np.ones((3, 4))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 39,
       "text": [
        "array([[ 1.,  1.,  1.,  1.],\n",
        "       [ 1.,  1.,  1.,  1.],\n",
        "       [ 1.,  1.,  1.,  1.]])"
       ]
      }
     ],
     "prompt_number": 39
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Like Python's range() function\n",
      "np.arange(10)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 40,
       "text": [
        "array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])"
       ]
      }
     ],
     "prompt_number": 40
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# 5 steps from 0 to 1\n",
      "np.linspace(0, 1, 5)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 41,
       "text": [
        "array([ 0.  ,  0.25,  0.5 ,  0.75,  1.  ])"
       ]
      }
     ],
     "prompt_number": 41
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# uninitialized array\n",
      "np.empty(10)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 42,
       "text": [
        "array([ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.])"
       ]
      }
     ],
     "prompt_number": 42
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# random numbers between 0 and 1\n",
      "np.random.rand(5)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 43,
       "text": [
        "array([ 0.48200098,  0.91255848,  0.43654199,  0.86788548,  0.36746416])"
       ]
      }
     ],
     "prompt_number": 43
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# standard-norm-distributed random numbers\n",
      "np.random.randn(5)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 44,
       "text": [
        "array([-0.86029106,  0.27795606, -1.59104791, -0.30107627,  0.46938077])"
       ]
      }
     ],
     "prompt_number": 44
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Some Strategies for Fast Computing with NumPy\n",
      "\n",
      "Here we'll discuss a couple strategies for fast computing with NumPy.\n",
      "In particular, we'll mention **universal functions**, which operate elementwise on arrays, and **aggregate functions**, which collapse arrays along particular dimensions."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Universal Functions\n",
      "\n",
      "Where the rubber hits the road with NumPy is with Universal functions: these are functions which operate *elementwise* on arrays. We saw this above with the ``np.sin`` function, which takes an array and returns an array with the elementwise sine:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x = np.linspace(0, 2 * np.pi)\n",
      "y = np.sin(x)\n",
      "print(x.shape)\n",
      "print(y.shape)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(50,)\n",
        "(50,)\n"
       ]
      }
     ],
     "prompt_number": 45
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.plot(x, y);"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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PVEUkaRh0zw7oga9NpwQMzcuFLp4Na8SDplNchYOfqIpIWE3IoBGw57xnOiVg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\nwU9EFGT+Pxvu78Bmq8eQAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x106cae9d0>"
       ]
      }
     ],
     "prompt_number": 46
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "NumPy also implements many arithmetic functions (e.g. ``+``, ``-``, ``*``, ``/``, ``**``) as element-wise ufuncs. So we can do things like this:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.plot(x, y)\n",
      "plt.plot(x, y + 1)\n",
      "plt.plot(x, -2 * y)\n",
      "plt.plot(x, 1 / (1 + y ** 2));"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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+vp6tW7cSExPDokWLqCmXURTBxGkXnms7W395m4nHttXz8OIUn2kApRr/BRBC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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x106ea1e90>"
       ]
      }
     ],
     "prompt_number": 47
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "You can find a lot of interesting ufuncs in NumPy: for example"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "for f in [np.sin, np.cos, np.exp, np.log, np.sinc]:\n",
      "    plt.plot(x, f(x), label='np.' + f.__name__)\n",
      "plt.legend()\n",
      "plt.ylim(-1, 5)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": [
        "-c:2: RuntimeWarning: divide by zero encountered in log\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 48,
       "text": [
        "(-1, 5)"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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IkPlPlyQpPHnVQzebzdx///08+uijPPbYY1RUVLB3715fxRYS+no0Wptd5Mgyc5IUVHxV\ngu5Edrudn/3sZ5SVlVFWVsb999+Pw+Hw/P65555j6tSplJWV8corr5CTk8ORI0f89RJP4fWQS0SE\ne9zY5XKh6zqxscG3IJU/Hapy30hkNMreuSQFE1+UoPuiZ555hh07dvDee+/x3nvvsWPHDp5++mkA\n/v3vf/P888/z6quvsn79ej766KPQu/Vf13XuueceGhsbueiii8jJyfFFXCHB5XTfGXreRSPrQ0yS\nBuOZZ57xyX5uv/32QW/jbQm6L3rjjTf45S9/SVJSEgB33XUX99xzD3fffTdvvfUW1157LWPHjgXg\nhz/84YB7/r7idUJXVZVHH32Uvr4+HnzwQSoqKigpKfH8vqKigoqKCs/PS5YswWKxePu0AWM2mz3x\n79/dTXpmJOkZgSuxNVgnxh9qQjl2CM/4DYaz3xU9lETsK96WoPuihoaGkzqt2dnZnu2ampqYMmWK\n53dDLWRhMBhO205WrVrl+b6kpOSkXAs+XJwrOjqac845hwMHDpz0JP09aaitn3yi42sVCyHYu6ub\nSdOiQ+r1hOL61ceFcuwQnvGH6gfUQEvQfVFGRgbV1dWeXnhtbS0ZGRkApKWlnVTrYah1HzRN67ed\nWCwWlixZcsZtvRpD7+rqore3F3DPeNm1axf5+fne7DJkNDe4UFVZM1SSQsVQStB90eWXX87TTz9N\nW1sbbW1tPPnkk1x55ZUAXHbZZaxatYqqqiqsVitPPfWUX17HmXjVQ+/o6GDFihXouo4QgvPOO49J\nkyb5KragdqjSTv44OVVRkkLF6UrQRUdHn1KCbvPmzbz00kun7GPZsmX09PSwcOFCABYtWsSyZcsA\nmD9/Pt/85je55pprUFWVZcuW8frrr2M2D98MOFmCbpAsFgv1dR1sWNvDwsviQm7d81A+7Q/l2CE8\n4w/F1zRcJegqKyu54IILOHz4MKo68MEQWYJumB3ab2dUgTnkkrkkSf71zjvvYLfb6ejo4MEHH+Si\niy4aVDL3lkzog+Rw6NQedZIn122RpJDlr6HSl19+mSlTpjBnzhxMJhO/+tWv/PI8pyMXHxmkg/t6\nSU03EhUtPwslKRT5swTdn//8Z7/sd6BkVhoETRPs2dXNmPGydy5JUvCRCX0Qqg85SEw2kZAkT2wk\nSQo+MqEPkK4JKvfYmHhOXKBDkSRJ6pdM6ANUfdiBJc5ASpocbpEkKTjJhD4Aui6o2mNn3ITIQIci\nSZJ0WjKhD0DtEQdRMSpJqXLsXJIkt2effZa777470GGcRGaos9B1QeVuO6XlUWf/Y0mSRozbbrst\n0CGcQvbQz6LuqJOIKIVk2TuXJCnIyYR+BkIXVO62MW5CpFyES5JCjK9K0K1YsYKysjKKioo477zz\nWL9+PQCPP/64p5deXV1NTk4Or732GtOnT2fSpEknFfbQdZ1nnnmGOXPmUFRUxMUXX+yXNa1kt/MM\n6mqcmMwKKenyMElSqDmxBJ3ZbGbx4sWsWrWKwsLCk0rQbd26lRtuuIHS0lLPiovHVVVVsXLlSt55\n5x3S0tKora3F5XJ59v9FmzdvZt26dRw4cIBFixZxySWXUFhYyO9+9zvWrFnDSy+9REFBAXv27Dmp\nwIavyEx1GkIIKitsFE+Jkr1zSfJCWtWPfbKfpsLBr4vibQk6g8GAw+Fg3759JCYmkp2d7fldfwvV\n3nXXXURERDBhwgQmTJjA7t27KSws5JVXXuG+++6joKAAYEDFNIZCJvTTaKh1ohoU0jLkIZIkbwwl\nEfuKtyXo8vPz+cUvfsETTzzB/v37mTdvHvfffz/p6en9Pt/xDw+AyMhI+vr6AKivrycvL88XL+mM\n5Bh6P3RdsG+XjaKJcuxcksLR8RJ0x9XU1HhKyX3R4sWLWb16NZs2bUJRFB588MFBP19WVhaHDx8e\nargDJhN6P44edGCOUEjLlL1zSQoXQylBd+DAAdavX4/dbsdsNhMRETGgwthftHTpUh555BEOHTqE\nEILdu3fT3t4+5NdyOjJjfYHTKdhfYWP63BjZO5ekMDKUEnQOh4OHHnqIyspKjEYj5eXlPPLII6fs\n7/jPp/Ptb38bu93O0qVLaWtrY+zYsbzwwgu+f42yBN3J9uy0YuvTOWdmTL+/D8WSWycK5fhDOXYI\nz/hD8TUNVwm6oZIl6HzE2qdz5ICD8aXyrlBJkkKPTOgn2LvTSl6hWVYjkqQwF67DqTJzHdPR5qK5\n0UXheLmioiSFM3+WoAs0mdBxX/3evcNK0cRIjKbw/OSWJCn8yYQONNa5cNgFufnmQIciSZI0ZCM+\noeu6YPenViZMiUJVZe9ckqTQNeLnoR+pchAdo5KWaQp0KJIUkiwWS6BDGBCDwYCmaYEOw69GdEK3\n23T277Yx6/zYQIciSSEplOagh+Kc+cEa0UMun223MirfTFzC4G/llSRJCjZe9dBbWlpYsWIFnZ2d\nKIrCBRdcwCWXXOKr2Pyqsc5JR5vG5PLoQIciSZLkE14ldKPRyI033kheXh42m4177rmH0tJScnJy\nfBWfX7icgl1b+5hcHo3RKC+ESpIUHrwacklISPCs8RsZGUl2drZfVhDztX2f2UhOM5KaIS+ESpIU\nPnw2ht7U1MThw4cZO3asr3bpFx2tLmqPOpgwRa7XIklSePHJLBebzcYTTzzBTTfdRGTkybfOV1RU\nUFFR4fl5yZIlAZvmpOuCde81MnVGIikp/a+meDZmszlkpmn1J5TjD+XYQcYfaKEeP8CqVas835eU\nlFBSUnLS771ePtflcvHwww8zZcoULr300gFtE6jlc6v22GhudDFz3tDXOg/1qU+hHH8oxw4y/kAL\n9fj9vnyuEILf/va3ZGdnDziZB0pvj0bVXjul02TRZ0mSwpNXQy779u1j3bp1jBo1iuXLlwPuUktT\npkzxSXC+IoRg5xYrhcURxMTKOeeSJIUnrxL6+PHjefXVV30Vi98cqnTgcgoKxkUEOhRJkiS/Cfs7\nRTvbXVTutjF1VrRcfEuSpAFxOp20tbVRW1sb6FAGJazXcnG5BNs+6qNkSpQcapEkycPlctHd3U1n\nZyfd3d10dXWd9HA4HFgsFpKTk8nOzg50uAMW1gm9YruV+CQDOXlynXNJGkl0Xaenp8eToDs7O7Fa\nrbS2ttLV1YXNZiM2Npa4uDjPo6CgwPN9dHR0SE6eCNuEXl/joKXRxXlfCu15p5Ik9c9ut9PZ2elJ\n2Me/Hu91R0VFER8f70nS+fn5FBUVERcXR0xMDKoafiPOYZnQrX06O7dYmT43BpMsKSdJIUkIQV9f\nHx0dHZ5EfeLD5XIRHx/vSdpJSUnk5+d7ErjReHJ6C/V56AMRdgld6IJtH/dSMC6CxOSwe3mSFFaE\nEPT09NDR0XFS4j7+vclk8iTt+Ph4Ro8e7fk+VIdF/CnsMl7lHjuKolA4Xk5RlKRgIISgt7eX9vZ2\nOjs7PV+PJ+3IyEji4+NJSEggPj6ecePGeZJ2RIR8Hw9GWCX0lkYnh6vszL3QgiKnKErSsLLZbLS3\nt9PR0eH5evxhNptJSEjwPDIzMz1J22yWkxZ8JWwSem+PxtaP+iibFU1UdPhd7JCkYKBpmqeXfWLy\nbm9vR9M0EhMTSUxMJCEhgTFjxpCYmCh72sMoLBK60yn4ZF0v40oiSUmXa5xLkrfsdjttbW20t7d7\nvh4f346NjfUk7oyMDMaPH09iYqIc0w4CIZ/QhRBs/7iXpBQjeYXy1E2SBurEse22tjbPo729HafT\nSWJiIklJSSQmJlJcXExOTg5Go/GU2SNS8Aj5/5m9u2w4nYJps+UqipLUn+MzSY4n7NbWVs/3qqqS\nlJTkeRwfJomNjT3l/TQSpv2FupBO6LVHHNQecTD3QguqQSZzaWQ7Pm+7tbXVk7SPfzUajZ6knZ6e\nTnFxMUlJSURFycpd4SRkE3pHm4vPtluZOS+WiEh5EVQaWY6Pcbe0tNDa2kpLSwttbW0AJCcnk5yc\nTFpaGuPHj5eJewQJyYRus+ps3tDLpLIo4hPloltS+NJ1nY6ODlpaWjyP1tZWrFYrSUlJpKSkkJyc\nTEFBAcnJyfLC5AgXcgndYdf56D895BVGkJUrL4JK4cNut3uSdnNzs6fXHR0dTWpqKsnJyUyYMIGU\nlBTi4uLCci0SyTshldBdTsGmD3tJzzLJO0GlkHX8ImVzc7MncTc3N3t63ampqaSlpVFSUkJycrK8\n8UYasJBJ6Jom2Ly+l7gEA8WlkfK0UgoJQgg6Oztpamqis7OTmpoampubURSF1NRUUlNTGTt2LLNn\nzyY+Pl72uiWvhERC13V3oQpThEJpmZyeKAUnIQQdHR00NTV5Hs3NzURERJCamkpOTg5TpkwhNTWV\nmJgY2Y4lnwv6hC6E4NPNfWiaYPqsGLlGixQUhBB0dXXR2NhIU1MTjY2NNDc3ExkZ6RkymTZtGmlp\naZ4ZJnIet+RvQZ3QhRBUbLfS26Mzc16snGsuBUxfXx9NTU00NDTQ2NhIY2MjBoOBtLQ00tPTT0ne\nkhQIQZvQhRDs2WmjtdnF7PmxGI0ymUvDw+Vy0dzc7EneDQ0N2Gw20tPTSU9PZ+LEiVxwwQXExsYG\nOlRJOklQJnQhBLu2Wulo05h1fiwms7xQJPlPd3c39fX1NDQ00NDQQEtLi2eJ11GjRjF9+nQSExPl\nmLcU9IIuoeu6YMemPqxWnVnzY2UJOcmndF2npaWFuro66uvrqa+vR9M0MjIyyMzMZPbs2aSlpcmp\nglJICqqErmmCrRt7EQJmnheLQQ6zSF5yOBw0NDRQV1dHXV0djY2NWCwWsrKyyMvLY9asWcTHx8ve\ntxQWgiahu5yCzRt6MZkVps6IlhdApSHp6+vzJO+6ujra29tJTU0lKyuLqVOnkpGRQWRkZKDDlCS/\nCIqE7nDofPJhL5Y4A6XTouTURGnA+vr6qK2tpaamhtraWnp6esjMzCQrK4u5c+eSnp4u1++WRoyA\nt/Tebo1P1vWSlmliwhR5B6h0ZlarldraWqqrq6mpqaG3t5esrCxycnKYMGECqamp8m5LacTyOqE/\n99xzbN++nbi4OB5//PFBbdvS6GTrR30UTYwkr1CuzSKdyuFweHrgdXV1tLW1kZWVRW5uLiUlJaSk\npMgELknHeJ3Q58+fz8UXX8yvf/3rQW13uMrO/gobZbOiZR1QyUPXdRobGzl69CjV1dU0NzeTlpZG\nbm4uX/7yl4mNjcVgkEsmS1J/vE7oxcXFNDU1DWqbXVv7aGlyMWdBLDEW+eYc6To7Ozl69ChHjhyh\ntrYWi8VCbm4u5eXlZGVlYTK5P/DlrfOSdGYBGUPv6dE59wILJrMcL/8ioWlg6wNFBaMRjEYUNbw+\n9FwuFzU1NZ4kbrfbGTVqFIWFhSxYsIDo6OhAhyiNcJousLl0HJogMSrglxoHzO+RVlRUUFFR4fl5\nyZIlnJP0LAc+TaDOkUC9M4lmPZleNZ2M+GhyEiLJiY8kNyGSDEsEhiCb8WI2m7FYLEPaVug6elM9\nWvUh9OpDaPXViO4uRHcnoqcLvbsTbFaUqGiELsDldD8UBYwmFJMZJTEZNTXj2CPd870hJw8l4uzT\n8byJ3xsdHR1UVlZSVVVFTU0N6enpjBkzhrKyMtLT0wd0MTxQsfuKjD+wzGYzsbGxtFtdVHfYqOm0\nUXPsa2OPgz6HhtWpYXXqODSdSKNKWmwEf7h2YqBD91i1apXn+5KSEkpKSk76vSKEEN4+SVNTEw8/\n/PCAL4o2HNqGYm8CWyMGRxNmZxOq1stnehn/7pzAwS6Fum4H7VaN7DgzJWlRlKRHU5IaTUKAPy0H\nc9ovWpsQu3fAgT2ImiPQUAMxFsgejZI9GjKyUSzx7n+LjYNYC0TFoJxwkU8IAbruTuwOB3S2QksT\norXJ/bWtCZoboLEOMnNRCsZBwXiUMeMh5dREOVzDFrquU19fz+HDhzl06BBWq5W8vDzy8vIYNWoU\nERGDvwge6kMuMv7hZ3fp7G+1UtFoZW+bnX1NvRhUhSyLmew407GvZlJjTMSYDESZVCKNKhFGBTXI\nZtxlZWWd9W8Ckh31iAyIyIA40AAHYLA3MLH9v0w1/glrwXT64udgI5rDHXYqmvr44EAnKz5uIDHK\nSElaNKUdJkMuAAAgAElEQVQZ0ZRlxRJlCp4ZDqKvB/buQuz51J3Irb0o40th3ETUuV9yJ9zomEHt\nU1EUMBjcj4hIsMRBTj5fbGrC6YAjBxAH9yJ2fIx4/UXQXCjFk1HOmQkTp6JE+ncow+l0cuTIEQ4e\nPMjhw4exWCzk5eWxcOHCAffCJckbuhDsabayra6X3U19HGy3MSo+gonp0VxTmkFutCAuMnSGUAbL\n6x76U089xZ49e+ju7iY+Pp4lS5Ywf/78M25TV1d32t+pzjai2z8ksmcnNssU+hLOQzclAO5xrSPH\nEvy2ul72tliZnBHD3NEWyrJjiTT6P7l/sZcirH2IbR8hNv0HDu6HMUUoE6agFE+BnLyTetvDTbQ2\nIz7bitjxMVTtgbElRM06H3tRKUpcgk+eo6+vj0OHDnHgwAFqa2vJyMigoKCAgoICn5+eh2IP8UQy\nfv/QhWBfi5UNR7rZcLQbS4SB6dmxTEyPpiglytPpC9b4B2ogPXSfDLkM1pkS+nGqq5uojvVEdW2l\nO/Uy7JbJp/xNl11jU3U36492s7/FyjmZMczNi6M8Oxajn8beLRYLXe3tULEdsek/iM+2QtEk1Jnn\nw6RpKObgnE8v+noRu7Zg/Gwrzk83Q14h6nlfgikzUIyDmzba09PDgQMHqKqqorm5mdGjR1NQUEBe\nXt6QhlIGKtTfkDJ+3zrYZuM/hzrZcLSbSKPK3NFxzBltITe+/zYYbPEPVkgn9OOMtlriGv+CMyqf\n7pTLQO1/FbxOm4uPq3v4z6FOGnucfHlsAheNTSDBh6dXoqUR0/p/Yf/wX5CehTLjfJRpc1Bi43z2\nHP5msVjoamt1n1V8+C401KDMWYgy9yKU1IzTbtfd3U1VVRVVVVW0tbWRn59PYWEho0aNGrZb60P9\nDSnj955TE3xU3c0/9rXT0udkQUE8546OY3TC2TsSwRC/N8IioQMouh1L8xsY7XV0pn8VLeL0iQfc\nn9xv729nY3U35VmxXFqUyLiUoVeSEQf2It57E7F3JxHzL8E5awFKWuaQ9xdIpwwZ1dcgPnwX8fG/\nYfQY1PmXQmk5iqLQ19dHZWUl+/fvp729nYKCAgoLC8nNzQ3IzT2h/oaU8Q9da5+Tf1V18G5lBznx\nEVw6LpHpObGDmgUX6sc/bBI6AEIQ2b2N2JZ36Em+CFtcuXs63xl02zXeP9DB2/s7iI80cE1JMtNz\nYgd0cU5oGuz4GP29N6GzHWXhV1DmXEBcanpIN4rTNWrhsCO2bsT6/lscNEZRlVVIk81BXl4eRUVF\nAUviJwr1N6SMf/CqO+289lkrW+p6mDs6jkvGJQ6oN96fUD/+QTvLZUgUBVtcGc7IXOIb/oLZepCu\n9KtBOf1LsEQYuGJCMl8Zn8QnNT38ZVcLr37WwnWTUijP7j+xC11HbF6HWPMKxCWgXnQFTJkedjf3\nnEjTNA5X17C3rY/q1HHkxsUyoWY/l3S3YJo0FiU3F0Xebi8No5ouO6/uamVHfS9fGZ/It8vHEGuW\nbfBsQqeHfiLdSVzjq6i6nc7M6xHqwD6xdSHYVO1O7CZV4aulKZRlxaAoinu+96eb0N94GSKjUBdf\n755y+AWh/il/PH4hBI2Njezdu5f9+/eTlJREcXExhYWFREREuI/H3p3o/1gFrU0ol1yDMvuCgCb2\ncDn2oWo44q/rcvDqZy1sq+vlsvGJLCpKJNrkmzYX6sc/vIZcvkhoWJpWY3Q00ZF1E8Iw8DnWunBf\nWHl1ZysRRoUbk7oofv9P4HSgLr4BSqeddlgm1BuFoihs3ryZPXv2oOs6xcXFFBUVER8ff9ptRNVu\n9wdddyfqNd9AmVg2jBF/LtSPvYz/9Fr7nLz8aQuba3tYVORO5DE+7pGH+vEP74QOIHRiW97GbK2i\nI+ub6MbBzTbRao6w/s33eCm6lMKkCG6aP56MuDP39kOxUei6zpEjR6ioqKCuro4xY8YwYcIEMjIy\nBnyzj/sM5hP0v66E5DTUa25Cycn3b+BfEIrH/kQy/lPZXTpv7mljzb52vlSYwBUTkvw2tBLqxz/8\nEzqAEES3/4fI7i10ZN2Mbko6+yZ9vYi3/oLY9F+Uy67DMfsi3tzfyVv72vlyYQJXlSSf9g7UUGoU\nXV1d7N69m927dxMTE0NJSQlTp07F4XAMeZ/C5UJ8+E/E319FmTwd5fKvoSSc/Zj7Qigd+/7I+D8n\nhGDj0W5Wbm9iTFIU35iaSnqsfwtzh/rxHxkJ/Ziojo+Ibv8PHVnfRItI7/dvhK4jPvoAsfollNJy\nlCtucK+lckxLn5M/bW/ms8Y+rp+Syvn5caes5xDsjUIIwdGjR9m5cyf19fUUFRV5CkGA7+IXfT2I\nt19DbHgf5dIlKPMX+X18PdiP/dnI+N0Ottl4fksjVpfOzWVpTEof3HIYQxXqx39EJXSAiO7txLa8\nTUfWzafMVReHK9Ff+R0A6tLvoOSNPe1+9rVYeX5LIyZV4dYZGeSccOdZsDYKu93O7t272bVrF0aj\nkdLSUoqKijxriR/n6/hFQw36n38D1l7UG27lTMfVW8F67AdqpMdvdeq8/Gkz6450sbQ0lYVj4od1\nNdVQP/4jLqEDRHR/6k7q2begmVMRdhvijZcRmz9EueLrKLPmD2h9FU0X/LOyg7/samFRUSJXTUjG\nZFCCrlG0tbWxY8cOKisrGT16NKWlpWRmZg7rRV0hBOKjfyNeX4ky7VyUxdejRPl+IbBgO/aDNZLj\n31Lbw+82NzAxPZpvTE0nLkLemDZYIzKhA0R2bSGm7X3arHNxvfQiypjxKEtuQbEM/hb95l4nv9vc\nQGOPk1tnZFJekBbwRiGEoLa2lm3bttHY2MikSZOYNGkSMTFnP3X1Z6MWPV2Iv65EVGxHve5bKGWz\nfbr/UH9DjsT4O2wuXtjSSGWrje9Nz2BK5vAMr/Qn1I//iE3ooq+XyPXPEpPSSrtpEWLSPO/2JwQb\njnbzwtYmzitI4rqSeJ/NjR0MTdOoqqpi27ZtuFwuzjnnHMaPHz+otVSGo1GL/Z+hv/QcSvZolK99\nb0gfpP0J9TfkSIpfCMEHBzt5cUczC/Lj+WppChHDsBrqmYT68R+RCV18uhn95d+gTJpGzJeKiLLu\noCP72+hG75dy7bZr/HlXO9tqOlk2K5OJ6cNTKs3lclFRUcG2bduIi4tj6tSp5OXlDWl98eFq1MJh\nR7z5MmLTh6hf+657TXYvhfobcqTE32Z18euP62mzurhtZiZjks5eSWs4hPrxH1EJXdj6EP/3PGJ/\nBeqNt6EUTQIgum0tkT27aM/+FsLg/emexWLhgz31rPikgXl5cXxtcgpmg396Hk6nk127drF9+3bS\n0tIoLy8nI+PMC5OdzXA3alG5G/2PT6GMKUa57lsoMbFD3leovyFHQvwbjnbxu82NfKkwgSUTUzAZ\ngqeoSagf/xGT0EXVHvQ/PIkyvhRlyc0okSesrCgEMa3vYrZW0pF1C8Iw9FUX4fNG0WVz8dwnjdR0\n2blrdhYFPuyF2O12du7cyY4dO8jOzqa8vJzU1FSf7DsQjVrYbYjXVyJ2fIL69R+gTJw6pP2E+hsy\nnOPvsWv8fksjla1W7pidRZEXq5v6S6gf/7BP6MLlQvz9/xDr/oV6/fdPf1ovBLEtb2G019GR9c3T\nrqk+ECc2CiEE/z3cxR+2NrFovHsmjDfTsJxOJzt27GD79u2MHj2aadOmkZycPOT99SeQjVrs+RR9\n5TMok8tRrv7GoIuBhPobMlzj31Hfy7Mf1zM9J5Ybz0kblsphQxHqxz+sE7poqEF/4Qn3iog33oYS\nn3iWDXQsTX/D4OqkI/ProA6uSs9x/TWK5l4nz35cj80l+OGczEHf8aZpGp999hmbN28mKyuLWbNm\nkZh4ltczRIFu1KKvB/HSc4j6atRv/chdLHuAAh27t8Itfqem86cdzWw42s1tMzM5J4AzWAYi1I9/\nWCZ0IQRi/XuIv/0J5fKlKPMuHvjFQaER1/B/KOh0ZiwFZfAzVU7XKHQheHNPG6t3t/Gd8nTmjD77\nzA5d19m3bx+bNm0iMTGRWbNmkZaWNuiYBiMYGrUQArHxA8Rf/4jylaUo5w/s/zAYYvdGOMVf2+Xg\n8Q21pESb+MHMzIDMKx+sUD/+YZfQhbUP8dIKRN1R1O8sR8nMHcJOXMTXv4RQo+lKvwaUwZ0enq1R\nVLZaeWx9HaUZ0dxSln7aqVpHjhxh/fr1mM1mZs+eTXZ29qDiGKpgatSioRb9hcchIQn1xtvPOr0x\nmGIfinCJ/4ODnfxxWxNfLU3h4rEJQ5ptFQihfvzDKqGLw5Xov38UpeQclGu+6V0xZt1JQt0fcZnT\n6Em9/KyVj040kEbR59T4zSeNHGq38aM5WeQlfn7BtKOjgw8//JD29nbOPfdcCgoKhvUNEWyNWric\niDf+7J7eePOd/a5Bf1ywxT5YoR6/ISKaxz6ooqrNxt3nntyuQ0GoH/+wSOhCCHc9z3++7p7PXDbH\nJzEouo2E2v/FEVVAb/KXB5zUB9oohBD8+1AXf9zWxNLSFOaPimLLli3s3r2bsrIyJk+ePGzFlU8U\nrI1a7N6O/oen3ENol17Tb4WoYI19oEI5/qpWG49vrGdiWiQ3l6UH7YXPMwnl4w9hkNBFTxf6H56C\nni73BbQzVKUfCkXrJbH2BewxxfQmXTigpD7YRlHdaeN3b28itX0fRYX5zJ0ze0C36PtLMDdq0dGK\n/vzjYDCg3nIXStzJF4aDOfaBCMX4hRC8U9nBX3a2sGzuaKal+3eJW38KxeN/ooEk9KD9mBUH9qI/\ncCdKZi7q8od8nswBhCGG9uybMffuIab1XfDxZ1traysfvbuGSWoj6rg5vGkbQ7Mj+C8eBYqSkIx6\n1wMoBUXoD9yJ2Lcr0CGNaH1Ojcc31PGvqg4evmg08wt9O4VW8r2gKxIthECsfQvx9mvum1CmzPDv\n8xli6ci+hYS6P6C06vQkXzyoMfX+uFwutmzZws6dO5k5cyaTJk1CURQ+ONjJfWurufGcVBaOSfDR\nKwgvisGAsvh6xNgS9OcfQzn/EpRLrg7rIt3B6HC7jYfX1TExPYqHLxod8HVYpIEJqiEXYe1DX/kM\ntDSifvcev/TKT0fRrCTU/S/OyNH0pCw6bVI/22lbXV0da9euJTExkXnz5mGxnLyGzNFOOw9/WMu4\nlCi+W376WTD+EkqnnaK9Ff2Fx8BoRr3lh8RlZYdM7P0JlWP//oEOXtzezDenpjG/4PMCMKES/+mE\nevwhNYYuqg+h//YhlOLJKNfegmIa/rE6d1L/A87IHHpSLut3SuPpGoXdbmfjxo0cPHiQefPmMWbM\nmNPOXrG5dH7zSQOH2uzcc1422XHD91pDrVELTUOsfgmxeR2xd/4ca8YQpqoGiWA/9naXzm83N7K/\nxco952UzKv7kmWTBHv/ZhHr8IZPQ9Q3vI/66EuW6b6HO8G6pW28pmo2E+j/iMmfQnXr5KUm9v0ZR\nX1/Pu+++S05ODueeey6RkWefziWE4F9Vnbz8aTPfnZ7O7FG+WWL2bIbUqIWGwdmOqnWjar2oWg+q\nqwdF60HVrQjFiFBMoJoRigmhmhGKGc2UiGZKQTMlDukmrpNC2P4x4s/PwaJr3cMwITL3+UTBnFDq\nux08vK6W3LgIvj8jo9+ausEc/0CEevzDktB37NjBypUr0XWdBQsWsHjx4rNuczyhC6cD8ZffIyp3\no37vXpSsUd6E4jOKbie+7kV0YyxdaVeftPbLiY1C13U2b97Mrl27mD9/PmPGjBn0c1W2WnlkXS2z\nR8Vxw5RUjH4uyTWQRq26OjHZqjHaqt1f7bUIQwyaMQ5hiEE3xJ7wiEIRGopwgO5EEU4U3Ymi2zC4\n2jA6WlC1bjRjgju5m1NwRmTjjByNbkwY1PWK6N4uuh/7KUrWKJQbbj15EbYQEKwJZVN1Nys2NXDt\npBQuGXf6G4WCNf6BCvX4/Z7QdV1n2bJl3HfffSQlJfHjH/+YZcuWkZOTc8bt6urqEM0N6L99GCU1\nA+Wm21Aih2dt8QHTnViaV2N0NNGZeQO60T2W6FltsauLd999F6PRyIUXXkhs7NCXhe2yazy5oQ6b\nS+fuudkkRfnvWnW/jVp3YrZWEdHzGea+KhSh4YzMwRmZiysyF2dErnerVOpODK42DI4WjM5mjLYa\nTLajADgjRx17jMYVmQ3K6V+7xWKhq6UF8cpvEYf2o37vxyiZZ25rwWRoZ0cCRe9DdXVj0LpQtF4U\n3YUiXCDcX93fa6AYEarp2FnSsa+KGd0Qg26MQzfEnrSGkaYLXv60mf8e7mL53OyzrpAY6gkx1OMf\nSEL3KnNUVVWRkZHhWX9kzpw5bNmy5awJXeza6l4j+5KrUS74SnCePqsmutOuIbrjvyRWP0dn5vW4\nIt3jt/v27ePDDz9k6tSpTJ061ev44yIM3Dc/h1W7WvnhO4f50ZwsSvxcPEPR7Zh79xHRW4G5bz8u\ncyb22BL6khagGZO8nulzEtWEZk5HM6fjOP5vQqC6OjDZjmCyHSWy5VMMjhackaNxRo/BEVWIKyLz\nlCEvJSICbrod1r+H/si9qNd/z2c3mwWM7sDobMHgaMbgbMboaMHgbHUPcbl6EKoZ3WhBN1jQDTEI\nxYxQjYDhWOI2gBLpTu5aH6pwuM+ShBNFtx8bJjt5X3bFwrYWE2Nc8XxtXh4RMe1ouoJQQ+vuT58T\n2gnDit0owoE9dlKgoxowrxJ6W1vbScu7JiUlUVVVddbt9D/92t27GjvBm6f3P0WhL/F8XKY0Eupf\npCPpUv7+3y6OHDnC5Zdf7tOFtFRF4brSFMalRPLw+lqunJDE5eOTfPthJ3TUrj3ENX6IuXc/zqhR\n2GMm0p2yCOGDik6DoijopkTspkTslinuf9KsmKwHMVsPENe4ClXrxhFVgDOqAEf0GBCxxzZVUOZe\nhBhVgP6bh1AO7EW58kaUANx5OyhCd5+lOOox2usw2usxOhpQtV40UzIuUyqaOQVH9DhcpuR+e9Xe\nPr+iWznS3MSaXUeYm6lxYY4do/0zDD2tGJ2tCNWMy5SCZkpFM6fiMh/73pTkmxgCSeiozg4Mrg5U\nVzsGZycGVzuqqwODq9N9XUi3ohuijw0nWtCMCSGV0L0acvn444/ZsWMH3/3udwH48MMPqaqq4pvf\n/OYZt6vdU3H25W6DjKP9AHF1L3K4L4uk0pswR/ivJ9PU4+ThdbWkxpi4fVaG1/VLVWcHkd1biera\ngmKKpTe2DFvsZK+Lffib6urCZD2Auc+d5FVc2CPzcUSNwRlVgGZKRvR2o//vE2C3oX7nnuBpV8KF\n0dF0LHG7HyZHI7oaiSsiC2dEJi5zFq6IjGPXEvw/fVUIwT/2t7NqVyu3zcykPCf2i3+AqnVjcLZi\ncDRjdDR5zhhUrQthTsZpTDqW8FM810R0g8W3Z3RDJfRjPesODM4O9zCfsx2Dsw3V1YbB1YWuRqEb\nE9wX7I0Jx75PQDfGoxks7qpmx/4vxNYN6G+/hvr/PY5iCPx9EH4fQ9+/fz+vvfYaP/nJTwBYvXo1\niqKcdGG0oqKCiooKz89LliwJuXGs2tpaXn/9dWZOncB56bvQFRPO3GsREb6pItQfh0vn1xuO8ml9\nNz+/qJD8pEEmX6Ghdn6GsXUDau9htMQyXMmzMSWMweFwnH37IGTWu9DaK1C792Po2Q9CoMfkoUWN\nwrZ1P9b31hP9vfswjh/mHpWzG9VWj2KrR7XWovZVo9gaEBHJ6FG5iOgc9KhcjPH5OHQf9bYHyerU\nePy/hznSbuUXXyokK26QHRLdgVnvwNVTh2pvRrE1odibUO1NoNkQ5iSEOdH9MCUhzAkIUwLCGAuG\naIQxGtTIoSV+oYPWh+LsRnG5Hxz/3tmB4mhHcbShODvAEHksliR0czLCnIKISEaYkzHFZuBwnT3d\nCZcL21+ex/nJh0Tf+XOMBUWDj9kPLBYLq1at8vxcUlJCSUnJSX/jVULXNI077rhjSBdFQ8Xu3bvZ\nsGEDF1xwAQUFBVhio9Gq3yG6/UP6EubSlzjX6yl5Z7L2QAcrtzfz7WnpzM07+9RG1dlBVNdmIru2\noJkSscWVY4ud5JmpE8oXhk6K3TMGX43JXoPRVo3RWo3eYcNpykDLnYxuSsZlSkYzJSEMsUPvRQqB\noluPnap3unt/zmaMjkaMjkYQGq5j1whcERk4I7JxmTNOqYwVqGNf2+XgoQ9rKEz27ma208Wv6HZP\nr1h1dR47Th0YXF3uMX3diqL1oQgXwhCFrka6L+CiHOsNq6CoCNTPZ0l5rgM4QLgQauTnM6uMse4L\nvYZYdGMcmjHR3cM2JpxxeGogx190tKH//hGIiHKvJxQzzEORZzAs0xa3b99+0rTFK6644qzbhEJC\n1zSN9evXc+TIERYtWkRSknsM8XijUJ1tWJrfxODqpCv1ClxRA6+8M1gH22w8vK6W8mx3ia9TCu8K\nHXNfJVFdmzBZD2OzTMYaNwMt4tQ7bcM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88Rni7F9g9jwMDz4CBYtRJtj5oEC2v3B0Is5+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\nkiRJUUIWdEmSpCghC7okSVKU+F9eANu8YcMRKAAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x106ecfb50>"
       ]
      }
     ],
     "prompt_number": 48
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Other interesting functions can be found in ``scipy.special``. For example, here are some Bessell functions:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from scipy import special\n",
      "x = np.linspace(0, 30, 500)\n",
      "plt.plot(x, special.j0(x), label='j0')\n",
      "plt.plot(x, special.j1(x), label='j1')\n",
      "plt.plot(x, special.jn(3, x), label='j3')\n",
      "plt.legend();"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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01m9SioFVl8Wy6+0hTGYdKT6UrPbGy8jXXkD3le8j8oonfC6iLIhr70AuWon9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\n6MH+P1QJ9EYJTBG4AAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x106e84b90>"
       ]
      }
     ],
     "prompt_number": 67
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "There are **far, far** more options available, and if you want some sort of specialized mathematical function, you can probably find a ufunc version of it in ``scipy.special``.\n",
      "Perhaps the best way to explore this is to use IPython's help or tab-completion features:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from scipy import special\n",
      "special?"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 68
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Notice the key here **UFuncs loop over data for you, so you don't have to write these loops by hand in Python**."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Aggregate Functions\n",
      "\n",
      "Aggregate function are those which collapse an array along a particular dimension.\n",
      "For example, the minimum of an array can be found using NumPy's ``min()`` aggregate:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x = np.random.random(100)\n",
      "x.min()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 50,
       "text": [
        "0.0040929643153089224"
       ]
      }
     ],
     "prompt_number": 50
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Other aggregates exist as well:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Maximum value\n",
      "x.max()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 51,
       "text": [
        "0.96697914536521146"
       ]
      }
     ],
     "prompt_number": 51
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Sum\n",
      "x.sum()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 52,
       "text": [
        "49.430117531542443"
       ]
      }
     ],
     "prompt_number": 52
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Mean\n",
      "x.mean()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 53,
       "text": [
        "0.49430117531542445"
       ]
      }
     ],
     "prompt_number": 53
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Product\n",
      "x.prod()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 54,
       "text": [
        "4.6730597420222299e-46"
       ]
      }
     ],
     "prompt_number": 54
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Standard Deviation\n",
      "x.std()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 55,
       "text": [
        "0.28299025459860538"
       ]
      }
     ],
     "prompt_number": 55
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Variance\n",
      "x.var()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 56,
       "text": [
        "0.080083484197783508"
       ]
      }
     ],
     "prompt_number": 56
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Median\n",
      "np.median(x)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 57,
       "text": [
        "0.51601049164335466"
       ]
      }
     ],
     "prompt_number": 57
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Quantiles\n",
      "np.percentile(x, [25, 50, 75])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 58,
       "text": [
        "array([ 0.25034498,  0.51601049,  0.71508313])"
       ]
      }
     ],
     "prompt_number": 58
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "For multi-dimensional arrays, we can compute aggregates along certain specified dimensions:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "y = np.arange(12).reshape(3, 4)\n",
      "y"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 59,
       "text": [
        "array([[ 0,  1,  2,  3],\n",
        "       [ 4,  5,  6,  7],\n",
        "       [ 8,  9, 10, 11]])"
       ]
      }
     ],
     "prompt_number": 59
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# sum of each column\n",
      "y.sum(0)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 60,
       "text": [
        "array([12, 15, 18, 21])"
       ]
      }
     ],
     "prompt_number": 60
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# sum of each row\n",
      "y.sum(1)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 61,
       "text": [
        "array([ 6, 22, 38])"
       ]
      }
     ],
     "prompt_number": 61
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Keep the dimensions (NumPy 1.7 or later)\n",
      "y.sum(1, keepdims=True)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 62,
       "text": [
        "array([[ 6],\n",
        "       [22],\n",
        "       [38]])"
       ]
      }
     ],
     "prompt_number": 62
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "np.std(y, 0)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 63,
       "text": [
        "array([ 3.26598632,  3.26598632,  3.26598632,  3.26598632])"
       ]
      }
     ],
     "prompt_number": 63
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "As with ufuncs, the key is this: **Aggregates loop over data for you, so you don't have to write the loops yourself in Python.**"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Last Thoughts; Where to Learn More\n",
      "\n",
      "We've just scratched the surface here: there is much more to using NumPy effectively and efficiently. We haven't covered topics like advanced indexing & slicing, masked arrays, structured arrays, linear algebra, fourier transforms, and the many more utilities that are available.\n",
      "\n",
      "If there's one thing to take away from this brief introduction, it's this:\n",
      "\n",
      "<big><font color=\"red\"> If you write Python loops which scan over your data, you're (most likely) doing it wrong. </font></big>\n",
      "<br>\n",
      "\n",
      "NumPy provides routines to replace *loops* with *vectorized* operations, as we've seen above, and this is where it gains its efficiency.\n",
      "\n",
      "For a more in-depth presentiation on the subject of efficient computing with NumPy, you can see [this 1.5 hour tutorial](http://vimeo.com/79820956) I gave at PyData 2013 (view the notebook [here](http://nbviewer.ipython.org/github/jakevdp/2014_fall_ASTR599/blob/master/notebooks/11_EfficientNumpy.ipynb))."
     ]
    }
   ],
   "metadata": {}
  }
 ]
}