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Add new numpy notebooks 

Source: https://github.com/jakevdp/PythonDataScienceHandbook unmodified
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Donne Martin 2017-03-13 04:31:53 -04:00
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<!--BOOK_INFORMATION-->\n",
"<img align=\"left\" style=\"padding-right:10px;\" src=\"figures/PDSH-cover-small.png\">\n",
"*This notebook contains an excerpt from the [Python Data Science Handbook](http://shop.oreilly.com/product/0636920034919.do) by Jake VanderPlas; the content is available [on GitHub](https://github.com/jakevdp/PythonDataScienceHandbook).*\n",
"\n",
"*The text is released under the [CC-BY-NC-ND license](https://creativecommons.org/licenses/by-nc-nd/3.0/us/legalcode), and code is released under the [MIT license](https://opensource.org/licenses/MIT). If you find this content useful, please consider supporting the work by [buying the book](http://shop.oreilly.com/product/0636920034919.do)!*\n",
"\n",
"*No changes were made to the contents of this notebook from the original.*"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<!--NAVIGATION-->\n",
"< [More IPython Resources](01.08-More-IPython-Resources.ipynb) | [Contents](Index.ipynb) | [Understanding Data Types in Python](02.01-Understanding-Data-Types.ipynb) >"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Introduction to NumPy\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This chapter, along with chapter 3, outlines techniques for effectively loading, storing, and manipulating in-memory data in Python.\n",
"The topic is very broad: datasets can come from a wide range of sources and a wide range of formats, including be collections of documents, collections of images, collections of sound clips, collections of numerical measurements, or nearly anything else.\n",
"Despite this apparent heterogeneity, it will help us to think of all data fundamentally as arrays of numbers.\n",
"\n",
"For example, images–particularly digital images–can be thought of as simply two-dimensional arrays of numbers representing pixel brightness across the area.\n",
"Sound clips can be thought of as one-dimensional arrays of intensity versus time.\n",
"Text can be converted in various ways into numerical representations, perhaps binary digits representing the frequency of certain words or pairs of words.\n",
"No matter what the data are, the first step in making it analyzable will be to transform them into arrays of numbers.\n",
"(We will discuss some specific examples of this process later in [Feature Engineering](05.04-Feature-Engineering.ipynb))\n",
"\n",
"For this reason, efficient storage and manipulation of numerical arrays is absolutely fundamental to the process of doing data science.\n",
"We'll now take a look at the specialized tools that Python has for handling such numerical arrays: the NumPy package, and the Pandas package (discussed in Chapter 3).\n",
"\n",
"This chapter will cover NumPy in detail. NumPy (short for *Numerical Python*) provides an efficient interface to store and operate on dense data buffers.\n",
"In some ways, NumPy arrays are like Python's built-in ``list`` type, but NumPy arrays provide much more efficient storage and data operations as the arrays grow larger in size.\n",
"NumPy arrays form the core of nearly the entire ecosystem of data science tools in Python, so time spent learning to use NumPy effectively will be valuable no matter what aspect of data science interests you.\n",
"\n",
"If you followed the advice outlined in the Preface and installed the Anaconda stack, you already have NumPy installed and ready to go.\n",
"If you're more the do-it-yourself type, you can go to http://www.numpy.org/ and follow the installation instructions found there.\n",
"Once you do, you can import NumPy and double-check the version:"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"'1.11.1'"
]
},
"execution_count": 1,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"import numpy\n",
"numpy.__version__"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"For the pieces of the package discussed here, I'd recommend NumPy version 1.8 or later.\n",
"By convention, you'll find that most people in the SciPy/PyData world will import NumPy using ``np`` as an alias:"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"import numpy as np"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Throughout this chapter, and indeed the rest of the book, you'll find that this is the way we will import and use NumPy."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Reminder about Built In Documentation\n",
"\n",
"As you read through this chapter, don't forget that IPython gives you the ability to quickly explore the contents of a package (by using the tab-completion feature), as well as the documentation of various functions (using the ``?`` character – Refer back to [Help and Documentation in IPython](01.01-Help-And-Documentation.ipynb)).\n",
"\n",
"For example, to display all the contents of the numpy namespace, you can type this:\n",
"\n",
"```ipython\n",
"In [3]: np.<TAB>\n",
"```\n",
"\n",
"And to display NumPy's built-in documentation, you can use this:\n",
"\n",
"```ipython\n",
"In [4]: np?\n",
"```\n",
"\n",
"More detailed documentation, along with tutorials and other resources, can be found at http://www.numpy.org."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<!--NAVIGATION-->\n",
"< [More IPython Resources](01.08-More-IPython-Resources.ipynb) | [Contents](Index.ipynb) | [Understanding Data Types in Python](02.01-Understanding-Data-Types.ipynb) >"
]
}
],
"metadata": {
"anaconda-cloud": {},
"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
}

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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<!--BOOK_INFORMATION-->\n",
"<img align=\"left\" style=\"padding-right:10px;\" src=\"figures/PDSH-cover-small.png\">\n",
"*This notebook contains an excerpt from the [Python Data Science Handbook](http://shop.oreilly.com/product/0636920034919.do) by Jake VanderPlas; the content is available [on GitHub](https://github.com/jakevdp/PythonDataScienceHandbook).*\n",
"\n",
"*The text is released under the [CC-BY-NC-ND license](https://creativecommons.org/licenses/by-nc-nd/3.0/us/legalcode), and code is released under the [MIT license](https://opensource.org/licenses/MIT). If you find this content useful, please consider supporting the work by [buying the book](http://shop.oreilly.com/product/0636920034919.do)!*\n",
"\n",
"*No changes were made to the contents of this notebook from the original.*"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<!--NAVIGATION-->\n",
"< [Introduction to NumPy](02.00-Introduction-to-NumPy.ipynb) | [Contents](Index.ipynb) | [The Basics of NumPy Arrays](02.02-The-Basics-Of-NumPy-Arrays.ipynb) >"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Understanding Data Types in Python"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Effective data-driven science and computation requires understanding how data is stored and manipulated.\n",
"This section outlines and contrasts how arrays of data are handled in the Python language itself, and how NumPy improves on this.\n",
"Understanding this difference is fundamental to understanding much of the material throughout the rest of the book.\n",
"\n",
"Users of Python are often drawn-in by its ease of use, one piece of which is dynamic typing.\n",
"While a statically-typed language like C or Java requires each variable to be explicitly declared, a dynamically-typed language like Python skips this specification. For example, in C you might specify a particular operation as follows:\n",
"\n",
"```C\n",
"/* C code */\n",
"int result = 0;\n",
"for(int i=0; i<100; i++){\n",
" result += i;\n",
"}\n",
"```\n",
"\n",
"While in Python the equivalent operation could be written this way:\n",
"\n",
"```python\n",
"# Python code\n",
"result = 0\n",
"for i in range(100):\n",
" result += i\n",
"```\n",
"\n",
"Notice the main difference: in C, the data types of each variable are explicitly declared, while in Python the types are dynamically inferred. This means, for example, that we can assign any kind of data to any variable:\n",
"\n",
"```python\n",
"# Python code\n",
"x = 4\n",
"x = \"four\"\n",
"```\n",
"\n",
"Here we've switched the contents of ``x`` from an integer to a string. The same thing in C would lead (depending on compiler settings) to a compilation error or other unintented consequences:\n",
"\n",
"```C\n",
"/* C code */\n",
"int x = 4;\n",
"x = \"four\"; // FAILS\n",
"```\n",
"\n",
"This sort of flexibility is one piece that makes Python and other dynamically-typed languages convenient and easy to use.\n",
"Understanding *how* this works is an important piece of learning to analyze data efficiently and effectively with Python.\n",
"But what this type-flexibility also points to is the fact that Python variables are more than just their value; they also contain extra information about the type of the value. We'll explore this more in the sections that follow."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## A Python Integer Is More Than Just an Integer\n",
"\n",
"The standard Python implementation is written in C.\n",
"This means that every Python object is simply a cleverly-disguised C structure, which contains not only its value, but other information as well. For example, when we define an integer in Python, such as ``x = 10000``, ``x`` is not just a \"raw\" integer. It's actually a pointer to a compound C structure, which contains several values.\n",
"Looking through the Python 3.4 source code, we find that the integer (long) type definition effectively looks like this (once the C macros are expanded):\n",
"\n",
"```C\n",
"struct _longobject {\n",
" long ob_refcnt;\n",
" PyTypeObject *ob_type;\n",
" size_t ob_size;\n",
" long ob_digit[1];\n",
"};\n",
"```\n",
"\n",
"A single integer in Python 3.4 actually contains four pieces:\n",
"\n",
"- ``ob_refcnt``, a reference count that helps Python silently handle memory allocation and deallocation\n",
"- ``ob_type``, which encodes the type of the variable\n",
"- ``ob_size``, which specifies the size of the following data members\n",
"- ``ob_digit``, which contains the actual integer value that we expect the Python variable to represent.\n",
"\n",
"This means that there is some overhead in storing an integer in Python as compared to an integer in a compiled language like C, as illustrated in the following figure:"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"![Integer Memory Layout](figures/cint_vs_pyint.png)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Here ``PyObject_HEAD`` is the part of the structure containing the reference count, type code, and other pieces mentioned before.\n",
"\n",
"Notice the difference here: a C integer is essentially a label for a position in memory whose bytes encode an integer value.\n",
"A Python integer is a pointer to a position in memory containing all the Python object information, including the bytes that contain the integer value.\n",
"This extra information in the Python integer structure is what allows Python to be coded so freely and dynamically.\n",
"All this additional information in Python types comes at a cost, however, which becomes especially apparent in structures that combine many of these objects."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## A Python List Is More Than Just a List\n",
"\n",
"Let's consider now what happens when we use a Python data structure that holds many Python objects.\n",
"The standard mutable multi-element container in Python is the list.\n",
"We can create a list of integers as follows:"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]"
]
},
"execution_count": 1,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"L = list(range(10))\n",
"L"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"int"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"type(L[0])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Or, similarly, a list of strings:"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"['0', '1', '2', '3', '4', '5', '6', '7', '8', '9']"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"L2 = [str(c) for c in L]\n",
"L2"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"str"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"type(L2[0])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Because of Python's dynamic typing, we can even create heterogeneous lists:"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"[bool, str, float, int]"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"L3 = [True, \"2\", 3.0, 4]\n",
"[type(item) for item in L3]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"But this flexibility comes at a cost: to allow these flexible types, each item in the list must contain its own type info, reference count, and other information–that is, each item is a complete Python object.\n",
"In the special case that all variables are of the same type, much of this information is redundant: it can be much more efficient to store data in a fixed-type array.\n",
"The difference between a dynamic-type list and a fixed-type (NumPy-style) array is illustrated in the following figure:"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"![Array Memory Layout](figures/array_vs_list.png)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"At the implementation level, the array essentially contains a single pointer to one contiguous block of data.\n",
"The Python list, on the other hand, contains a pointer to a block of pointers, each of which in turn points to a full Python object like the Python integer we saw earlier.\n",
"Again, the advantage of the list is flexibility: because each list element is a full structure containing both data and type information, the list can be filled with data of any desired type.\n",
"Fixed-type NumPy-style arrays lack this flexibility, but are much more efficient for storing and manipulating data."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Fixed-Type Arrays in Python\n",
"\n",
"Python offers several different options for storing data in efficient, fixed-type data buffers.\n",
"The built-in ``array`` module (available since Python 3.3) can be used to create dense arrays of a uniform type:"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array('i', [0, 1, 2, 3, 4, 5, 6, 7, 8, 9])"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"import array\n",
"L = list(range(10))\n",
"A = array.array('i', L)\n",
"A"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Here ``'i'`` is a type code indicating the contents are integers.\n",
"\n",
"Much more useful, however, is the ``ndarray`` object of the NumPy package.\n",
"While Python's ``array`` object provides efficient storage of array-based data, NumPy adds to this efficient *operations* on that data.\n",
"We will explore these operations in later sections; here we'll demonstrate several ways of creating a NumPy array.\n",
"\n",
"We'll start with the standard NumPy import, under the alias ``np``:"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"import numpy as np"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Creating Arrays from Python Lists\n",
"\n",
"First, we can use ``np.array`` to create arrays from Python lists:"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([1, 4, 2, 5, 3])"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# integer array:\n",
"np.array([1, 4, 2, 5, 3])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Remember that unlike Python lists, NumPy is constrained to arrays that all contain the same type.\n",
"If types do not match, NumPy will upcast if possible (here, integers are up-cast to floating point):"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([ 3.14, 4. , 2. , 3. ])"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"np.array([3.14, 4, 2, 3])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"If we want to explicitly set the data type of the resulting array, we can use the ``dtype`` keyword:"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([ 1., 2., 3., 4.], dtype=float32)"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"np.array([1, 2, 3, 4], dtype='float32')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Finally, unlike Python lists, NumPy arrays can explicitly be multi-dimensional; here's one way of initializing a multidimensional array using a list of lists:"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([[2, 3, 4],\n",
" [4, 5, 6],\n",
" [6, 7, 8]])"
]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# nested lists result in multi-dimensional arrays\n",
"np.array([range(i, i + 3) for i in [2, 4, 6]])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The inner lists are treated as rows of the resulting two-dimensional array."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Creating Arrays from Scratch\n",
"\n",
"Especially for larger arrays, it is more efficient to create arrays from scratch using routines built into NumPy.\n",
"Here are several examples:"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0])"
]
},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Create a length-10 integer array filled with zeros\n",
"np.zeros(10, dtype=int)"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([[ 1., 1., 1., 1., 1.],\n",
" [ 1., 1., 1., 1., 1.],\n",
" [ 1., 1., 1., 1., 1.]])"
]
},
"execution_count": 13,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Create a 3x5 floating-point array filled with ones\n",
"np.ones((3, 5), dtype=float)"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([[ 3.14, 3.14, 3.14, 3.14, 3.14],\n",
" [ 3.14, 3.14, 3.14, 3.14, 3.14],\n",
" [ 3.14, 3.14, 3.14, 3.14, 3.14]])"
]
},
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Create a 3x5 array filled with 3.14\n",
"np.full((3, 5), 3.14)"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([ 0, 2, 4, 6, 8, 10, 12, 14, 16, 18])"
]
},
"execution_count": 15,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Create an array filled with a linear sequence\n",
"# Starting at 0, ending at 20, stepping by 2\n",
"# (this is similar to the built-in range() function)\n",
"np.arange(0, 20, 2)"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([ 0. , 0.25, 0.5 , 0.75, 1. ])"
]
},
"execution_count": 16,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Create an array of five values evenly spaced between 0 and 1\n",
"np.linspace(0, 1, 5)"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([[ 0.99844933, 0.52183819, 0.22421193],\n",
" [ 0.08007488, 0.45429293, 0.20941444],\n",
" [ 0.14360941, 0.96910973, 0.946117 ]])"
]
},
"execution_count": 17,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Create a 3x3 array of uniformly distributed\n",
"# random values between 0 and 1\n",
"np.random.random((3, 3))"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([[ 1.51772646, 0.39614948, -0.10634696],\n",
" [ 0.25671348, 0.00732722, 0.37783601],\n",
" [ 0.68446945, 0.15926039, -0.70744073]])"
]
},
"execution_count": 18,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Create a 3x3 array of normally distributed random values\n",
"# with mean 0 and standard deviation 1\n",
"np.random.normal(0, 1, (3, 3))"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([[2, 3, 4],\n",
" [5, 7, 8],\n",
" [0, 5, 0]])"
]
},
"execution_count": 19,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Create a 3x3 array of random integers in the interval [0, 10)\n",
"np.random.randint(0, 10, (3, 3))"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([[ 1., 0., 0.],\n",
" [ 0., 1., 0.],\n",
" [ 0., 0., 1.]])"
]
},
"execution_count": 20,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Create a 3x3 identity matrix\n",
"np.eye(3)"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([ 1., 1., 1.])"
]
},
"execution_count": 21,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Create an uninitialized array of three integers\n",
"# The values will be whatever happens to already exist at that memory location\n",
"np.empty(3)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## NumPy Standard Data Types\n",
"\n",
"NumPy arrays contain values of a single type, so it is important to have detailed knowledge of those types and their limitations.\n",
"Because NumPy is built in C, the types will be familiar to users of C, Fortran, and other related languages.\n",
"\n",
"The standard NumPy data types are listed in the following table.\n",
"Note that when constructing an array, they can be specified using a string:\n",
"\n",
"```python\n",
"np.zeros(10, dtype='int16')\n",
"```\n",
"\n",
"Or using the associated NumPy object:\n",
"\n",
"```python\n",
"np.zeros(10, dtype=np.int16)\n",
"```"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"| Data type\t | Description |\n",
"|---------------|-------------|\n",
"| ``bool_`` | Boolean (True or False) stored as a byte |\n",
"| ``int_`` | Default integer type (same as C ``long``; normally either ``int64`` or ``int32``)| \n",
"| ``intc`` | Identical to C ``int`` (normally ``int32`` or ``int64``)| \n",
"| ``intp`` | Integer used for indexing (same as C ``ssize_t``; normally either ``int32`` or ``int64``)| \n",
"| ``int8`` | Byte (-128 to 127)| \n",
"| ``int16`` | Integer (-32768 to 32767)|\n",
"| ``int32`` | Integer (-2147483648 to 2147483647)|\n",
"| ``int64`` | Integer (-9223372036854775808 to 9223372036854775807)| \n",
"| ``uint8`` | Unsigned integer (0 to 255)| \n",
"| ``uint16`` | Unsigned integer (0 to 65535)| \n",
"| ``uint32`` | Unsigned integer (0 to 4294967295)| \n",
"| ``uint64`` | Unsigned integer (0 to 18446744073709551615)| \n",
"| ``float_`` | Shorthand for ``float64``.| \n",
"| ``float16`` | Half precision float: sign bit, 5 bits exponent, 10 bits mantissa| \n",
"| ``float32`` | Single precision float: sign bit, 8 bits exponent, 23 bits mantissa| \n",
"| ``float64`` | Double precision float: sign bit, 11 bits exponent, 52 bits mantissa| \n",
"| ``complex_`` | Shorthand for ``complex128``.| \n",
"| ``complex64`` | Complex number, represented by two 32-bit floats| \n",
"| ``complex128``| Complex number, represented by two 64-bit floats| "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"More advanced type specification is possible, such as specifying big or little endian numbers; for more information, refer to the [NumPy documentation](http://numpy.org/).\n",
"NumPy also supports compound data types, which will be covered in [Structured Data: NumPy's Structured Arrays](02.09-Structured-Data-NumPy.ipynb)."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<!--NAVIGATION-->\n",
"< [Introduction to NumPy](02.00-Introduction-to-NumPy.ipynb) | [Contents](Index.ipynb) | [The Basics of NumPy Arrays](02.02-The-Basics-Of-NumPy-Arrays.ipynb) >"
]
}
],
"metadata": {
"anaconda-cloud": {},
"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"
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"nbformat": 4,
"nbformat_minor": 0
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<!--BOOK_INFORMATION-->\n",
"<img align=\"left\" style=\"padding-right:10px;\" src=\"figures/PDSH-cover-small.png\">\n",
"*This notebook contains an excerpt from the [Python Data Science Handbook](http://shop.oreilly.com/product/0636920034919.do) by Jake VanderPlas; the content is available [on GitHub](https://github.com/jakevdp/PythonDataScienceHandbook).*\n",
"\n",
"*The text is released under the [CC-BY-NC-ND license](https://creativecommons.org/licenses/by-nc-nd/3.0/us/legalcode), and code is released under the [MIT license](https://opensource.org/licenses/MIT). If you find this content useful, please consider supporting the work by [buying the book](http://shop.oreilly.com/product/0636920034919.do)!*\n",
"\n",
"*No changes were made to the contents of this notebook from the original.*"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<!--NAVIGATION-->\n",
"< [Sorting Arrays](02.08-Sorting.ipynb) | [Contents](Index.ipynb) | [Data Manipulation with Pandas](03.00-Introduction-to-Pandas.ipynb) >"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Structured Data: NumPy's Structured Arrays"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"While often our data can be well represented by a homogeneous array of values, sometimes this is not the case. This section demonstrates the use of NumPy's *structured arrays* and *record arrays*, which provide efficient storage for compound, heterogeneous data. While the patterns shown here are useful for simple operations, scenarios like this often lend themselves to the use of Pandas ``Dataframe``s, which we'll explore in [Chapter 3](03.00-Introduction-to-Pandas.ipynb)."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"import numpy as np"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Imagine that we have several categories of data on a number of people (say, name, age, and weight), and we'd like to store these values for use in a Python program.\n",
"It would be possible to store these in three separate arrays:"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"name = ['Alice', 'Bob', 'Cathy', 'Doug']\n",
"age = [25, 45, 37, 19]\n",
"weight = [55.0, 85.5, 68.0, 61.5]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"But this is a bit clumsy. There's nothing here that tells us that the three arrays are related; it would be more natural if we could use a single structure to store all of this data.\n",
"NumPy can handle this through structured arrays, which are arrays with compound data types.\n",
"\n",
"Recall that previously we created a simple array using an expression like this:"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"x = np.zeros(4, dtype=int)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can similarly create a structured array using a compound data type specification:"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[('name', '<U10'), ('age', '<i4'), ('weight', '<f8')]\n"
]
}
],
"source": [
"# Use a compound data type for structured arrays\n",
"data = np.zeros(4, dtype={'names':('name', 'age', 'weight'),\n",
" 'formats':('U10', 'i4', 'f8')})\n",
"print(data.dtype)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Here ``'U10'`` translates to \"Unicode string of maximum length 10,\" ``'i4'`` translates to \"4-byte (i.e., 32 bit) integer,\" and ``'f8'`` translates to \"8-byte (i.e., 64 bit) float.\"\n",
"We'll discuss other options for these type codes in the following section.\n",
"\n",
"Now that we've created an empty container array, we can fill the array with our lists of values:"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[('Alice', 25, 55.0) ('Bob', 45, 85.5) ('Cathy', 37, 68.0)\n",
" ('Doug', 19, 61.5)]\n"
]
}
],
"source": [
"data['name'] = name\n",
"data['age'] = age\n",
"data['weight'] = weight\n",
"print(data)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"As we had hoped, the data is now arranged together in one convenient block of memory.\n",
"\n",
"The handy thing with structured arrays is that you can now refer to values either by index or by name:"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array(['Alice', 'Bob', 'Cathy', 'Doug'], \n",
" dtype='<U10')"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Get all names\n",
"data['name']"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"('Alice', 25, 55.0)"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Get first row of data\n",
"data[0]"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"'Doug'"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Get the name from the last row\n",
"data[-1]['name']"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Using Boolean masking, this even allows you to do some more sophisticated operations such as filtering on age:"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array(['Alice', 'Doug'], \n",
" dtype='<U10')"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Get names where age is under 30\n",
"data[data['age'] < 30]['name']"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Note that if you'd like to do any operations that are any more complicated than these, you should probably consider the Pandas package, covered in the next chapter.\n",
"As we'll see, Pandas provides a ``Dataframe`` object, which is a structure built on NumPy arrays that offers a variety of useful data manipulation functionality similar to what we've shown here, as well as much, much more."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Creating Structured Arrays\n",
"\n",
"Structured array data types can be specified in a number of ways.\n",
"Earlier, we saw the dictionary method:"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"dtype([('name', '<U10'), ('age', '<i4'), ('weight', '<f8')])"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"np.dtype({'names':('name', 'age', 'weight'),\n",
" 'formats':('U10', 'i4', 'f8')})"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"For clarity, numerical types can be specified using Python types or NumPy ``dtype``s instead:"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"dtype([('name', '<U10'), ('age', '<i8'), ('weight', '<f4')])"
]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"np.dtype({'names':('name', 'age', 'weight'),\n",
" 'formats':((np.str_, 10), int, np.float32)})"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"A compound type can also be specified as a list of tuples:"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"dtype([('name', 'S10'), ('age', '<i4'), ('weight', '<f8')])"
]
},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"np.dtype([('name', 'S10'), ('age', 'i4'), ('weight', 'f8')])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"If the names of the types do not matter to you, you can specify the types alone in a comma-separated string:"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"dtype([('f0', 'S10'), ('f1', '<i4'), ('f2', '<f8')])"
]
},
"execution_count": 13,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"np.dtype('S10,i4,f8')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The shortened string format codes may seem confusing, but they are built on simple principles.\n",
"The first (optional) character is ``<`` or ``>``, which means \"little endian\" or \"big endian,\" respectively, and specifies the ordering convention for significant bits.\n",
"The next character specifies the type of data: characters, bytes, ints, floating points, and so on (see the table below).\n",
"The last character or characters represents the size of the object in bytes.\n",
"\n",
"| Character | Description | Example |\n",
"| --------- | ----------- | ------- | \n",
"| ``'b'`` | Byte | ``np.dtype('b')`` |\n",
"| ``'i'`` | Signed integer | ``np.dtype('i4') == np.int32`` |\n",
"| ``'u'`` | Unsigned integer | ``np.dtype('u1') == np.uint8`` |\n",
"| ``'f'`` | Floating point | ``np.dtype('f8') == np.int64`` |\n",
"| ``'c'`` | Complex floating point| ``np.dtype('c16') == np.complex128``|\n",
"| ``'S'``, ``'a'`` | String | ``np.dtype('S5')`` |\n",
"| ``'U'`` | Unicode string | ``np.dtype('U') == np.str_`` |\n",
"| ``'V'`` | Raw data (void) | ``np.dtype('V') == np.void`` |"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## More Advanced Compound Types\n",
"\n",
"It is possible to define even more advanced compound types.\n",
"For example, you can create a type where each element contains an array or matrix of values.\n",
"Here, we'll create a data type with a ``mat`` component consisting of a $3\\times 3$ floating-point matrix:"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"(0, [[0.0, 0.0, 0.0], [0.0, 0.0, 0.0], [0.0, 0.0, 0.0]])\n",
"[[ 0. 0. 0.]\n",
" [ 0. 0. 0.]\n",
" [ 0. 0. 0.]]\n"
]
}
],
"source": [
"tp = np.dtype([('id', 'i8'), ('mat', 'f8', (3, 3))])\n",
"X = np.zeros(1, dtype=tp)\n",
"print(X[0])\n",
"print(X['mat'][0])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now each element in the ``X`` array consists of an ``id`` and a $3\\times 3$ matrix.\n",
"Why would you use this rather than a simple multidimensional array, or perhaps a Python dictionary?\n",
"The reason is that this NumPy ``dtype`` directly maps onto a C structure definition, so the buffer containing the array content can be accessed directly within an appropriately written C program.\n",
"If you find yourself writing a Python interface to a legacy C or Fortran library that manipulates structured data, you'll probably find structured arrays quite useful!"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## RecordArrays: Structured Arrays with a Twist\n",
"\n",
"NumPy also provides the ``np.recarray`` class, which is almost identical to the structured arrays just described, but with one additional feature: fields can be accessed as attributes rather than as dictionary keys.\n",
"Recall that we previously accessed the ages by writing:"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([25, 45, 37, 19], dtype=int32)"
]
},
"execution_count": 15,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"data['age']"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"If we view our data as a record array instead, we can access this with slightly fewer keystrokes:"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([25, 45, 37, 19], dtype=int32)"
]
},
"execution_count": 16,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"data_rec = data.view(np.recarray)\n",
"data_rec.age"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The downside is that for record arrays, there is some extra overhead involved in accessing the fields, even when using the same syntax. We can see this here:"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"1000000 loops, best of 3: 241 ns per loop\n",
"100000 loops, best of 3: 4.61 µs per loop\n",
"100000 loops, best of 3: 7.27 µs per loop\n"
]
}
],
"source": [
"%timeit data['age']\n",
"%timeit data_rec['age']\n",
"%timeit data_rec.age"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Whether the more convenient notation is worth the additional overhead will depend on your own application."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## On to Pandas\n",
"\n",
"This section on structured and record arrays is purposely at the end of this chapter, because it leads so well into the next package we will cover: Pandas.\n",
"Structured arrays like the ones discussed here are good to know about for certain situations, especially in case you're using NumPy arrays to map onto binary data formats in C, Fortran, or another language.\n",
"For day-to-day use of structured data, the Pandas package is a much better choice, and we'll dive into a full discussion of it in the chapter that follows."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<!--NAVIGATION-->\n",
"< [Sorting Arrays](02.08-Sorting.ipynb) | [Contents](Index.ipynb) | [Data Manipulation with Pandas](03.00-Introduction-to-Pandas.ipynb) >"
]
}
],
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"display_name": "Python 3",
"language": "python",
"name": "python3"
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