mirror of
https://github.com/donnemartin/data-science-ipython-notebooks.git
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1570 lines
32 KiB
Python
1570 lines
32 KiB
Python
{
|
||
"cells": [
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
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||
"source": [
|
||
"<!--BOOK_INFORMATION-->\n",
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||
"<img align=\"left\" style=\"padding-right:10px;\" src=\"figures/PDSH-cover-small.png\">\n",
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||
"*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.*"
|
||
]
|
||
},
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||
{
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||
"cell_type": "markdown",
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||
"metadata": {},
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||
"source": [
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"<!--NAVIGATION-->\n",
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||
"< [Understanding Data Types in Python](02.01-Understanding-Data-Types.ipynb) | [Contents](Index.ipynb) | [Computation on NumPy Arrays: Universal Functions](02.03-Computation-on-arrays-ufuncs.ipynb) >"
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||
]
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||
},
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||
{
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||
"cell_type": "markdown",
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||
"metadata": {},
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"source": [
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"# The Basics of NumPy Arrays"
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||
]
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||
},
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||
{
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||
"cell_type": "markdown",
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"metadata": {},
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||
"source": [
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||
"Data manipulation in Python is nearly synonymous with NumPy array manipulation: even newer tools like Pandas ([Chapter 3](03.00-Introduction-to-Pandas.ipynb)) are built around the NumPy array.\n",
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||
"This section will present several examples of using NumPy array manipulation to access data and subarrays, and to split, reshape, and join the arrays.\n",
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||
"While the types of operations shown here may seem a bit dry and pedantic, they comprise the building blocks of many other examples used throughout the book.\n",
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||
"Get to know them well!\n",
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||
"\n",
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||
"We'll cover a few categories of basic array manipulations here:\n",
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||
"\n",
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||
"- *Attributes of arrays*: Determining the size, shape, memory consumption, and data types of arrays\n",
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||
"- *Indexing of arrays*: Getting and setting the value of individual array elements\n",
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||
"- *Slicing of arrays*: Getting and setting smaller subarrays within a larger array\n",
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||
"- *Reshaping of arrays*: Changing the shape of a given array\n",
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||
"- *Joining and splitting of arrays*: Combining multiple arrays into one, and splitting one array into many"
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||
]
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||
},
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||
{
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||
"cell_type": "markdown",
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"metadata": {},
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"source": [
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||
"## NumPy Array Attributes"
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||
]
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||
},
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||
{
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||
"cell_type": "markdown",
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||
"metadata": {},
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||
"source": [
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||
"First let's discuss some useful array attributes.\n",
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||
"We'll start by defining three random arrays, a one-dimensional, two-dimensional, and three-dimensional array.\n",
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||
"We'll use NumPy's random number generator, which we will *seed* with a set value in order to ensure that the same random arrays are generated each time this code is run:"
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||
]
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||
},
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||
{
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||
"cell_type": "code",
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||
"execution_count": 1,
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||
"metadata": {
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||
"collapsed": false
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||
},
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||
"outputs": [],
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||
"source": [
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||
"import numpy as np\n",
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||
"np.random.seed(0) # seed for reproducibility\n",
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"\n",
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"x1 = np.random.randint(10, size=6) # One-dimensional array\n",
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"x2 = np.random.randint(10, size=(3, 4)) # Two-dimensional array\n",
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||
"x3 = np.random.randint(10, size=(3, 4, 5)) # Three-dimensional array"
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||
]
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||
},
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||
{
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||
"cell_type": "markdown",
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||
"metadata": {},
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||
"source": [
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||
"Each array has attributes ``ndim`` (the number of dimensions), ``shape`` (the size of each dimension), and ``size`` (the total size of the array):"
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||
]
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||
},
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||
{
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||
"cell_type": "code",
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||
"execution_count": 2,
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||
"metadata": {
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||
"collapsed": false
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||
},
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||
"outputs": [
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||
{
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||
"name": "stdout",
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||
"output_type": "stream",
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||
"text": [
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||
"x3 ndim: 3\n",
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||
"x3 shape: (3, 4, 5)\n",
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||
"x3 size: 60\n"
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||
]
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||
}
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||
],
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||
"source": [
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||
"print(\"x3 ndim: \", x3.ndim)\n",
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||
"print(\"x3 shape:\", x3.shape)\n",
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||
"print(\"x3 size: \", x3.size)"
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||
]
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||
},
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||
{
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||
"cell_type": "markdown",
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||
"metadata": {},
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||
"source": [
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||
"Another useful attribute is the ``dtype``, the data type of the array (which we discussed previously in [Understanding Data Types in Python](02.01-Understanding-Data-Types.ipynb)):"
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||
]
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||
},
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||
{
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||
"cell_type": "code",
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||
"execution_count": 3,
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||
"metadata": {
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||
"collapsed": false
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||
},
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||
"outputs": [
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||
{
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||
"name": "stdout",
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||
"output_type": "stream",
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||
"text": [
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||
"dtype: int64\n"
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||
]
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||
}
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||
],
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||
"source": [
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||
"print(\"dtype:\", x3.dtype)"
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||
]
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||
},
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||
{
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||
"cell_type": "markdown",
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||
"metadata": {},
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||
"source": [
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||
"Other attributes include ``itemsize``, which lists the size (in bytes) of each array element, and ``nbytes``, which lists the total size (in bytes) of the array:"
|
||
]
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||
},
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||
{
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||
"cell_type": "code",
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||
"execution_count": 4,
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||
"metadata": {
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||
"collapsed": false
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||
},
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||
"outputs": [
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||
{
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||
"name": "stdout",
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||
"output_type": "stream",
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||
"text": [
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||
"itemsize: 8 bytes\n",
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||
"nbytes: 480 bytes\n"
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||
]
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||
}
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||
],
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||
"source": [
|
||
"print(\"itemsize:\", x3.itemsize, \"bytes\")\n",
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||
"print(\"nbytes:\", x3.nbytes, \"bytes\")"
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||
]
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||
},
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||
{
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||
"cell_type": "markdown",
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||
"metadata": {},
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||
"source": [
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||
"In general, we expect that ``nbytes`` is equal to ``itemsize`` times ``size``."
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||
]
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||
},
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||
{
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||
"cell_type": "markdown",
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||
"metadata": {},
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||
"source": [
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||
"## Array Indexing: Accessing Single Elements"
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||
]
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||
},
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||
{
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||
"cell_type": "markdown",
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||
"metadata": {},
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||
"source": [
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||
"If you are familiar with Python's standard list indexing, indexing in NumPy will feel quite familiar.\n",
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||
"In a one-dimensional array, the $i^{th}$ value (counting from zero) can be accessed by specifying the desired index in square brackets, just as with Python lists:"
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||
]
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||
},
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||
{
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||
"cell_type": "code",
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||
"execution_count": 5,
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||
"metadata": {
|
||
"collapsed": false
|
||
},
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||
"outputs": [
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||
{
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||
"data": {
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||
"text/plain": [
|
||
"array([5, 0, 3, 3, 7, 9])"
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||
]
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||
},
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||
"execution_count": 5,
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||
"metadata": {},
|
||
"output_type": "execute_result"
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||
}
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||
],
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||
"source": [
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||
"x1"
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||
]
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||
},
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||
{
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||
"cell_type": "code",
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||
"execution_count": 6,
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||
"metadata": {
|
||
"collapsed": false
|
||
},
|
||
"outputs": [
|
||
{
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||
"data": {
|
||
"text/plain": [
|
||
"5"
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||
]
|
||
},
|
||
"execution_count": 6,
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||
"metadata": {},
|
||
"output_type": "execute_result"
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||
}
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||
],
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||
"source": [
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||
"x1[0]"
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||
]
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||
},
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||
{
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||
"cell_type": "code",
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||
"execution_count": 7,
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||
"metadata": {
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||
"collapsed": false
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||
},
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||
"outputs": [
|
||
{
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||
"data": {
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||
"text/plain": [
|
||
"7"
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||
]
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||
},
|
||
"execution_count": 7,
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||
"metadata": {},
|
||
"output_type": "execute_result"
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||
}
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||
],
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||
"source": [
|
||
"x1[4]"
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||
]
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||
},
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||
{
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||
"cell_type": "markdown",
|
||
"metadata": {},
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||
"source": [
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||
"To index from the end of the array, you can use negative indices:"
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||
]
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||
},
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||
{
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||
"cell_type": "code",
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||
"execution_count": 8,
|
||
"metadata": {
|
||
"collapsed": false
|
||
},
|
||
"outputs": [
|
||
{
|
||
"data": {
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||
"text/plain": [
|
||
"9"
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||
]
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||
},
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||
"execution_count": 8,
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||
"metadata": {},
|
||
"output_type": "execute_result"
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||
}
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||
],
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||
"source": [
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||
"x1[-1]"
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||
]
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||
},
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||
{
|
||
"cell_type": "code",
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||
"execution_count": 9,
|
||
"metadata": {
|
||
"collapsed": false
|
||
},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"7"
|
||
]
|
||
},
|
||
"execution_count": 9,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
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||
"source": [
|
||
"x1[-2]"
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||
]
|
||
},
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||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"In a multi-dimensional array, items can be accessed using a comma-separated tuple of indices:"
|
||
]
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||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 10,
|
||
"metadata": {
|
||
"collapsed": false
|
||
},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"array([[3, 5, 2, 4],\n",
|
||
" [7, 6, 8, 8],\n",
|
||
" [1, 6, 7, 7]])"
|
||
]
|
||
},
|
||
"execution_count": 10,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"x2"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 11,
|
||
"metadata": {
|
||
"collapsed": false
|
||
},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"3"
|
||
]
|
||
},
|
||
"execution_count": 11,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"x2[0, 0]"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 12,
|
||
"metadata": {
|
||
"collapsed": false
|
||
},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"1"
|
||
]
|
||
},
|
||
"execution_count": 12,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"x2[2, 0]"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 13,
|
||
"metadata": {
|
||
"collapsed": false
|
||
},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"7"
|
||
]
|
||
},
|
||
"execution_count": 13,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"x2[2, -1]"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"Values can also be modified using any of the above index notation:"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 14,
|
||
"metadata": {
|
||
"collapsed": false
|
||
},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"array([[12, 5, 2, 4],\n",
|
||
" [ 7, 6, 8, 8],\n",
|
||
" [ 1, 6, 7, 7]])"
|
||
]
|
||
},
|
||
"execution_count": 14,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"x2[0, 0] = 12\n",
|
||
"x2"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"Keep in mind that, unlike Python lists, NumPy arrays have a fixed type.\n",
|
||
"This means, for example, that if you attempt to insert a floating-point value to an integer array, the value will be silently truncated. Don't be caught unaware by this behavior!"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 15,
|
||
"metadata": {
|
||
"collapsed": false
|
||
},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"array([3, 0, 3, 3, 7, 9])"
|
||
]
|
||
},
|
||
"execution_count": 15,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"x1[0] = 3.14159 # this will be truncated!\n",
|
||
"x1"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Array Slicing: Accessing Subarrays"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"Just as we can use square brackets to access individual array elements, we can also use them to access subarrays with the *slice* notation, marked by the colon (``:``) character.\n",
|
||
"The NumPy slicing syntax follows that of the standard Python list; to access a slice of an array ``x``, use this:\n",
|
||
"``` python\n",
|
||
"x[start:stop:step]\n",
|
||
"```\n",
|
||
"If any of these are unspecified, they default to the values ``start=0``, ``stop=``*``size of dimension``*, ``step=1``.\n",
|
||
"We'll take a look at accessing sub-arrays in one dimension and in multiple dimensions."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"### One-dimensional subarrays"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 16,
|
||
"metadata": {
|
||
"collapsed": false
|
||
},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])"
|
||
]
|
||
},
|
||
"execution_count": 16,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"x = np.arange(10)\n",
|
||
"x"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 17,
|
||
"metadata": {
|
||
"collapsed": false
|
||
},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"array([0, 1, 2, 3, 4])"
|
||
]
|
||
},
|
||
"execution_count": 17,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"x[:5] # first five elements"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 18,
|
||
"metadata": {
|
||
"collapsed": false
|
||
},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"array([5, 6, 7, 8, 9])"
|
||
]
|
||
},
|
||
"execution_count": 18,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"x[5:] # elements after index 5"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 19,
|
||
"metadata": {
|
||
"collapsed": false
|
||
},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"array([4, 5, 6])"
|
||
]
|
||
},
|
||
"execution_count": 19,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"x[4:7] # middle sub-array"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 20,
|
||
"metadata": {
|
||
"collapsed": false
|
||
},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"array([0, 2, 4, 6, 8])"
|
||
]
|
||
},
|
||
"execution_count": 20,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"x[::2] # every other element"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 21,
|
||
"metadata": {
|
||
"collapsed": false
|
||
},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"array([1, 3, 5, 7, 9])"
|
||
]
|
||
},
|
||
"execution_count": 21,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"x[1::2] # every other element, starting at index 1"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"A potentially confusing case is when the ``step`` value is negative.\n",
|
||
"In this case, the defaults for ``start`` and ``stop`` are swapped.\n",
|
||
"This becomes a convenient way to reverse an array:"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 22,
|
||
"metadata": {
|
||
"collapsed": false
|
||
},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"array([9, 8, 7, 6, 5, 4, 3, 2, 1, 0])"
|
||
]
|
||
},
|
||
"execution_count": 22,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"x[::-1] # all elements, reversed"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 23,
|
||
"metadata": {
|
||
"collapsed": false
|
||
},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"array([5, 3, 1])"
|
||
]
|
||
},
|
||
"execution_count": 23,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"x[5::-2] # reversed every other from index 5"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"### Multi-dimensional subarrays\n",
|
||
"\n",
|
||
"Multi-dimensional slices work in the same way, with multiple slices separated by commas.\n",
|
||
"For example:"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 24,
|
||
"metadata": {
|
||
"collapsed": false
|
||
},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"array([[12, 5, 2, 4],\n",
|
||
" [ 7, 6, 8, 8],\n",
|
||
" [ 1, 6, 7, 7]])"
|
||
]
|
||
},
|
||
"execution_count": 24,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"x2"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 25,
|
||
"metadata": {
|
||
"collapsed": false
|
||
},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"array([[12, 5, 2],\n",
|
||
" [ 7, 6, 8]])"
|
||
]
|
||
},
|
||
"execution_count": 25,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"x2[:2, :3] # two rows, three columns"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 26,
|
||
"metadata": {
|
||
"collapsed": false
|
||
},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"array([[12, 2],\n",
|
||
" [ 7, 8],\n",
|
||
" [ 1, 7]])"
|
||
]
|
||
},
|
||
"execution_count": 26,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"x2[:3, ::2] # all rows, every other column"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"Finally, subarray dimensions can even be reversed together:"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 27,
|
||
"metadata": {
|
||
"collapsed": false
|
||
},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"array([[ 7, 7, 6, 1],\n",
|
||
" [ 8, 8, 6, 7],\n",
|
||
" [ 4, 2, 5, 12]])"
|
||
]
|
||
},
|
||
"execution_count": 27,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"x2[::-1, ::-1]"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"#### Accessing array rows and columns\n",
|
||
"\n",
|
||
"One commonly needed routine is accessing of single rows or columns of an array.\n",
|
||
"This can be done by combining indexing and slicing, using an empty slice marked by a single colon (``:``):"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 28,
|
||
"metadata": {
|
||
"collapsed": false
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"[12 7 1]\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"print(x2[:, 0]) # first column of x2"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 29,
|
||
"metadata": {
|
||
"collapsed": false
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"[12 5 2 4]\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"print(x2[0, :]) # first row of x2"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"In the case of row access, the empty slice can be omitted for a more compact syntax:"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 30,
|
||
"metadata": {
|
||
"collapsed": false
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"[12 5 2 4]\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"print(x2[0]) # equivalent to x2[0, :]"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"### Subarrays as no-copy views\n",
|
||
"\n",
|
||
"One important–and extremely useful–thing to know about array slices is that they return *views* rather than *copies* of the array data.\n",
|
||
"This is one area in which NumPy array slicing differs from Python list slicing: in lists, slices will be copies.\n",
|
||
"Consider our two-dimensional array from before:"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 31,
|
||
"metadata": {
|
||
"collapsed": false
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"[[12 5 2 4]\n",
|
||
" [ 7 6 8 8]\n",
|
||
" [ 1 6 7 7]]\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"print(x2)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"Let's extract a $2 \\times 2$ subarray from this:"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 32,
|
||
"metadata": {
|
||
"collapsed": false
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"[[12 5]\n",
|
||
" [ 7 6]]\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"x2_sub = x2[:2, :2]\n",
|
||
"print(x2_sub)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"Now if we modify this subarray, we'll see that the original array is changed! Observe:"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 33,
|
||
"metadata": {
|
||
"collapsed": false
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"[[99 5]\n",
|
||
" [ 7 6]]\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"x2_sub[0, 0] = 99\n",
|
||
"print(x2_sub)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 34,
|
||
"metadata": {
|
||
"collapsed": false
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"[[99 5 2 4]\n",
|
||
" [ 7 6 8 8]\n",
|
||
" [ 1 6 7 7]]\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"print(x2)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"This default behavior is actually quite useful: it means that when we work with large datasets, we can access and process pieces of these datasets without the need to copy the underlying data buffer."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"### Creating copies of arrays\n",
|
||
"\n",
|
||
"Despite the nice features of array views, it is sometimes useful to instead explicitly copy the data within an array or a subarray. This can be most easily done with the ``copy()`` method:"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 35,
|
||
"metadata": {
|
||
"collapsed": false
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"[[99 5]\n",
|
||
" [ 7 6]]\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"x2_sub_copy = x2[:2, :2].copy()\n",
|
||
"print(x2_sub_copy)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"If we now modify this subarray, the original array is not touched:"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 36,
|
||
"metadata": {
|
||
"collapsed": false
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"[[42 5]\n",
|
||
" [ 7 6]]\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"x2_sub_copy[0, 0] = 42\n",
|
||
"print(x2_sub_copy)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 37,
|
||
"metadata": {
|
||
"collapsed": false
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"[[99 5 2 4]\n",
|
||
" [ 7 6 8 8]\n",
|
||
" [ 1 6 7 7]]\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"print(x2)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Reshaping of Arrays\n",
|
||
"\n",
|
||
"Another useful type of operation is reshaping of arrays.\n",
|
||
"The most flexible way of doing this is with the ``reshape`` method.\n",
|
||
"For example, if you want to put the numbers 1 through 9 in a $3 \\times 3$ grid, you can do the following:"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 38,
|
||
"metadata": {
|
||
"collapsed": false
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"[[1 2 3]\n",
|
||
" [4 5 6]\n",
|
||
" [7 8 9]]\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"grid = np.arange(1, 10).reshape((3, 3))\n",
|
||
"print(grid)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"Note that for this to work, the size of the initial array must match the size of the reshaped array. \n",
|
||
"Where possible, the ``reshape`` method will use a no-copy view of the initial array, but with non-contiguous memory buffers this is not always the case.\n",
|
||
"\n",
|
||
"Another common reshaping pattern is the conversion of a one-dimensional array into a two-dimensional row or column matrix.\n",
|
||
"This can be done with the ``reshape`` method, or more easily done by making use of the ``newaxis`` keyword within a slice operation:"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 39,
|
||
"metadata": {
|
||
"collapsed": false
|
||
},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"array([[1, 2, 3]])"
|
||
]
|
||
},
|
||
"execution_count": 39,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"x = np.array([1, 2, 3])\n",
|
||
"\n",
|
||
"# row vector via reshape\n",
|
||
"x.reshape((1, 3))"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 40,
|
||
"metadata": {
|
||
"collapsed": false
|
||
},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"array([[1, 2, 3]])"
|
||
]
|
||
},
|
||
"execution_count": 40,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"# row vector via newaxis\n",
|
||
"x[np.newaxis, :]"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 41,
|
||
"metadata": {
|
||
"collapsed": false
|
||
},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"array([[1],\n",
|
||
" [2],\n",
|
||
" [3]])"
|
||
]
|
||
},
|
||
"execution_count": 41,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"# column vector via reshape\n",
|
||
"x.reshape((3, 1))"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 42,
|
||
"metadata": {
|
||
"collapsed": false
|
||
},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"array([[1],\n",
|
||
" [2],\n",
|
||
" [3]])"
|
||
]
|
||
},
|
||
"execution_count": 42,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"# column vector via newaxis\n",
|
||
"x[:, np.newaxis]"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"We will see this type of transformation often throughout the remainder of the book."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Array Concatenation and Splitting\n",
|
||
"\n",
|
||
"All of the preceding routines worked on single arrays. It's also possible to combine multiple arrays into one, and to conversely split a single array into multiple arrays. We'll take a look at those operations here."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"### Concatenation of arrays\n",
|
||
"\n",
|
||
"Concatenation, or joining of two arrays in NumPy, is primarily accomplished using the routines ``np.concatenate``, ``np.vstack``, and ``np.hstack``.\n",
|
||
"``np.concatenate`` takes a tuple or list of arrays as its first argument, as we can see here:"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 43,
|
||
"metadata": {
|
||
"collapsed": false
|
||
},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"array([1, 2, 3, 3, 2, 1])"
|
||
]
|
||
},
|
||
"execution_count": 43,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"x = np.array([1, 2, 3])\n",
|
||
"y = np.array([3, 2, 1])\n",
|
||
"np.concatenate([x, y])"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"You can also concatenate more than two arrays at once:"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 44,
|
||
"metadata": {
|
||
"collapsed": false
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"[ 1 2 3 3 2 1 99 99 99]\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"z = [99, 99, 99]\n",
|
||
"print(np.concatenate([x, y, z]))"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"It can also be used for two-dimensional arrays:"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 45,
|
||
"metadata": {
|
||
"collapsed": false
|
||
},
|
||
"outputs": [],
|
||
"source": [
|
||
"grid = np.array([[1, 2, 3],\n",
|
||
" [4, 5, 6]])"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 46,
|
||
"metadata": {
|
||
"collapsed": false
|
||
},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"array([[1, 2, 3],\n",
|
||
" [4, 5, 6],\n",
|
||
" [1, 2, 3],\n",
|
||
" [4, 5, 6]])"
|
||
]
|
||
},
|
||
"execution_count": 46,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"# concatenate along the first axis\n",
|
||
"np.concatenate([grid, grid])"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 47,
|
||
"metadata": {
|
||
"collapsed": false
|
||
},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"array([[1, 2, 3, 1, 2, 3],\n",
|
||
" [4, 5, 6, 4, 5, 6]])"
|
||
]
|
||
},
|
||
"execution_count": 47,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"# concatenate along the second axis (zero-indexed)\n",
|
||
"np.concatenate([grid, grid], axis=1)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"For working with arrays of mixed dimensions, it can be clearer to use the ``np.vstack`` (vertical stack) and ``np.hstack`` (horizontal stack) functions:"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 48,
|
||
"metadata": {
|
||
"collapsed": false
|
||
},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"array([[1, 2, 3],\n",
|
||
" [9, 8, 7],\n",
|
||
" [6, 5, 4]])"
|
||
]
|
||
},
|
||
"execution_count": 48,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"x = np.array([1, 2, 3])\n",
|
||
"grid = np.array([[9, 8, 7],\n",
|
||
" [6, 5, 4]])\n",
|
||
"\n",
|
||
"# vertically stack the arrays\n",
|
||
"np.vstack([x, grid])"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 49,
|
||
"metadata": {
|
||
"collapsed": false
|
||
},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"array([[ 9, 8, 7, 99],\n",
|
||
" [ 6, 5, 4, 99]])"
|
||
]
|
||
},
|
||
"execution_count": 49,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"# horizontally stack the arrays\n",
|
||
"y = np.array([[99],\n",
|
||
" [99]])\n",
|
||
"np.hstack([grid, y])"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"Similary, ``np.dstack`` will stack arrays along the third axis."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"### Splitting of arrays\n",
|
||
"\n",
|
||
"The opposite of concatenation is splitting, which is implemented by the functions ``np.split``, ``np.hsplit``, and ``np.vsplit``. For each of these, we can pass a list of indices giving the split points:"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 50,
|
||
"metadata": {
|
||
"collapsed": false
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"[1 2 3] [99 99] [3 2 1]\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"x = [1, 2, 3, 99, 99, 3, 2, 1]\n",
|
||
"x1, x2, x3 = np.split(x, [3, 5])\n",
|
||
"print(x1, x2, x3)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"Notice that *N* split-points, leads to *N + 1* subarrays.\n",
|
||
"The related functions ``np.hsplit`` and ``np.vsplit`` are similar:"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 51,
|
||
"metadata": {
|
||
"collapsed": false
|
||
},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"array([[ 0, 1, 2, 3],\n",
|
||
" [ 4, 5, 6, 7],\n",
|
||
" [ 8, 9, 10, 11],\n",
|
||
" [12, 13, 14, 15]])"
|
||
]
|
||
},
|
||
"execution_count": 51,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"grid = np.arange(16).reshape((4, 4))\n",
|
||
"grid"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 52,
|
||
"metadata": {
|
||
"collapsed": false
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"[[0 1 2 3]\n",
|
||
" [4 5 6 7]]\n",
|
||
"[[ 8 9 10 11]\n",
|
||
" [12 13 14 15]]\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"upper, lower = np.vsplit(grid, [2])\n",
|
||
"print(upper)\n",
|
||
"print(lower)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 53,
|
||
"metadata": {
|
||
"collapsed": false
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"[[ 0 1]\n",
|
||
" [ 4 5]\n",
|
||
" [ 8 9]\n",
|
||
" [12 13]]\n",
|
||
"[[ 2 3]\n",
|
||
" [ 6 7]\n",
|
||
" [10 11]\n",
|
||
" [14 15]]\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"left, right = np.hsplit(grid, [2])\n",
|
||
"print(left)\n",
|
||
"print(right)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"Similarly, ``np.dsplit`` will split arrays along the third axis."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"<!--NAVIGATION-->\n",
|
||
"< [Understanding Data Types in Python](02.01-Understanding-Data-Types.ipynb) | [Contents](Index.ipynb) | [Computation on NumPy Arrays: Universal Functions](02.03-Computation-on-arrays-ufuncs.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
|
||
}
|