深入学习NumPy：Python科学计算库指南

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"Python的NumPy模块是一份详尽的参考文档，涵盖了从基础到高级的NumPy使用知识，包括数据类型、数组创建、输入/输出、索引、广播、字节顺序转换、结构化数组、性能优化以及与C、Fortran、C++等语言的接口。这份文档适用于学习和提升NumPy技能的Python开发人员。" NumPy是Python科学计算的核心库，提供了高效的多维数组对象和一系列用于处理这些数组的工具。以下是关于NumPy的一些关键知识点： 1. **什么是NumPy?** NumPy是Numerical Python的简称，它是Python编程语言的一个库，专为处理大型多维数组和矩阵而设计。它提供了大量的数学和逻辑操作，使得数据处理变得高效且简洁。 2. **数据类型(Datatypes)** NumPy支持多种数据类型，如int, float, bool, complex等，以及特定大小的整数和浮点数类型，如int32、float64等。它还允许创建自定义数据类型，以适应特定的应用需求。 3. **数组创建(Array creation)** NumPy提供了多种创建数组的方法，如`numpy.array()`、`numpy.zeros()`、`numpy.ones()`、`numpy.empty()`等。此外，可以使用列表推导式或直接从已有的序列创建数组。 4. **输入/输出(I/O with Numpy)** NumPy能够读写各种数据文件，如文本文件、二进制文件等，主要通过`numpy.save()`、`numpy.load()`、`numpy.savetxt()`和`numpy.loadtxt()`等函数。 5. **索引(Indexing)** NumPy数组支持多维索引，包括单个元素的索引、切片索引、整数索引和布尔索引。这使得对数组的子集进行选择、修改和操作变得非常方便。 6. **广播(Broadcasting)** 广播是NumPy处理不同形状数组间运算的一种机制，允许小数组在尺寸上“扩展”以匹配大数组，从而实现对它们的并行操作，无需显式地复制数据。 7. **字节顺序转换(Byte-swapping)** NumPy支持在不同的字节顺序之间转换数组，这对于跨平台的数据交换至关重要。 8. **结构化数组(Structured arrays, aka “Record arrays”)** 结构化数组允许在一个数组中存储不同类型的元素，类似于数据库中的记录，每个元素都是一个包含多个字段的结构。 9. **子类化ndarray** NumPy的`ndarray`类可以被子类化，以便扩展其功能或添加自定义行为。 10. **性能(Performance)** NumPy数组操作通常比Python内置的列表操作更快，因为它们在底层使用了高效的C代码。此外，使用向量化操作可以进一步提高性能，避免循环和条件语句。 11. **与其他语言的接口** NumPy提供了与C、Fortran和C++等语言的接口，允许直接操作和使用NumPy数组，以实现更高效的计算或利用现有库。 12. **NumPy C-API** NumPy的C-API允许开发者用C或C++编写与NumPy数组交互的低级代码，用于性能关键的部分。 13. **编写自己的通用函数(Ufuncs)** NumPy的通用函数（Ufuncs）是用于数组操作的一类高效函数，可以使用C API来编写自定义的Ufuncs，以实现特定的数值运算。 14. **方法vs.函数(Methods vs. Functions)** NumPy中的数组方法和函数在功能上类似，但调用方式不同。方法是针对特定数组对象的，而函数则是全局的，可以作用于任何数组。这份文档详细解释了NumPy的各个方面，无论你是初学者还是有经验的开发者，都可以从中找到有价值的信息来提升你的Python数据处理能力。

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NumPy User Guide , Release 1.9.0.dev-ce6f348

and types

>>> x = np.array([[ 1.+0.j, 2.+0.j], [ 0.+0.j, 0.+0.j], [ 1.+1.j, 3.+0.j]])

2.2.3 Intrinsic Numpy Array Creation

Numpy has built-in functions for creating arrays from scratch:

zeros(shape) will create an array ﬁlled with 0 values with the speciﬁed shape. The default dtype is ﬂoat64.

>>> np.zeros((2, 3)) array([[ 0., 0., 0.], [ 0., 0., 0.]])

ones(shape) will create an array ﬁlled with 1 values. It is identical to zeros in all other respects.

arange() will create arrays with regularly incrementing values. Check the docstring for complete information on the

various ways it can be used. A few examples will be given here:

>>> np.arange(10)

array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])

>>> np.arange(2, 10, dtype=np.float)

array([ 2., 3., 4., 5., 6., 7., 8., 9.])

>>> np.arange(2, 3, 0.1)

array([ 2. , 2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 2.7, 2.8, 2.9])

Note that there are some subtleties regarding the last usage that the user should be aware of that are described in the

arange docstring.

linspace() will create arrays with a speciﬁed number of elements, and spaced equally between the speciﬁed beginning

and end values. For example:

>>> np.linspace(1., 4., 6)

array([ 1. , 1.6, 2.2, 2.8, 3.4, 4. ])

The advantage of this creation function is that one can guarantee the number of elements and the starting and end

point, which arange() generally will not do for arbitrary start, stop, and step values.

indices() will create a set of arrays (stacked as a one-higher dimensioned array), one per dimension with each repre-

senting variation in that dimension. An example illustrates much better than a verbal description:

>>> np.indices((3,3))

array([[[0, 0, 0], [1, 1, 1], [2, 2, 2]], [[0, 1, 2], [0, 1, 2], [0, 1, 2]]])

This is particularly useful for evaluating functions of multiple dimensions on a regular grid.

2.2.4 Reading Arrays From Disk

This is presumably the most common case of large array creation. The details, of course, depend greatly on the format

of data on disk and so this section can only give general pointers on how to handle various formats.

Standard Binary Formats

Various ﬁelds have standard formats for array data. The following lists the ones with known python libraries to read

them and return numpy arrays (there may be others for which it is possible to read and convert to numpy arrays so

check the last section as well)

HDF5: PyTables

FITS: PyFITS

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Examples of formats that cannot be read directly but for which it is not hard to convert are those formats supported by

libraries like PIL (able to read and write many image formats such as jpg, png, etc).

Common ASCII Formats

Comma Separated Value ﬁles (CSV) are widely used (and an export and import option for programs like Excel). There

are a number of ways of reading these ﬁles in Python. There are CSV functions in Python and functions in pylab (part

of matplotlib).

More generic ascii ﬁles can be read using the io package in scipy.

Custom Binary Formats

There are a variety of approaches one can use. If the ﬁle has a relatively simple format then one can write a simple

I/O library and use the numpy fromﬁle() function and .toﬁle() method to read and write numpy arrays directly (mind

your byteorder though!) If a good C or C++ library exists that read the data, one can wrap that library with a variety of

techniques though that certainly is much more work and requires signiﬁcantly more advanced knowledge to interface

with C or C++.

Use of Special Libraries

There are libraries that can be used to generate arrays for special purposes and it isn’t possible to enumerate all of

them. The most common uses are use of the many array generation functions in random that can generate arrays of

random values, and some utility functions to generate special matrices (e.g. diagonal).

2.3 I/O with Numpy

2.3.1 Importing data with genfromtxt

Numpy provides several functions to create arrays from tabular data. We focus here on the genfromtxt function.

In a nutshell, genfromtxt runs two main loops. The ﬁrst loop converts each line of the ﬁle in a sequence of strings.

The second loop converts each string to the appropriate data type. This mechanism is slower than a single loop, but

gives more ﬂexibility. In particular, genfromtxt is able to take missing data into account, when other faster and

simpler functions like loadtxt cannot.

Note: When giving examples, we will use the following conventions:

>>> import numpy as np

>>> from StringIO import StringIO

Deﬁning the input

The only mandatory argument of genfromtxt is the source of the data. It can be a string corresponding to the name

of a local or remote ﬁle, or a ﬁle-like object with a read method (such as an actual ﬁle or a StringIO.StringIO

object). If the argument is the URL of a remote ﬁle, this latter is automatically downloaded in the current directory.

The input ﬁle can be a text ﬁle or an archive. Currently, the function recognizes gzip and bz2 (bzip2) archives. The

type of the archive is determined by examining the extension of the ﬁle: if the ﬁlename ends with ’.gz’, a gzip

archive is expected; if it ends with ’bz2’, a bzip2 archive is assumed.

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Splitting the lines into columns

The delimiter argument

Once the ﬁle is deﬁned and open for reading, genfromtxt splits each non-empty line into a sequence of strings.

Empty or commented lines are just skipped. The delimiter keyword is used to deﬁne how the splitting should take

place.

Quite often, a single character marks the separation between columns. For example, comma-separated ﬁles (CSV) use

a comma (,) or a semicolon (;) as delimiter:

>>> data = "1, 2, 3\n4, 5, 6"

>>> np.genfromtxt(StringIO(data), delimiter=",")

array([[ 1., 2., 3.],

[ 4., 5., 6.]])

Another common separator is "\t", the tabulation character. However, we are not limited to a single character, any

string will do. By default, genfromtxt assumes delimiter=None, meaning that the line is split along white

spaces (including tabs) and that consecutive white spaces are considered as a single white space.

Alternatively, we may be dealing with a ﬁxed-width ﬁle, where columns are deﬁned as a given number of characters.

In that case, we need to set delimiter to a single integer (if all the columns have the same size) or to a sequence of

integers (if columns can have different sizes):

>>> data = " 1 2 3\n 4 5 67\n890123 4"

>>> np.genfromtxt(StringIO(data), delimiter=3)

array([[ 1., 2., 3.],

[ 4., 5., 67.],

[ 890., 123., 4.]])

>>> data = "123456789\n 4 7 9\n 4567 9"

>>> np.genfromtxt(StringIO(data), delimiter=(4, 3, 2))

array([[ 1234., 567., 89.],

[ 4., 7., 9.],

[ 4., 567., 9.]])

The autostrip argument

By default, when a line is decomposed into a series of strings, the individual entries are not stripped of leading nor

trailing white spaces. This behavior can be overwritten by setting the optional argument autostrip to a value of

True:

>>> data = "1, abc , 2\n 3, xxx, 4"

>>> # Without autostrip

>>> np.genfromtxt(StringIO(data), dtype="|S5")

array([[’1’, ’ abc ’, ’ 2’],

[’3’, ’ xxx’, ’ 4’]],

dtype=’|S5’)

>>> # With autostrip

>>> np.genfromtxt(StringIO(data), dtype="|S5", autostrip=True)

array([[’1’, ’abc’, ’2’],

[’3’, ’xxx’, ’4’]],

dtype=’|S5’)

The comments argument

The optional argument comments is used to deﬁne a character string that marks the beginning of a comment. By

default, genfromtxt assumes comments=’#’. The comment marker may occur anywhere on the line. Any

character present after the comment marker(s) is simply ignored:

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>>> data = """#

... # Skip me !

... # Skip me too !

... 1, 2

... 3, 4

... 5, 6 #This is the third line of the data

... 7, 8

... # And here comes the last line

... 9, 0

... """

>>> np.genfromtxt(StringIO(data), comments="#", delimiter=",")

[[ 1. 2.]

[ 3. 4.]

[ 5. 6.]

[ 7. 8.]

[ 9. 0.]]

Note: There is one notable exception to this behavior: if the optional argument names=True, the ﬁrst commented

line will be examined for names.

Skipping lines and choosing columns

The skip_header and skip_footer arguments

The presence of a header in the ﬁle can hinder data processing. In that case, we need to use the skip_header

optional argument. The values of this argument must be an integer which corresponds to the number of lines to skip

at the beginning of the ﬁle, before any other action is performed. Similarly, we can skip the last n lines of the ﬁle by

using the skip_footer attribute and giving it a value of n:

>>> data = "\n".join(str(i) for i in range(10))

>>> np.genfromtxt(StringIO(data),)

array([ 0., 1., 2., 3., 4., 5., 6., 7., 8., 9.])

>>> np.genfromtxt(StringIO(data),

... skip_header=3, skip_footer=5)

array([ 3., 4.])

By default, skip_header=0 and skip_footer=0, meaning that no lines are skipped.

The usecols argument

In some cases, we are not interested in all the columns of the data but only a few of them. We can select which

columns to import with the usecols argument. This argument accepts a single integer or a sequence of integers

corresponding to the indices of the columns to import. Remember that by convention, the ﬁrst column has an index of

0. Negative integers behave the same as regular Python negative indexes.

For example, if we want to import only the ﬁrst and the last columns, we can use usecols=(0, -1):

>>> data = "1 2 3\n4 5 6"

>>> np.genfromtxt(StringIO(data), usecols=(0, -1))

array([[ 1., 3.],

[ 4., 6.]])

If the columns have names, we can also select which columns to import by giving their name to the usecols

argument, either as a sequence of strings or a comma-separated string:

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>>> data = "1 2 3\n4 5 6"

>>> np.genfromtxt(StringIO(data),

... names="a, b, c", usecols=("a", "c"))

array([(1.0, 3.0), (4.0, 6.0)],

dtype=[(’a’, ’<f8’), (’c’, ’<f8’)])

>>> np.genfromtxt(StringIO(data),

... names="a, b, c", usecols=("a, c"))

array([(1.0, 3.0), (4.0, 6.0)],

dtype=[(’a’, ’<f8’), (’c’, ’<f8’)])

Choosing the data type

The main way to control how the sequences of strings we have read from the ﬁle are converted to other types is to set

the dtype argument. Acceptable values for this argument are:

• a single type, such as dtype=float. The output will be 2D with the given dtype, unless a name has been

associated with each column with the use of the names argument (see below). Note that dtype=float is the

default for genfromtxt.

• a sequence of types, such as dtype=(int, float, float).

• a comma-separated string, such as dtype="i4,f8,|S3".

• a dictionary with two keys ’names’ and ’formats’.

• a sequence of tuples (name, type), such as dtype=[(’A’, int), (’B’, float)].

• an existing numpy.dtype object.

• the special value None. In that case, the type of the columns will be determined from the data itself (see below).

In all the cases but the ﬁrst one, the output will be a 1D array with a structured dtype. This dtype has as many ﬁelds as

items in the sequence. The ﬁeld names are deﬁned with the names keyword.

When dtype=None, the type of each column is determined iteratively from its data. We start by checking whether a

string can be converted to a boolean (that is, if the string matches true or false in lower cases); then whether it can

be converted to an integer, then to a ﬂoat, then to a complex and eventually to a string. This behavior may be changed

by modifying the default mapper of the StringConverter class.

The option dtype=None is provided for convenience. However, it is signiﬁcantly slower than setting the dtype

explicitly.

Setting the names

The names argument

A natural approach when dealing with tabular data is to allocate a name to each column. A ﬁrst possibility is to use an

explicit structured dtype, as mentioned previously:

>>> data = StringIO("1 2 3\n 4 5 6")

>>> np.genfromtxt(data, dtype=[(_, int) for _ in "abc"])

array([(1, 2, 3), (4, 5, 6)],

dtype=[(’a’, ’<i8’), (’b’, ’<i8’), (’c’, ’<i8’)])

Another simpler possibility is to use the names keyword with a sequence of strings or a comma-separated string:

>>> data = StringIO("1 2 3\n 4 5 6")

>>> np.genfromtxt(data, names="A, B, C")

16 Chapter 2. Numpy basics

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