Python NumPy入门教程：科学计算基石

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Numpy官方教程是一份详细的指南，旨在为Python中的科学计算入门者提供NumPy库的安装与关键功能使用方法。NumPy是Python中不可或缺的库，它为数据处理和分析提供了强大的支持，包括多维数组（ndarray）对象、其他衍生类型如掩码数组和矩阵，以及一系列高效的数组操作函数。这些操作覆盖了数学运算（如基本线性代数、统计操作）、逻辑操作、形状变换、排序选择、I/O功能、离散傅立叶变换、随机模拟等多个领域。本教程的结构分为多个章节： 1. **设置**：这部分介绍了NumPy的基本概念，解释了它是如何作为Python科学计算的核心包，以及它提供的核心组件——ndarray，即多维度数组，其高效性和灵活性对于数据处理至关重要。 2. **快速入门教程**：这个部分可能包含简短的步骤和示例，帮助读者快速掌握如何安装NumPy，并通过实际操作了解其基础用法。 3. **NumPy基础知识**：深入讲解了NumPy的数组操作、索引和切片、广播规则、数组创建、形状和维度管理等核心概念，为后续更复杂的运算打下坚实的基础。 4. **杂项**：这部分涵盖了更高级的主题，如NumPy与其他Python库的交互，例如Pandas和SciPy，以及一些高级特性，如并行计算和向量化操作。 5. **针对Matlab用户的NumPy**：考虑到NumPy与MATLAB的相似之处，这部分可能会介绍如何让MATLAB用户更快地适应NumPy的思维方式和语法。 6. **从源代码构建**：对于开发者而言，这部分可能涉及如何编译和自定义NumPy库，适合那些想要深入了解库内部工作原理或进行扩展的人。 7. **使用NumPy C-API**：C API允许直接访问NumPy的底层功能，对高级开发者或者需要定制化接口的用户来说，这部分内容尤为重要。 Numpy官方教程为不同层次的用户提供了全面且深入的指导，无论是初学者还是专业人员都能从中获益良多。通过学习这份教程，读者将能够熟练地在Python环境中进行大规模的数据处理和科学计算任务。

NumPy User Guide, Release 1.13.0

[40, 41, 42, 43]])

>>> b[2,3]

>>> b[0:5, 1] # each row in the second column of b

array([ 1, 11, 21, 31, 41])

>>> b[ : ,1] # equivalent to the previous example

array([ 1, 11, 21, 31, 41])

>>> b[1:3, : ] # each column in the second and third row of b

array([[10, 11, 12, 13],

[20, 21, 22, 23]])

When fewer indices are provided than the number of axes, the missing indices are considered complete slices:

>>> b[-1] # the last row. Equivalent to b[-1,:]

array([40, 41, 42, 43])

The expression within brackets in b[i] is treated as an i followed by as many instances of : as needed to represent

the remaining axes. NumPy also allows you to write this using dots as b[i,...].

The dots (...) represent as many colons as needed to produce a complete indexing tuple. For example, if x is a rank

5 array (i.e., it has 5 axes), then

• x[1,2,...] is equivalent to x[1,2,:,:,:],

• x[...,3] to x[:,:,:,:,3] and

• x[4,...,5,:] to x[4,:,:,5,:].

>>> c = np.array( [[[ 0, 1, 2], # a 3D array (two stacked 2D arrays)

... [ 10, 12, 13]],

... [[100,101,102],

... [110,112,113]]])

>>> c.shape

(2, 2, 3)

>>> c[1,...] # same as c[1,:,:] or c[1]

array([[100, 101, 102],

[110, 112, 113]])

>>> c[...,2] # same as c[:,:,2]

array([[ 2, 13],

[102, 113]])

Iterating over multidimensional arrays is done with respect to the ﬁrst axis:

>>> for row in b:

... print(row)

...

[0 1 2 3]

[10 11 12 13]

[20 21 22 23]

[30 31 32 33]

[40 41 42 43]

However, if one wants to perform an operation on each element in the array, one can use the flat attribute which is

an iterator over all the elements of the array:

>>> for element in b.flat:

... print(element)

...

12 Chapter 2. Quickstart tutorial

NumPy User Guide, Release 1.13.0

The function column_stack stacks 1D arrays as columns into a 2D array. It is equivalent to hstack only for 2D

arrays:

>>> from numpy import newaxis

>>> np.column_stack((a,b)) # with 2D arrays

array([[ 8., 8., 1., 8.],

[ 0., 0., 0., 4.]])

>>> a = np.array([4.,2.])

>>> b = np.array([3.,8.])

>>> np.column_stack((a,b)) # returns a 2D array

array([[ 4., 3.],

[ 2., 8.]])

>>> np.hstack((a,b)) # the result is different

array([ 4., 2., 3., 8.])

>>> a[:,newaxis] # this allows to have a 2D columns vector

array([[ 4.],

[ 2.]])

>>> np.column_stack((a[:,newaxis],b[:,newaxis]))

array([[ 4., 3.],

[ 2., 8.]])

>>> np.hstack((a[:,newaxis],b[:,newaxis])) # the result is the same

array([[ 4., 3.],

[ 2., 8.]])

On the other hand, the function row_stack is equivalent to vstack for any input arrays. In general, for arrays of

with more than two dimensions, hstack stacks along their second axes, vstack stacks along their ﬁrst axes, and

concatenate allows for an optional arguments giving the number of the axis along which the concatenation should

happen.

Note

In complex cases, r_ and c_ are useful for creating arrays by stacking numbers along one axis. They allow the use of

range literals (”:”)

>>> np.r_[1:4,0,4]

array([1, 2, 3, 0, 4])

When used with arrays as arguments, r_ and c_ are similar to vstack and hstack in their default behavior, but

allow for an optional argument giving the number of the axis along which to concatenate.

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