3.9小节完成
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XiongNeng
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cookbook/c03/p09_array_numpy.py
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55
cookbook/c03/p09_array_numpy.py
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#!/usr/bin/env python
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# -*- encoding: utf-8 -*-
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"""
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Topic: 利用numpy执行数组运算
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Desc :
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"""
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import numpy as np
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def array_numpy():
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x = [1, 2, 3, 4]
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y = [5, 6, 7, 8]
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print(x * 2)
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print(x + y)
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# Numpy arrays
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ax = np.array([1, 2, 3, 4])
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ay = np.array([5, 6, 7, 8])
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print(ax * 2)
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print(ax + ay)
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print(ax * ay)
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print(f(ax))
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print(np.sqrt(ax))
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print(np.cos(ax))
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# 大数组
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grid = np.zeros(shape=(10000, 10000), dtype=float)
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grid += 10
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print(grid)
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print(np.sin(grid))
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# 二维数组的索引操作
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a = np.array([[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12]])
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print(a)
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print(a[1]) # Select row 1
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print(a[:, 1]) # Select column 1
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# Select a subregion and change it
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print(a[1:3, 1:3])
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a[1:3, 1:3] += 10
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print(a)
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# Broadcast a row vector across an operation on all rows
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print(a + [100, 101, 102, 103])
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# Conditional assignment on an array
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print(np.where(a < 10, a, 10))
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def f(x):
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return 3 * x ** 2 - 2 * x + 7
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if __name__ == '__main__':
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array_numpy()
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@@ -1,18 +1,180 @@
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============================
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========================
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3.9 大型数组运算
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============================
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========================
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----------
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问题
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----------
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todo...
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你需要在大数据集(比如数组或网格)上面执行计算。
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----------
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解决方案
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----------
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todo...
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涉及到数组的重量级运算操作，可以使用NumPy库。
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NumPy的一个主要特征是它会给Python提供一个数组对象，相比标准的Python列表而已更适合用来做数学运算。
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下面是一个简单的小例子，向你展示标准列表对象和NumPy数组对象之间的差别：
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.. code-block:: python
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>>> # Python lists
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>>> x = [1, 2, 3, 4]
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>>> y = [5, 6, 7, 8]
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>>> x * 2
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[1, 2, 3, 4, 1, 2, 3, 4]
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>>> x + 10
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Traceback (most recent call last):
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File "<stdin>", line 1, in <module>
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TypeError: can only concatenate list (not "int") to list
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>>> x + y
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[1, 2, 3, 4, 5, 6, 7, 8]
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>>> # Numpy arrays
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>>> import numpy as np
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>>> ax = np.array([1, 2, 3, 4])
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>>> ay = np.array([5, 6, 7, 8])
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>>> ax * 2
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array([2, 4, 6, 8])
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>>> ax + 10
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array([11, 12, 13, 14])
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>>> ax + ay
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array([ 6, 8, 10, 12])
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>>> ax * ay
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array([ 5, 12, 21, 32])
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>>>
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正如所见，两种方案中数组的基本数学运算结果并不相同。
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特别的，numpy中的标量运算(比如ax * 2或ax + 10)会作用在每一个元素上。
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另外，当两个操作数都是数组的时候执行元素对等位置计算，并最终生成一个新的数组。
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对整个数组中所有元素同时执行数学运算可以使得作用在整个数组上的函数运算简单而又快速。
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比如，如果你想计算多项式的值，可以这样做：
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.. code-block:: python
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>>> def f(x):
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... return 3*x**2 - 2*x + 7
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...
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>>> f(ax)
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array([ 8, 15, 28, 47])
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>>>
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NumPy还为数组操作提供了大量的通用函数，这些函数可以作为math模块中类似函数的替代。比如：
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.. code-block:: python
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>>> np.sqrt(ax)
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array([ 1. , 1.41421356, 1.73205081, 2. ])
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>>> np.cos(ax)
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array([ 0.54030231, -0.41614684, -0.9899925 , -0.65364362])
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>>>
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使用这些通用函数要比循环数组并使用math模块中的函数执行计算要快的多。
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因此，只要有可能的话尽量选择numpy的数组方案。
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底层实现中，NumPy数组使用了C或者Fortran语言的机制分配内存。
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也就是说，它们是一个非常大的连续的并由同类型数据组成的内存区域。
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所以，你可以构造一个比普通Python列表大的多的数组。比如，如果你想构造一个10,000*10,000的浮点数二维网格，很轻松：
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.. code-block:: python
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>>> grid = np.zeros(shape=(10000,10000), dtype=float)
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>>> grid
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array([[ 0., 0., 0., ..., 0., 0., 0.],
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[ 0., 0., 0., ..., 0., 0., 0.],
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[ 0., 0., 0., ..., 0., 0., 0.],
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...,
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[ 0., 0., 0., ..., 0., 0., 0.],
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[ 0., 0., 0., ..., 0., 0., 0.],
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[ 0., 0., 0., ..., 0., 0., 0.]])
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>>>
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所有的普通操作还是会同时作用在所有元素上：
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.. code-block:: python
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>>> grid += 10
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>>> grid
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array([[ 10., 10., 10., ..., 10., 10., 10.],
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[ 10., 10., 10., ..., 10., 10., 10.],
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[ 10., 10., 10., ..., 10., 10., 10.],
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...,
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[ 10., 10., 10., ..., 10., 10., 10.],
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[ 10., 10., 10., ..., 10., 10., 10.],
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[ 10., 10., 10., ..., 10., 10., 10.]])
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>>> np.sin(grid)
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array([[-0.54402111, -0.54402111, -0.54402111, ..., -0.54402111,
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-0.54402111, -0.54402111],
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[-0.54402111, -0.54402111, -0.54402111, ..., -0.54402111,
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-0.54402111, -0.54402111],
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[-0.54402111, -0.54402111, -0.54402111, ..., -0.54402111,
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-0.54402111, -0.54402111],
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...,
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[-0.54402111, -0.54402111, -0.54402111, ..., -0.54402111,
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-0.54402111, -0.54402111],
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[-0.54402111, -0.54402111, -0.54402111, ..., -0.54402111,
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-0.54402111, -0.54402111],
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[-0.54402111, -0.54402111, -0.54402111, ..., -0.54402111,
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-0.54402111, -0.54402111]])
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>>>
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关于NumPy有一点需要特别的主意，那就是它扩展Python列表的索引功能 - 特别是对于多维数组。
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为了说明清楚，先构造一个简单的二维数组并试着做些试验：
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.. code-block:: python
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>>> a = np.array([[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12]])
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>>> a
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array([[ 1, 2, 3, 4],
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[ 5, 6, 7, 8],
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[ 9, 10, 11, 12]])
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>>> # Select row 1
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>>> a[1]
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array([5, 6, 7, 8])
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>>> # Select column 1
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>>> a[:,1]
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array([ 2, 6, 10])
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>>> # Select a subregion and change it
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>>> a[1:3, 1:3]
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array([[ 6, 7],
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[10, 11]])
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>>> a[1:3, 1:3] += 10
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>>> a
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array([[ 1, 2, 3, 4],
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[ 5, 16, 17, 8],
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[ 9, 20, 21, 12]])
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>>> # Broadcast a row vector across an operation on all rows
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>>> a + [100, 101, 102, 103]
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array([[101, 103, 105, 107],
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[105, 117, 119, 111],
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[109, 121, 123, 115]])
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>>> a
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array([[ 1, 2, 3, 4],
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[ 5, 16, 17, 8],
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[ 9, 20, 21, 12]])
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>>> # Conditional assignment on an array
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>>> np.where(a < 10, a, 10)
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array([[ 1, 2, 3, 4],
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[ 5, 10, 10, 8],
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[ 9, 10, 10, 10]])
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>>>
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----------
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讨论
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----------
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todo...
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NumPy是Python领域中很多科学与工程库的基础，同时也是被广泛使用的最大最复杂的模块。
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即便如此，在刚开始的时候通过一些简单的例子和玩具程序也能帮我们完成一些有趣的事情。
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通常我们导入NumPy模块的时候会使用语句import numpy as np。
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这样的话你就不用再你的程序里面一遍遍的敲入numpy，只需要输入np就行了，节省了不少时间。
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如果想获取更多的信息，你当然得去NumPy官网逛逛了，网址是： http://www.numpy.org
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