目录

简介

沿其他轴向广播

通过广播设置数组的值

ufunc高级应用

自定义的ufunc

架构化和记录式数组

其他排序算法

结束

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简介

广播指的是不同形状数组之间的算术运算的执行方式。它是一种非常强大的功能

>>> import numpy as np >>> arr = np.arange(5) >>> arr array([0, 1, 2, 3, 4]) >>> arr*4 array([ 0, 4, 8, 12, 16]) >>> arr = randn(4,3) >>> arr.mean(0) array([-0.43115904, -0.04193137, -0.55604705]) >>> demeaned = arr-arr.mean(0) >>> demeaned array([[ 0.28172111, -0.03730437, 0.15310302], [-0.65851004, -2.0032837 , -0.50386558], [ 0.90069608, 1.24842358, 1.39446594], [-0.52390714, 0.79216448, -1.04370338]])

沿其他轴向广播

根据广播的原则，较小数组的广播维必须为1

于是就有一个非常普遍的问题，即专门为了广播而添加一个长度为一的新轴，办法为使用全切片来插入新轴

>>> arr = np.zeros((4,4)) >>> arr_3d = arr[:,np.newaxis,:] >>> arr_3d.shape (4L, 1L, 4L) >>> arr_1d = np.random.normal(size=3) >>> arr_1d[:,np.newaxis] array([[-2.28070615], [ 1.45676407], [-0.33501704]]) >>> arr_1d[np.newaxis,:] array([[-2.28070615, 1.45676407, -0.33501704]])

如果我们有三维数组，并希望对轴2进行距平化，那么只需要编写下面这样的代码即可。

>>> arr = randn(3,4,5) >>> arr array([[[ 0.14355889, 0.91471291, -1.48453369, -0.42455771, 1.35064972], [-1.6315615 , -0.28652536, -0.22573702, -0.02694076, -0.43670708], [-0.30708186, 0.44396068, -0.20062503, -0.35479536, -0.67984063], [ 1.08344408, -0.48893 , 0.16412084, 1.23980658, -0.6989953 ]], [[ 0.23317469, 0.91435539, 0.85500396, -0.76785453, -1.06678174], [ 0.04440929, 1.47382479, -0.29530241, -0.12223287, 0.58623605], [ 1.21833979, 1.25049874, 0.60785443, 0.98217354, -0.31913215], [-1.48977066, -1.21858972, 0.16373654, -1.13013772, -0.19680737]], [[-1.09171845, -0.30966571, 0.74153601, 1.07080261, -0.89091987], [ 0.66661656, -0.61741408, -0.64890451, -0.23578853, 0.45262463], [-0.57686182, -0.62548638, 0.12317945, 0.23243517, -1.67882355], [ 0.1218588 , 0.92471459, 0.68252696, 0.4598333 , 0.29009011]]]) >>> depth_means = arr.mean(2) >>> depth_means array([[ 0.09996603, -0.52149434, -0.21967644, 0.25988924], [ 0.03357955, 0.33738697, 0.74794687, -0.77431379], [-0.09599308, -0.07657319, -0.50511143, 0.49580475]]) >>> demeaned = arr - depth_means[:,:,np.newaxis] >>> demeaned.mean(2) array([[ 0.00000000e+00, -6.66133815e-17, -3.33066907e-17, -4.44089210e-17], [ 0.00000000e+00, 6.66133815e-17, -4.44089210e-17, 1.11022302e-16], [ 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, -3.33066907e-17]])

通过广播设置数组的值

>>> arr = np.zeros((4,3)) >>> arr[:] = 5 >>> arr array([[5., 5., 5.], [5., 5., 5.], [5., 5., 5.], [5., 5., 5.]]) >>> col = np.array([1.28,-0.42,0.44,1.6]) >>> arr[:] = col[:,np.newaxis] >>> arr array([[ 1.28, 1.28, 1.28], [-0.42, -0.42, -0.42], [ 0.44, 0.44, 0.44], [ 1.6 , 1.6 , 1.6 ]]) >>> arr[:2] = [[-1.37],[0.509]] >>> arr array([[-1.37 , -1.37 , -1.37 ], [ 0.509, 0.509, 0.509], [ 0.44 , 0.44 , 0.44 ], [ 1.6 , 1.6 , 1.6 ]])

ufunc高级应用

>>> arr = np.arange(10) >>> np.add.reduce(arr) 45 >>> arr.sum() 45

 arr[::2]对每个第三行进行操作

>>> arr = randn(5,5) >>> arr[::2].sort(1) >>> arr array([[-1.77863628, -1.27039208, -0.90102076, -0.47784934, 1.53919358], [-0.06052154, -0.47682076, 0.65163751, -0.95954794, -3.60159995], [-0.50752957, -0.50483839, -0.05569555, 0.34798383, 1.69232614], [-0.05763389, -0.54338055, 0.93306287, 0.9971338 , -0.87589324], [-2.07027641, -1.51301557, -0.54804822, 0.06283581, 0.69473061]]) >>> arr[:,:-1] < arr[:,1:] array([[ True, True, True, True], [False, True, False, False], [ True, True, True, True], [False, True, True, False], [ True, True, True, True]])

logical_and.reduce与all方法等价

>>> np.logical_and.reduce(arr[:,:-1] < arr[:,1:],axis=1) array([ True, False, True, False, True])

outer用于计算两个数组的差积，out输出的结果是两个维度之和

>>> arr = np.arange(3).repeat([1,2,2]) >>> arr array([0, 1, 1, 2, 2]) >>> np.multiply.outer(arr,np.arange(5)) array([[0, 0, 0, 0, 0], [0, 1, 2, 3, 4], [0, 1, 2, 3, 4], [0, 2, 4, 6, 8], [0, 2, 4, 6, 8]])

自定义的ufunc

两种方法

>>> def add_elements(x,y): ... return x + y ... >>> add_them = np.frompyfunc(add_elements,2,1) >>> add_them(np.arange(8),np.arange(8)) array([0, 2, 4, 6, 8, 10, 12, 14], dtype=object) >>> add_them = np.vectorize(add_elements,otypes=[np.float64]) >>> add_them(np.arange(8),np.arange(8)) array([ 0., 2., 4., 6., 8., 10., 12., 14.])

架构化和记录式数组

结构化数组是一种特殊的ndarray,其中的各个元素可以被看作C语言中的结构体或SQL中带有多个命名字段的行

>>> dtype = [('x',np.float64),('y',np.int32)] >>> sarr = np.array([(1.5,6),(np.pi,-2)],type = dtype) >>> sarr = np.array([(1.5,6),(np.pi,-2)],dtype = dtype) >>> sarr array([(1.5 , 6), (3.14159265, -2)], dtype=[('x', '<f8'), ('y', '<i4')])

定义架构化dtype的方式有很多，最典型的是元组列表，各元组的格式为（field_name,field_data_type）.这样数组元素就成了元组式的对象。该对象可以向字典那样访问。

下例：以类型为索引

>>> sarr[0] (1.5, 6) >>> sarr[0]['y'] 6

其他排序算法

结束