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numpy.testing.utils

assert_(val, msg='') Assert that works in release mode. assert_almost_equal(actual, desired, decimal=7, err_msg='', verbose=True) Raise an assertion if two items are not equal up to desired precision. The test is equivalent to abs(desired-actual) < 0.5 * 10**(-decimal) Given two objects (numbers or ndarrays), check that all elements of these objects are almost equal. An exception is raised at conflicting values. For ndarrays this delegates to assert_array_almost_equal Parameters ---------- actual : number or ndarray The object to check. desired : number or ndarray The expected object. decimal : integer (decimal=7) desired precision err_msg : string The error message to be printed in case of failure. verbose : bool If True, the conflicting values are appended to the error message. Raises ------ AssertionError If actual and desired are not equal up to specified precision. See Also -------- assert_array_almost_equal: compares array_like objects assert_equal: tests objects for equality Examples -------- >>> npt.assert_almost_equal(2.3333333333333, 2.33333334) >>> npt.assert_almost_equal(2.3333333333333, 2.33333334, decimal=10) ... <type 'exceptions.AssertionError'>: Items are not equal: ACTUAL: 2.3333333333333002 DESIRED: 2.3333333399999998 >>> npt.assert_almost_equal(np.array([1.0,2.3333333333333]), np.array([1.0,2.33333334]), decimal=9) ... <type 'exceptions.AssertionError'>: Arrays are not almost equal <BLANKLINE> (mismatch 50.0%) x: array([ 1. , 2.33333333]) y: array([ 1. , 2.33333334]) assert_approx_equal(actual, desired, significant=7, err_msg='', verbose=True) Raise an assertion if two items are not equal up to significant digits. Given two numbers, check that they are approximately equal. Approximately equal is defined as the number of significant digits that

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机器学习基础与实践(三)----数据降维之PCA

写在前面:本来这篇应该是上周四更新,但是上周四写了一篇深度学习的反向传播法的过程,就推迟更新了。本来想参考PRML来写,但是发现里面涉及到比较多的数学知识,写出来可能不好理解,我决定还是用最通俗的方法解释PCA,并举一个实例一步步计算,然后再进行数学推导,最后再介绍一些变种以及相应的程序。(数学推导及变种下次再写好了) 正文:   在数据处理中,经常会遇到特征维度比样本数量多得多的情况,如果拿到实际工程中去跑,效果不一定好。一是因为冗余的特征会带来一些噪音,影响计算的结果;二是因为无关的特征会加大计算量,耗

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Python数据分析(中英对照)·Building and Examining NumPy Arrays 构建和检查 NumPy 数组

NumPy provides a couple of ways to construct arrays with fixed,start, and end values, such that the other elements are uniformly spaced between them. NumPy提供了两种方法来构造具有固定值、起始值和结束值的数组,以便其他元素在它们之间均匀分布。 To construct an array of 10 linearly spaced elements starting with 0 and ending with 100, we can use the NumPy linspace function. 要构造一个由10个线性间隔元素组成的数组,从0开始到100结束,我们可以使用NumPy linspace函数。 In this case, I’m going to type np.linspace. 在本例中,我将键入np.linspace。 The first argument is the starting point, which is 0. 第一个参数是起点,即0。 The second is the ending point, which will be included in the NumPy array that gets generated. 第二个是结束点,它将包含在生成的NumPy数组中。 And the final argument is the number of points I would like to have in my array. 最后一个参数是数组中的点数。 In this case, NumPy has created a linearly spaced array starting at 0 and ending at 100. 在本例中,NumPy创建了一个从0开始到100结束的线性间隔阵列。 Now, to construct an average of 10 logarithmically spaced elements between 10 and 100, we can do the following. 现在,要构造10个10到100之间的对数间隔元素的平均值,我们可以执行以下操作。 In this case we use the NumPy logspace command. 在本例中,我们使用NumPy logspace命令。 But now careful, the first argument that goes into logspace is going to be the log of the starting point. 但是现在要小心,进入日志空间的第一个参数将是起点的日志。 If you want the sequence to start at 10, the first argument has to be the log of 10 which is 1. 如果希望序列从10开始,则第一个参数必须是10的log,即1。 The second argument is the endpoint of the array, which is 100. 第二个参数是数组的端点,它是100。 And again, we need to put in the log of that, which is 2. 再一次,我们需要把它放到日志中,也就是2。 And the third argument as before, is the number of elements in our array. 和前面一样,第三个参数是数组中的元素数。 in this case, what NumPy has constructed is an array consisting of 10 elements where the first element is 10 and the last element is 100. 在本例中,NumPy构造了一个由10个元素组成的数组,其中第一个元素是10,最后一个元素是100。 All of the other elements are uniformly spaced between those two extreme points in the logarithmic space. 所有其他元素均匀分布在对数空间的两个端点之间。 To construct array of ten logarithmically spaced elements between numbers say 250 and 500,

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Python数据分析(中英对照)·Random Walks 随机游走

This is a good point to introduce random walks. 这是引入随机游动的一个很好的观点。 Random walks have many uses. 随机游动有许多用途。 They can be used to model random movements of molecules, 它们可以用来模拟分子的随机运动, but they can also be used to model spatial trajectories of people, 但它们也可以用来模拟人的空间轨迹, the kind we might be able to measure using GPS or similar technologies. 我们可以用GPS或类似的技术来测量。 There are many different kinds of random walks, and properties of random walks 有许多不同种类的随机游动,以及随机游动的性质 are central to many areas in physics and mathematics. 是物理学和数学许多领域的核心。 Let’s look at a very basic type of random walk on the white board. 让我们看看白板上一种非常基本的随机行走。 We’re first going to set up a coordinate system. 我们首先要建立一个坐标系。 Let’s call this axis "y" and this "x". 我们把这个轴叫做“y”,这个叫做“x”。 We’d like to have the random walk start from the origin. 我们想让随机游动从原点开始。 So this is position 1 for the random walk. 这是随机游动的位置1。 To get the position of the random walker at time 1, we can pick a step size. 为了得到时间1时随机行走者的位置,我们可以选择一个步长。 In this case, I’m just going to randomly draw an arrow. 在这种情况下,我将随机画一个箭头。 And this gives us the location of the random walker at time 1. 这给了我们时间1的随机游走者的位置。 So this point here is time is equal to 0. 这里的时间等于0。 And this point here corresponds to time equal to 1. 这一点对应于等于1的时间。 We can take another step. 我们可以再走一步。 Perhaps in this case, we go down, say over here. 也许在这种情况下,我们下去,比如说在这里。 And this is our location for the random walker at time t is equal to 2. 这是时间t等于2时,随机游走者的位置。 This is the basic idea behind all random walks. 这是所有随机游动背后的基本思想。 You have some location at time t, and from that location 你在时间t有一个位置,从这个位置开始 you take a step in a random direction and that generates your location 你在一个随机的方向上迈出一步,这就产生了你的位置 at time t plus 1. 在时间t加1时。 Let’s look at these a little bit more mathematically. 让我们从数学的角度来看这些。 First, we’re going to start with the location of the random walk at time t 首先,我们从时间t的随机游动的位置开始 is equal to 0. 等于0。 So position x at time t is equal to 0 is whatever 所以时间t处的位置x等于0是什么 the location of the random walke

02

Python数据分析(中英对照)·Using the NumPy Random Module 使用 NumPy 随机模块

NumPy makes it possible to generate all kinds of random variables. NumPy使生成各种随机变量成为可能。 We’ll explore just a couple of them to get you familiar with the NumPy random module. 为了让您熟悉NumPy随机模块,我们将探索其中的几个模块。 The reason for using NumPy to deal with random variables is that first, it has a broad range of different kinds of random variables. 使用NumPy来处理随机变量的原因是,首先,它有广泛的不同种类的随机变量。 And second, it’s also very fast. 第二,速度也很快。 Let’s start with generating numbers from the standard uniform distribution,which is a the completely flat distribution between 0 and 1 such that any floating point number between these two endpoints is equally likely. 让我们从标准均匀分布开始生成数字,这是一个0和1之间完全平坦的分布,因此这两个端点之间的任何浮点数的可能性相等。 We will first important NumPy as np as usual. 我们会像往常一样,先做一个重要的事情。 To generate just one realization from this distribution,we’ll type np dot random dot random. 为了从这个分布生成一个实现,我们将键入np-dot-random-dot-random。 And this enables us to generate one realization from the 0 1 uniform distribution. 这使我们能够从01均匀分布生成一个实现。 We can use the same function to generate multiple realizations or an array of random numbers from the same distribution. 我们可以使用同一个函数从同一个分布生成多个实现或一个随机数数组。 If I wanted to generate a 1d array of numbers,I will simply insert the size of that array, say 5 in this case. 如果我想生成一个一维数字数组,我只需插入该数组的大小,在本例中为5。 And that would generate five random numbers drawn from the 0 1 uniform distribution. 这将从0-1均匀分布中产生五个随机数。 It’s also possible to use the same function to generate a 2d array of random numbers. 也可以使用相同的函数生成随机数的2d数组。 In this case, inside the parentheses we need to insert as a tuple the dimensions of that array. 在本例中,我们需要在括号内插入该数组的维度作为元组。 The first argument is the number of rows,and the second argument is the number of columns. 第一个参数是行数,第二个参数是列数。 In this case, we have generated a table — a 2d table of random numbers with five rows and three columns. 在本例中,我们生成了一个表——一个由五行三列随机数组成的二维表。 Let’s then look at the normal distribution. 让我们看看正态分布。 It requires the mean and the standard deviation as its input parameters. 它需

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