blocks|key|216487|text|numpy.correlate只是返回两个向量的互相关值。|type|unstyled|depth|inlineStyleRanges|offset|length|style|CODE|entityRanges|data|216488|如果您需要了解交叉相关，那么从http://en.wikipedia.org/wiki/Cross-correlation开始。|216489|一个很好的例子可以通过查看自相关函数(与自身相互关联的向量)来看到：|216490|import+numpy+as+np

#+create+a+vector
vector+=+np.random.normal(0,1,size=1000)+

#+insert+a+signal+into+vector
vector[::50]%2B=10

#+perform+cross-correlation+for+all+data+points
output+=+np.correlate(vector,vector,mode='full')|code-block|syntax|javascript|216491|​|216492|📷|atomic|216493|216494|当两个数据集重叠时，这将返回一个带有最大值的comb/shah函数。由于这是一种自相关，因此在两个输入信号之间不会有“滞后”。因此，相关性的最大值是vector.size-1。|216495|如果您只需要重叠数据的相关值，则可以使用mode='valid'。|216496|entityMap|0|LINK|mutability|MUTABLE|url|http://en.wikipedia.org/wiki/Cross-correlation|1|IMAGE|IMMUTABLE|imageUrl|https://ask.qcloudimg.com/http-save/yehe-900000/f8cb028c1e255acfe73f47c0f58aaca1.png|imageAlt^0|0|F|0|F|1A|0|0|0|0|0|0|1|1|0|0|0|K|C|0^^$0|@$1|2|3|4|5|6|7|1C|8|@$9|1D|A|1E|B|C]]|D|@]|E|$]]|$1|F|3|G|5|6|7|1F|8|@]|D|@$9|1G|A|1H|1|1I]]|E|$]]|$1|H|3|I|5|6|7|1J|8|@]|D|@]|E|$]]|$1|J|3|K|5|L|7|1K|8|@]|D|@]|E|$M|N]]|$1|O|3|P|5|6|7|1L|8|@]|D|@]|E|$]]|$1|Q|3|R|5|S|7|1M|8|@]|D|@$9|1N|A|1O|1|1P]]|E|$]]|$1|T|3|P|5|6|7|1Q|8|@]|D|@]|E|$]]|$1|U|3|V|5|6|7|1R|8|@]|D|@]|E|$]]|$1|W|3|X|5|6|7|1S|8|@$9|1T|A|1U|B|C]]|D|@]|E|$]]|$1|Y|3|-4|5|6|7|1V|8|@]|D|@]|E|$]]]|Z|$10|$5|11|12|13|E|$14|15]]|16|$5|17|12|18|E|$19|1A|1B|-4]]]]

<code>numpy.correlate</code> simply returns the cross-correlation of two vectors. 

if you need to understand cross-correlation, then start with <a href="http://en.wikipedia.org/wiki/Cross-correlation">http://en.wikipedia.org/wiki/Cross-correlation</a>.

A good example might be seen by looking at the autocorrelation function (a vector cross-correlated with itself):

<pre><code>import numpy as np

# create a vector
vector = np.random.normal(0,1,size=1000) 

# insert a signal into vector
vector[::50]+=10

# perform cross-correlation for all data points
output = np.correlate(vector,vector,mode='full')
</code></pre>

<img src="https://i.stack.imgur.com/PpAjv.png" alt="Code graph">

This will return a comb/shah function with a maximum when both data sets are overlapping. As this is an autocorrelation there will be no "lag" between the two input signals. The maximum of the correlation is therefore vector.size-1. 

if you only want the value of the correlation for overlapping data, you can use <code>mode='valid'</code>.

blocks|key|434654|text|目前我只能对numpy.correlate发表评论。这是一个强大的工具。我使用它有两个目的。第一种方法是在另一个模式中找到另一个模式：|type|unstyled|depth|inlineStyleRanges|offset|length|style|CODE|entityRanges|data|434655|import+numpy+as+np
import+matplotlib.pyplot+as+plt

some_data+=+np.random.uniform(0,1,size=100)
subset+=+some_data[42:50]

mean+=+np.mean(some_data)
some_data_normalised+=+some_data+-+mean
subset_normalised+=+subset+-+mean

correlated+=+np.correlate(some_data_normalised,+subset_normalised)
max_index+=+np.argmax(correlated)++#+42+!|code-block|syntax|javascript|434656|我使用它的第二个用途(以及如何解释结果)是用于频率检测：|434657|hz_a+=+np.cos(np.linspace(0,np.pi*6,100))
hz_b+=+np.cos(np.linspace(0,np.pi*4,100))

f,+axarr+=+plt.subplots(2,+sharex=True)

axarr[0].plot(hz_a)
axarr[0].plot(hz_b)
axarr[0].grid(True)

hz_a_autocorrelation+=+np.correlate(hz_a,hz_a,'same')[round(len(hz_a)/2):]
hz_b_autocorrelation+=+np.correlate(hz_b,hz_b,'same')[round(len(hz_b)/2):]

axarr[1].plot(hz_a_autocorrelation)
axarr[1].plot(hz_b_autocorrelation)
axarr[1].grid(True)

plt.show()|434658|​|434659|📷|atomic|434660|434661|找出第二个峰值的指数。由此，您可以返回以找到频率。|434662|first_min_index+=+np.argmin(hz_a_autocorrelation)
second_max_index+=+np.argmax(hz_a_autocorrelation[first_min_index:])
frequency+=+1/second_max_index|434663|entityMap|0|IMAGE|mutability|IMMUTABLE|imageUrl|https://ask.qcloudimg.com/http-save/yehe-900000/a14be1293b53be53c54f0f559ef2a704.png|imageAlt^0|6|F|0|0|0|0|0|0|1|0|0|0|0|0^^$0|@$1|2|3|4|5|6|7|17|8|@$9|18|A|19|B|C]]|D|@]|E|$]]|$1|F|3|G|5|H|7|1A|8|@]|D|@]|E|$I|J]]|$1|K|3|L|5|6|7|1B|8|@]|D|@]|E|$]]|$1|M|3|N|5|H|7|1C|8|@]|D|@]|E|$I|J]]|$1|O|3|P|5|6|7|1D|8|@]|D|@]|E|$]]|$1|Q|3|R|5|S|7|1E|8|@]|D|@$9|1F|A|1G|1|1H]]|E|$]]|$1|T|3|P|5|6|7|1I|8|@]|D|@]|E|$]]|$1|U|3|V|5|6|7|1J|8|@]|D|@]|E|$]]|$1|W|3|X|5|H|7|1K|8|@]|D|@]|E|$I|J]]|$1|Y|3|-4|5|6|7|1L|8|@]|D|@]|E|$]]]|Z|$10|$5|11|12|13|E|$14|15|16|-4]]]]

I can only comment on <code>numpy.correlate</code> at the moment. It's a powerful tool. I have used it for two purposes. The first is to find a pattern inside another pattern:

<pre><code>import numpy as np
import matplotlib.pyplot as plt

some_data = np.random.uniform(0,1,size=100)
subset = some_data[42:50]

mean = np.mean(some_data)
some_data_normalised = some_data - mean
subset_normalised = subset - mean

correlated = np.correlate(some_data_normalised, subset_normalised)
max_index = np.argmax(correlated) # 42 !
</code></pre>

The second use I have used it for (and how to interpret the result) is for frequency detection:

<pre><code>hz_a = np.cos(np.linspace(0,np.pi*6,100))
hz_b = np.cos(np.linspace(0,np.pi*4,100))

f, axarr = plt.subplots(2, sharex=True)

axarr[0].plot(hz_a)
axarr[0].plot(hz_b)
axarr[0].grid(True)

hz_a_autocorrelation = np.correlate(hz_a,hz_a,'same')[round(len(hz_a)/2):]
hz_b_autocorrelation = np.correlate(hz_b,hz_b,'same')[round(len(hz_b)/2):]

axarr[1].plot(hz_a_autocorrelation)
axarr[1].plot(hz_b_autocorrelation)
axarr[1].grid(True)

plt.show()
</code></pre>

<a href="https://i.stack.imgur.com/GNKri.png" rel="noreferrer"><img src="https://i.stack.imgur.com/GNKri.png" alt="three hz and two hz with autocorrelation show beneath"></a>

Find the index of the second peaks. From this you can work back to find the frequency.

<pre><code>first_min_index = np.argmin(hz_a_autocorrelation)
second_max_index = np.argmax(hz_a_autocorrelation[first_min_index:])
frequency = 1/second_max_index
</code></pre>

I have two 1D arrays and I want to see their inter-relationships. What procedure should I use in numpy? I am using <code>numpy.corrcoef(arrayA, arrayB)</code> and <code>numpy.correlate(arrayA, arrayB)</code> and both are giving some results that I am not able to comprehend or understand.

Can somebody please shed light on how to understand and interpret those numerical results (preferably, using an example)?

How to interpret the values returned by numpy.correlate and numpy.corrcoef?

我有两个一维数组，我想看看它们之间的关系。我应该在numpy中使用什么过程？我使用的是numpy.corrcoef(arrayA, arrayB)和numpy.correlate(arrayA, arrayB)，它们都给出了一些我无法理解或理解的结果。有没有人能解释一下如何理解和解释这些数值结果(最好是用一个例子)？

问如何解释numpy.correlate和numpy.corrcoef的返回值？
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