blocks|key|1923469|text|NumPy的ufuncs有accumulate()|type|unstyled|depth|inlineStyleRanges|offset|length|style|CODE|entityRanges|data|1923470|In+[22]:+np.multiply.accumulate([[1,+2,+3],+[4,+5,+6]],+axis=1)
Out[22]:+
array([[++1,+++2,+++6],
+++++++[++4,++20,+120]])|code-block|syntax|javascript|1923471|不幸的是，在frompyfunc()'ed+Python函数上调用accumulate()失败，并显示一个奇怪的错误：|1923472|In+[32]:+uadd+=+np.frompyfunc(lambda+x,+y:+x+%2B+y,+2,+1)

In+[33]:+uadd.accumulate([1,+2,+3])
---------------------------------------------------------------------------
ValueError++++++++++++++++++++++++++++++++Traceback+(most+recent+call+last)

ValueError:+could+not+find+a+matching+type+for+<lambda>+(vectorized).accumulate,+
++++++++++++requested+type+has+type+code+'l'|1923473|它使用的是NumPy+1.6.1和Python2.7.3。|1923474|entityMap|0|LINK|mutability|MUTABLE|url|http://docs.scipy.org/doc/numpy/reference/generated/numpy.ufunc.accumulate.html^0|D|C|D|C|0|0|0|6|C|X|C|0|0|0^^$0|@$1|2|3|4|5|6|7|Y|8|@$9|Z|A|10|B|C]]|D|@$9|11|A|12|1|13]]|E|$]]|$1|F|3|G|5|H|7|14|8|@]|D|@]|E|$I|J]]|$1|K|3|L|5|6|7|15|8|@$9|16|A|17|B|C]|$9|18|A|19|B|C]]|D|@]|E|$]]|$1|M|3|N|5|H|7|1A|8|@]|D|@]|E|$I|J]]|$1|O|3|P|5|6|7|1B|8|@]|D|@]|E|$]]|$1|Q|3|-4|5|6|7|1C|8|@]|D|@]|E|$]]]|R|$S|$5|T|U|V|E|$W|X]]]]

NumPy's ufuncs have <a href="http://docs.scipy.org/doc/numpy/reference/generated/numpy.ufunc.accumulate.html"><code>accumulate()</code></a>:

<pre><code>In [22]: np.multiply.accumulate([[1, 2, 3], [4, 5, 6]], axis=1)
Out[22]: 
array([[ 1, 2, 6],
 [ 4, 20, 120]])
</code></pre>

Unfortunately, calling <code>accumulate()</code> on a <code>frompyfunc()</code>'ed Python function fails with a strange error:

<pre><code>In [32]: uadd = np.frompyfunc(lambda x, y: x + y, 2, 1)

In [33]: uadd.accumulate([1, 2, 3])
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)

ValueError: could not find a matching type for &lt;lambda&gt; (vectorized).accumulate, 
 requested type has type code 'l'
</code></pre>

This is using NumPy 1.6.1 with Python 2.7.3.

blocks|key|1709993|text|上面的ValueError仍然是一个使用Numpy+1.20.1+(使用Python3.9.1)的bug。|type|unstyled|depth|inlineStyleRanges|entityRanges|data|1709994|幸运的是，发现了一种使用强制转换的解决方法：https://groups.google.com/forum/#!topic/numpy/JgUltPe2hqw|offset|length|1709995|import+numpy+as+np
uadd+=+np.frompyfunc(lambda+x,+y:+x+%2B+y,+2,+1)
uadd.accumulate([1,2,3],+dtype=object).astype(int)
#+array([1,+3,+6])|code-block|syntax|javascript|1709996|请注意，由于自定义操作在对象类型上工作，因此它不会从numpy的有效内存管理中受益。因此，对于非常大的数组，该操作可能比不需要强制转换为object的操作慢。|1709997|entityMap|0|LINK|mutability|MUTABLE|url|https://groups.google.com/forum/#!topic/numpy/JgUltPe2hqw^0|0|M|1L|0|0|0|0^^$0|@$1|2|3|4|5|6|7|U|8|@]|9|@]|A|$]]|$1|B|3|C|5|6|7|V|8|@]|9|@$D|W|E|X|1|Y]]|A|$]]|$1|F|3|G|5|H|7|Z|8|@]|9|@]|A|$I|J]]|$1|K|3|L|5|6|7|10|8|@]|9|@]|A|$]]|$1|M|3|-4|5|6|7|11|8|@]|9|@]|A|$]]]|N|$O|$5|P|Q|R|A|$S|T]]]]

The ValueError above is still a bug using Numpy 1.20.1 (with Python 3.9.1).
Luckily a workaround was discovered that uses casting:
<a href="https://groups.google.com/forum/#!topic/numpy/JgUltPe2hqw" rel="nofollow noreferrer">https://groups.google.com/forum/#!topic/numpy/JgUltPe2hqw</a>
<pre><code>import numpy as np
uadd = np.frompyfunc(lambda x, y: x + y, 2, 1)
uadd.accumulate([1,2,3], dtype=object).astype(int)
# array([1, 3, 6])
</code></pre>
Note that since the custom operation works on an object type, it won't benefit from the efficient memory management of numpy. So the operation may be slower than one that didn't need casting to object for extremely large arrays.

Is there a function in numpy or scipy (or some other library) that generalizes the idea of cumsum and cumprod to arbitrary function. For example, consider the (theoretical) function

<pre><code>cumf( func, array) 
</code></pre>

func is a function that accepts two floats, and returns a float. Particular cases 

<pre><code>lambda x,y: x+y 
</code></pre>

and 

<pre><code>lambda x,y: x*y 
</code></pre>

are cumsum and cumprod respectively. For example, if 

<pre><code>func = lambda x,prev_x: x^2*prev_x 
</code></pre>

and I apply it to:

<pre><code>cumf(func, np.array( 1, 2, 3) )
</code></pre>

I would like 

<pre><code>np.array( 1, 4, 9*4 )
</code></pre>

generalized cumulative functions in NumPy/SciPy?

内存管理

Python

在numpy或scipy (或其他库)中，有没有一个函数可以将cumsum和cumprod的概念推广到任意函数。例如，考虑(理论)函数cumf( func, array) func是一个接受两个浮点数的函数，并返回一个浮点数。特殊情况lambda x,y: x+y 和lambda x,y: x*y 分别是cumsum和...

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