平均值取决于与第二个变量有关的装仓

问题描述

我正在使用python/numpy.作为输入数据，我具有大量的值对(x,y).我基本上想绘制<y>(x)，即某个数据仓x的y平均值.目前，我使用普通的for循环来实现此目标，这非常慢.

I am working with python / numpy. As input data I have a large number of value pairs (x,y). I basically want to plot <y>(x), i.e., the mean value of y for a certain data bin x. At the moment I use a plain for loop to achieve this, which is terribly slow.

# create example data
x = numpy.random.rand(1000)
y = numpy.random.rand(1000)
# set resolution
xbins = 100
# find x bins
H, xedges, yedges = numpy.histogram2d(x, y, bins=(xbins,xbins) )
# calculate mean and std of y for each x bin
mean = numpy.zeros(xbins)
std = numpy.zeros(xbins)
for i in numpy.arange(xbins):
    mean[i] = numpy.mean(y[ numpy.logical_and( x>=xedges[i], x<xedges[i+1] ) ])
    std[i]  = numpy.std (y[ numpy.logical_and( x>=xedges[i], x<xedges[i+1] ) ])

是否可以为其进行矢量化写作?

Is it possible to have a kind of vectorized writing for it?

推荐答案

您不必要地使事情复杂化.您需要知道的是，对于x中的每个bin，什么是n，sy和sy2，该x bin中的y值的数量，这些y的总和值及其平方和.您可以通过以下方式获得它们:

You are complicating things unnecessarily. All you need to know is, for every bin in x, what are n, sy and sy2, the number of y values in that x bin, the sum of those y values, and the sum of their squares. You can get those as:

>>> n, _ = np.histogram(x, bins=xbins)
>>> sy, _ = np.histogram(x, bins=xbins, weights=y)
>>> sy2, _ = np.histogram(x, bins=xbins, weights=y*y)

从那些:

>>> mean = sy / n
>>> std = np.sqrt(sy2/n - mean*mean)

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