Performing grouped average and standard deviation with NumPy arrays

Question

I have a set of data (X,Y). My independent variable values X are not unique, so there are multiple repeated values, I want to output a new array containing : X_unique, which is a list of unique values of X. Y_mean, the mean of all of the Y values corresponding to X_unique. Y_std, the standard deviation of all the Y values corresponding to X_unique.

x = data[:,0]
y = data[:,1]

Answer 1

You can use binned_statistic from scipy.stats that supports various statistic functions to be applied in chunks across a 1D array. To get the chunks, we need to sort and get positions of the shifts (where chunks change), for which np.unique would be useful. Putting all those, here's an implementation -

from scipy.stats import binned_statistic as bstat

# Sort data corresponding to argsort of first column
sdata = data[data[:,0].argsort()]

# Unique col-1 elements and positions of breaks (elements are not identical)
unq_x,breaks = np.unique(sdata[:,0],return_index=True)
breaks = np.append(breaks,data.shape[0])

# Use binned statistic to get grouped average and std deviation values
idx_range = np.arange(data.shape[0])
avg_y,_,_ = bstat(x=idx_range, values=sdata[:,1], statistic='mean', bins=breaks)
std_y,_,_ = bstat(x=idx_range, values=sdata[:,1], statistic='std', bins=breaks)

From the docs of binned_statistic, one can also use a custom statistic function :

function : a user-defined function which takes a 1D array of values, and outputs a single numerical statistic. This function will be called on the values in each bin. Empty bins will be represented by function([]), or NaN if this returns an error.

Sample input, output -

In [121]: data
Out[121]: 
array([[2, 5],
       [2, 2],
       [1, 5],
       [3, 8],
       [0, 8],
       [6, 7],
       [8, 1],
       [2, 5],
       [6, 8],
       [1, 8]])

In [122]: np.column_stack((unq_x,avg_y,std_y))
Out[122]: 
array([[ 0.        ,  8.        ,  0.        ],
       [ 1.        ,  6.5       ,  1.5       ],
       [ 2.        ,  4.        ,  1.41421356],
       [ 3.        ,  8.        ,  0.        ],
       [ 6.        ,  7.5       ,  0.5       ],
       [ 8.        ,  1.        ,  0.        ]])

Answer 2

x_unique  = np.unique(x)
y_means = np.array([np.mean(y[x==u]) for u in x_unique])
y_stds = np.array([np.std(y[x==u]) for u in x_unique])