不规则时间间隔的平均值

Question

I have several pairs of arrays of measurements and the times at which the measurements were taken that I want to average. Unfortunately the times at which these measurements were taken isn't regular or the same for each pair.

My idea for averaging them is to create a new array with the value at each second then average these. It works but it seems a bit clumsy and means I have to create many unnecessarily long arrays.

Example Inputs

m1 = [0.4, 0.6, 0.2]
t1 = [0.0, 2.4, 5.2]

m2 = [1.0, 1.4, 1.0]
t2 = [0.0, 3.6, 4.8]

Generated Regular Arrays for values at each second

r1 = [0.4, 0.4, 0.4, 0.6, 0.6, 0.6, 0.2]
r2 = [1.0, 1.0, 1.0, 1.0, 1.4, 1.0]

Average values up to length of shortest array

a = [0.7, 0.7, 0.7, 0.8, 1.0, 0.8]

My attempt given list of measurement arrays measurements and respective list of time interval arrays times

def granulate(values, times):
    count = 0
    regular_values = []
    for index, x in enumerate(times):
        while count <= x:
            regular_values.append(values[index])
            count += 1
    return np.array(regular_values)

processed_measurements = [granulate(m, t) for m, t in zip(measurements, times)]
min_length = min(len(m) for m in processed_measurements )
processed_measurements = [m[:min_length] for m in processed_measurements]
average_measurement = np.mean(processed_measurements, axis=0)

Is there a better way to do it, ideally using numpy functions?

Answer 1

This will average to closest second:

time_series = np.arange(np.stack((t1, t2)).max())
np.mean([m1[abs(t1-time_series[:,None]).argmin(axis=1)], m2[abs(t2-time_series[:,None]).argmin(axis=1)]], axis=0)

If you want to floor times to each second (with possibility of generalizing to more arrays):

m = [m1, m2]
t = [t1, t2]
m_t=[]
time_series = np.arange(np.stack(t).max())
for i in range(len(t)):
  time_diff = time_series-t[i][:,None]
  m_t.append(m[i][np.where(time_diff > 0, time_diff, np.inf).argmin(axis=0)])
average = np.mean(m_t, axis=0)

output:

[0.7 0.7 0.7 0.8 1.  0.8]

Answer 2

You can do (a bit more numpy-ish solution):

import numpy as np

# oddly enough - numpy doesn't have it's own ffill function:

def np_ffill(arr):
    mask = np.arange(len(arr))
    mask[np.isnan(arr)]=0
    np.maximum.accumulate(mask, axis=0, out=mask)
    return arr[mask]


t1=np.ceil(t1).astype("int")
t2=np.ceil(t2).astype("int")
r1=np.empty(max(t1)+1)
r2=np.empty(max(t2)+1)
r1[:]=np.nan
r2[:]=np.nan
r1[t1]=m1
r2[t2]=m2

r1=np_ffill(r1)
r2=np_ffill(r2)

>>> print(r1,r2)

[0.4 0.4 0.4 0.6 0.6 0.6 0.2] [1.  1.  1.  1.  1.4 1. ]

#in order to get avg:

r3=np.vstack([r1[:len(r2)],r2[:len(r1)]]).mean(axis=0)

>>> print(r3)
[0.7 0.7 0.7 0.8 1.  0.8]

Answer 3

I see two possible solutions:

1. Create a 'bucket' for each time step, lets say 1 second, and insert all measurements that were taken at the time step +/- 1 second in the bucket. Average all values in the bucket.
2. Interpolate every measurement row, so that they have equal time steps. Average all measurements for every time step