I'm looking for a way to do a simple linear interpolation between two numpy arrays that represent a start and endpoint in time.
The two arrays have the same length:
fst = np.random.random_integers(5, size=(10.))
>>> array([4, 4, 1, 3, 1, 4, 3, 2, 5, 2])
snd = np.random.random_integers(5, size=(10.))
>>> array([1, 1, 3, 4, 1, 5, 5, 5, 4, 3])
Between my start and endpoint there are 3 timesteps. How can I interpolate between fst and snd? I want to be able, taking the first entry of fst and snd as an example, to retrieve the value of each timestep like
np.interp(1, [1,5], [4,1])
np.interp(2, [1,5], [4,1])
...
# that is
np.interp([1,2,3,4,5], [1,5], [4,1])
>>> array([ 4. , 3.25, 2.5 , 1.75, 1. ])
But than not just for the first entry but over the whole array.
Obviously, this won't do it:
np.interp(1, [1,5], [fst,snd])
Well I know I get there in a loop, e.g.
[np.interp(2, [1,5], [item,snd[idx]]) for idx,item in enumerate(fst)]
>>> [3.25, 3.25, 1.5, 3.25, 1.0, 4.25, 3.5, 2.75, 4.75, 2.25]
but I believe when you are lopping over numpy arrays you are doing something fundamentally wrong.
The facilities in scipy.interpolate.interp1d allow this to be done quite easily if you form your samples into a 2D matrix. In your case, you can construct a 2xN array, and construct an interpolation function that operates down the columns:
from scipy.interpolate import interp1d
fst = np.array([4, 4, 1, 3, 1, 4, 3, 2, 5, 2])
snd = np.array([1, 1, 3, 4, 1, 5, 5, 5, 4, 3])
linfit = interp1d([1,5], np.vstack([fst, snd]), axis=0)
You can then generate an interpolated vector at any time of interest. For example linfit(2) produces:
array([ 3.25, 3.25, 1.5 , 3.25, 1. , 4.25, 3.5 , 2.75, 4.75, 2.25])
or you can invoke linfit() with a vector of time values, e.g. linfit([1,2,3]) gives:
array([[ 4. , 4. , 1. , 3. , 1. , 4. , 3. , 2. , 5. , 2. ],
[ 3.25, 3.25, 1.5 , 3.25, 1. , 4.25, 3.5 , 2.75, 4.75, 2.25],
[ 2.5 , 2.5 , 2. , 3.5 , 1. , 4.5 , 4. , 3.5 , 4.5 , 2.5 ]])
If you're only doing linear interpolation, you could also just do something like:
((5-t)/(5-1)) * fst + ((t-1)/(5-1)) * snd
to directly compute the interpolated vector at any time t.