Interpolating/crossfading a stack of matrices

[raphael at mameghani.de]

>> Hi,
>>
>> I want to interpolate (with quadratic splines) a stack of 2D-arrays/matrices
>> y1, y2, y3, ... in a third dimension (which I call x) e.g. for crossfading 
>> images. I already have a working code which unfortunately still contains two 
>> explicit loops over the rows and colums of the matrices. Inside these loops I 
>> simply use 'interp1d' from scipy suitable for 1D-interpolations. Is anybody 
>> here aware of a better, more efficient solution of my problem? Maybe 
>> somewhere out there a compiled routine for my problem already exists in a 
>> python library... :-) 

> Since numpy arrays make it so easy to form linear combinations of
> arrays without loops I would probably eliminate the loops and just 
> form the appropriate combinations of the image arrays. For example, to 
> use linear interpolation you could do:
> 
> 
> 
> def interp_frames_linear(times, frames, t):
> 
>     '''times is a vector of floats
> 
>     frames is a 3D array whose nth page is the image for time t[n]
> 
>     t is the time to interpolate for
> 
>     '''
> 
>     # Find the two frames to interpolate between
> 
>     # Probably a better way of doing this
> 
>     for n in range(len(t)-1):
> 
>         if times[n] <= t < times[n+1]:
> 
>             break
> 
>     else:
> 
>         raise OutOfBoundsError
> 
> 
> 
>     # Interpolate between the two images
> 
>     alpha = (t - times[n]) / (times[n+1] - times[n])
> 
>     return (1 - alpha) * frames[:, :, n] + alpha * frames[:, :, n+1]
> 
> 
> 
> I'm not really sure how quadratic interpolation is supposed to work
> (I've only ever used linear and cubic) but you should be able to do
> the same sort of thing.
> 
> Oscar

Indeed, the 'manual' reimplementation of the interpolation formula using numpy arrays significantly sped up the code. The numexpr package made it even faster. Thanks a lot for your advice!

Raphael