I have several values that are defined on the same irregular grid (x, y, z)
that I want to interpolate onto a new grid (x1, y1, z1)
. i.e., I have f(x, y, z), g(x, y, z), h(x, y, z)
and I want to calculate f(x1, y1, z1), g(x1, y1, z1), h(x1, y1, z1)
.
At the moment I am doing this using scipy.interpolate.griddata
and it works well. However, because I have to perform each interpolation separately and there are many points, it is quite slow, with a great deal of duplication in the calculation (i.e finding which points are closest, setting up the grids etc...).
Is there a way to speedup the calculation and reduce the duplicated calculations? i.e something along the lines of defining the two grids, then changing the values for the interpolation?
There are several things going on every time you make a call to
scipy.interpolate.griddata
:sp.spatial.qhull.Delaunay
is made to triangulate the irregular grid coordinates.The first three steps are identical for all your interpolations, so if you could store, for each new grid point, the indices of the vertices of the enclosing simplex and the weights for the interpolation, you would minimize the amount of computations by a lot. This is unfortunately not easy to do directly with the functionality available, although it is indeed possible:
The function
interp_weights
does the calculations for the first three steps I listed above. Then the functioninterpolate
uses those calcualted values to do step 4 very fast:So first, it does the same as
griddata
, which is good. Second, setting up the interpolation, i.e. computingvtx
andwts
takes roughly the same as a call togriddata
. But third, you can now interpolate for different values on the same grid in virtually no time.The only thing that
griddata
does that is not contemplated here is assigningfill_value
to points that have to be extrapolated. You could do that by checking for points for which at least one of the weights is negative, e.g.: