python-二维插值，一次一维

Question

I am trying to implement some interpolation techniques - specifically using the scipy pchip routine.

What I am trying to determine is whether I can perform interpolation of regularly space 2d data by interpolating each coordinate separately.

For example, if I have:

(1 x m) vector of X coordinates
(1 x n) vector of Y coordinates

(m x n) matrix of Z coordinates //Z value corresponding to (x,y) pair

Is it possible to perform pchip interpolation over each dimension in succession, therefore creating an interpolated surface?

Pchip expects data in the form of pchip(X,Z) - where both X and Z are 1D arrays. What then is the best way to interpolate each dimension? Should I do, for example, pchip(X,Z) for each column of my Z matrix? Then pchip(Y,Z*) over each row of the matrix resulting from the first interpolation?

Thank you for the help. I have seen pv post about performing tensor rpoduct interpolation with pchip, but it results in a pesky divide by zero error I can't get rid of, even with his updates on github.

EDIT:

I found this ticket posted regarding the warning I have using pchip: http://projects.scipy.org/scipy/ticket/1838

Could anyone please tell me what it means when it says "The infs/nans so generated are filtered out by applying a boolean condition mask, but the mask could be applied before division to avoid the warnings altogether. "

How do I got about applying this to avoid the warning?

Answer 1

Take a look at the top picture in Bilinear interpolation .
Find the rows y1, y2 nearest y,
pchip x in those to get R1 R2 (blue),
then linearly interpolate those to get P (green).
(You could also do that in the other order, and average the values x-then-y, y-then-x.)

However if pchip is nearly linear between knots (is it for your data ?),
then it would be simpler to do bilinear directly, either with scipy BivariateSpline
or with scipy.ndimage.interpolation.map_coordinates ( ... order=1 ) and (ahem) the wrapper Intergrid .