How do you interpolate 2D data with unique y-arrays for each x-array value in Python?

Question

I'm struggling to produce an interpolation function for some 2-dimensional data I have. My data isn't standard as each value in the x-array corresponds to a unique y-array. For example:

x = [0.1, 0.2]

y1 = [13.719, 10.488, 9.885, 9.704]       #Corresponding to x=0.1

y2 = [13.34, 10.259,  9.275,  8.724]      #Corresponding to x=0.2

z1 = [1395., 2209., 2411., 2555.]         #Corresponding to y1

z2 = [1570., 2261., 2519., 2682.]         #Corresponding to y2

Ideally I would like to generate a function, f(x, y) that will return an interpolated value of z.

So far my only attempts have been through using:

from scipy.interpolate import interp2d

interpolation = interp2d(x, [y1, y2], [z1, z2])

Which, not unsurprisingly, results in the following error message:

ValueError: x and y must have equal lengths for non rectangular grid

I understand why I'm getting this message and appreciate that interp2d is not the function I should be using, but I'm unsure where to go from here.

Mikhail Genkin · Accepted Answer · 2019-11-07 14:33:24Z

1

The problem is that interp2d works with data arranged on a rectangular grid. You only have 8 data points that are not arranged in a rectangular xy grid.

You can consider a rectangle 2x8 that consists of all possible combinations of your x and y data, but you only have 8 data points (z values).

Below is an example solution with more generic scipy.interpolate.griddata function:

x = [0.1, 0.2]
y1 = [13.719, 10.488, 9.885, 9.704]       #Corresponding to x=0.1
y2 = [13.34, 10.259,  9.275,  8.724]      #Corresponding to x=0.2
z1 = [1395., 2209., 2411., 2555.]         #Corresponding to y1
z2 = [1570., 2261., 2519., 2682.]         #Corresponding to y2

y=np.concatenate((y1,y2))  # collapse all y-data into a single array

# obtain x- and y- grids
grid_x, grid_y =np.meshgrid(np.array(x), y)[0].T, np.meshgrid(np.array(x), y)[1].T
points=np.stack((np.repeat(x,4).T,y))  #obtain xy corrdinates for data points
values=np.concatenate((z1,z2)) #obtain values 
grid_z0 = griddata(points.T, values, (grid_x, grid_y), method='nearest') #Nearest neighbour interpolation

You can generalize this code for other interpolation options / denser grids and so on.

answered Nov 7, 2019 at 14:33

Mikhail Genkin

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2 Comments

Carterini Over a year ago

Great, thanks for the response. I wasn't aware of grid data before and this has definitely solved my problem. For any future readers of this question, to actually extract new values of z for a given x/y adjust the final line to: grid_z0 = griddata(points.T, values, (new_x, new_y), method='cubic'). Cubic is optional, but 'nearest' won't interpolate between points.

Mikhail Genkin Over a year ago

Sure. I just showed a simple solution, and one should use their own parameters (interpolation type and the grid)

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