28

I have a xarray dataset with irregular spaced latitude and longitudes coordinates. My goal is to find the value of a variable at the point nearest a certain lat/lon.

Since the x and y dimensions are not the lat/lon values, it doesn't seem that the ds.sel() method can be used by itself in this case. Is there a xarray-centric method to locate the point nearest a desired lat/lon by referencing the multi-dimensional lat/lon dimensions? For example, I want to pluck out the SPEED value nearest lat=21.2 and lon=-122.68.

Below is an example dataset...

lats = np.array([[21.138  , 21.14499, 21.15197, 21.15894, 21.16591],
                 [21.16287, 21.16986, 21.17684, 21.18382, 21.19079],
                 [21.18775, 21.19474, 21.20172, 21.2087 , 21.21568],
                 [21.21262, 21.21962, 21.22661, 21.23359, 21.24056],
                 [21.2375 , 21.2445 , 21.25149, 21.25848, 21.26545]])  

lons = np.array([[-122.72   , -122.69333, -122.66666, -122.63999, -122.61331],
                 [-122.7275 , -122.70082, -122.67415, -122.64746, -122.62078],
                 [-122.735  , -122.70832, -122.68163, -122.65494, -122.62825],
                 [-122.7425 , -122.71582, -122.68912, -122.66243, -122.63573],
                 [-122.75001, -122.72332, -122.69662, -122.66992, -122.64321]])

speed = np.array([[10.934007, 10.941321, 10.991583, 11.063932, 11.159435],
                  [10.98778 , 10.975482, 10.990983, 11.042522, 11.131154],
                  [11.013505, 11.001573, 10.997754, 11.03566 , 11.123781],
                  [11.011163, 11.000227, 11.010223, 11.049   , 11.1449  ],
                  [11.015698, 11.026604, 11.030653, 11.076904, 11.201464]])

ds = xarray.Dataset({'SPEED':(('x', 'y'),speed)},
                    coords = {'latitude': (('x', 'y'), lats),
                              'longitude': (('x', 'y'), lons)},
                    attrs={'variable':'Wind Speed'})

The value of ds:

<xarray.Dataset>
Dimensions:    (x: 5, y: 5)
Coordinates:
    latitude   (x, y) float64 21.14 21.14 21.15 21.16 ... 21.25 21.26 21.27
    longitude  (x, y) float64 -122.7 -122.7 -122.7 ... -122.7 -122.7 -122.6
Dimensions without coordinates: x, y
Data variables:
SPEED      (x, y) float64 10.93 10.94 10.99 11.06 ... 11.03 11.03 11.08 11.2
Attributes:
    variable:  Wind Speed

Again, ds.sel(latitude=21.2, longitude=-122.68) doesn't work because latitude and longitude are not the dataset dimensions.

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2
  • Any reason the arrays are 5x5? Commented Nov 8, 2019 at 4:50
  • The 5x5 is just a subset of a much larger dataset (5000x5000) for example purposes Commented Nov 8, 2019 at 6:02

6 Answers 6

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21

A bit late to the party here, but I've come back to this question multiple times. If your x and y coordinates are in a geospatial coordinate system, you can transform the lat/lon point to that coordinate system using cartopy. Constructing the cartopy projection is usually straightforward if you look at the metadata from the netcdf.

import cartopy.crs as ccrs

# Example - your x and y coordinates are in a Lambert Conformal projection
data_crs = ccrs.LambertConformal(central_longitude=-100)

# Transform the point - src_crs is always Plate Carree for lat/lon grid
x, y = data_crs.transform_point(-122.68, 21.2, src_crs=ccrs.PlateCarree())

# Now you can select data
ds.sel(x=x, y=y)
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4 Comments

Ah, yes, this is true. Thanks for pointing that out. Just takes a bit of data prep to put those x/y coordinates in the projection coordinates. Thanks @karl-schneider
The last select statement doesn't seem to work for the data format in the question. I'll add an answer with the data prep required.
This is the best answer. Note that you can also use .sel(..., method="nearest") to select the nearest point in x, y. Note that this might not be the nearest point in some if your projection warps space sufficiently.
This method works really well. Some MetPy features can make this easy to do: 1) Use MetPy's ds.metpy.parse_cf method to parse the CF metadata from the file if it's available (if not, use ds.metpy.assign_crs to add the crs information). 2) Use ds.metpy.assign_y_x to change the x/y dim values from index values to projection coordinate values. 3) then data_crs.tranforms_point to convert lat/lon to crs coordinate 4) Then ds.sel(x=x, y=y) as you say. My posted answer performs about the same, but when you scale this up to matching >15 points, this method wins in performance.
18

I came up with a method that doesn't purely use xarray. I first find the index of the nearest neighbor manually, and then use that index to access the xarray dimensions.

# A 2D plot of the SPEED variable, assigning the coordinate values,
# and plot the verticies of each point
ds.SPEED.plot(x='longitude', y='latitude')
plt.scatter(ds.longitude, ds.latitude)

# I want to find the speed at a certain lat/lon point.
lat = 21.22
lon = -122.68

# First, find the index of the grid point nearest a specific lat/lon.   
abslat = np.abs(ds.latitude-lat)
abslon = np.abs(ds.longitude-lon)
c = np.maximum(abslon, abslat)

([xloc], [yloc]) = np.where(c == np.min(c))

# Now I can use that index location to get the values at the x/y diminsion
point_ds = ds.sel(x=xloc, y=yloc)

# Plot requested lat/lon point blue
plt.scatter(lon, lat, color='b')
plt.text(lon, lat, 'requested')

# Plot nearest point in the array red
plt.scatter(point_ds.longitude, point_ds.latitude, color='r')
plt.text(point_ds.longitude, point_ds.latitude, 'nearest')

plt.title('speed at nearest point: %s' % point_ds.SPEED.data)

2d grid of wind speed for the example dataset

Another potential solution (again, not xarray) is to use scipy's KDTree, or even better, scikit-learn's BallTree (https://scikit-learn.org/stable/modules/generated/sklearn.neighbors.BallTree.html) or use https://github.com/xarray-contrib/xoak.

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6 Comments

I cannot get my head around the way you calculate the shortest distance. Please can you explain. I have also provided another answer where I just basically use pythogoras.
My method is most easily understood if you plot the results of abslon and abslat with pcolormesh. These are the absolute difference between the gridded coordinates and the requested point coordinate. The intersection of the minimum values of abslon and abslat (now graph the value of c) is the nearest grid point to the requested point. I then used the where function to locate the minimum value. Hope this helps. It looks like it's practically the same you did in your other example.
I describe the method in more detail here: github.com/blaylockbk/pyBKB_v3/blob/master/demo/…. The original purpose of my question was to see if there was a way already built into xarray to do this sort of indexing for multi-dimensional coordinates, but it looks like there isn't, yet.
Coming to this later, but if you go to his notebook above, you get a nice visualization that shows this answer is taking the minimum of the l-infinity norm (math.stackexchange.com/questions/2842541/… ). Doing np.min(np.maximum(abslon, abslat)) is the l-infinity norm, and doing np.min(abslon**2 + abslat**2) is doing the L2 norm minimum. Both seem like they'd work here.
if your grid is 45° rotated, can't you have a point that is
|
7

I think you need to create your dataset in a different way to make sure latitude and longitude have interpretable dimensions (see article Basic data structure of xarray).

For example:

import numpy as np
import pandas as pd
import xarray
import matplotlib.pyplot as plt
from scipy.interpolate import griddata

lats = np.array([21.138, 21.14499, 21.15197, 21.15894, 21.16591,
                 21.16287, 21.16986, 21.17684, 21.18382, 21.19079,
                 21.18775, 21.19474, 21.20172, 21.2087, 21.21568,
                 21.21262, 21.21962, 21.22661, 21.23359, 21.24056,
                 21.2375, 21.2445, 21.25149, 21.25848, 21.26545])

lons = np.array([-122.72, -122.69333, -122.66666, -122.63999, -122.61331,
                 -122.7275, -122.70082, -122.67415, -122.64746, -122.62078,
                 -122.735, -122.70832, -122.68163, -122.65494, -122.62825,
                 -122.7425, -122.71582, -122.68912, -122.66243, -122.63573,
                 -122.75001, -122.72332, -122.69662, -122.66992, -122.64321])

speed = np.array([10.934007, 10.941321, 10.991583, 11.063932, 11.159435,
                  10.98778, 10.975482, 10.990983, 11.042522, 11.131154,
                  11.013505, 11.001573, 10.997754, 11.03566, 11.123781,
                  11.011163, 11.000227, 11.010223, 11.049, 11.1449,
                  11.015698, 11.026604, 11.030653, 11.076904, 11.201464])

fig, (ax1, ax2) = plt.subplots(ncols=2, figsize=(12, 5))

idx = pd.MultiIndex.from_arrays(arrays=[lons, lats], names=["lon", "lat"])
s = pd.Series(data=speed, index=idx)
da = xarray.DataArray.from_series(s)
print(da)
da.plot(ax=ax1)

print('-'*80)
print(da.sel(lat=21.2, lon=-122.68, method='nearest'))

# define grid.
num_points = 100
lats_i = np.linspace(np.min(lats), np.max(lats), num_points)
lons_i = np.linspace(np.min(lons), np.max(lons), num_points)

# grid the data.
speed_i = griddata((lats, lons), speed,
                   (lats_i[None, :], lons_i[:, None]), method='cubic')

# contour the gridded data
ax2.contour(lats_i, lons_i, speed_i, 15, linewidths=0.5, colors='k')
contour = ax2.contourf(lats_i, lons_i, speed_i, 15, cmap=plt.cm.jet)
plt.colorbar(contour, ax=ax2)

# plot data points.
for i, (lat, lon) in enumerate(zip(lats, lons)):
    label = f'{speed[i]:0.2f}'
    ax2.annotate(label, (lat, lon))

ax2.scatter(lats, lons, marker='o', c='b', s=5)

ax2.set_title(f'griddata test {num_points} points')

plt.subplots_adjust(wspace=0.2)
plt.show()

Result

<xarray.DataArray (lat: 25, lon: 25)>
array([[      nan,       nan,       nan,       nan,       nan, 10.934007,
              nan,       nan,       nan,       nan,       nan,       nan,
              nan,       nan,       nan,       nan,       nan,       nan,
              nan,       nan,       nan,       nan,       nan,       nan,
              nan],
       [      nan,       nan,       nan,       nan,       nan,       nan,
              nan,       nan,       nan,       nan, 10.941321,       nan,
              nan,       nan,       nan,       nan,       nan,       nan,
              nan,       nan,       nan,       nan,       nan,       nan,
              nan],
       [      nan,       nan,       nan,       nan,       nan,       nan,
              nan,       nan,       nan,       nan,       nan,       nan,
              nan,       nan,       nan, 10.991583,       nan,       nan,
              nan,       nan,       nan,       nan,       nan,       nan,
              nan],
       [      nan,       nan,       nan,       nan,       nan,       nan,
              nan,       nan,       nan,       nan,       nan,       nan,
              nan,       nan,       nan,       nan,       nan,       nan,
              nan,       nan, 11.063932,       nan,       nan,       nan,
              nan],
       [      nan,       nan,       nan, 10.98778 ,       nan,       nan,
              nan,       nan,       nan,       nan,       nan,       nan,
              nan,       nan,       nan,       nan,       nan,       nan,
              nan,       nan,       nan,       nan,       nan,       nan,
              nan],
       [      nan,       nan,       nan,       nan,       nan,       nan,
              nan,       nan,       nan,       nan,       nan,       nan,
              nan,       nan,       nan,       nan,       nan,       nan,
              nan,       nan,       nan,       nan,       nan,       nan,
        11.159435],
       [      nan,       nan,       nan,       nan,       nan,       nan,
              nan,       nan, 10.975482,       nan,       nan,       nan,
              nan,       nan,       nan,       nan,       nan,       nan,
              nan,       nan,       nan,       nan,       nan,       nan,
              nan],
       [      nan,       nan,       nan,       nan,       nan,       nan,
              nan,       nan,       nan,       nan,       nan,       nan,
              nan, 10.990983,       nan,       nan,       nan,       nan,
              nan,       nan,       nan,       nan,       nan,       nan,
              nan],
       [      nan,       nan,       nan,       nan,       nan,       nan,
              nan,       nan,       nan,       nan,       nan,       nan,
              nan,       nan,       nan,       nan,       nan,       nan,
        11.042522,       nan,       nan,       nan,       nan,       nan,
              nan],
       [      nan,       nan, 11.013505,       nan,       nan,       nan,
              nan,       nan,       nan,       nan,       nan,       nan,
              nan,       nan,       nan,       nan,       nan,       nan,
              nan,       nan,       nan,       nan,       nan,       nan,
              nan],
       [      nan,       nan,       nan,       nan,       nan,       nan,
              nan,       nan,       nan,       nan,       nan,       nan,
              nan,       nan,       nan,       nan,       nan,       nan,
              nan,       nan,       nan,       nan,       nan, 11.131154,
              nan],
       [      nan,       nan,       nan,       nan,       nan,       nan,
              nan, 11.001573,       nan,       nan,       nan,       nan,
              nan,       nan,       nan,       nan,       nan,       nan,
              nan,       nan,       nan,       nan,       nan,       nan,
              nan],
       [      nan,       nan,       nan,       nan,       nan,       nan,
              nan,       nan,       nan,       nan,       nan,       nan,
        10.997754,       nan,       nan,       nan,       nan,       nan,
              nan,       nan,       nan,       nan,       nan,       nan,
              nan],
       [      nan,       nan,       nan,       nan,       nan,       nan,
              nan,       nan,       nan,       nan,       nan,       nan,
              nan,       nan,       nan,       nan,       nan, 11.03566 ,
              nan,       nan,       nan,       nan,       nan,       nan,
              nan],
       [      nan, 11.011163,       nan,       nan,       nan,       nan,
              nan,       nan,       nan,       nan,       nan,       nan,
              nan,       nan,       nan,       nan,       nan,       nan,
              nan,       nan,       nan,       nan,       nan,       nan,
              nan],
       [      nan,       nan,       nan,       nan,       nan,       nan,
              nan,       nan,       nan,       nan,       nan,       nan,
              nan,       nan,       nan,       nan,       nan,       nan,
              nan,       nan,       nan,       nan, 11.123781,       nan,
              nan],
       [      nan,       nan,       nan,       nan,       nan,       nan,
        11.000227,       nan,       nan,       nan,       nan,       nan,
              nan,       nan,       nan,       nan,       nan,       nan,
              nan,       nan,       nan,       nan,       nan,       nan,
              nan],
       [      nan,       nan,       nan,       nan,       nan,       nan,
              nan,       nan,       nan,       nan,       nan, 11.010223,
              nan,       nan,       nan,       nan,       nan,       nan,
              nan,       nan,       nan,       nan,       nan,       nan,
              nan],
       [      nan,       nan,       nan,       nan,       nan,       nan,
              nan,       nan,       nan,       nan,       nan,       nan,
              nan,       nan,       nan,       nan, 11.049   ,       nan,
              nan,       nan,       nan,       nan,       nan,       nan,
              nan],
       [11.015698,       nan,       nan,       nan,       nan,       nan,
              nan,       nan,       nan,       nan,       nan,       nan,
              nan,       nan,       nan,       nan,       nan,       nan,
              nan,       nan,       nan,       nan,       nan,       nan,
              nan],
       [      nan,       nan,       nan,       nan,       nan,       nan,
              nan,       nan,       nan,       nan,       nan,       nan,
              nan,       nan,       nan,       nan,       nan,       nan,
              nan,       nan,       nan, 11.1449  ,       nan,       nan,
              nan],
       [      nan,       nan,       nan,       nan, 11.026604,       nan,
              nan,       nan,       nan,       nan,       nan,       nan,
              nan,       nan,       nan,       nan,       nan,       nan,
              nan,       nan,       nan,       nan,       nan,       nan,
              nan],
       [      nan,       nan,       nan,       nan,       nan,       nan,
              nan,       nan,       nan, 11.030653,       nan,       nan,
              nan,       nan,       nan,       nan,       nan,       nan,
              nan,       nan,       nan,       nan,       nan,       nan,
              nan],
       [      nan,       nan,       nan,       nan,       nan,       nan,
              nan,       nan,       nan,       nan,       nan,       nan,
              nan,       nan, 11.076904,       nan,       nan,       nan,
              nan,       nan,       nan,       nan,       nan,       nan,
              nan],
       [      nan,       nan,       nan,       nan,       nan,       nan,
              nan,       nan,       nan,       nan,       nan,       nan,
              nan,       nan,       nan,       nan,       nan,       nan,
              nan, 11.201464,       nan,       nan,       nan,       nan,
              nan]])
Coordinates:
  * lat      (lat) float64 21.14 21.14 21.15 21.16 ... 21.24 21.25 21.26 21.27
  * lon      (lon) float64 -122.8 -122.7 -122.7 -122.7 ... -122.6 -122.6 -122.6
--------------------------------------------------------------------------------
<xarray.DataArray ()>
array(10.997754)
Coordinates:
    lat      float64 21.2
    lon      float64 -122.7

and a plot including gridding just for the fun of it enter image description here

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Comments

4

I like the answer given by @blaylockbk, but I cannot get my head around the way the shortest distance is calculated to a datapoint. Below I provide an alternative that just makes use of Pythagoras plus a way to grid the dataset ds. In order not to confuse the (x, y) in the dataset with x, y geodetic co-ordinates I have renamed them to (i, j).

import numpy as np
import xarray
import matplotlib.pyplot as plt
from scipy.interpolate import griddata

lats = np.array([[21.138, 21.14499, 21.15197, 21.15894, 21.16591],
                 [21.16287, 21.16986, 21.17684, 21.18382, 21.19079],
                 [21.18775, 21.19474, 21.20172, 21.2087, 21.21568],
                 [21.21262, 21.21962, 21.22661, 21.23359, 21.24056],
                 [21.2375, 21.2445, 21.25149, 21.25848, 21.26545]])

lons = np.array([[-122.72, -122.69333, -122.66666, -122.63999, -122.61331],
                 [-122.7275, -122.70082, -122.67415, -122.64746, -122.62078],
                 [-122.735, -122.70832, -122.68163, -122.65494, -122.62825],
                 [-122.7425, -122.71582, -122.68912, -122.66243, -122.63573],
                 [-122.75001, -122.72332, -122.69662, -122.66992, -122.64321]])

speed = np.array([[10.934007, 10.941321, 10.991583, 11.063932, 11.159435],
                  [10.98778, 10.975482, 10.990983, 11.042522, 11.131154],
                  [11.013505, 11.001573, 10.997754, 11.03566, 11.123781],
                  [11.011163, 11.000227, 11.010223, 11.049, 11.1449],
                  [11.015698, 11.026604, 11.030653, 11.076904, 11.201464]])

ds = xarray.Dataset({'SPEED': (('i', 'j'), speed)},
                    coords={'latitude': (('i', 'j'), lats),
                            'longitude': (('i', 'j'), lons)},
                    attrs={'variable': 'Wind Speed'})

lat_min = float(np.min(ds.latitude))
lat_max = float(np.max(ds.latitude))
lon_min = float(np.min(ds.longitude))
lon_max = float(np.max(ds.longitude))
margin = 0.02

fig, ((ax1, ax2)) = plt.subplots(nrows=1, ncols=2, figsize=(12, 5))

ax1.set_xlim(lat_min - margin, lat_max + margin)
ax1.set_ylim(lon_min - margin, lon_max + margin)
ax1.axis('equal')
ds.SPEED.plot(ax=ax1, x='latitude', y='longitude', cmap=plt.cm.jet)
ax1.scatter(ds.latitude, ds.longitude, color='black')

# find nearest_point for a requested lat/ lon
lat_requested = 21.22
lon_requested = -122.68

d_lat = ds.latitude - lat_requested
d_lon = ds.longitude - lon_requested
r2_requested = d_lat**2 + d_lon**2
i_j_loc = np.where(r2_requested == np.min(r2_requested))

nearest_point = ds.sel(i=i_j_loc[0], j=i_j_loc[1])

# Plot nearest point in the array red# Plot nearest point in the array red
ax1.scatter(lat_requested, lon_requested, color='green')
ax1.text(lat_requested, lon_requested, 'requested')
ax1.scatter(nearest_point.latitude, nearest_point.longitude, color='red')
ax1.text(nearest_point.latitude, nearest_point.longitude, 'nearest')
ax1.set_title(f'speed at nearest point: {float(nearest_point.SPEED.data):.2f}')

# define grid from the dataset
num_points = 100
lats_i = np.linspace(lat_min, lat_max, num_points)
lons_i = np.linspace(lon_min, lon_max, num_points)

# grid and contour the data.
speed_i = griddata((ds.latitude.values.flatten(), ds.longitude.values.flatten()),
                   ds.SPEED.values.flatten(),
                   (lats_i[None, :], lons_i[:, None]), method='cubic')

ax2.set_xlim(lat_min - margin, lat_max + margin)
ax2.set_ylim(lon_min - margin, lon_max + margin)
ax2.axis('equal')
ax2.set_title(f'griddata test {num_points} points')

ax2.contour(lats_i, lons_i, speed_i, 15, linewidths=0.5, colors='k')
contour = ax2.contourf(lats_i, lons_i, speed_i, 15, cmap=plt.cm.jet)
plt.colorbar(contour, ax=ax2)

# plot data points and labels
ax2.scatter(ds.latitude, ds.longitude, marker='o', c='b', s=5)

for i, (lat, lon) in enumerate(zip(ds.latitude.values.flatten(),
                                   ds.longitude.values.flatten())):
    text_label = f'{ds.SPEED.values.flatten()[i]:0.2f}'
    ax2.text(lat, lon, text_label)

# Plot nearest point in the array red
ax2.scatter(lat_requested, lon_requested, color='green')
ax2.text(lat_requested, lon_requested, 'requested')
ax2.scatter(nearest_point.latitude, nearest_point.longitude, color='red')

plt.subplots_adjust(wspace=0.2)
plt.show()

result: result

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Comments

4

To do the lookup based on projection on this data format as mentioned in another answer, you unfortunately have to add the projection information back into the data.

import cartopy.crs as ccrs

# Projection may vary
projection = ccrs.LambertConformal(central_longitude=-97.5,
                             central_latitude=38.5,
                             standard_parallels=[38.5])
transform = np.vectorize(lambda x, y: projection.transform_point(x, y, ccrs.PlateCarree()))

# The grid should be aligned such that the projection x and y are the same
# at every y and x index respectively
grid_y = ds.isel(x=0)
grid_x = ds.isel(y=0)

_, proj_y = transform(grid_y.longitude, grid_y.latitude)
proj_x, _ = transform(grid_x.longitude, grid_x.latitude)

# ds.sel only works on the dimensions, so we can't just add
# proj_x and proj_y as additional coordinate variables
ds["x"] = proj_x
ds["y"] = proj_y

desired_x, desired_y = transform(-122.68, 21.2)
nearest_point = ds.sel(x=desired_x, y=desired_y, method="nearest")

print(nearest_point.SPEED)

Output:

<xarray.DataArray 'SPEED' ()>
array(10.934007)
Coordinates:
    latitude   float64 21.14
    longitude  float64 -122.7
    x          float64 -2.701e+06
    y          float64 -1.581e+06
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Comments

2

Just a comment and some runtimes:
For 5000 × 5000 data points, each single query takes time and space proportional to 25 million. The following, which I think is equivalent to your code, takes ~ 1 sec per query on my old 2.7 GHz iMac:

import sys
import numpy as np
from scipy.spatial.distance import cdist

n = 5000
nask = 1
dim = 2
# to change these params, run this.py  a=1  b=None  'c = expr' ... in sh or ipython --
for arg in sys.argv[1:]:
    exec( arg )
rng = np.random.default_rng( seed=0 )

X = rng.uniform( -100, 100, size=(n*n, dim) )  # data, n^2 × 2
ask = rng.uniform( -100, 100, size=(nask, dim) )  # query points

dist = cdist( X, ask, "chebyshev" )  # -> n^2 × nask

    # 1d index -> 2d index, e.g. 60003 -> row 12, col 3
jminflat = dist[:,0].argmin()
jmin = np.unravel_index( jminflat, (n,n) )
print( "cdist  N %g  dim %d  ask %s: dist %.2g to X[%s] = %s " % (
        n*n, dim, ask[0], dist[jminflat], jmin, X[jminflat] ))
# cdist  N 25000000  dim 2  ask [-4.6 94]: dist 0.0079 to X[(4070, 2530)] = [-4.6 94]

For comparison, scipy KDTree takes ~ 30 sec to build a tree for 25M 2d points, then each query takes milliseconds. Advantages: the input points can be scattered any which way, and finding 5 or 10 nearest neighbors to interpolate takes not much longer than 1.

See also: scipy cdist
difference-between-reproject-match-and-interp-like on gis.stack
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