How to find the nearest point for 71 points?

Hey all,

I have coordinates.mat which includes the name of 71 climate stations and corresponding latitude and longitude. I want to know the nearest stations. I want something like this:

Station lat lon NEAR_STATION *(NEW COLUMN IN FRONT OF EACH ROW)*

------------------------------------------------------------------------------------------

Ahvaz 20.32 33.3 Abadan

Abadan 20.30 33 Ahvaz

Tehran 36.72 52.5 Qum

I want to find the nearest stations for all these 71 stations. once I know what is the name of the nearest station I can go ahead and using linear regression to reconstruct missing data.

thank you in advance

I attached coordinates.mat

[Walter Roberson]

Which distance measure are you using? Is Euclidean distance good enough for your purposes? If not, then is Sphere an acceptable approximation https://www.mathworks.com/matlabcentral/fileexchange/23026-compute-the-great-circle-distance-between-two-points or do you need a reference ellipsoid? https://www.mathworks.com/help/map/ref/distance.html ?

You can use pdist() . If you need something other than Euclidean distance then you can pass a handle to the distance function like

pdist(Points, @(Z1,Z2) distance(Z1(1), Z1(2), Z2(1), Z2(2)))

It is common to want to use squareform() on the output of pdist()

[BN]

Is there any chance for dsearchn? I'm new to this topic. I have 71 points (latitude and longitude creates a point actually) I want to find the nearest points for all these 71's. So I want to find one nearest point for every 71 points that I have. I think it would be great if the distance between them can be calculated by kilometer. I don't have any idea to do this. any help is appreciated.

Thank you and Best Regards

[Walter Roberson]

dsearchn always uses Euclidean distance. That might or might not be acceptable to you. depending on the span of latitudes and the distance from the equator. If map distance is needed then use https://www.mathworks.com/help/stats/knnsearch.html knnsearch with the 'Distance' option naming a function handle such as the distance() function from the Mapping Toolbox

I think it would be great if the distance between them can be calculated by kilometer

With the span of latitudes that you have, you cannot get kilometer accuracy using Euclidean distance.

>> 69*1.6093*cosd(20.3)

ans =

          104.144781710494

>> 69*1.6093*cosd(36.72)

ans =

          89.0073606639364

so you have a difference of about 15 kilometer per degree of longitude because of latitude effects.

[BN]

Ok, thank you for very useful information.

I'll go ahead and modify my question. really helpful information from you. Best Regards.

[Walter Roberson]

I notice that your example coordinates are pretty far off from reality. It might be the case that your actual coordinates are all close enough together that you can use Euclidean distance. However, at your lowest latitude, 20.30, an additional 1.44 degrees north makes a difference of 1 kilometer per degree of longitude due to spherical correction, so your stations would have to be really close together or closer yet to the equator to get kilometer accuracy using Euclidean distance.

[BN]

Yes, you are right. all the latitude and longitude stands for climate stations in a country. The biggest problem that is I have 2 things (latitude and longitude) and I want to search along 2 columns (latitude and longitude). I could handle it if they are just one point using this code:

Ahvaz = coordinates(5,{'lat','lon'})
All = coordinates(:,{'lat','lon'})
%compute Euclidean distances:
distances = sqrt(sum(bsxfun(@minus, All, Ahvaz).^2,2));
%find the smallest distance and use that as an index into All:
closest = All(find(distances==min(distances)),:);

If I knew how to automatically finde the nearest station for Ahvaz (in station_name column) and prints the name of it. I could repeat the process for all stations and find my answer. I want to use the Euclidean distance.

[BN]

In fact the distance between them no important for me. I just want to know which station is more near to Ahvaz to use its data.

[Mohammad Sami]

You can try to use interp2, it will help you interpolate in 2 dimension.

Vq = interp2(X,Y,V,Xq,Yq,'nearest'); % use the method nearest

X = lat, Y = lon, V = StationID, Xq = lat_of_missing, Yq = lon_of_missing.

Do note as Walter mentioned, that this is will not use Euclidean distance.

[BN]

For each point, I need to compute the distance to all other points, and pick the one with the smallest distance. I want to save some computation by realizing that the distances are symmetric, and so need to compute only n*(n-1)/2 distances.

[BN]

Dear @Mohammad Sami,

This is not fill missing problem, I jsut want to find nearest station.

[Walter Roberson]

I would tend to suspect you should be using

Ahvaz = coordinates{5,{'lat','lon'}};
All = coordinates{:,{'lat','lon'}};

Caution:

closest = All(find(distances==min(distances)),:);

Your All data includes Ahvaz so the minimum distance is going to be 0, which is not going to be of much use to you.

[BN]

Ah, you right. I didn't consider that. after running the code, the output is Ahvaz :(

[BN]

I modify my question and post it. Thank you I learn so many things here.

[BN]

I moved my question to this link and modify it: https://www.mathworks.com/matlabcentral/answers/501995-help-me-to-find-nearest-latitude-and-longitude-between-a-bunch-of-latitudes-and-longitudes

thank you all