Nearest
Nearest[{elem1,elem2,…},x]
gives the list of elemi to which x is nearest.
Nearest[{elem1v1,elem2v2,…},x]
gives the vi corresponding to the elemi to which x is nearest.
Nearest[{elem1,elem2,…}{v1,v2,…},x]
gives the same result.
Nearest[{elem1,elem2,…}prop,x]
gives the property prop for the elemi to which x is nearest.
Nearest[data,{x1,x2,…}]
effectively gives {Nearest[data,x1],Nearest[data,x2],…}.
Nearest[data,x,n]
gives the n nearest elemi to x.
Nearest[data,x,{n,r}]
gives the n or fewer nearest elemi to x that are within radius r of x.
Nearest[data]
generates a NearestFunction[…] that can be applied repeatedly to different x.
Details and Options
- Nearest works for a variety of data, including numerical, geospatial, textual, and visual, as well as dates and times.
- The data can also be given as an association. In this case, Nearest[<key1val1,key2val2,…>] is equivalent to Nearest[{val1key1,val2key2,…}].
- In Nearest[{elem1,elem2,…}prop,…], possible forms for prop include:
-
"Element" the elemi found to be nearest "Index" the index i of the elemi found to be nearest "Distance" the distance to the nearest elemi {prop1,prop2,…} a list of multiple forms All an association giving element, index and distance - When Nearest returns several elements elemi, the nearest ones are given first.
- If several elements are at the same distance, they are returned in the order they appear in data.
- Nearest[data,x,{All,r}] can be used to get all elemi within radius r.
- The following options can be given:
-
DistanceFunction Automatic the distance metric to use Method Automatic method to use WorkingPrecision Automatic precision to use for numeric data - By default, the following distance functions are used for different types of elemi:
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Norm[#1-#2]& numeric data JaccardDissimilarity Boolean data EditDistance strings ColorDistance colors ImageDistance images DateDifference dates and times GeoDistance geospatial data - Nearest with geospatial data uses GeoDistance to compute distances. The data can be given as a list of GeoPosition objects, or a GeoPosition containing an array of points.
- For images or colors and a distance function f, DistanceFunction->f is passed to ImageDistance and ColorDistance, respectively. »
- All images are conformed using ConformImages. With DistanceFunction->Automatic, dimensionality reduction based on discrete cosine transform is applied to the set of images.
- Using Norm[#1-#2,p]& for
or named distance functions such as ManhattanDistance, ChessboardDistance, and EuclideanDistance can invoke special optimizations for numeric vector data. - Possible settings for Method include "Octree", "KDtree", and "Scan".
- Possible settings for the WorkingPrecision option are:
-
MachinePrecision use machine-precision numbers p use precision p Automatic use adaptive precision to resolve nearest points
Examples
open all close allBasic Examples (5)
Scope (9)
Give the elements within radius 2:
Give at most 3 nearest elements within radius 2:
Find which element is nearest to {2,3} in 2D and return the appropriate label:
Compute the same using an Association:
Return the index for the nearest string:
Return an Association giving the string element, index, and distance:
Find the 3 elements nearest to 20, simultaneously reporting the elements and their distance to 20:
For uniform random points in 3D, give the distances for the 10 nearest to the origin:
For each of the 10 nearest, give an Association including the point element, index and distance:
Create a lookup function for future use:
Find the date nearest to a given DateObject:
Find out which of these {lat,lon} points on Earth is closest to you:
Express the input as a list of separate GeoPosition objects instead:
Report simultaneously the closest point and the distance to it:
Options (6)
DistanceFunction (3)
By default, normal Euclidean distance is used for points:
Use the ManhattanDistance, which sums the length of each side:
The ChessboardDistance only takes into account the dimension with the largest separation:
The DistanceFunction can be given as a symbol:
Find nearest colors using a color distance different from the default distance in ColorDistance:
Method (2)
Compare different methods for machine-precision data:
In three dimensions, the "KDtree" method is faster:
In 20 dimensions, a simple scan is faster:
The setting Method->{"KDtree","LeafSize"->s} may be used to control the maximum number of points in any leaf of the KD tree constructed:
WorkingPrecision (1)
Using WorkingPrecision->MachinePrecision ensures the fastest evaluation method is used:
The results may not be correct if the numbers are not all distinct to machine precision:
All the points are effectively the same to machine precision:
Applications (8)
Plot the Nearest of a list of:
Use a 1-norm ("taxicab distance"):
Highlight the 200 random points closest to the origin:
Create a nearest function from all the words in a dictionary:
Look up words closest to a given word:
Find the outputs from running a sequence of elementary cellular automata:
Generate a complete list of outputs from all 256 elementary cellular automata:
Find which rules give outputs nearest the specified sequences:
Use a negative distance function to find the element farthest away from the given element:
Show the returned element for all values between 1 and 5:
Compute the nearest of the points of that polygon from your current geo location:
Properties & Relations (2)
In the case of a tie, all nearest elements are returned in order:
The single argument form of Nearest returns a NearestFunction object:
This is an optimized lookup function, which is faster than calling Nearest repeatedly:
Text
Wolfram Research (2007), Nearest, Wolfram Language function, https://reference.wolfram.com/language/ref/Nearest.html (updated 2017).
CMS
Wolfram Language. 2007. "Nearest." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2017. https://reference.wolfram.com/language/ref/Nearest.html.
APA
Wolfram Language. (2007). Nearest. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Nearest.html