# rangesearch

Find all neighbors within specified distance using searcher object

## Description

searches for all neighbors (i.e., points, rows, or observations) in
`Idx`

= rangesearch(`Mdl`

,`Y`

,`r`

)`Mdl.X`

within radius `r`

of each point (i.e.,
row or observation) in the query data `Y`

using an exhaustive
search or a *K*d-tree. `rangesearch`

returns
`Idx`

, which is a column vector of the indices of
`Mdl.X`

within `r`

units.

returns the indices of the observation in `Idx`

= rangesearch(`Mdl`

,`Y`

,`r`

,`Name,Value`

)`Mdl.X`

within radius
`r`

of each observation in `Y`

with additional
options specified by one or more `Name,Value`

pair arguments. For
example, you can specify to use a different distance metric than is stored in
`Mdl.Distance`

or a different distance metric parameter than is
stored in `Mdl.DistParameter`

.

`[`

additionally returns the matrix `Idx`

,`D`

]
= rangesearch(___)`D`

using any of the input
arguments in the previous syntaxes. `D`

contains the distances
between the observations in `Mdl.X`

within radius
`r`

of each observation in `Y`

. By default,
the function arranges the columns of `D`

in ascending order by
closeness, with respect to the distance metric.

## Examples

### Search for Neighbors Within a Radius Using *K*d-tree and Exhaustive Search

`rangesearch`

accepts `ExhaustiveSearcher`

or `KDTreeSearcher`

model objects to search the training data for the nearest neighbors to the query data. An `ExhaustiveSearcher`

model invokes the exhaustive searcher algorithm, and a `KDTreeSearcher`

model defines a *K*d-tree, which `rangesearch`

uses to search for nearest neighbors.

Load Fisher's iris data set. Randomly reserve five observations from the data for query data. Focus on the petal dimensions.

load fisheriris rng(1); % For reproducibility n = size(meas,1); idx = randsample(n,5); X = meas(~ismember(1:n,idx),3:4); % Training data Y = meas(idx,3:4); % Query data

Grow a default two-dimensional *K*d-tree.

MdlKDT = KDTreeSearcher(X)

MdlKDT = KDTreeSearcher with properties: BucketSize: 50 Distance: 'euclidean' DistParameter: [] X: [145x2 double]

`MdlKDT`

is a `KDTreeSearcher`

model object. You can alter its writable properties using dot notation.

Prepare an exhaustive nearest neighbor searcher.

MdlES = ExhaustiveSearcher(X)

MdlES = ExhaustiveSearcher with properties: Distance: 'euclidean' DistParameter: [] X: [145x2 double]

`MdlES`

is an `ExhaustiveSearcher`

model object. It contains the options, such as the distance metric, to use to find nearest neighbors.

Alternatively, you can grow a *K*d-tree or prepare an exhaustive nearest neighbor searcher using `createns`

.

Search training data for the nearest neighbor indices that correspond to each query observation that are within a 0.5 cm radius. Conduct both types of searches and use the default settings.

```
r = 0.15; % Search radius
IdxKDT = rangesearch(MdlKDT,Y,r);
IdxES = rangesearch(MdlES,Y,r);
[IdxKDT IdxES]
```

`ans=`*5×2 cell array*
{[ 1 4 8 27 32 45 47 2 35 37 41 6 17 12 36 3 7 10 26 33 38 46 39 40 19 9 31]} {[ 1 4 8 27 32 45 47 2 35 37 41 6 17 12 36 3 7 10 26 33 38 46 39 40 19 9 31]}
{[ 13]} {[ 13]}
{[6 17 39 40 1 4 8 27 32 45 47 19 2 35 37 41 16 3 7 10 26 33 38 46 15 21 30]} {[6 17 39 40 1 4 8 27 32 45 47 19 2 35 37 41 16 3 7 10 26 33 38 46 15 21 30]}
{[ 64 66]} {[ 64 66]}
{1x0 double } {1x0 double }

`IdxKDT`

and `IdxES`

are cell arrays of vectors corresponding to the indices of `X`

that are within 0.15 cm of the observations in `Y`

. Each row of the index matrices corresponds to a query observation.

Compare the results between the methods.

cellfun(@isequal,IdxKDT,IdxES)

`ans = `*5x1 logical array*
1
1
1
1
1

In this case, the results are the same.

Plot the results for the setosa irises.

setosaIdx = strcmp(species(~ismember(1:n,idx)),'setosa'); XSetosa = X(setosaIdx,:); ySetosaIdx = strcmp(species(idx),'setosa'); YSetosa = Y(ySetosaIdx,:); figure; plot(XSetosa(:,1),XSetosa(:,2),'.k'); hold on; plot(YSetosa(:,1),YSetosa(:,2),'*r'); for j = 1:sum(ySetosaIdx) c = YSetosa(j,:); circleFun = @(x1,x2)r^2 - (x1 - c(1)).^2 - (x2 - c(2)).^2; fimplicit(circleFun,[c(1) + [-1 1]*r, c(2) + [-1 1]*r],'b-') end xlabel 'Petal length (cm)'; ylabel 'Petal width (cm)'; title 'Setosa Petal Measurements'; legend('Observations','Query Data','Search Radius'); axis equal hold off

### Search for Neighbors Within a Radius Using the Mahalanobis Distance

Load Fisher's iris data set.

`load fisheriris`

Remove five irises randomly from the predictor data to use as a query set.

rng(1); % For reproducibility n = size(meas,1); % Sample size qIdx = randsample(n,5); % Indices of query data X = meas(~ismember(1:n,qIdx),:); Y = meas(qIdx,:);

Prepare a default exhaustive nearest neighbor searcher.

Mdl = ExhaustiveSearcher(X)

Mdl = ExhaustiveSearcher with properties: Distance: 'euclidean' DistParameter: [] X: [145x4 double]

`Mdl`

is an `ExhaustiveSearcher`

model.

Find the indices of the training data (`X`

) that are within 0.15 cm of each point in the query data (`Y`

). Specify that the distances are with respect to the Mahalanobis metric.

r = 1; Idx = rangesearch(Mdl,Y,r,'Distance','mahalanobis')

`Idx=`*5×1 cell array*
{[26 38 7 17 47 4 27 46 25 10 39 20 21 2 33]}
{[ 6 21 25 4 19]}
{[ 1 34 33 22 24 2]}
{[ 84]}
{[ 69]}

Idx{3}

`ans = `*1×6*
1 34 33 22 24 2

Each cell of `Idx`

corresponds to a query data observation and contains in `X`

a vector of indices of the neighbors within 0.15cm of the query data. `rangesearch`

arranges the indices in ascending order by distance. For example, using the Mahalanobis distance, the second nearest neighbor of `Y(3,:)`

is `X(34,:)`

.

### Compute Distances of Neighbors Within a Radius

Load Fisher's iris data set.

`load fisheriris`

Remove five irises randomly from the predictor data to use as a query set.

rng(4); % For reproducibility n = size(meas,1); % Sample size qIdx = randsample(n,5); % Indices of query data X = meas(~ismember(1:n,qIdx),:); Y = meas(qIdx,:);

Grow a four-dimensional *K*d-tree using the training data. Specify to use the Minkowski distance for finding nearest neighbors.

Mdl = KDTreeSearcher(X);

`Mdl`

is a `KDTreeSearcher`

model. By default, the distance metric for finding nearest neighbors is the Euclidean metric.

Find the indices of the training data (`X`

) that are within 0.5 cm from each point in the query data (`Y`

).

r = 0.5; [Idx,D] = rangesearch(Mdl,Y,r);

`Idx`

and `D`

are five-element cell arrays of vectors. The vector values in `Idx`

are the indices in `X`

. The `X`

indices represent the observations that are within 0.5 cm of the query data, `Y`

. `D`

contains the distances that correspond to the observations.

Display the results for query observation 3.

Idx{3}

`ans = `*1×2*
127 122

D{3}

`ans = `*1×2*
0.2646 0.4359

The closest observation to `Y(3,:)`

is `X(127,:)`

, which is `0.2646`

cm away. The next closest is `X(122,:)`

, which is `0.4359`

cm away. All other observations are greater than `0.5`

cm away from `Y(5,:)`

.

## Input Arguments

`Mdl`

— Nearest neighbor searcher

`ExhaustiveSearcher`

model object | `KDTreeSearcher`

model object | `hnswSearcher`

model object

Nearest neighbor searcher, specified as an `ExhaustiveSearcher`

, `KDTreeSearcher`

, or `hnswSearcher`

model object.

If `Mdl`

is an `ExhaustiveSearcher`

model, then
`rangesearch`

searches for nearest neighbors using an exhaustive
search. If `Mdl`

is a `KDTreeSearcher`

model,
`rangesearch`

uses the grown *K*d-tree to search
for nearest neighbors. If `Mdl`

is an `hnswSearcher`

model, `rangesearch`

uses the Hierarchical Navigable Small Worlds
approximate neighbor search algorithm. For descriptions, see k-Nearest Neighbor Search and Radius Search.

`Y`

— Query data

numeric matrix

Query data, specified as a numeric matrix.

`Y`

is an *m*-by-*K* matrix.
Rows of `Y`

correspond to observations (i.e., examples),
and columns correspond to predictors (i.e., variables or features). `Y`

must
have the same number of columns as the training data stored in `Mdl.X`

.

**Data Types: **`single`

| `double`

### Name-Value Arguments

Specify optional pairs of arguments as
`Name1=Value1,...,NameN=ValueN`

, where `Name`

is
the argument name and `Value`

is the corresponding value.
Name-value arguments must appear after other arguments, but the order of the
pairs does not matter.

*
Before R2021a, use commas to separate each name and value, and enclose*
`Name`

*in quotes.*

**Example: **`'Distance','minkowski','P',3`

specifies to find all
observations in `Mdl.X`

within distance `r`

of
each observation in `Y`

, using the Minkowski distance metric with
exponent `3`

.

**For Both Nearest Neighbor Searchers**

`Distance`

— Distance metric

`Mdl.Distance`

(default) | `'cityblock'`

| `'euclidean'`

| `'mahalanobis'`

| `'minkowski'`

| `'seuclidean'`

| function handle | ...

Distance metric used to find neighbors of the training data to the query observations, specified as one of the values in this table or function handle.

For all types of nearest neighbor searchers, `rangesearch`

supports these
distance metrics.

Value | Description |
---|---|

`'chebychev'` | Chebychev distance (maximum coordinate difference) |

`'cityblock'` | City block distance |

`'euclidean'` | Euclidean distance |

`'minkowski'` | Minkowski distance. The default exponent is 2. To specify a different exponent, use the
`'P'` name-value
argument. |

If `Mdl`

is an `ExhaustiveSearcher`

model object, then
`rangesearch`

also supports these distance metrics.

Value | Description |
---|---|

`'correlation'` | One minus the sample linear correlation between observations (treated as sequences of values) |

`'cosine'` | One minus the cosine of the included angle between observations (treated as row vectors) |

`'fasteuclidean'` | Euclidean distance computed by using an alternative algorithm that saves time
when the number of predictors is at least 10. In some cases, this faster algorithm can
reduce accuracy. This distance metric is available only when
`NSMethod` is `'exhaustive'` . Algorithms
starting with `'fast'` do not support sparse data. For details, see
Algorithms. |

`'fastseuclidean'` | Standardized Euclidean distance computed by using an alternative algorithm that
saves time when the number of predictors is at least 10. In some cases, this faster
algorithm can reduce accuracy. This distance metric is available only when
`NSMethod` is `'exhaustive'` . Algorithms
starting with `'fast'` do not support sparse data. For details, see
Algorithms. |

`'hamming'` | Hamming distance, which is the percentage of coordinates that differ |

`'jaccard'` | One minus the Jaccard coefficient, which is the percentage of nonzero coordinates that differ |

`'mahalanobis'` | Mahalanobis distance, computed using a positive definite covariance matrix. To change the
value of the covariance matrix, use the `'Cov'` name-value
argument. |

`'seuclidean'` | Standardized Euclidean distance. Each coordinate difference between the rows in
`X` and the query matrix `Y` is scaled by
dividing by the corresponding element of the standard deviation computed from
`X` . To specify a different scaling, use the
`'Scale'` name-value argument. |

`'spearman'` | One minus the sample Spearman's rank correlation between observations (treated as sequences of values) |

If `Mdl`

is an `hnswSearcher`

model object,
`rangesearch`

supports all the distances in the
`ExhaustiveSearcher`

table except for those beginning with
`fast`

: `"fasteuclidean"`

and
`"fastseuclidean"`

.

If `Mdl`

is an `ExhaustiveSearcher`

model object, then you
can also specify a function handle for a custom distance metric
by using `@`

(for example,
`@distfun`

). The custom distance
function must:

Have the form

`function D2 = distfun(ZI,ZJ)`

.Take as arguments:

A 1-by-

*K*vector`ZI`

containing a single row from`Mdl.X`

or`Y`

, where*K*is the number of columns of`Mdl.X`

.An

*m*-by-*K*matrix`ZJ`

containing multiple rows of`Mdl.X`

or`Y`

, where*m*is a positive integer.

Return an

*m*-by-1 vector of distances`D2`

, where`D2(`

is the distance between the observations)`j`

`ZI`

and`ZJ(`

.,:)`j`

For more details, see Distance Metrics.

**Example: **`'Distance','minkowski'`

**Data Types: **`char`

| `string`

| `function_handle`

`P`

— Exponent for Minkowski distance metric

`2`

(default) | positive scalar

Exponent for the Minkowski distance metric, specified as a positive scalar. This argument is
valid only when `Distance`

is
`"minkowski"`

.

The value of `P`

sets the value of the
`DistParameter`

property in the model
object.

**Example: **`P=3`

**Data Types: **`single`

| `double`

`SortIndices`

— Flag to sort returned indices according to distance

`true`

(`1`

) (default) | `false`

(`0`

)

Flag to sort returned indices according to distance, specified as the
comma-separated pair consisting of `'SortIndices'`

and
either `true`

(`1`

) or
`false`

(`0`

).

For faster performance when `Y`

contains many
observations that have many nearest points, you can set
`SortIndices`

to `false`

. In
this case, `rangesearch`

returns the indices of the
nearest points in no particular order. When
`SortIndices`

is `true`

, the
function arranges the indices of the nearest points in ascending order
by distance.

**Example: **`'SortIndices',false`

**Data Types: **`logical`

**For Exhaustive Nearest Neighbor Searchers**

`Cov`

— Covariance matrix for Mahalanobis distance metric

`cov(Mdl.X,'omitrows')`

(default) | positive definite matrix

Covariance matrix for the Mahalanobis distance metric, specified as the comma-separated pair
consisting of `'Cov'`

and a positive definite matrix.
`Cov`

is a *K*-by-*K* matrix,
where *K* is the number of columns of `Mdl.X`

. If you
specify `Cov`

and do not specify
`'`

`Distance`

`','mahalanobis'`

,
then `rangesearch`

returns an error message.

**Example: **`'Cov',eye(3)`

**Data Types: **`single`

| `double`

`Scale`

— Scale parameter value for standardized Euclidean distance metric

`std(Mdl.X,'omitnan')`

(default) | nonnegative numeric vector

Scale parameter value for the standardized Euclidean distance metric, specified as the
comma-separated pair consisting of `'Scale'`

and a nonnegative numeric
vector. `Scale`

has length *K*, where
*K* is the number of columns of `Mdl.X`

.

The software scales each difference between the training and query data using the
corresponding element of `Scale`

. If you specify
`Scale`

and do not specify
`'`

`Distance`

`','seuclidean'`

,
then `rangesearch`

returns an error message.

**Example: **```
'Scale',quantile(Mdl.X,0.75) -
quantile(Mdl.X,0.25)
```

**Data Types: **`single`

| `double`

**Note**

If you specify
`'`

`Distance`

`'`

,
`'`

`Cov`

`'`

,
`'`

`P`

`'`

, or
`'`

`Scale`

`'`

, then
`Mdl.Distance`

and `Mdl.DistParameter`

do
not change value.

## Output Arguments

`Idx`

— Training data indices of nearest neighbors

cell array of numeric vectors

Training data indices of nearest neighbors, returned as a cell array of numeric vectors.

`Idx`

is an
*m*-by-`1`

cell array such that cell
`j`

(`Idx{j}`

) contains an
*m _{j}*-dimensional vector of
indices of the observations in

`Mdl.X`

that are within
`r`

units to the query observation
`Y(j,:)`

. If `SortIndices`

is
`true`

, then `rangesearch`

arranges
the elements of the vectors in ascending order by distance.`D`

— Distances of nearest neighbors to the query data

cell array of numeric vectors

Distances of the neighbors to the query data, returned as a numeric matrix or cell array of numeric vectors.

`D`

is an *m*-by-`1`

cell array such that cell `j`

(`D{j}`

)
contains an *m _{j}*-dimensional vector
of the distances that the observations in

`Mdl.X`

are from
the query observation `Y(j,:)`

. All elements of the vector
are less than `r`

. If `SortIndices`

is
`true`

, then `rangesearch`

arranges
the elements of the vectors in ascending order.## Tips

`knnsearch`

finds the *k*
(positive integer) points in `Mdl.X`

that are
*k*-nearest for each `Y`

point. In contrast,
`rangesearch`

finds all the points in `Mdl.X`

that are within distance `r`

(positive scalar) of each
`Y`

point.

## Alternative Functionality

`rangesearch`

is an object function that requires an `ExhaustiveSearcher`

or a `KDTreeSearcher`

model object, query data, and a distance. Under equivalent
conditions, `rangesearch`

returns the same results as `rangesearch`

when you specify the name-value pair argument
`'NSMethod','exhaustive'`

or
`'NSMethod','kdtree'`

, respectively.

## Extended Capabilities

### C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

This table contains notes about the arguments of

`rangesearch`

. Arguments not included in this table are fully supported.Argument Notes and Limitations `Mdl`

There are two ways to use

`Mdl`

in code generation. For an example, see Code Generation for Nearest Neighbor Searcher.Use

`saveLearnerForCoder`

,`loadLearnerForCoder`

, and`codegen`

(MATLAB Coder) to generate code for the`rangesearch`

function. Save a trained model by using`saveLearnerForCoder`

. Define an entry-point function that loads the saved model by using`loadLearnerForCoder`

and calls the`rangesearch`

function. Then use`codegen`

to generate code for the entry-point function.Include

`coder.Constant(Mdl)`

in the`-args`

value of`codegen`

(MATLAB Coder).

If

`Mdl`

is a`KDTreeSearcher`

object, and the code generation build type is a MEX function, then`codegen`

(MATLAB Coder) generates a MEX function using Intel^{®}Threading Building Blocks (TBB) for parallel computation. Otherwise,`codegen`

generates code using`parfor`

(MATLAB Coder).MEX function for the

*k*d-tree search algorithm —`codegen`

generates an optimized MEX function using Intel TBB for parallel computation on multicore platforms. You can use the MEX function to accelerate MATLAB^{®}algorithms. For details on Intel TBB, see https://www.intel.com/content/www/us/en/developer/tools/oneapi/onetbb.html.If you generate the MEX function to test the generated code of the

`parfor`

version, you can disable the usage of Intel TBB. Set the`ExtrinsicCalls`

property of the MEX configuration object to`false`

. For details, see`coder.MexCodeConfig`

(MATLAB Coder).MEX function for the exhaustive search algorithm and standalone C/C++ code for both algorithms — The generated code of

`rangesearch`

uses`parfor`

(MATLAB Coder) to create loops that run in parallel on supported shared-memory multicore platforms in the generated code. If your compiler does not support the Open Multiprocessing (OpenMP) application interface or you disable OpenMP library, MATLAB Coder™ treats the`parfor`

-loops as`for`

-loops. To find supported compilers, see Supported Compilers. To disable OpenMP library, set the`EnableOpenMP`

property of the configuration object to`false`

. For details, see`coder.CodeConfig`

(MATLAB Coder).

`'Distance'`

Cannot be a custom distance function.

Must be a compile-time constant; its value cannot change in the generated code.

`'SortIndices'`

Not supported. The output arguments are always sorted. Name-value pair arguments Names in name-value arguments must be compile-time constants. For example, to allow a user-defined exponent for the Minkowski distance in the generated code, include

`{coder.Constant('Distance'),coder.Constant('Minkowski'),coder.Constant('P'),0}`

in the`-args`

value of`codegen`

(MATLAB Coder).`Idx`

The sorted order of tied distances in the generated code can be different from the order in MATLAB due to numerical precision.

`rangesearch`

returns integer-type (`int32`

) indices in generated standalone C/C++ code. Therefore, the function allows for strict single-precision support when you use single-precision inputs. For MEX code generation, the function still returns double-precision indices to match the MATLAB behavior.*Before R2020a:*`rangesearch`

returns double-precision indices in generated standalone C/C++ code.

For more information, see Introduction to Code Generation and Code Generation for Nearest Neighbor Searcher.

## Version History

**Introduced in R2011b**

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