# stdist

Standard distance of geographic points

## Syntax

``dist = stdist(lat,lon)``
``dist = stdist(lat,lon,units)``
``dist = stdist(lat,lon,ellipsoid)``
``dist = stdist(lat,lon,ellipsoid,units)``
``dist = stdist(lat,lon,ellipsoid,units,method)``

## Description

example

````dist = stdist(lat,lon)` computes the standard distance of the geographic points specified by `lat` and `lon`. This syntax references the points to a unit sphere, assumes the points are specified in degrees, and returns the standard distance in degrees.Standard distance measures the dispersion of great-circle distances from each point to the geographic mean (centroid) of the points. For more information about the geographic mean, see `meanm`.```
````dist = stdist(lat,lon,units)` specifies the angle units `units` for the points and standard distance.```

example

````dist = stdist(lat,lon,ellipsoid)` specifies the reference ellipsoid for the geographic points. This syntax returns the standard distance as a linear distance in the same units as the semimajor axis of the reference ellipsoid.```
````dist = stdist(lat,lon,ellipsoid,units)` specifies the reference ellipsoid and units for the geographic points. This syntax returns the standard distance as a linear distance in the same units as the semimajor axis of the reference ellipsoid.```

example

````dist = stdist(lat,lon,ellipsoid,units,method)` specifies the calculation method. By default, the function calculates the average great-circle distance of the points from the geographic mean of the points.```

## Examples

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Specify the latitude and longitude coordinates of Paris, London, Rome, Madrid, Berlin, and Athens.

```lat = [48.87 51.52 41.93 40.43 52.43 38.02]; lon = [2.41 -0.13 12.5 -3.68 13.08 23.52];```

Find the standard distance of the points.

`dist = stdist(lat,lon)`
```dist = 8.1833 ```

Compare the `stdist` function to the `sdtm` function, which independently calculates the standard deviations for the latitudes and longitudes.

`[latdev,londev] = stdm(lat,lon) `
```latdev = 6.1805 ```
```londev = 7.5871 ```

Specify the latitude and longitude coordinates of Paris, London, Rome, Madrid, Berlin, and Athens.

```lat = [48.87 51.52 41.93 40.43 52.43 38.02]; lon = [2.41 -0.13 12.5 -3.68 13.08 23.52];```

Create a World Geodetic System of 1984 (WGS84) reference ellipsoid with a length unit of kilometers.

`wgs84 = wgs84Ellipsoid("km");`

Find the standard distance of the points referenced to the ellipsoid. When you specify a reference ellipsoid as input, the `stdist` function returns the standard distance in the same length unit as the ellipsoid.

`dist = stdist(lat,lon,wgs84)`
```dist = 911.0339 ```

Specify the latitude and longitude coordinates of Paris, London, Rome, Madrid, Berlin, and Athens.

```lat = [48.87 51.52 41.93 40.43 52.43 38.02]; lon = [2.41 -0.13 12.5 -3.68 13.08 23.52];```

Create a World Geodetic System of 1984 (WGS84) reference ellipsoid with a length unit of kilometers.

`wgs84 = wgs84Ellipsoid("km");`

Find the standard distance of the points using a quadratic calculation method.

`distQ = stdist(lat,lon,wgs84,"degrees","quadratic")`
```distQ = 976.4035 ```

Find the standard distance of the point using a cubic calculation method.

`distC = stdist(lat,lon,wgs84,"degrees","cubic")`
```distC = 1.0398e+03 ```

## Input Arguments

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Latitude coordinates, specified as a vector or a matrix.

Data Types: `double`

Longitude coordinates, specified as a vector or a matrix.

Data Types: `double`

Angle unit, specified as one of these options:

• `"degrees"` — Degrees

• `"radians"` — Radians

If you do not specify a reference ellipsoid, this argument determines the angle units for the input points and the output standard distance. If you specify a reference ellipsoid, this argument only determines the angle units for the input points.

Data Types: `char` | `string`

Reference ellipsoid, specified as a `referenceSphere` object, a `referenceEllipsoid` object, an `oblateSpheroid` object, or a two-element vector of the form `[semimajor_axis eccentricity]`, where `semimajor_axis` is the length of the semimajor axis and `eccentricity` is the eccentricity. The values `semimajor_axis` and `eccentricity` must be of data type `double`.

The default value of `[1 0]` represents the unit sphere.

Calculation method, specified as one of these options:

• `"linear"``dist` is the average of the great-circle distances from each geographic point to the geographic mean of the points.

• `"quadratic"``dist` is the square root of the average of the squared great-circle distances.

• `"cubic"``dist` is the cube root of the average of the cubed great-circle distances.

Data Types: `char` | `string`

## Output Arguments

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Standard distance of the geographic points, returned as a scalar or a row vector.

• When `lat` and `lon` are vectors, `dist` is a scalar.

• When `lat` and `lon` are matrices, `dist` is a row vector. Each element of the vector is the standard distance for the corresponding column of `lat` and `lon`.

Data Types: `double`

## Version History

Introduced in R2006a