# stdist

Standard distance for geographic points

## Syntax

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

## Description

`dist = stdist(lat,lon)` computes the average standard distance for geographic data. This function assumes that the data is distributed on a sphere. In contrast, `std` assumes that the data is distributed on a Cartesian plane. The result is a single value based on the great-circle distance of the data points from their geographic mean point. When `lat` and `lon` are vectors, a single distance is returned. When `lat` and `lon` are matrices, a row vector of distances is given, providing the distances for each column of `lat` and `lon`. N-dimensional arrays are not allowed. Distances are returned in degrees of angle units.

`dist = stdist(lat,lon,units)` indicates the angular units of the data. When the standard angle units is omitted, `'degrees'` is assumed. Output measurements are in terms of these `units` (as arc length distance).

`dist = stdist(lat,lon,ellipsoid)` specifies the shape of the Earth to be used with `ellipsoid`, which can be a `referenceSphere`, `referenceEllipsoid`, or `oblateSpheroid` object, or a vector of the form ```[semimajor_axis eccentricity]```. The default is a unit sphere. Output measurements are in terms of the distance units of the semimajor axis of the `ellipsoid`.

`dist = stdist(lat,lon,ellipsoid,units,method)` specifies the method of calculating the standard distance of the data. The default, `'linear'`, is simply the average great circle distance of the data points from the centroid. Using `'quadratic'` results in the square root of the average of the squared distances, and `'cubic'` results in the cube root of the average of the cubed distances.

## Background

The function `stdm` provides independent standard deviations in latitude and longitude of data points. `stdist` provides a means of examining data scatter that does not separate these components. The result is a standard distance, which can be interpreted as a measure of the scatter in the great circle distance of the data points from the centroid as returned by `meanm`.

The output distance can be thought of as the radius of a circle centered on the geographic mean position, which gives a measure of the spread of the data.

## Examples

Create latitude and longitude lists using the `worldcities` data set and obtain standard distance deviation for group (compare with the example for `stdm`):

```cities = shaperead('worldcities.shp', 'UseGeoCoords', true); Paris = strcmp('Paris',{cities(:).Name}); London = strcmp('London',{cities(:).Name}); Rome = strcmp('Rome',{cities(:).Name}); Madrid = strcmp('Madrid',{cities(:).Name}); Berlin = strcmp('Berlin',{cities(:).Name}); Athens = strcmp('Athens',{cities(:).Name}); lat = [cities(Paris).Lat cities(London).Lat... cities(Rome).Lat cities(Madrid).Lat... cities(Berlin).Lat cities(Athens).Lat] lon = [cities(Paris).Lon cities(London).Lon... cities(Rome).Lon cities(Madrid).Lon... cities(Berlin).Lon cities(Athens).Lon] dist = stdist(lat,lon) lat = 48.8708 51.5188 41.9260 40.4312 52.4257 38.0164 lon = 2.4131 -0.1300 12.4951 -3.6788 13.0802 23.5183 dist = 8.1827``` 