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

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.

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.

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

Calculate Standard Distance of Geographic Points

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

Calculate Standard Distance of Geographic Points on Ellipsoid

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

Calculate Standard Distance Using Specified Method

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

lat — Latitude coordinates

vector | matrix

Latitude coordinates, specified as a vector or a matrix.

Data Types: double

lon — Longitude coordinates

vector | matrix

Longitude coordinates, specified as a vector or a matrix.

Data Types: double

units — Angle unit

"degrees" (default) | "radians"

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

ellipsoid — Reference ellipsoid

[1 0] (default) | referenceSphere object | referenceEllipsoid object | oblateSpheroid object | two-element numeric vector

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.

method — Calculation method

"linear" (default) | "quadratic | "cubic"

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

dist — Standard distance of geographic points

scalar | row vector

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