stdm

Standard deviation of geographic points

Syntax

[latdev,londev] = stdm(lat,lon)

[latdev,londev] = stdm(lat,lon,units)

[latdev,londev] = stdm(lat,lon,ellipsoid)

[latdev,londev] = stdm(lat,lon,ellipsoid,units)

mat = stdm(___)

Description

[latdev,londev] = stdm(lat,lon) calculates the standard deviations latdev and londev 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 deviations in degrees.

[latdev,londev] = stdm(lat,lon,units) specifies the angle units units for the points and standard deviations.

[latdev,londev] = stdm(lat,lon,ellipsoid) specifies the reference ellipsoid for the geographic points. This syntax returns the standard deviations as linear distances in the same units as the semimajor axis of the reference ellipsoid.

[latdev,londev] = stdm(lat,lon,ellipsoid,units) specifies the reference ellipsoid and units for the geographic points. This syntax returns the standard deviations as linear distances in the same units as the semimajor axis of the reference ellipsoid.

mat = stdm(___) returns the standard deviations of the geographic points in the matrix mat, using any combination of input arguments from the previous syntaxes.

Examples

Calculate Standard Deviation 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 deviations of the latitude and longitude coordinates.

[latdev,londev] = stdm(lat,lon)

latdev = 
6.1805

londev = 
7.5871

Compare the stdm function to the stdist function, which calculates the standard distance of the points.

dist = stdist(lat,lon)

dist = 
8.1833

Calculate Standard Deviation 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 deviations of the points referenced to the ellipsoid. When you specify a reference ellipsoid as input, the stdm function returns the standard deviations in the same length unit as the ellipsoid.

[latdev,londev] = stdm(lat,lon,wgs84)

latdev = 
688.0321

londev = 
845.8243

Input Arguments

lat — Latitude coordinates

vector | matrix

Latitude coordinates, specified as a vector or a matrix. The sizes of lat and lon must match.

Data Types: single | double

lon — Longitude coordinates

vector | matrix

Longitude coordinates, specified as a vector or a matrix. The sizes of lon and lat must match.

Data Types: single | 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 deviations. 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.

Output Arguments

latdev — Standard deviation of latitude coordinates

scalar | row vector

Standard deviation of the latitude coordinates, returned as a scalar or a row vector. The size of latdev depends on the sizes of lat and lon.

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

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

The function calculates the standard deviation of the latitude coordinates using angular measurements.

londev — Standard deviation of longitude coordinates

row vector

Standard deviation of the longitude coordinates, returned as a scalar or a row vector. The size of londev depends on the sizes of lat and lon.

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

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

The function calculates the standard deviation of the longitude coordinates using departure distances. For more information about departure, see departure.

mat — Standard deviation of latitude and longitude coordinates

row vector

Standard deviation of the latitude and longitude coordinates, returned as a matrix equivalent to [latdev londev].

Algorithms

• The function calculates the mean position of the latitude and longitude coordinates using the meanm function.

• The function normalizes the standard deviations by n–1, where n is the number of geographic points.

Version History

Introduced before R2006a