## Linear trend of vectors

version 1.0.1 (4.63 KB) by
The function RM_vectrend calculates the parameters of the linear trend of vector processes.

Updated 25 Sep 2021

The decomposition of acceleration vectors into orthogonal and collinear components relative to the mean vector. The decomposition makes it possible to estimate an increase or decrease in the average velocity and regularity of change in the angular velocity of direction of the mean vector.
M.A. Lipatov, V.A. Volkov, R.I. May. Linear trends in sea ice drift fields in the Arctic Ocean// Oceanology. Vol.61, No.3.2021. 297-304 pp.
[pu, pv, aL1, aL2, aD1, bL1, bL2, bD1, acol, aort, ao]=RM_vectrend(u, v, t, alfa)
INPUT
u, v - components of vectors
t - time
alfa - confidence interval for standard error ellipse
OUTPUT
pu - parameters of linear trend of U-component; pu=[a, b], a is acceleration and b is mean velocity of U;
pv - parameters of linear trend of V-component; pu=[a, b], a is acceleration and b is mean velocity of V;
aL1 - semimajor axes of standard error ellipse for the acceleration vector
aL2 - semiminor axes of standard error ellipse for the acceleration vector
aD1 - direction (azimuth) of the major axis of confidence interval of the acceleration vector
bL1 - semimajor axes of standard error ellipse for the mean vector
bL2 - semiminor axes of standard error ellipse for the mean vector
bD1 - direction (azimuth) of the major axis of standard error ellipse for mean vector
acol - the collinear component of acceleration vector. The collinear component acol indicates changes in the velocity of the mean vector: positive values correspond to an increase in velocity; negative values, to a decrease.
aort - the orthogonal component of acceleration vector. The orthogonal component aort shows the trend of the change in direction of the mean vector. Positive values a_|_ indicate the rotation of the mean vector to the right, negative – to the left.
ao - angular rate of mean vector change. Angular rate ao of the change in direction of the mean vector shows how many degrees(clockwise “+” or counterclockwise “–”) the direction of the mean vector has changed per unit time.

### Cite As

Ruslan May (2022). Linear trend of vectors (https://www.mathworks.com/matlabcentral/fileexchange/75239-linear-trend-of-vectors), MATLAB Central File Exchange. Retrieved .

M.A. Lipatov, V.A. Volkov, R.I. May. Linear trends in sea ice drift fields in the Arctic Ocean// Oceanology. Vol.61, No.3.2021. 297-304 pp.

##### MATLAB Release Compatibility
Created with R2020a
Compatible with any release
##### Platform Compatibility
Windows macOS Linux

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