POD - Proper Orthogonal Decomposition (Wrapper)

Version 2.0.1 (3.98 KB) by
By Fernando Zigunov, 2019 [U, S, V] = POD(X) returns the proper orthogonal decomposition
Updated 13 Apr 2021

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This function is just a nice wrapper for Matlab's built-in SVD function, which
only operates in 2D data sets. The wrapper just reshapes the matrices
before and after applying SVD such that the input series X can be
n-dimensional and ensures the output modes U are also n-dimensional.
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%POD has several names (POD, SVD, PCA, ...) and is a mathematical tool that
%highlights the principal modes of a random series of variables (i.e.,
%financial measurements, fluid flow fields, structural vibrations, neuron
%firing patterns, video frames, and basically anything imaginable!)

%The POD tool is extremely useful in data analysis to identify the most
%energetic modes of a complex system by simply performing measurements when
%its operating. (But if you're already here you already know all of this.)

%============Inputs:=============
%X - Time series or snapshots to be analyzed. Can be a n-dimensional matrix
%(n>=2). First dimension is time/snapshot, and all other dimensions are
%conserved for output.

%============Outputs:=============
%U - Mode matrix, has the same size of X. First dimension of X was
%"time/snapshot", therefore first dimension of U will be "mode". Modes are
%automatically organized from most energetic U(1,:,:...) to least
%energetic.

%S - Mode eigenvalues. S.^2 gives the mode energies. S is a diagonal
%matrix, so returns just the vector S to save one line of post-processing.

%V - Mode time-series or snapshot coefficients - V contains the
%contribution of each mode to a specific snapshot of X. U*S*V gives back X
%(given U and X are reshaped into 2D matrices again).

Cite As

Fernando Zigunov (2024). POD - Proper Orthogonal Decomposition (Wrapper) (https://www.mathworks.com/matlabcentral/fileexchange/72022-pod-proper-orthogonal-decomposition-wrapper), MATLAB Central File Exchange. Retrieved .

MATLAB Release Compatibility
Created with R2018a
Compatible with any release
Platform Compatibility
Windows macOS Linux
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Version Published Release Notes
2.0.1

For some reason Matlab Exchange is not updating the thumbnail

2.0.0

Updated bug when the number of sensors was smaller than the number of snapshots.
Included example of usage with a solution of the wave equation for learning purposes.

1.0.1

Updated description

1.0.0