Plugin WindLab
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| Description |
|---|
| This plugin implement various WindLab features. Plugin version: 1.0 Last modified: 2024-04-15 LabRPS version: All Author: Koffi Daniel |
| Author |
| Koffi Daniel |
| Download |
| None |
| Features |
| Cholesky Decomposition Horizontal Uniform Distribution |
| Plugin Version |
| 1.0 |
| Date last modified |
| 2024-04-15 |
| LabRPS Version(s) |
| All |
| Default shortcut |
| None |
| See also |
| None |
You can find the source code of this plugin on the following Github repository: Get the code here!. This plugin is one of the official plugins provided by LabRPS. It provides very useful features (tools) for the simulation of random wind velocity. Plugins are very easy to create in LabRPS, therefore, anyone can develop plugin for any random phenomenon in LabRPS. Go to this page to see how to create new plugin for LabRPS. You can get quick assistance from LabRPS community by sending your concern to the community forum.
Cholesky Decomposition
This feature performs the Cholesky decomposition of a positive Hermitian power spectrum matrix and returns the lower triangular matrix (L) of the decomposition. The Cholesky decomposition is a numerical method used to decompose a positive-definite matrix into the product of a lower triangular matrix and its conjugate transpose. Specifically, for a matrix A, the decomposition is given by:
[math]\displaystyle{ \mathbf{A} = \mathbf{L L}^{*}, }[/math]
[math]\displaystyle{ L_{j,j} = \sqrt{ A_{j,j} - \sum_{k=1}^{j-1} L_{j,k}^*L_{j,k} }, }[/math]
[math]\displaystyle{ L_{i,j} = \frac{1}{L_{j,j}} \left( A_{i,j} - \sum_{k=1}^{j-1} L_{j,k}^* L_{i,k} \right) \quad \text{for } i\gt j. }[/math]
where [math]\displaystyle{ L }[/math] is a lower triangular matrix with real and positive diagonal entries, and [math]\displaystyle{ L^* }[/math] denotes the conjugate transpose of [math]\displaystyle{ L }[/math].
The feature is optimized for performance and can handle large matrices efficiently using [math]\displaystyle{ O(n^3) }[/math] computational complexity in the worst case. It checks if the input matrix is indeed positive-definite and Hermitian before performing the decomposition and raises an error if the matrix does not meet these conditions. The feature belong to the PSD Decomposition Method feature group.
Scripting
The feature can be used from the python console as follows:
import WindLab
import WindLabObjects
from LabRPS import Vector as vec
import numpy
# get an existing WindLab simulation called "Simulation"
sim = WindLab.getSimulation("Simulation")
# check if the simulation does really exist
if not sim:
LabRPS.Console.PrintError("The simulation does not exist.\n")
return None
featureType = "Cholesky Decomposition"
featureGroup = "Spectrum Decomposition Method"
# create the feature and add it to the existing simulation (you may refer to the WindLab Workbench page in
# case you don't understand the next line)
decomposedPSD = WindLabObjects.makeFeature("MyNewFeature", sim.Name, featureType, featureGroup)
# check if the created feature is good
if not decomposedPSD :
LabRPS.Console.PrintError("Error on creating the spectrum decomposition method.\n")
return None
# get the active simulation points feature and compute the simulation points coordinates
simPoints = sim.computeLocationCoordinateMatrixP3()
# use a vector to represent a simulation point based on its coordinates
v1 = vec(simPoints[0][1], simPoints[0][2], simPoints[0][3])
v2 = vec(simPoints[1][1], simPoints[1][2], simPoints[1][3])
v3 = vec(simPoints[2][1], simPoints[2][2], simPoints[2][3])
# This is feature is used to decompose power spectrum matrices which may vary in time. Let's assume that
# the active power spectrun density function in this example is stationary. Meanning it is not varying in time.
#Then, we use time instant of 0 second.
time = 0.0
# compute the decomposed cross spectrum between points 1 and 3, at time instant of 0 second and for all frequency
# increments note that when the following code is ran, WindLab will try to identify the active frequency distribution,
# the active power spectrum feature, the active coherence function feature and others. It WindLab fails to find any
# of these dependency features, the computation will fails and specific error messages will be sent to the report view.
psd13 = sim.computeDecomposedCrossSpectrumVectorF(v1, v3, time)
# psd13 can be converted to numpy vector and be used for some other purposes.
arr = numpy.asarray(psd13)