Dakota Reference Manual
Version 6.4
LargeScale Engineering Optimization and Uncertainty Analysis

Design of Computer Experiments  Centroidal Voronoi Tessellation
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Alias: none
Argument(s): none
Required/Optional  Description of Group  Dakota Keyword  Dakota Keyword Description  

Optional  samples  Number of samples for samplingbased methods  
Optional  seed  Seed of the random number generator  
Optional  latinize  Adjust samples to improve the discrepancy of the marginal distributions  
Optional  quality_metrics  Calculate metrics to assess the quality of quasiMonte Carlo samples  
Optional  variance_based_decomp  Activates global sensitivity analysis based on decomposition of response variance into contributions from variables  
Optional  fixed_seed  Reuses the same seed value for multiple random sampling sets  
Optional  trial_type  Specify how the trial samples are generated  
Optional  num_trials  The number of secondary sample points generated to adjust the location of the primary sample points  
Optional  max_iterations  Stopping criterion based on number of iterations  
Optional  model_pointer  Identifier for model block to be used by a method 
The FSU Centroidal Voronoi Tessellation method (fsu_cvt
) produces a set of sample points that are (approximately) a Centroidal Voronoi Tessellation. The primary feature of such a set of points is that they have good volumetric spacing; the points tend to arrange themselves in a pattern of cells that are roughly the same shape.
To produce this set of points, an almost arbitrary set of initial points is chosen, and then an internal set of iterations is carried out. These iterations repeatedly replace the current set of sample points by an estimate of the centroids of the corresponding Voronoi subregions. [17].
The user may generally ignore the details of this internal iteration. If control is desired, however, there are a few variables with which the user can influence the iteration. The user may specify:
This method generates sets of uniform random variables on the interval [0,1]. If the user specifies lower and upper bounds for a variable, the [0,1] samples are mapped to the [lower, upper] interval.
This method is designed to generate samples with the goal of low discrepancy. Discrepancy refers to the nonuniformity of the sample points within the hypercube.
Discrepancy is defined as the difference between the actual number and the expected number of points one would expect in a particular set B (such as a hyperrectangle within the unit hypercube), maximized over all such sets. Low discrepancy sequences tend to cover the unit hypercube reasonably uniformly.
Centroidal Voronoi Tessellation does very well volumetrically: it spaces the points fairly equally throughout the space, so that the points cover the region and are isotropically distributed with no directional bias in the point placement. There are various measures of volumetric uniformity which take into account the distances between pairs of points, regularity measures, etc. Note that Centroidal Voronoi Tessellation does not produce lowdiscrepancy sequences in lower dimensions. The lowerdimension (such as 1D) projections of Centroidal Voronoi Tessellation can have high discrepancy.
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