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We are now going to adjust the coordinates of the points to achieve the Latin Hypercube property. The approach used here is quite simple. A Latin Square dataset is typically a two dimensional dataset of N points in the unit square, with the property that, if both the x and y axes are divided up into N equal subintervals, exactly one dataset point has an x or y coordinate in each subinterval. However, a CVT dataset in a regular domain, such as the unit hypercube, has the tendency for the projections of the points to cluster together in any coordinate axis. This program is mainly an attempt to explore whether a dataset can be computed using techniques similar to those of a CVT, but with the constraint whether imposed or expected that the point projections do not clump up. The fact that the projection of a Latin Square dataset onto any coordinate axis is either exactly evenly spaced, or approximately so depending on the algorithm , turns out to be an attractive feature for many uses. Our hope is that the process of adjusting the point coordinates does not too severely damage the nice dispersion properties inherent in the CVT point placement. We assume that the bounding region is the unit hypercube.

Lcvt


We assume that the bounding region is the unit hypercube. The fact that the projection of a Latin Square dataset onto any coordinate axis is either exactly evenly spaced, or approximately so depending on the algorithm , turns out to be an attractive feature for many uses. Related Data and Programs: A Latin Square dataset is typically a two dimensional dataset of N points in the unit square, with the property that, if both the x and y axes are divided up into N equal subintervals, exactly one dataset point has an x or y coordinate in each subinterval. The fact that the projection of a Latin Square dataset onto any coordinate axis is either exactly evenly spaced, or approximately so depending on the algorithm , turns out to be an attractive feature for many uses. Now this process guarantees that we get a Latin Hypercube. Latin squares can easily be extended to the case of M dimensions, and may be pedantically called Latin Hypersquares or Latin Hypercubes in such a case. Statisticians like Latin Squares, as do experiment designers, and and people who need to approximate scalar functions of many variables. The approach used here is quite simple. However, a CVT dataset in a regular domain, such as the unit hypercube, has the tendency for the projections of the points to cluster together in any coordinate axis. This program is mainly an attempt to explore whether a dataset can be computed using techniques similar to those of a CVT, but with the constraint whether imposed or expected that the point projections do not clump up. However, a CVT dataset in a regular domain, such as the unit hypercube, has the tendency for the projections of the points to cluster together in any coordinate axis. We assume that the bounding region is the unit hypercube. Statisticians like Latin Squares, as do experiment designers, and and people who need to approximate scalar functions of many variables. The approach used here is quite simple. We are now going to adjust the coordinates of the points to achieve the Latin Hypercube property. A Latin Square dataset is typically a two dimensional dataset of N points in the unit square, with the property that, if both the x and y axes are divided up into N equal subintervals, exactly one dataset point has an x or y coordinate in each subinterval. Latin squares can easily be extended to the case of M dimensions, and may be pedantically called "Latin Hypersquares" or "Latin Hypercubes" in such a case. Our hope is that the process of adjusting the point coordinates does not too severely damage the nice dispersion properties inherent in the CVT point placement. This program is mainly an attempt to explore whether a dataset can be computed using techniques similar to those of a CVT, but with the constraint whether imposed or expected that the point projections do not clump up. Now this process guarantees that we get a Latin Hypercube. We are now going to adjust the coordinates of the points to achieve the Latin Hypercube property. Our hope is that the process of adjusting the point coordinates does not too severely damage the nice dispersion properties inherent in the CVT point placement.

Lcvt

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Brataxe

23.02.2018 at 10:12 pm
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This program is mainly an attempt to explore whether a dataset can be computed using techniques similar to those of a CVT, but with the constraint whether imposed or expected that the point projections do not clump up.

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