# Preselection: Selection of an initial spread set In SpotSampling: SPatial and Optimally Temporal (SPOT) Sampling

## Description

Select an initial spread set using the flight phase of the local cube method. Some inclusion probabilities are set to 0. The others probabilities are also modified so as not to change the sum of the inclusion probabilities.

## Usage

 `1` ```Preselection(pik, coord, L = 1, EPS = 1e-09) ```

## Arguments

 `pik` a matrix of temporal inclusion probabilities. Columns of `pik` correspond to the times, and rows correspond to the units. Inclusion probabilities can be totally unequal. `coord` a matrix that contains spatial coordinates in columns. The number of columns can be more than two. Matrix rows correspond to the units. `L` a parameter to achieve good spatial balanced (see details). Default value is 1. `EPS` a tolerance parameter. Default value is 1e-9.

## Details

`L` is used to achieve good spatial balance. It must be equal to or larger than one.

## Value

a matrix with the same size as `pik` that contains new temporal inclusion probabilities. Some inclusion probabilities are updated to 0.

## Author(s)

Esther Eustache esther.eustache@unine.ch

## References

Grafstrom, A., Lundstrom, N. L. P., and Schelin, L. (2012). Spatially balanced sampling through the pivotal method. Biometrics, 68(2):514-520.

`fastflightcube`
 ```1 2 3 4 5 6 7 8 9``` ```## Coordinates in two dimensions of 4 units ## coord <- matrix(c(0.5,0.6,0.2,0.3,0.8,0.9,0.4,0.7), ncol=2) ## Temporal inclusion probabilities with 3 waves and 4 units ## pik <- matrix(c(0.6,0.3,0.3, 0.2,0.4,0.9, 0.3,0.2,0.5, 0.9,0.1,0.3), ncol = 3, byrow = TRUE) ## Selection of an initial spread set ## Preselection(pik, coord) ```