# gridweights

0th

Percentile

##### Compute Quadrature Weights Based on Grid Counts

Computes quadrature weights for a given set of points, using the counting weights'' for a grid of rectangular tiles.

Keywords
spatial, datagen
##### Usage
gridweights(X, ntile, …, window=NULL, verbose=FALSE, npix=NULL, areas=NULL)
##### Arguments
X

Data defining a point pattern.

ntile

Number of tiles in each row and column of the rectangular grid. An integer vector of length 1 or 2.

Ignored.

window

Default window for the point pattern

verbose

Logical flag. If TRUE, information will be printed about the computation of the grid weights.

npix

Dimensions of pixel grid to use when computing a digital approximation to the tile areas.

areas

Vector of areas of the tiles, if they are already known.

##### Details

This function computes a set of quadrature weights for a given pattern of points (typically comprising both data'' and dummy'' points). See quad.object for an explanation of quadrature weights and quadrature schemes.

The weights are computed by the counting weights'' rule based on a regular grid of rectangular tiles. First X and (optionally) window are converted into a point pattern object. Then the bounding rectangle of the window of the point pattern is divided into a regular ntile * ntile grid of rectangular tiles. The weight attached to a point of X is the area of the tile in which it lies, divided by the number of points of X lying in that tile.

For non-rectangular windows the tile areas are currently calculated by approximating the window as a binary mask. The accuracy of this approximation is controlled by npix, which becomes the argument dimyx of as.mask.

##### Value

Vector of nonnegative weights for each point in X.

quad.object, dirichletWeights

• gridweights
##### Examples
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