R: Compute Quadrature Weights Based on Grid Counts

gridweights {spatstat.geom} | R Documentation

## Compute Quadrature Weights Based on Grid Counts

### Description

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

### 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[1] * ntile[2]` 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`.

### Author(s)

Adrian Baddeley Adrian.Baddeley@curtin.edu.au

and Rolf Turner r.turner@auckland.ac.nz

### See Also

`quad.object`, `dirichletWeights`

### Examples

      Q <- quadscheme(runifrect(15))
      X <- as.ppp(Q) # data and dummy points together
      w <- gridweights(X, 10)
      w <- gridweights(X, c(10, 10))

[Package spatstat.geom version 2.3-2 Index]