R: Integral of a Measure

integral.msr {spatstat.core} | R Documentation

## Integral of a Measure

### Description

Computes the integral (total value) of a measure over its domain.

### Usage

    ## S3 method for class 'msr'
    integral(f, domain=NULL, ...)

### Arguments

`f` | A signed measure or vector-valued measure (object of class `"msr"`).
`domain` | Optional window specifying the domain of integration. Alternatively a tessellation.
`...` | Ignored.

### Details

The integral (total value of the measure over its domain) is calculated.

If `domain` is a window (class `"owin"`) then the integration will be restricted to this window. If `domain` is a tessellation (class `"tess"`) then the integral of `f` in each tile of `domain` will be computed.

For a multitype measure `m`, use `split.msr` to separate the contributions for each type of point, as shown in the Examples.

### Value

A numeric value, vector, or matrix.

`integral(f)` returns a numeric value (for a signed measure) or a vector of values (for a vector-valued measure).

If `domain` is a tessellation then `integral(f, domain)` returns a numeric vector with one entry for each tile (if `f` is a signed measure) or a numeric matrix with one row for each tile (if `f` is a vector-valued measure).

### Author(s)

Adrian Baddeley Adrian.Baddeley@curtin.edu.au, Rolf Turner r.turner@auckland.ac.nz and Ege Rubak rubak@math.aau.dk.

### See Also

`msr`, `integral`

### Examples

       fit <- ppm(cells ~ x)
       rr <- residuals(fit)
       integral(rr)

       # vector-valued measure
       rs <- residuals(fit, type="score")
       integral(rs)

       # multitype
       fitA <- ppm(amacrine ~ x)
       rrA <- residuals(fitA)
       sapply(split(rrA), integral)

       # multitype and vector-valued
       rsA <- residuals(fitA, type="score")
       sapply(split(rsA), integral)

       ## integral over a subregion
       integral(rr, domain=square(0.5))
       ## integrals over the tiles of a tessellation
       integral(rr, domain=quadrats(cells, 2))

[Package spatstat.core version 1.65-5 Index]