R: Heat Kernel for a One-Dimensional Rod

hotrod {spatstat.geom} | R Documentation

## Heat Kernel for a One-Dimensional Rod

### Description

Calculate values of the heat kernel on a one-dimensional rod. The ends of the rod may be assumed to be insulated, or absorbing.

### Usage

    hotrod(len, xsource, xquery, sigma, ends=c("insulated", "absorbing"), nmax=20)

### Arguments

`len` | Length of the rod. A single number or numeric vector.
`xsource` | Positions of the source points, from the left end of the rod (in the same distance units as `len`). A single number or numeric vector.
`xquery` | Positions of the query points, from the left end of the rod (in the same distance units as `len`). A single number or numeric vector.
`sigma` | Bandwidth for kernel. A single number or a numeric vector.
`ends` | Character string (partially matched) specifying whether the ends of the rod are assumed to be insulated or absorbing.
`nmax` | Number of terms in the infinite sum to use. A single integer or an integer vector.

### Details

Computes the heat kernel as an infinite sum.

### Value

Number or numeric vector.

### Author(s)

Greg McSwiggan and Adrian Baddeley Adrian.Baddeley@curtin.edu.au.

### Examples

      curve(hotrod(1, 0.1, x, 0.7))

      # check it's a probability density
      f <- function(x) hotrod(1, 0.1, x, 0.7)
      integrate(f, 0, 1)

      ## absorbing ends
      curve(hotrod(1, 0.1, x, 0.7, ends="a"))

[Package spatstat.geom version 2.2-0 Index]