# hotrod: Heat Kernel for a One-Dimensional Rod In spatstat.geom: Geometrical Functionality of the 'spatstat' Family

## 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

 `1` ```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.

## Examples

 ```1 2 3 4 5 6 7 8``` ``` 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")) ```

spatstat.geom documentation built on April 15, 2021, 9:06 a.m.