designs: Design functions

In SSN: Spatial Modeling on Stream Networks

Design functions

Description

Functions to generate points on a network.

Usage

binomialDesign(n, replications=1, rep.variable = "Time", rep.values)
poissonDesign(lambda, replications=1, rep.variable = "Time", rep.values)
hardCoreDesign(n, inhibition_region, replications=1, rep.variable = "Time", rep.values)
systematicDesign(spacing, replications=1, rep.variable = "Time", rep.values)
noPoints

Arguments

n	A numeric vector having length 1 or the same length as the number of networks. This represents the number of points to be spread across a network.
lambda	A numeric vector having length 1 or the same length as the number of networks. This represents the rate at which points occur on a network.
inhibition_region	A numeric vector having length 1 or the same length as the number of networks. This represents the size of the inhibition region on a network.
spacing	A numeric vector having length 1 or the same length as the number of networks. This represents the desired spacing for the regular grid of points.
replications	The number of replications of each point.
rep.variable	The name of the variable that will distinguish between the replicated points.
rep.values	The values that will be given to the variable named rep.variable. rep.values[1] will be assigned for replication 1, rep.values[2] for replication 2, etc. Defaults to 1:replications if no value is given.

Details

These design functions are intended to be used in the obsDesign or predDesign inputs of the createSSN function. The binomialDesign function represents a binomial process - A number n[i] of points are distributed randomly and uniformly across network i (or n points if n is a single number).

The poissonDesign function represents a poisson process, where points occur at rate lambda[i] on network i (or lambda if lambda is a single number).

The hardCoreDesign function represents a hard-core process where n[i] (or n if n has length 1) points are distributed uniformly and randomly on network i, and then points are removed until all points are at least inhibition_region[i] distant from each other (or inhibition_region if inhibition_region has length 1).

The systematicDesign function gives a deterministic and regular set of points. Starting from the outlet points are placed upwards along the network, at a fixed distance from the previous point. Note that while the generated grids are regular in a certain sense, they can appear non-regular at certains points from visual inspection. This is because it is impossible to generate a grid of truly equal-spaced points on a network.

The noPoints function simply generates zero points across all networks. Note that this cannot be used as the design for the observed points as there must be at least one observed point. Also this is used directly without any parameters, unlike the other design functions.

A design function must have the form

	function(tree.graphs, edge_lengths, locations, edge_updist, distance_matrices)

All inputs to the design function are lists of length n where n is the number of trees. Input tree.graphs[[i]] is an object of class igraph which represent the ith generated network in a graph theoretic sense; without any specific locations assigned to the vertices. edge_lengths[[i]] contains the lengths of the edges for the ith tree, in the same order as the edges appear in the corresponding igraph object. Input locations[[i]] is a matrix with n[i] rows and 2 columns giving the locations of the points on that network. edge_updist[[i]] is a numeric vector which gives the upstream distance from the downstream point of every stream segment, in the same order as these edges appear in the corresponding igraph object. distance_matrices[[i]] is a matrix with n[i] rows and columns, giving the network distance between the downstream points of a pair of edges, where the edges are ordered in the same way as in the igraph object. To summarise, on tree number i if edge number k has downstream point k_ and edge number l has downstream point l_ then edge_lengths[[i]][k] gives the length of edge number k, edge_updist[[i]][k] gives the distance from point k_ to the outlet of the stream network, and distance_matrices[[i]][k, l] gives the network distance between points k_ and l_. Note that some of these inputs may have associated row or column names, but these should be ignored.

Value

A design function having the signature mentioned above.

Author(s)

Rohan Shah [e-mail]

See Also

createSSN

SSN documentation built on March 7, 2023, 5:30 p.m.