library (dodgr)
The dodgr
package includes three functions for allocating and aggregating
flows throughout network, based on defined properties of a set of origin and
destination points. The three primary functions for flows are
dodgr_flows_aggregate()
,
dodgr_flows_disperse()
,
and
dodgr_flows_si()
,
each of which is now described in detail.
The first of the above functions aggregates ''flows'' throughout a
network from a set of origin (from
) and destination (to
) points. Flows
commonly arise in origin-destination matrices used in transport studies, but may
be any kind of generic flows on graphs. A flow matrix specifies the flow between
each pair of origin and destination points, and the
dodgr_flows_aggregate()
function aggregates all of these flows throughout a network and assigns a
resultant aggregate flow to each edge.
For a set of nf
points of origin and nt
points of destination, flows are
defined by a simple nf
-by-nt
matrix of values, as in the following code:
graph <- weight_streetnet (hampi, wt_profile = "foot") set.seed (1) from <- sample (graph$from_id, size = 10) to <- sample (graph$to_id, size = 10) flows <- matrix (10 * runif (length (from) * length (to)), nrow = length (from) )
This flows
matrix is then submitted to
dodgr_flows_aggregate()
,
which simply appends an additional column of flows
to the submitted graph
:
graph_f <- dodgr_flows_aggregate (graph, from = from, to = to, flows = flows) head (graph_f)
Most flows are zero because they have only been calculated between very few points in the graph.
summary (graph_f$flow)
The second function,
dodgr_flows_disperse()
,
uses only a vector a origin (from
) points, and aggregates flows as they
disperse throughout the network
according to a simple exponential model. In place of the matrix of flows
required by
dodgr_flows_aggregate()
,
dispersal requires an equivalent vector of densities dispersing from all origin
(from
) points. This is illustrated in
the following code, using the same graph as the previous example.
dens <- rep (1, length (from)) # uniform densities graph_f <- dodgr_flows_disperse (graph, from = from, dens = dens) summary (graph_f$flow)
Note that flows from both
dodgr_flows_aggregate()
and
dodgr_flows_disperse()
are directed, so the flow from 'A' to 'B' will not necessarily equal the flow
from 'B' to 'A'. It is often desirable to aggregate flows in an undirected
manner, for example for visualisations where plotting pairs of directed flows
between each edge if often not feasible for large graphs. Directed flows can be
aggregated to equivalent undirected flows with the merge_directed_graph()
function:
graph_undir <- merge_directed_graph (graph_f)
Resultant graphs produced by
merge_directed_graph()
only include those edges having non-zero flows, and so:
nrow (graph_f) nrow (graph_undir) # the latter is much smaller
The resultant graph can readily be merged with the original graph to regain the original data on vertex coordinates through
graph <- graph [graph_undir$edge_id, ] graph$flow <- graph_undir$flow
This graph may then be used to visualise flows with the
dodgr_flowmap()
function:
graph_f <- graph_f [graph_f$flow > 0, ] dodgr_flowmap (graph_f, linescale = 5)
An additional function,
dodgr_flows_si()
enables flows to be aggregated according to exponential spatial interaction
models. The function is called just as the dodgr_flows_aggregate()
call
demonstrated above, but without the flows
matrix specifying strengths of
flows between each pair of points.
graph_f <- dodgr_flows_si (graph, from = from, to = to) graph_undir <- merge_directed_graph (graph_f) graph <- graph [graph_undir$edge_id, ] graph$flow <- graph_undir$flow graph_f <- graph_f [graph_f$flow > 0, ] png (file.path (here::here (), "vignettes", "hampi-flowmap2.png"), width = 480, height = 480, units = "px" ) dodgr_flowmap (graph_f, linescale = 5) dev.off (which = dev.cur ())
graph_f <- dodgr_flows_si (graph, from = from, to = to) graph_undir <- merge_directed_graph (graph_f) graph <- graph [graph_undir$edge_id, ] graph$flow <- graph_undir$flow graph_f <- graph_f [graph_f$flow > 0, ] dodgr_flowmap (graph_f, linescale = 5)
Flows in that graph are are notably lower than in the previous one, because that previous one aggregated flows between all pairs of points with no attenuation. Spatial interaction models attenuate both attraction based on how far apart two points are, as well as flows along paths between those points based on an exponential decay model. The documentation for that function describes the several ways this attenuation can be controlled, the easiest of which is via a single numeric value. Reducing the attenuation gives the following result:
graph <- weight_streetnet (hampi, wt_profile = "foot") graph_f <- dodgr_flows_si (graph, from = from, to = to, k = 1e6) graph_undir <- merge_directed_graph (graph_f) graph <- graph [graph_undir$edge_id, ] graph$flow <- graph_undir$flow graph_f <- graph_f [graph_f$flow > 0, ] png (file.path (here::here (), "vignettes", "hampi-flowmap3.png"), width = 480, height = 480, units = "px" ) dodgr_flowmap (graph_f, linescale = 5) dev.off (which = dev.cur ())
graph <- weight_streetnet (hampi, wt_profile = "foot") graph_f <- dodgr_flows_si (graph, from = from, to = to, k = 1e6) graph_undir <- merge_directed_graph (graph_f) graph <- graph [graph_undir$edge_id, ] graph$flow <- graph_undir$flow graph_f <- graph_f [graph_f$flow > 0, ] dodgr_flowmap (graph_f, linescale = 5)
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