Aggregate flows throughout a network using a spatial interaction model.
Source:R/flows.R
dodgr_flows_si.Rd
Aggregate flows throughout a network using an exponential Spatial Interaction (SI) model between a specified set of origin and destination points, and associated vectors of densities.
Usage
dodgr_flows_si(
graph,
from,
to,
k = 500,
dens_from = NULL,
dens_to = NULL,
contract = TRUE,
norm_sums = TRUE,
heap = "BHeap",
tol = 0.000000000001,
quiet = TRUE
)
Arguments
- graph
data.frame
or equivalent object representing the network graph (see Details)- from
Vector or matrix of points from which route distances are to be calculated, specified as one of the following:
Single character vector precisely matching node numbers or names given in
graph$from
orgraph$to
.Single vector of integer-ish values, in which case these will be presumed to specify indices into dodgr_vertices, and NOT to correspond to values in the 'from' or 'to' columns of the graph. See the example below for a demonstration.
Matrix or equivalent of longitude and latitude coordinates, in which case these will be matched on to the nearest coordinates of 'from' and 'to' points in the graph.
- to
Vector or matrix of points to which route distances are to be calculated. If
to
isNULL
, pairwise distances will be calculated from allfrom
points to all other nodes ingraph
. If bothfrom
andto
areNULL
, pairwise distances are calculated between all nodes ingraph
.- k
Width of exponential spatial interaction function (exp (-d / k)), in units of 'd', specified in one of 3 forms: (i) a single value; (ii) a vector of independent values for each origin point (with same length as 'from' points); or (iii) an equivalent matrix with each column holding values for each 'from' point, so 'nrow(k)==length(from)'. See Note.
- dens_from
Vector of densities at origin ('from') points
- dens_to
Vector of densities at destination ('to') points
- contract
If
TRUE
(default), calculate flows on contracted graph before mapping them back on to the original full graph (recommended as this will generally be much faster).FALSE
should only be used if thegraph
has already been contracted.- norm_sums
Standardise sums from all origin points, so sum of flows throughout entire network equals sum of densities from all origins (see Note).
- heap
Type of heap to use in priority queue. Options include Fibonacci Heap (default;
FHeap
), Binary Heap (BHeap
), Trinomial Heap (TriHeap
), Extended Trinomial Heap (TriHeapExt
, and 2-3 Heap (Heap23
).- tol
Relative tolerance below which flows towards
to
vertices are not considered. This will generally have no effect, but can provide speed gains when flow matrices represent spatial interaction models, in which case this parameter effectively reduces the radius from eachfrom
point over which flows are aggregated. To remove any such effect, settol = 0
.- quiet
If
FALSE
, display progress messages on screen.
Note
Spatial Interaction models are often fitted through trialling a range of values of 'k'. The specification above allows fitting multiple values of 'k' to be done with a single call, in a way that is far more efficient than making multiple calls. A matrix of 'k' values may be entered, with each column holding a different vector of values, one for each 'from' point. For a matrix of 'k' values having 'n' columns, the return object will be a modified version in the input 'graph', with an additional 'n' columns, named 'flow1', 'flow2', ... up to 'n'. These columns must be subsequently matched by the user back on to the corresponding columns of the matrix of 'k' values.
The norm_sums
parameter should be used whenever densities at origins
and destinations are absolute values, and ensures that the sum of resultant
flow values throughout the entire network equals the sum of densities at all
origins. For example, with norm_sums = TRUE
(the default), a flow from a
single origin with density one to a single destination along two edges will
allocate flows of one half to each of those edges, such that the sum of flows
across the network will equal one, or the sum of densities from all origins.
The norm_sums = TRUE
option is appropriate where densities are relative
values, and ensures that each edge maintains relative proportions. In the
above example, flows along each of two edges would equal one, for a network
sum of two, or greater than the sum of densities.
With norm_sums = TRUE
, the sum of network flows (sum(output$flow)
) should
equal the sum of origin densities (sum(dens_from)
). This may nevertheless
not always be the case, because origin points may simply be too far from any
destination (to
) points for an exponential model to yield non-zero values
anywhere in a network within machine tolerance. Such cases may result in sums
of output flows being less than sums of input densities.
See also
Other distances:
dodgr_distances()
,
dodgr_dists()
,
dodgr_dists_categorical()
,
dodgr_dists_nearest()
,
dodgr_flows_aggregate()
,
dodgr_flows_disperse()
,
dodgr_isochrones()
,
dodgr_isodists()
,
dodgr_isoverts()
,
dodgr_paths()
,
dodgr_times()
Examples
graph <- weight_streetnet (hampi)
from <- sample (graph$from_id, size = 10)
to <- sample (graph$to_id, size = 5)
to <- to [!to %in% from]
flows <- matrix (10 * runif (length (from) * length (to)),
nrow = length (from)
)
graph <- dodgr_flows_aggregate (graph, from = from, to = to, flows = flows)
# graph then has an additonal 'flows' column of aggregate flows along all
# edges. These flows are directed, and can be aggregated to equivalent
# undirected flows on an equivalent undirected graph with:
graph_undir <- merge_directed_graph (graph)
# This graph will only include those edges having non-zero flows, and so:
nrow (graph)
#> [1] 6813
nrow (graph_undir) # the latter is much smaller
#> [1] 855