Description Usage Arguments Value Note Examples
Aggregate flows throughout a network based using an exponential Spatial Interaction (SI) model between a specified set of origin and destination points, and associated vectors of densities.
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graph 

from 
Vector or matrix of points from which aggregate flows are to be calculated (see Details) 
to 
Vector or matrix of points to which aggregate flows are to be calculated (see Details) 
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 
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; 
tol 
Relative tolerance below which flows towards 
quiet 
If 
Modified version of graph with additional flow
column added.
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$flow)
) should
equal the sum of origin densities (sum(dens_from)
). This may nevertheless
not always be the case, because origin points may simply be too far from any
destination (to
) points for an exponential model to yield nonzero values
anywhere in a network within machine tolerance. Such cases may result in sums
of output flows being less than sums of input densities.
1 2 3 4 5 6 7 8 9 10 11 12 13  graph < weight_streetnet (hampi)
from < sample (graph$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 nonzero flows, and so:
nrow (graph); nrow (graph_undir) # the latter is much smaller

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