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add dists-categorical vignette; closes #144
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Package: dodgr | ||
Title: Distances on Directed Graphs | ||
Version: 0.2.10.024 | ||
Version: 0.2.10.025 | ||
Authors@R: c( | ||
person("Mark", "Padgham", , "[email protected]", role = c("aut", "cre")), | ||
person("Andreas", "Petutschnig", role = "aut"), | ||
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@@ -32,6 +32,7 @@ Imports: | |
Rcpp (>= 0.12.6), | ||
RcppParallel | ||
Suggests: | ||
bench, | ||
dplyr, | ||
geodist, | ||
ggplot2, | ||
|
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--- | ||
title: "Aggregating distances along categories of edges" | ||
author: "Mark Padgham" | ||
date: "`r Sys.Date()`" | ||
output: | ||
html_document: | ||
toc: true | ||
toc_float: true | ||
number_sections: false | ||
theme: flatly | ||
vignette: > | ||
%\VignetteIndexEntry{4 dodgr_dists_categorical} | ||
%\VignetteEngine{knitr::rmarkdown} | ||
%\VignetteEncoding{UTF-8} | ||
--- | ||
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```{r pkg-load, echo = FALSE, message = FALSE} | ||
library (dodgr) | ||
``` | ||
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The [`dodgr_dists_categorical` | ||
function](https://atfutures.github.io/dodgr/reference/dodgr_dists_categorical.html) | ||
enables multiple distances to be aggregated along distinct categories of edges | ||
with a single query. This is particularly useful to examine information on | ||
proportions of total distances routed along different edge categories. The | ||
following three sub-sections describe the three main uses and interfaces of the | ||
[`dodgr_dists_categorical` | ||
function](https://atfutures.github.io/dodgr/reference/dodgr_dists_categorical.html). | ||
Each of these requires an input `graph` to have an additional column named | ||
`"edge_type"`, which labels discrete categories of edges. These can be any kind | ||
of discrete labels at all, from integer values to character labels or factors. | ||
The labels are retained in the result, as demonstrated below. | ||
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# 1 Full Distance Information for Edge Categories | ||
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The "default" interface of the | ||
[`dodgr_dists_categorical` | ||
function](https://atfutures.github.io/dodgr/reference/dodgr_dists_categorical.html) | ||
requires the same three mandatory parameters as | ||
[`dodgr_distances`](https://atfutures.github.io/dodgr/reference/dodgr_dists.html), of | ||
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1. A weighted `graph` on which the distances are to be calculated; | ||
2. A vector of `from` points from which distances are to be calculated; and | ||
3. A corresponding vector of `to` points. | ||
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As for | ||
[`dodgr_distances`](https://atfutures.github.io/dodgr/reference/dodgr_dists.html), | ||
the `from` and `to` arguments can be either vertex identifiers (generally as | ||
`from_id` and `to_id` columns of the input `graph`), or two-column coordinates | ||
for spatial graphs. The following code illustrates the procedure, using the | ||
internal data set, | ||
[`hampi`](https://atfutures.github.io/dodgr/reference/hampi.html), initially | ||
starting by reducing to the largest connected component only, to ensure all | ||
points are mutually reachable. | ||
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```{r hampi-edge-types} | ||
graph <- weight_streetnet (hampi, wt_profile = "foot") | ||
graph <- graph [graph$component == 1, ] | ||
graph$edge_type <- graph$highway | ||
table (graph$edge_type) | ||
``` | ||
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That network then has `r length (unique (graph$edge_type))` distinct edge | ||
types. Submitting this graph to the function, and calculating pairwise | ||
distances between all points, then gives the following result: | ||
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```{r full-dists1} | ||
v <- dodgr_vertices (graph) | ||
from <- to <- v$id | ||
d <- dodgr_dists_categorical (graph, from, to) | ||
class (d) | ||
length (d) | ||
sapply (d, dim) | ||
``` | ||
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The result has the dedicated class, `dodgr_dists_categorical`, which it itself | ||
a list of matrices, one for each distinct edge type. This class enables | ||
a convenient `summary` method which converts data on aggregate distances along | ||
each category of edges into overall proportions: | ||
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```{r summary-full-dists, eval = FALSE} | ||
summary (d) | ||
``` | ||
```{r summary-out, echo = FALSE, collapse = TRUE} | ||
s <- summary (d) | ||
``` | ||
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# 2. Proportional Distances along each Edge Category | ||
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If `summary` results like those immediately above are all that is desired, | ||
without any additional information from the full distance matrices, then | ||
a `proportions_only` parameter can be used to directly return those: | ||
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```{r prop-only} | ||
dodgr_dists_categorical (graph, from, to, | ||
proportions_only = TRUE) | ||
``` | ||
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Queries with `proportions_only = TRUE` are constructed in a different way in | ||
the underlying C++ code, with the main difference being that the full list of | ||
matrices is not stored, and these queries will generally use considerably less | ||
memory. For most jobs, this should translate to faster queries, as illustrated | ||
in the following benchmark: | ||
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```{r prop-only-benchmark, warning = FALSE} | ||
bench::mark (full = dodgr_dists_categorical (graph, from, to), | ||
prop_only = dodgr_dists_categorical (graph, from, to, | ||
proportions_only = TRUE), | ||
check = FALSE, time_unit = "s") [, 1:3] | ||
``` | ||
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# 3. Proportional Distances within a Threshold Distance | ||
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The third and final use of the [`dodgr_dists_categorical` | ||
function](https://atfutures.github.io/dodgr/reference/dodgr_dists_categorical.html) | ||
is through the `dlimit` parameter, used to specify a distance threshold below | ||
which categorical distances are to be aggregated. This is useful to examine | ||
relative proportions of different edges types necessary in travelling in any | ||
and all directions away from each point or vertex of a graph. | ||
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When a `dlimit` parameter is specified, the `to` parameter is ignored, and | ||
distances are aggregated along all possible routes away from each `from` point, | ||
out to the specified `dlimit`. The value of `dlimit` must be specified relative | ||
to the edge distance values contained in the input graph. For spatial graphs | ||
obtained with [`dodgr_streetnet()` or | ||
`dodgr_streetnet_sc()`](https://atfutures.github.io/dodgr/reference/dodgr_streetnet.html), | ||
for example, as well as the internal [`hampi` | ||
data](https://atfutures.github.io/dodgr/reference/hampi.html), these distances | ||
are in metres, and so `dlimit` must be specified in metres. | ||
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The result in then a single matrix in which each row represents one of the | ||
`from` points, and there is one column of aggregate distances for each edge | ||
type, plus an initial column of overall distances. The following code | ||
illustrates: | ||
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```{r dists-dlimit} | ||
dlimit <- 2000 # in metres | ||
d <- dodgr_dists_categorical (graph, from, dlimit = dlimit) | ||
dim (d) | ||
head (d) | ||
``` | ||
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The row names of the resultant `data.frame` are the vertex identifiers | ||
specified in the `from` parameter. Such results can easily be combined with | ||
spatial information on the vertices obtained from the [`dodgr_vertices()~ | ||
function](https://atfutures.github.io/dodgr/reference/dodgr_vertices.html) to | ||
generate spatial maps of relative proportions around each point in a graph or | ||
network. Summary statistics can also readily be extracted, for example, | ||
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```{r hist-path} | ||
hist (d$path / d$distance, | ||
xlab = "Relative proportions of trips along paths", main = "") | ||
``` | ||
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Trips along paths are roughly evenly distributed between 0 and 1. In contrast, | ||
proportions of trips along service ways -- used to facilitate motorised | ||
vehicular access in the otherwise car-free area of Hampi, India -- are | ||
distinctly different: | ||
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```{r hist-track} | ||
hist (d$service / d$distance, | ||
xlab = "Relative proportions of trips along service ways", main = "") | ||
``` | ||
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These distributions provide more detailed and nuanced insights than those | ||
provided by the overall `summary` functions above, which only revealed overall | ||
respective relative proportions of `r round (s [["path"]], digits = 2)` and | ||
`r round (s [["service"]], digits = 2)` for paths and service ways. The results | ||
within the distance threshold reveal that the distributional forms of | ||
proportional distances differ as much as the aggregate values, and that both | ||
aspects of the function provide distinct insights into proportional distances | ||
along categories of edge types. | ||
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Finally, this use of the function also utilizes distinct difference in the | ||
underlying C++ code that are even more efficient that the previous case of | ||
proportional distances. The following code benchmarks the three modes: | ||
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```{r benchmark3, warning = FALSE} | ||
bench::mark (full = dodgr_dists_categorical (graph, from, to), | ||
prop_only = dodgr_dists_categorical (graph, from, to, | ||
proportions_only = TRUE), | ||
dlimit = dodgr_dists_categorical (graph, from, dlimit = 2000), | ||
check = FALSE, time_unit = "s") [, 1:3] | ||
``` | ||
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Finally, note that the efficiency of distance-threshold queries scales | ||
non-linearly with increases in `dlimit`, with queries quickly becoming less | ||
efficient for larger values of `dlimit`. |
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