# Floating Catchment Area (FCA) Methods

Floating Catchment Area (FCA) methods to Calculate Spatial Accessibility.

Perform various floating catchment area methods to calculate a spatial accessibility index (SPAI) for demand point data. The distance matrix used for weighting is normalized in a preprocessing step using common functions (gaussian, gravity, exponential or logistic).

## Installation

You can install the released version of fca from CRAN with:

``install.packages("fca")``

And the development version from GitHub with:

``remotes::install_github("egrueebler/fca")``

## Example

This is a basic example which shows you how to calculate a SPAI for demand point data using FCA methods.

Create an example population, supply and distances:

``````set.seed(123)

# Population df with column for size
pop <- data.frame(
orig_id = letters[1:10],
size = c(100, 200, 50, 100, 500, 50, 100, 100, 50, 500)
)

# Supply df with column for capacity
sup <- data.frame(
dest_id = as.character(1:3),
capacity = c(1000, 200, 500)
)

# Distance matrix with travel times from 0 to 30
D <- matrix(
runif(30, min = 0, max = 30),
ncol = 10, nrow = 3, byrow = TRUE,
dimnames = list(c(1:3), c(letters[1:10]))
)
D
#>           a        b        c        d        e         f         g         h
#> 1  8.627326 23.64915 12.26931 26.49052 28.21402  1.366695 15.843165 26.772571
#> 2 28.705000 13.60002 20.32712 17.17900  3.08774 26.994749  7.382632  1.261786
#> 3 26.686179 20.78410 19.21520 29.82809 19.67117 21.255914 16.321981 17.824261
#>           i         j
#> 1 16.543050 13.698442
#> 2  9.837622 28.635109
#> 3  8.674792  4.413409``````

Normalize distance matrix with gaussian function, apply a threshold of 20 minutes (to compute beta for the function) and formatting input data as named vectors for the FCA method (match IDs of distance weight matrix with demand and supply data).

``````library(fca)

# Normalize distances
W <- dist_normalize(
D,
d_max = 20,
imp_function = "gaussian", function_d_max = 0.01
)

# Ensure order of ids
pop <- pop[order(pop\$orig_id), ]
sup <- sup[order(sup\$dest_id), ]

# Named vectors
(p <- setNames(pop\$size, as.character(pop\$orig_id)))
#>   a   b   c   d   e   f   g   h   i   j
#> 100 200  50 100 500  50 100 100  50 500
(s <- setNames(sup\$capacity, as.character(sup\$dest_id)))
#>    1    2    3
#> 1000  200  500``````

Apply FCA method on formatted input, get SPAI for each origin location (`p`):

``````(spai <- spai_3sfca(p, s, W))
#>        step3
#> a 3.97260949
#> b 0.03678999
#> c 1.46747735
#> d 0.01079342
#> e 0.28782748
#> f 9.11410451
#> g 0.19596873
#> h 0.31194607
#> i 0.37539987
#> j 1.10349481``````