Returns a stepped weighting function to be used inside accessibility calculating functions.

This function is generic over any kind of numeric travel cost, such as distance, time and money.

decay_stepped(steps, weights)

## Arguments

steps

A numeric vector or a list of numeric vectors. The travel cost steps, in ascending order. Please do not include travel cost 0 as a step: this is already handled by the function.

weights

A numeric vector with same length as steps or a list of numeric vectors whose lengths are equal to the lengths of the elements of same index in steps. The values, between 0 and 1, that the function assumes at each step. Please do not include weight 1 as the first value: this is already handled by the function. The function considers the steps' intervals "open on the right", meaning that the function assumes the step value at the actual step, not right after it. Please see the illustrative examples for effects of this assumption on the results.

## Value

A function that takes a generic travel cost vector (numeric) as an input and returns a vector of weights (numeric).

## Details

When both steps and weights parameters are given lists, their content are matched element-wise to define each stepped weighting function

• i.e. the first element of steps is matched to the first element of weights, the second element of steps is matched to the second of weights, etc. When using a function created with decay_stepped(), the output is named after the combination of steps ("s") and weights ("w")

• e.g. given the steps c(10, 20, 30) and the weights c(0.66, 0.33, 0), the output will be named "s(10,20,30);w(0.66,0.33,0)".

Other decay functions: decay_binary(), decay_exponential(), decay_linear(), decay_power()

## Examples

weighting_function <- decay_stepped(
c(10, 20, 30, 40),
weights = c(0.75, 0.5, 0.25, 0)
)

weighting_function(c(5, 25, 35, 45))
#> $s(10,20,30,40);w(0.75,0.5,0.25,0) #>  1.00 0.50 0.25 0.00 #> weighting_function <- decay_stepped( list(c(10, 20, 30, 40), c(10, 20, 30, 40)), weights = list(c(0.75, 0.5, 0.25, 0), c(0.8, 0.6, 0.4, 0.2)) ) weighting_function(c(5, 25, 35, 45)) #>$s(10,20,30,40);w(0.75,0.5,0.25,0)
#>  1.00 0.50 0.25 0.00
#>
#> $s(10,20,30,40);w(0.8,0.6,0.4,0.2) #>  1.0 0.6 0.4 0.2 #> # intervals are open on the right, so the values change exactly at each step weighting_function(c(0, 10, 20, 30, 40)) #>$s(10,20,30,40);w(0.75,0.5,0.25,0)
#>  1.00 0.75 0.50 0.25 0.00
#>
#> \$s(10,20,30,40);w(0.8,0.6,0.4,0.2)
#>  1.0 0.8 0.6 0.4 0.2
#>