Calculate the cumulative Eddington number

Description

This function is much like E_num except it provides a cumulative Eddington number over the vector rather than a single summary number.

Usage

E_cum(rides)

Arguments

Value

An integer vector the same length as rides.

See Also

E_next, E_num, E_req, E_sat

Get the number of rides required to increment to the next Eddington number

Description

Get the number of rides required to increment to the next Eddington number.

Usage

E_next(rides)

Arguments

Value

A named list with the current Eddington number (E) and the number of rides required to increment by one (req).

See Also

E_cum, E_num, E_req, E_sat

Get the Eddington number for cycling

Description

Gets the Eddington number for cycling. The Eddington Number for cycling, E, is the maximum number where a cyclist has ridden E miles on E distinct days.

Usage

E_num(rides)

Arguments

Details

The Eddington Number for cycling is related to computing the rank of an integer partition, which is the same as computing the side length of its Durfee square. Another relevant application of this metric is computing the Hirsch index (doi:10.1073/pnas.0507655102) for publications.

This is not to be confused with the Eddington Number in astrophysics, N_{Edd}, which represents the number of protons in the observable universe.

Value

An integer which is the Eddington cycling number for the data provided.

See Also

E_cum, E_next, E_req, E_sat

Examples

# Randomly generate a set of 15 rides
rides <- rgamma(15, shape = 2, scale = 10)

# View the rides sorted in decreasing order
stats::setNames(sort(rides, decreasing = TRUE), seq_along(rides))

# Get the Eddington number
E_num(rides)

Determine the number of additional rides required to achieve a specified Eddington number

Description

Determine the number of additional rides required to achieve a specified Eddington number.

Usage

E_req(rides, candidate)

Arguments

Value

An integer vector of length 1. Returns 0L if E is already achieved.

See Also

E_cum, E_next, E_num, E_sat

Determine if a dataset satisfies a specified Eddington number

Description

Indicates whether a certain Eddington number is satisfied, given the data.

Usage

E_sat(rides, candidate)

Arguments

Value

A logical vector of length 1.

See Also

E_cum, E_next, E_num, E_req

An R6 Class for Tracking Eddington Numbers for Cycling

Description

The class will maintain the state of the algorithm, allowing for efficient updates as new rides come in.

Warnings

The implementation uses an experimental base R feature utils::hashtab.

Cloning of Eddington objects is disabled. Additionally, Eddington objects cannot be serialized; they cannot be carried between sessions using base::saveRDS or base::save and then loaded later using base::readRDS or base::load.

Active bindings

Methods

Public methods

• Eddington$new()

• Eddington$print()

• Eddington$update()

• Eddington$getNumberToTarget()

• Eddington$isSatisfied()

Method new()

Create a new Eddington object.

Usage

Eddington$new(rides, store.cumulative = FALSE)

Arguments

Returns

A new Eddington object

Method print()

Print the current Eddington number.

Usage

Eddington$print()

Method update()

Add new rides to the existing Eddington object.

Usage

Eddington$update(rides)

Arguments

Method getNumberToTarget()

Get the number of rides of a specified length to get to a target Eddington number.

Usage

Eddington$getNumberToTarget(target)

Arguments

Returns

An integer representing the number of rides of target length needed to achieve the target number.

Method isSatisfied()

Test if an Eddington number is satisfied.

Usage

Eddington$isSatisfied(target)

Arguments

Returns

Logical

Examples

# Randomly generate a set of 15 rides
rides <- rgamma(15, shape = 2, scale = 10)

# View the rides sorted in decreasing order
stats::setNames(sort(rides, decreasing = TRUE), seq_along(rides))

# Create the Eddington object
e <- Eddington$new(rides, store.cumulative = TRUE)

# Get the Eddington number
e$current

# Update with new data
e$update(rep(25, 10))

# See the new data
e$cumulative

An Rcpp Module for Tracking Eddington Numbers for Cycling

Description

A stateful C++ object for computing Eddington numbers.

Arguments

Fields

new

Constructor. Parameter list may either be empty, store_cumulative, or rides and store_cumulative

current

The current Eddington number.

cumulative

A vector of Eddington numbers or NULL if store_cumulative is FALSE.

hashmap

A data.frame containing the distances and counts above the current Eddington number.

update

Update the class state with new data.

getNumberToNext

Get the number of additional distances required to reach the next Eddington number.

getNumberToTarget

Get the number of additional distances required to reach a target Eddington number.

Warning

EddingtonModule objects cannot be serialized at this time; they cannot be carried between sessions using base::saveRDS or base::save and then loaded later using base::readRDS or base::load.

Examples

# Create a class instance with some initial data
e <- EddingtonModule$new(c(3, 3, 2), store_cumulative = TRUE)
e$current

# Update with new data and look at the vector of cumulative Eddington numbers.
e$update(c(3, 3, 5))
e$cumulative

# Get the number of rides required to reach the next Eddington number and
# an Eddington number of 4.
e$getNumberToNext()
e$getNumberToTarget(4)

Compute the distance between two points using the Haversine formula

Description

Uses the Haversine great-circle distance formula to compute the distance between two latitude/longitude points.

Usage

get_haversine_distance(
  lat_1,
  lon_1,
  lat_2,
  lon_2,
  units = c("miles", "kilometers")
)

Arguments

Value

The distance between two points in the requested units.

References

https://en.wikipedia.org/wiki/Haversine_formula

Examples

# In NYC, 20 blocks == 1 mile. Thus, computing the distance between two
# points along 7th Ave from W 39 St to W 59 St should return ~1 mile.
w39_coords <- list(lat=40.75406905512651, lon=-73.98830604245481)
w59_coords <- list(lat=40.76684156255418, lon=-73.97908243833855)

get_haversine_distance(
  w39_coords$lat,
  w39_coords$lon,
  w59_coords$lat,
  w59_coords$lon,
  "miles"
)

# The total distance along a sequence of points can be computed. Consider the
# following sequence of points along Park Ave in the form of a list of points
# where each point is a list containing a `lat` and `lon` tag.
park_ave_coords <- list(
  list(lat=40.735337983655434, lon=-73.98973648773142),  # E 15 St
  list(lat=40.74772623378332, lon=-73.98066078090876),   # E 35 St
  list(lat=40.76026319186414, lon=-73.97149360922498),   # E 55 St
  list(lat=40.77301604875587, lon=-73.96217737679450)    # E 75 St
)

# We can create a function to compute the total distance as follows:
compute_total_distance <- function(coords) {
  sum(
    sapply(
      seq_along(coords)[-1],
      \(i) get_haversine_distance(
        coords[[i]]$lat,
        coords[[i]]$lon,
        coords[[i - 1]]$lat,
        coords[[i - 1]]$lon,
        "miles"
      )
    )
  )
}

# Then applying the function to our sequence results in a total distance.
compute_total_distance(park_ave_coords)

Read a GPX file into a data frame containing dates and distances

Description

Reads in a GPS Exchange Format XML document and outputs a data.frame containing distances. The corresponding dates for each track segment (trkseg) will be included if present in the source file, else the date column will be populated with NAs.

Usage

read_gpx(file, units = c("miles", "kilometers"))

Arguments

Details

Distances are computed using the Haversine formula and do not account for elevation changes.

This function treats the first timestamp of each trkseg as the date of record. Thus overnight track segments will all count toward the day in which the journey began.

Value

A data frame containing up to two columns:

date

The date of the ride. See description and details.

distance

The distance of the track segment in the requested units.

Examples

## Not run: 
# Get a list of all GPX export files in a directory tree
gpx_export_files <- list.files(
  "/path/to/gpx/exports/",
  pattern = "\\.gpx$",
  full.names = TRUE,
  recursive = TRUE
)

# Read in all files and combine them into a single data frame
rides <- do.call(rbind, lapply(gpx_export_files, read_gpx))

## End(Not run)

A year of simulated bicycle ride mileages

Description

Simulated dates and distances of rides occurring in 2009.

Usage

rides

Format

A data frame with 250 rows and 2 variables:

ride_date

date the ride occurred

ride_length

the length in miles

Details

The dataset contains a total of 3,419 miles spread across 178 unique days. The Eddington number for the year was 29.