Computation of Spatial Data by Hierarchical and Objective Partitioning of Inputs for Parallel Processing

Objective

This package automates parallelization in spatial operations with chopin functions as well as sf/terra functions. With GDAL-compatible files and database tables, chopin functions help to calculate spatial variables from vector and raster data with no external software requirements. All who need to perform geospatial operations with large datasets may find this package useful to accelerate the covariate calculation process for further analysis and modeling may find the main functions useful. We assume that users have basic knowledge of geographic information system data models, coordinate systems and transformations, spatial operations, and raster-vector overlay.

Overview

chopin encapsulates the parallel processing of spatial computation into three steps. First, users will define the parallelization strategy, which is one of many supported in future and future.mirai packages. Users always need to register parallel workers with future before running the par_*() functions that will be introduced below.

future::plan(future.mirai::mirai_multisession, workers = 4L)
# future::multisession, future::cluster are available,
# See future.batchtools and future.callr for other options
# the number of workers are up to users' choice

Second, users choose the proper data parallelization configuration by creating a grid partition of the processing extent, defining the field name with values that are hierarchically coded, or entering multiple raster file paths into par_multirasters(). Finally, users run par_*() function with the configurations set above to compute spatial variables from input data in parallel:

par_grid: parallelize over artificial grid polygons that are generated from the maximum extent of inputs. par_pad_grid is used to generate the grid polygons before running this function.
par_hierarchy: parallelize over hierarchy coded in identifier fields (for example, census blocks in each county in the US)
par_multirasters: parallelize over multiple raster files
Each of the par_* functions introduced above has mirai version with a suffix _mirai after the function names: par_grid_mirai, par_hierarchy_mirai, and par_multirasters. These functions will work properly after creating daemons with mirai::daemons.

mirai::daemons(4L, dispatcher = "process")

For grid partitioning, the entire study area will be divided into partly overlapped grids. We suggest two flowcharts to help which function to use for parallel processing below. The upper flowchart is raster-oriented and the lower is vector-oriented. They are supplementary to each other. When a user follows the raster-oriented one, they might visit the vector-oriented flowchart at each end of the raster-oriented flowchart.

Processing functions accept terra/sf classes for spatial data. Raster-vector overlay is done with exactextractr. Three helper functions encapsulate multiple geospatial data calculation steps over multiple CPU threads.

extract_at: extract raster values with point buffers or polygons with or without kernel weights
summarize_sedc: calculate sums of exponentially decaying contributions
summarize_aw: area-weighted covariates based on target and reference polygons

Function selection guide

We provide two flowcharts to help users choose the right function for parallel processing. The raster-oriented flowchart is for users who want to start with raster data, and the vector-oriented flowchart is for users with large vector data.

In raster-oriented selection, we suggest four factors to consider:

Number of raster files: for multiple files, par_multirasters is recommended. When there are multiple rasters that share the same extent and resolution, consider stacking the rasters into multilayer SpatRaster object by calling terra::rast(filenames).
Raster resolution: We suggest 100 meters as a threshold. Rasters with resolution coarser than 100 meters and a few layers would be better for the direct call of exactextractr::exact_extract().
Raster extent: Using SpatRaster in exactextractr::exact_extract() is often minimally affected by the raster extent.
Memory size: max_cells_in_memory argument value of exactextractr::exact_extract(), raster resolution, and the number of layers in SpatRaster are multiplicatively related to the memory usage.

For vector-oriented selection, we suggest three factors to consider:

Number of features: When the number of features is over 100,000, consider using par_grid or par_hierarchy to split the data into smaller chunks.
Hierarchical structure: If the data has a hierarchical structure, consider using par_hierarchy to parallelize the operation.
Data grouping: If the data needs to be grouped in similar sizes, consider using par_pad_balanced or par_pad_grid with mode = "grid_quantile".

Installation

chopin can be installed using remotes::install_github (also possible with pak::pak or devtools::install_github).

rlang::check_installed("remotes")
remotes::install_github("ropensci/chopin")

or you can also set repos in install.packages() as ROpenSci repository:

install.packages("chopin", repos = "https://ropensci.r-universe.dev")

Examples

Examples will navigate par_grid, par_hierarchy, and par_multirasters functions in chopin to parallelize geospatial operations.

# check and install packages to run examples
pkgs <- c("chopin", "dplyr", "sf", "terra", "future", "future.mirai", "mirai")
# install packages if anything is unavailable
rlang::check_installed(pkgs)

library(chopin)
library(dplyr)
#> 
#> Attaching package: 'dplyr'
#> The following objects are masked from 'package:stats':
#> 
#>     filter, lag
#> The following objects are masked from 'package:base':
#> 
#>     intersect, setdiff, setequal, union
library(sf)
#> Linking to GEOS 3.12.1, GDAL 3.8.4, PROJ 9.3.1; sf_use_s2() is TRUE
library(terra)
#> terra 1.7.83
library(future)
library(future.mirai)
library(mirai)

# disable spherical geometries
sf::sf_use_s2(FALSE)
#> Spherical geometry (s2) switched off

# parallelization-safe random number generator
set.seed(2024, kind = "L'Ecuyer-CMRG")

`par_grid`: parallelize over artificial grid polygons

Please refer to a small example below for extracting mean altitude values at circular point buffers and census tracts in North Carolina. Before running code chunks below, set the cloned chopin repository as your working directory with setwd()

ncpoly <- system.file("shape/nc.shp", package = "sf")
ncsf <- sf::read_sf(ncpoly)
ncsf <- sf::st_transform(ncsf, "EPSG:5070")
plot(sf::st_geometry(ncsf))

Generate random points in NC

Ten thousands random point locations were generated inside the counties of North Carolina.

ncpoints <- sf::st_sample(ncsf, 1e4)
ncpoints <- sf::st_as_sf(ncpoints)
ncpoints$pid <- sprintf("PID-%05d", seq(1, 1e4))
plot(sf::st_geometry(ncpoints))

Target raster dataset: Shuttle Radar Topography Mission

We use an elevation dataset with and a moderate spatial resolution (approximately 400 meters or 0.25 miles).

# data preparation
wdir <- system.file("extdata", package = "chopin")
srtm <- file.path(wdir, "nc_srtm15_otm.tif")

# terra SpatRaster objects are wrapped when exported to rds file
srtm_ras <- terra::rast(srtm)
terra::crs(srtm_ras) <- "EPSG:5070"
srtm_ras
#> class       : SpatRaster 
#> dimensions  : 1534, 2281, 1  (nrow, ncol, nlyr)
#> resolution  : 391.5026, 391.5026  (x, y)
#> extent      : 1012872, 1905890, 1219961, 1820526  (xmin, xmax, ymin, ymax)
#> coord. ref. : NAD83 / Conus Albers (EPSG:5070) 
#> source      : nc_srtm15_otm.tif 
#> name        :    srtm15 
#> min value   : -3589.291 
#> max value   :  1946.400
terra::plot(srtm_ras)

# ncpoints_tr <- terra::vect(ncpoints)
system.time(
  ncpoints_srtm <-
    chopin::extract_at(
      x = srtm,
      y = ncpoints,
      id = "pid",
      mode = "buffer",
      radius = 1e4L  # 10,000 meters (10 km)
    )
)
#> Input is a character. Attempt to read it with terra::rast...
#>    user  system elapsed 
#>   5.009   0.067   4.719

Generate regular grid computational regions

chopin::par_pad_grid() takes a spatial dataset to generate regular grid polygons with nx and ny arguments with padding. Users will have both overlapping (by the degree of radius) and non-overlapping grids, both of which will be utilized to split locations and target datasets into sub-datasets for efficient processing.

compregions <-
  chopin::par_pad_grid(
    ncpoints,
    mode = "grid",
    nx = 2L,
    ny = 2L,
    padding = 1e4L
  )
#> Switch sf class to terra...
#> Switch terra class to sf...

compregions is a list object with two elements named original (non-overlapping grid polygons) and padded (overlapping by padding). The figures below illustrate the grid polygons with and without overlaps.

names(compregions)
#> [1] "original" "padded"

oldpar <- par()
par(mfrow = c(2, 1))
terra::plot(
  terra::vect(compregions$original),
  main = "Original grids"
)
terra::plot(
  terra::vect(compregions$padded),
  main = "Padded grids"
)

Parallel processing

Using the grid polygons, we distribute the task of averaging elevations at 10,000 circular buffer polygons, which are generated from the random locations, with 10 kilometers radius by chopin::par_grid(). Users always need to register multiple CPU threads (logical cores) for parallelization. chopin::par_*() functions are flexible in terms of supporting generic spatial operations in sf and terra, especially where two datasets are involved. Users can inject generic functions’ arguments (parameters) by writing them in the ellipsis (...) arguments, as demonstrated below:

future::plan(future.mirai::mirai_multisession, workers = 4L)

system.time(
  ncpoints_srtm_mthr <-
    par_grid(
      grids = compregions,
      fun_dist = extract_at,
      x = srtm,
      y = ncpoints,
      id = "pid",
      radius = 1e4L,
      .standalone = FALSE
    )
)
#> ℹ Input is not a character.
#> Input is a character. Attempt to read it with terra::rast...
#> ℹ Task at CGRIDID: 1 is successfully dispatched.
#> 
#> Input is a character. Attempt to read it with terra::rast...
#> ℹ Task at CGRIDID: 2 is successfully dispatched.
#> 
#> Input is a character. Attempt to read it with terra::rast...
#> ℹ Task at CGRIDID: 3 is successfully dispatched.
#> 
#> Input is a character. Attempt to read it with terra::rast...
#> ℹ Task at CGRIDID: 4 is successfully dispatched.
#>    user  system elapsed 
#>   0.325   0.023   7.433

ncpoints_srtm <-
  extract_at(
    x = srtm,
    y = ncpoints,
    id = "pid",
    radius = 1e4L
  )
#> Input is a character. Attempt to read it with terra::rast...

colnames(ncpoints_srtm_mthr)[2] <- "mean_par"
ncpoints_compar <- merge(ncpoints_srtm, ncpoints_srtm_mthr)
# Are the calculations equal?
all.equal(ncpoints_compar$mean, ncpoints_compar$mean_par)
#> [1] TRUE

ncpoints_s <-
  merge(ncpoints, ncpoints_srtm)
ncpoints_m <-
  merge(ncpoints, ncpoints_srtm_mthr)

plot(ncpoints_s[, "mean"], main = "Single-thread", pch = 19, cex = 0.33)

plot(ncpoints_m[, "mean_par"], main = "Multi-thread", pch = 19, cex = 0.33)

The same workflow operates on mirai dispatchers.

future::plan(future::sequential)
mirai::daemons(n = 4L, dispatcher = "process")
#> [1] 4

system.time(
  ncpoints_srtm_mthr <-
    par_grid_mirai(
      grids = compregions,
      fun_dist = extract_at,
      x = srtm,
      y = ncpoints,
      id = "pid",
      radius = 1e4L,
      .standalone = FALSE
    )
)
#> ℹ Input is not a character.
#>    user  system elapsed 
#>   0.074   0.000   9.284

# remove mirai::daemons
mirai::daemons(0L)
#> [1] 0

`chopin::par_hierarchy()`: parallelize geospatial computations using intrinsic data hierarchy

We usually have nested/exhaustive hierarchies in real-world datasets. For example, land is organized by administrative/jurisdictional borders where multiple levels exist. In the U.S. context, a state consists of several counties, counties are split into census tracts, and they have a group of block groups. chopin::par_hierarchy() leverages such hierarchies to parallelize geospatial operations, which means that a group of lower-level geographic units in a higher-level geography is assigned to a process. A demonstration below shows that census tracts are grouped by their counties then each county will be processed in a CPU thread.

Read data

# nc_hierarchy.gpkg includes two layers: county and tracts
path_nchrchy <- file.path(wdir, "nc_hierarchy.gpkg")

nc_data <- path_nchrchy
nc_county <- sf::st_read(nc_data, layer = "county")
#> Reading layer `county' from data source 
#>   `/tmp/RtmpXuCaOL/temp_libpath358e3adc6f09/chopin/extdata/nc_hierarchy.gpkg' 
#>   using driver `GPKG'
#> Simple feature collection with 100 features and 1 field
#> Geometry type: POLYGON
#> Dimension:     XY
#> Bounding box:  xmin: 1054155 ymin: 1341756 xmax: 1838923 ymax: 1690176
#> Projected CRS: NAD83 / Conus Albers
nc_tracts <- sf::st_read(nc_data, layer = "tracts")
#> Reading layer `tracts' from data source 
#>   `/tmp/RtmpXuCaOL/temp_libpath358e3adc6f09/chopin/extdata/nc_hierarchy.gpkg' 
#>   using driver `GPKG'
#> Simple feature collection with 2672 features and 1 field
#> Geometry type: MULTIPOLYGON
#> Dimension:     XY
#> Bounding box:  xmin: 1054155 ymin: 1341756 xmax: 1838923 ymax: 1690176
#> Projected CRS: NAD83 / Conus Albers

# reproject to Conus Albers Equal Area
nc_county <- sf::st_transform(nc_county, "EPSG:5070")
nc_tracts <- sf::st_transform(nc_tracts, "EPSG:5070")
nc_tracts$COUNTY <- substr(nc_tracts$GEOID, 1, 5)

Extract average SRTM elevations by single and multiple threads

future::plan(future.mirai::mirai_multisession, workers = 4L)

# single-thread
system.time(
  nc_elev_tr_single <-
    chopin::extract_at(
      x = srtm,
      y = nc_tracts,
      id = "GEOID"
    )
)
#> Input is a character. Attempt to read it with terra::rast...
#>    user  system elapsed 
#>   0.527   0.000   0.491

# hierarchical parallelization
system.time(
  nc_elev_tr_distr <-
    chopin::par_hierarchy(
      regions = nc_county, # higher level geometry
      regions_id = "GEOID", # higher level unique id
      fun_dist = extract_at,
      x = srtm,
      y = nc_tracts, # lower level geometry
      id = "GEOID", # lower level unique id
      func = "mean"
    )
)
#> ℹ Input is not a character.
#> ℹ GEOID is used to stratify the process.
#> Input is a character. Attempt to read it with terra::rast...ℹ Your input function at 37037 is dispatched.
#> Input is a character. Attempt to read it with terra::rast...ℹ Your input function at 37001 is dispatched.
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#>    user  system elapsed 
#>   0.396   0.041   7.102

`par_multirasters()`: parallelize over multiple rasters

There is a common case of having a large group of raster files at which the same operation should be performed. chopin::par_multirasters() is for such cases. An example below demonstrates where we have five elevation raster files to calculate the average elevation at counties in North Carolina.

# nccnty <- sf::st_read(nc_data, layer = "county")
ncelev <- terra::rast(srtm)
terra::crs(ncelev) <- "EPSG:5070"
names(ncelev) <- c("srtm15")
tdir <- tempdir()

terra::writeRaster(ncelev, file.path(tdir, "test1.tif"), overwrite = TRUE)
terra::writeRaster(ncelev, file.path(tdir, "test2.tif"), overwrite = TRUE)
terra::writeRaster(ncelev, file.path(tdir, "test3.tif"), overwrite = TRUE)
terra::writeRaster(ncelev, file.path(tdir, "test4.tif"), overwrite = TRUE)
terra::writeRaster(ncelev, file.path(tdir, "test5.tif"), overwrite = TRUE)

# check if the raster files were exported as expected
testfiles <- list.files(tdir, pattern = "*.tif$", full.names = TRUE)
testfiles
#> [1] "/tmp/Rtmpe3n6BN/test1.tif" "/tmp/Rtmpe3n6BN/test2.tif"
#> [3] "/tmp/Rtmpe3n6BN/test3.tif" "/tmp/Rtmpe3n6BN/test4.tif"
#> [5] "/tmp/Rtmpe3n6BN/test5.tif"

system.time(
  res <-
    chopin::par_multirasters(
      filenames = testfiles,
      fun_dist = extract_at,
      x = ncelev,
      y = nc_county,
      id = "GEOID",
      func = "mean"
    )
)
#> ℹ Input is not a character.
#> Input is a character. Attempt to read it with terra::rast...
#> ℹ Your input function at /tmp/Rtmpe3n6BN/test1.tif is dispatched.
#> 
#> Input is a character. Attempt to read it with terra::rast...
#> ℹ Your input function at /tmp/Rtmpe3n6BN/test2.tif is dispatched.
#> 
#> Input is a character. Attempt to read it with terra::rast...
#> ℹ Your input function at /tmp/Rtmpe3n6BN/test3.tif is dispatched.
#> 
#> Input is a character. Attempt to read it with terra::rast...
#> ℹ Your input function at /tmp/Rtmpe3n6BN/test4.tif is dispatched.
#> 
#> Input is a character. Attempt to read it with terra::rast...
#> ℹ Your input function at /tmp/Rtmpe3n6BN/test5.tif is dispatched.
#>    user  system elapsed 
#>   1.329   0.087   2.830
knitr::kable(head(res))

mean	base_raster
136.80203	/tmp/Rtmpe3n6BN/test1.tif
189.76170	/tmp/Rtmpe3n6BN/test1.tif
231.16968	/tmp/Rtmpe3n6BN/test1.tif
98.03845	/tmp/Rtmpe3n6BN/test1.tif
41.23463	/tmp/Rtmpe3n6BN/test1.tif
270.96933	/tmp/Rtmpe3n6BN/test1.tif

# remove temporary raster files
file.remove(testfiles)
#> [1] TRUE TRUE TRUE TRUE TRUE

Parallelization of a generic geospatial operation

Other than chopin processing functions, chopin::par_*() functions support generic geospatial operations. An example below uses terra::nearest(), which gets the nearest feature’s attributes, inside chopin::par_grid().

path_ncrd1 <- file.path(wdir, "ncroads_first.gpkg")

# Generate 5000 random points
pnts <- sf::st_sample(nc_county, 5000)
pnts <- sf::st_as_sf(pnts)
# assign identifiers
pnts$pid <- sprintf("RPID-%04d", seq(1, 5000))
rd1 <- sf::st_read(path_ncrd1)
#> Reading layer `ncroads_first' from data source 
#>   `/tmp/RtmpXuCaOL/temp_libpath358e3adc6f09/chopin/extdata/ncroads_first.gpkg' 
#>   using driver `GPKG'
#> Simple feature collection with 620 features and 4 fields
#> Geometry type: MULTILINESTRING
#> Dimension:     XY
#> Bounding box:  xmin: 1152512 ymin: 1390719 xmax: 1748367 ymax: 1662294
#> Projected CRS: NAD83 / Conus Albers

# reproject
pntst <- sf::st_transform(pnts, "EPSG:5070")
rd1t <- sf::st_transform(rd1, "EPSG:5070")

# generate grids
nccompreg <-
  chopin::par_pad_grid(
    input = pntst,
    mode = "grid",
    nx = 4L,
    ny = 2L,
    padding = 5e4L
  )
#> Switch sf class to terra...
#> Switch terra class to sf...

The figure below shows the padded grids (50 kilometers), primary roads, and points. Primary roads will be selected by a padded grid per iteration and used to calculate the distance from each point to the nearest primary road. Padded grids and their overlapping areas will look different according to padding argument in chopin::par_pad_grid().

# plot
terra::plot(nccompreg$padded, border = "orange")
terra::plot(terra::vect(ncsf), add = TRUE)
terra::plot(rd1t, col = "blue", add = TRUE)
#> Warning in plot.sf(rd1t, col = "blue", add = TRUE): ignoring all but the first
#> attribute
terra::plot(pntst, add = TRUE, cex = 0.3)
legend(1.02e6, 1.72e6,
       legend = c("Computation grids (50km padding)", "Major roads"),
       lty = 1, lwd = 1, col = c("orange", "blue"),
       cex = 0.5)

# terra::nearest run
system.time(
  restr <- terra::nearest(x = terra::vect(pntst), y = terra::vect(rd1t))
)
#>    user  system elapsed 
#>    0.38    0.00    0.36

pnt_path <- file.path(tdir, "pntst.gpkg")
sf::st_write(pntst, pnt_path)
#> Writing layer `pntst' to data source `/tmp/Rtmpe3n6BN/pntst.gpkg' using driver `GPKG'
#> Writing 5000 features with 1 fields and geometry type Point.

# we use four threads that were configured above
system.time(
  resd <-
    chopin::par_grid(
      grids = nccompreg,
      fun_dist = nearest,
      x = pnt_path,
      y = path_ncrd1,
      pad_y = TRUE
    )
)
#> ℹ Input is a character. Trying to read with terra .
#> ℹ Input is a character. Trying to read with terra .
#> ℹ Task at CGRIDID: 1 is successfully dispatched.
#> 
#> ℹ Input is a character. Trying to read with terra .
#> ℹ Input is a character. Trying to read with terra .
#> ℹ Task at CGRIDID: 2 is successfully dispatched.
#> 
#> ℹ Input is a character. Trying to read with terra .
#> ℹ Input is a character. Trying to read with terra .
#> ℹ Task at CGRIDID: 3 is successfully dispatched.
#> 
#> ℹ Input is a character. Trying to read with terra .
#> ℹ Input is a character. Trying to read with terra .
#> ℹ Task at CGRIDID: 4 is successfully dispatched.
#> 
#> ℹ Input is a character. Trying to read with terra .
#> ℹ Input is a character. Trying to read with terra .
#> ℹ Task at CGRIDID: 5 is successfully dispatched.
#> 
#> ℹ Input is a character. Trying to read with terra .
#> ℹ Input is a character. Trying to read with terra .
#> ℹ Task at CGRIDID: 6 is successfully dispatched.
#> 
#> ℹ Input is a character. Trying to read with terra .
#> ℹ Input is a character. Trying to read with terra .
#> ℹ Task at CGRIDID: 7 is successfully dispatched.
#> 
#> ℹ Input is a character. Trying to read with terra .
#> ℹ Input is a character. Trying to read with terra .
#> ℹ Task at CGRIDID: 8 is successfully dispatched.
#>    user  system elapsed 
#>   0.066   0.000   0.374

We will compare the results from the single-thread and multi-thread calculation.

resj <- merge(restr, resd, by = c("from_x", "from_y"))
all.equal(resj$distance.x, resj$distance.y)
#> [1] TRUE

Users should be mindful of caveats in the parallelization of nearest feature search, which may result in no or excess distance depending on the distribution of the target dataset to which the nearest feature is searched. For example, when one wants to calculate the nearest interstate from rural homes with fine grids, some grids may have no interstates then homes in such grids will not get any distance to the nearest interstate. Such problems can be avoided by choosing nx, ny, and padding values in par_pad_grid() meticulously.

Caveats

Why parallelization is slower than the ordinary function run?

Parallelization may underperform when the datasets are too small to take advantage of divide-and-compute approach, where parallelization overhead is involved. Overhead here refers to the required amount of computational resources for transferring objects to multiple processes. Since the demonstrations above use quite small datasets, the advantage of parallelization was not as noticeable as it was expected. Should a large amount of data (spatial/temporal resolution or number of files, for example) be processed, users could find the efficiency of this package. A vignette in this package demonstrates use cases extracting various climate/weather datasets.

Notes on data restrictions

chopin works best with two-dimensional (planar) geometries. Users should disable s2 spherical geometry mode in sf by setting sf::sf_use_s2(FALSE). Running any chopin functions at spherical or three-dimensional (e.g., including M/Z dimensions) geometries may produce incorrect or unexpected results.

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data		data
inst/extdata		inst/extdata
man		man
tests		tests
tools		tools
vignettes		vignettes
.Rbuildignore		.Rbuildignore
.gitignore		.gitignore
CITATION.cff		CITATION.cff
DESCRIPTION		DESCRIPTION
LICENSE		LICENSE
LICENSE.md		LICENSE.md
NAMESPACE		NAMESPACE
NEWS.md		NEWS.md
README.Rmd		README.Rmd
README.md		README.md
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Computation of Spatial Data by Hierarchical and Objective Partitioning of Inputs for Parallel Processing

Objective

Overview

Function selection guide

Installation

Examples

`par_grid`: parallelize over artificial grid polygons

Generate random points in NC

Target raster dataset: Shuttle Radar Topography Mission

Generate regular grid computational regions

Parallel processing

`chopin::par_hierarchy()`: parallelize geospatial computations using intrinsic data hierarchy

Read data

Extract average SRTM elevations by single and multiple threads

`par_multirasters()`: parallelize over multiple rasters

Parallelization of a generic geospatial operation

Caveats

Why parallelization is slower than the ordinary function run?

Notes on data restrictions

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Computation of Spatial Data by Hierarchical and Objective Partitioning of Inputs for Parallel Processing

Objective

Overview

Function selection guide

Installation

Examples

par_grid: parallelize over artificial grid polygons

Generate random points in NC

Target raster dataset: Shuttle Radar Topography Mission

Generate regular grid computational regions

Parallel processing

chopin::par_hierarchy(): parallelize geospatial computations using intrinsic data hierarchy

Read data

Extract average SRTM elevations by single and multiple threads

par_multirasters(): parallelize over multiple rasters

Parallelization of a generic geospatial operation

Caveats

Why parallelization is slower than the ordinary function run?

Notes on data restrictions

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`par_grid`: parallelize over artificial grid polygons

`chopin::par_hierarchy()`: parallelize geospatial computations using intrinsic data hierarchy

`par_multirasters()`: parallelize over multiple rasters

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