Type:	Package
Title:	Space-Filling Random and Quasi-Random Sequences
Version:	0.4.0
Maintainer:	Tyler Morgan-Wall <tylermw@gmail.com>
Description:	Generates random and quasi-random space-filling sequences. Supports the following sequences: 'Halton', 'Sobol', 'Owen'-scrambled 'Sobol', 'Owen'-scrambled 'Sobol' with errors distributed as blue noise, progressive jittered, progressive multi-jittered ('PMJ'), 'PMJ' with blue noise, 'PMJ02', and 'PMJ02' with blue noise. Includes a 'C++' 'API'. Methods derived from "Constructing Sobol sequences with better two-dimensional projections" (2012) <doi:10.1137/070709359> S. Joe and F. Y. Kuo, "Progressive Multi-Jittered Sample Sequences" (2018) https://graphics.pixar.com/library/ProgressiveMultiJitteredSampling/paper.pdf Christensen, P., Kensler, A. and Kilpatrick, C., and "A Low-Discrepancy Sampler that Distributes Monte Carlo Errors as a Blue Noise in Screen Space" (2019) E. Heitz, B. Laurent, O. Victor, C. David and I. Jean-Claude, <doi:10.1145/3306307.3328191>.
License:	MIT + file LICENSE
Imports:	Rcpp (≥ 1.0.0)
LinkingTo:	Rcpp
Encoding:	UTF-8
RoxygenNote:	7.3.2
URL:	https://github.com/tylermorganwall/spacefillr
BugReports:	https://github.com/tylermorganwall/spacefillr/issues
SystemRequirements:	C++17
Config/build/compilation-database:	true
NeedsCompilation:	yes
Packaged:	2025-02-23 23:50:25 UTC; tyler
Author:	Tyler Morgan-Wall [aut, cph, cre], Andrew Helmer [ctb, cph], Leonhard Grünschloß [ctb, cph], Eric Heitz [ctb, cph]
Repository:	CRAN
Date/Publication:	2025-02-24 00:30:02 UTC

Generate Halton Set (Faure Initialized)

Description

Generate a set of values from a Faure Halton set.

Usage

generate_halton_faure_set(n, dim)

Arguments

Value

An 'n' x 'dim' matrix listing all the

Examples

#Generate a 2D sample:
points2d = generate_halton_random_set(n=1000, dim=2)
plot(points2d)

#Extract a separate pair of dimensions
points2d = generate_halton_random_set(n=1000, dim=10)
plot(points2d[,5:6])

#Integrate the value of pi by counting the number of randomly generated points that fall
#within the unit circle.
pointset = matrix(generate_halton_faure_set(10000,dim=2),ncol=2)

pi_estimate = 4*sum(pointset[,1] * pointset[,1] + pointset[,2] * pointset[,2] < 1)/10000
pi_estimate

Generate Halton Value (Faure Initialized)

Description

Generate a single value from a seeded Halton set, initialized with a Faure sequence.

Note: This is much slower than generating the entire set ahead of time.

Usage

generate_halton_faure_single(i, dim)

Arguments

Value

A single numeric value representing the 'i'th element in the 'dim' dimension.

Examples

#Generate a 3D sample:
point3d = c(generate_halton_faure_single(10, dim = 1),
           generate_halton_faure_single(10, dim = 2),
           generate_halton_faure_single(10, dim = 3))
point3d

Generate Halton Set (Randomly Initialized)

Description

Generate a set of values from a seeded Halton set.

Usage

generate_halton_random_set(n, dim, seed = 0)

Arguments

Value

An 'n' x 'dim' matrix listing all the

Examples

#Generate a 2D sample:
points2d = generate_halton_random_set(n=1000, dim=2)
plot(points2d)

#Change the seed and extract a separate pair of dimensions
points2d = generate_halton_random_set(n=1000, dim=10,seed=2)
plot(points2d[,5:6])

#Integrate the value of pi by counting the number of randomly generated points that fall
#within the unit circle.
pointset = matrix(generate_halton_random_set(10000,dim=2),ncol=2)

pi_estimate = 4*sum(pointset[,1] * pointset[,1] + pointset[,2] * pointset[,2] < 1)/10000
pi_estimate

Generate Halton Value (Randomly Initialized)

Description

Generate a single value from a seeded Halton set.

Note: This is much slower than generating the entire set ahead of time.

Usage

generate_halton_random_single(i, dim, seed = 0)

Arguments

Value

A single numeric value representing the 'i'th element in the 'dim' dimension.

Examples

#Generate a 3D sample:
point3d = c(generate_halton_random_single(10, dim = 1),
           generate_halton_random_single(10, dim = 2),
           generate_halton_random_single(10, dim = 3))
point3d

#Change the random seed:
#'#Generate a 3D sample
point3d_2 = c(generate_halton_random_single(10, dim = 1, seed = 10),
             generate_halton_random_single(10, dim = 2, seed = 10),
             generate_halton_random_single(10, dim = 3, seed = 10))
point3d_2

Generate 2D Progressive Jittered Set

Description

Generate a set of values from a Progressive Jittered set.

Usage

generate_pj_set(n, seed = 0)

Arguments

Value

An 'n' x '2' matrix with all the calculated values from the set.

Examples

#Generate a 2D sample:
points2d = generate_pj_set(n=1000)
plot(points2d, xlim=c(0,1),ylim=c(0,1))

#Generate a longer sequence of values from that set
points2d = generate_pj_set(n=1500)
plot(points2d, xlim=c(0,1),ylim=c(0,1))

#Generate a new set by changing the seed
points2d = generate_pj_set(n=1500,seed=10)
plot(points2d, xlim=c(0,1),ylim=c(0,1))

#'#Integrate the value of pi by counting the number of randomly generated points that fall
#within the unit circle.
pointset = generate_pj_set(10000)

pi_estimate = 4*sum(pointset[,1] * pointset[,1] + pointset[,2] * pointset[,2] < 1)/10000
pi_estimate

Generate 2D Progressive Multi-Jittered (0, 2) Set

Description

Generate a set of values from a Progressive Multi-Jittered (0, 2) set.

Usage

generate_pmj02_set(n, seed = 0)

Arguments

Value

An 'n' x '2' matrix with all the calculated values from the set.

Examples

#Generate a 2D sample:
points2d = generate_pmj02_set(n=1000)
plot(points2d, xlim=c(0,1),ylim=c(0,1))

#Generate a longer sequence of values from that set
points2d = generate_pmj02_set(n=1500)
plot(points2d, xlim=c(0,1),ylim=c(0,1))

#Generate a new set by changing the seed
points2d = generate_pmj02_set(n=1500,seed=10)
plot(points2d, xlim=c(0,1),ylim=c(0,1))

#'#Integrate the value of pi by counting the number of randomly generated points that fall
#within the unit circle.
pointset = generate_pmj02_set(10000)

pi_estimate = 4*sum(pointset[,1] * pointset[,1] + pointset[,2] * pointset[,2] < 1)/10000
pi_estimate

Generate 2D Progressive Multi-Jittered (0, 2) (with blue noise) Set

Description

Generate a set of values from a Progressive Multi-Jittered (0, 2) (with blue noise) set.

Usage

generate_pmj02bn_set(n, seed = 0)

Arguments

Value

An 'n' x '2' matrix with all the calculated values from the set.

Examples

#Generate a 2D sample:
points2d = generate_pmj02bn_set(n=1000)
plot(points2d, xlim=c(0,1),ylim=c(0,1))

#Generate a longer sequence of values from that set
points2d = generate_pmj02bn_set(n=1500)
plot(points2d, xlim=c(0,1),ylim=c(0,1))

#Generate a new set by changing the seed
points2d = generate_pmj02bn_set(n=1500,seed=10)
plot(points2d, xlim=c(0,1),ylim=c(0,1))

#Integrate the value of pi by counting the number of randomly generated points that fall
#within the unit circle.
pointset = generate_pmj02bn_set(10000)

pi_estimate = 4*sum(pointset[,1] * pointset[,1] + pointset[,2] * pointset[,2] < 1)/10000
pi_estimate

Generate 2D Progressive Multi-Jittered Set

Description

Generate a set of values from a Progressive Multi-Jittered set.

Usage

generate_pmj_set(n, seed = 0)

Arguments

Value

An 'n' x '2' matrix with all the calculated values from the set.

Examples

#Generate a 2D sample:
points2d = generate_pmj_set(n=1000)
plot(points2d, xlim=c(0,1),ylim=c(0,1))

#Generate a longer sequence of values from that set
points2d = generate_pmj_set(n=1500)
plot(points2d, xlim=c(0,1),ylim=c(0,1))

#Generate a new set by changing the seed
points2d = generate_pmj_set(n=1500,seed=10)
plot(points2d, xlim=c(0,1),ylim=c(0,1))

#Integrate the value of pi by counting the number of randomly generated points that fall
#within the unit circle.
pointset = generate_pj_set(10000)

pi_estimate = 4*sum(pointset[,1] * pointset[,1] + pointset[,2] * pointset[,2] < 1)/10000
pi_estimate

Generate 2D Progressive Multi-Jittered (with blue noise) Set

Description

Generate a set of values from a Progressive Multi-Jittered (with blue noise) set.

Usage

generate_pmjbn_set(n, seed = 0)

Arguments

Value

An 'n' x '2' matrix with all the calculated values from the set.

Examples

#Generate a 2D sample:
points2d = generate_pmjbn_set(n=1000)
plot(points2d, xlim=c(0,1),ylim=c(0,1))

#Generate a longer sequence of values from that set
points2d = generate_pmjbn_set(n=1500)
plot(points2d, xlim=c(0,1),ylim=c(0,1))

#Generate a new set by changing the seed
points2d = generate_pmjbn_set(n=1500,seed=10)
plot(points2d, xlim=c(0,1),ylim=c(0,1))

#Integrate the value of pi by counting the number of randomly generated points that fall
#within the unit circle.
pointset = generate_pmjbn_set(10000)

pi_estimate = 4*sum(pointset[,1] * pointset[,1] + pointset[,2] * pointset[,2] < 1)/10000
pi_estimate

Generate Owen-scrambled Sobol Set

Description

Generate a set of values from an Owen-scrambled Sobol set.

Usage

generate_sobol_owen_set(n, dim, seed = 0)

Arguments

Value

An 'n' x 'dim' matrix with all the calculated values from the set.

Examples

#Generate a 2D sample:
points2d = generate_sobol_owen_set(n=1000, dim = 2)
plot(points2d, xlim=c(0,1),ylim=c(0,1))

#Generate a longer sequence of values from that set
points2d = generate_sobol_owen_set(n=1500, dim = 2)
plot(points2d, xlim=c(0,1),ylim=c(0,1))

#'#Integrate the value of pi by counting the number of randomly generated points that fall
#within the unit circle.
pointset = matrix(generate_sobol_owen_set(10000,dim=2),ncol=2)

pi_estimate = 4*sum(pointset[,1] * pointset[,1] + pointset[,2] * pointset[,2] < 1)/10000
pi_estimate

Generate Sobol Set

Description

Generate a set of values from a Sobol set.

Note: the Sobol sequences provided by spacefillr are different than those provided by randtoolbox, as spacefillr's Sobol sequences have better 2D projections (see "Constructing Sobol sequences with better two-dimensional projections" (2012) <doi:10.1137/070709359> S. Joe and F. Y. Kuo).

Usage

generate_sobol_set(n, dim, seed = 0)

Arguments

Value

A single numeric value representing the 'i'th element in the 'dim' dimension.

Examples

#Generate a 2D sample:
points2d = generate_sobol_set(n=1000, dim = 2)
plot(points2d, xlim=c(0,1),ylim=c(0,1))

#Generate a longer sequence of values from that set
points2d = generate_sobol_set(n=1500, dim = 2)
plot(points2d, xlim=c(0,1),ylim=c(0,1))

#'#Integrate the value of pi by counting the number of randomly generated points that fall
#within the unit circle.
pointset = matrix(generate_sobol_set(10000,dim=2),ncol=2)

pi_estimate = 4*sum(pointset[,1] * pointset[,1] + pointset[,2] * pointset[,2] < 1)/10000
pi_estimate