Package {pRepDOE}

Type:	Package
Title:	Construction of p-Rep Designs from Graph and Finite-Field Structures
Version:	0.1.0
Maintainer:	Vinaykumar L.N. <vinaymandya123@gmail.com>
Description:	Constructs partially replicated (p-rep) designs in which every treatment occurs in every location, once or twice in Methods I and III and q or q + 1 times in Method II, with constant overall replication. Method I decomposes the complete graph into Hamiltonian paths, Method II uses cyclic blocks derived from a Hamiltonian cycle, and Method III uses mutually orthogonal Latin squares over a Galois field. Three treatment-replacement extensions (block enlargement, block splitting, and replacement followed by column-wise splitting) can be applied to Methods I and II. Each design is checked for connectedness and is returned with its parameters, pairwise concurrence distribution, canonical efficiency factor (CEF), average variance factor (AVF) and a randomized layout. Background references: Vinaykumar et al. (2026) <doi:10.1007/s12355-025-01684-1>; Vinaykumar et al. (2024) <doi:10.1080/03610926.2023.2185753>; Williams et al. (2011) <doi:10.1002/bimj.201000102>.
License:	GPL (≥ 3)
Encoding:	UTF-8
Depends:	R (≥ 3.5.0)
Suggests:	testthat (≥ 3.0.0)
Config/testthat/edition:	3
Config/roxygen2/version:	8.0.0
NeedsCompilation:	no
Packaged:	2026-10-29 06:01:04 UTC; Vinaykumar LN
Author:	Vinaykumar L.N. [aut, cre], Cini Varghese [aut], Mohd Harun [aut], Sayantani Karmakar [aut], Vinayaka [aut]
Repository:	CRAN
Date/Publication:	2026-11-13 23:10:08 UTC

Construction of p-rep Designs

Description

Functions to construct p-rep designs by three methods (Hamiltonian path decomposition, cyclic blocks from a Hamiltonian cycle, and mutually orthogonal Latin squares) and to extend them by treatment replacement.

Details

• method1_prep: Method I, Hamiltonian path decomposition of the complete graph (even number of treatments).

• method2_prep: Method II, cyclic blocks taken from a Hamiltonian cycle.

• method3_prep: Method III, mutually orthogonal Latin squares over a Galois field (v = s^2).

• design_summary: one row per design, for building catalogues.

Methods I and II accept a treatment-replacement case: 1 (block enlargement), 2 (block splitting) and 3 (replacement followed by column-wise splitting). In Cases 2 and 3 the split blocks use a linked (twisted) matching, which keeps every extended design connected. Every design is verified to be connected before it is returned.

Author(s)

Maintainer: Vinaykumar L.N. vinaymandya123@gmail.com (ORCID)

Authors:

• Vinaykumar L.N. vinaymandya123@gmail.com (ORCID)

• Cini Varghese cini2204@gmail.com (ORCID)

• Mohd Harun harun.agribhu@gmail.com (ORCID)

• Sayantani Karmakar sayantanikarmakar20@gmail.com (ORCID)

• Vinayaka vinayaka.b3vs@gmail.com (ORCID)

One-Row-per-Design Summary

Description

Condenses the output of method1_prep, method2_prep or method3_prep into a data frame with one row per design, convenient for building catalogues.

Usage

design_summary(x)

Arguments

Value

A data frame with columns design, method, case, f, g, v, b, r, k, L, CEF, AVF, connected, n_nonestimable_pairs, concurrence_levels and concurrence_counts. The last two are comma-separated strings giving the distinct pairwise concurrence values and how many treatment pairs have each value.

Examples

design_summary(method1_prep(6))

## Several designs of one method (one row per feasible L)
design_summary(method2_prep(6, 5))

## Catalogue rows from different methods and cases
rows <- list(
  design_summary(method1_prep(6)),
  design_summary(method1_prep(6, case = 2, f = 2)),
  design_summary(method2_prep(10, 7)),
  design_summary(method3_prep(5))
)
catalogue <- do.call(rbind, rows)
catalogue[, c("method", "case", "v", "b", "r", "k", "L", "CEF", "AVF", "connected")]

Method I: Hamiltonian Path Decomposition

Description

Constructs a p-rep design from a decomposition of the complete graph on v vertices into v/2 edge-disjoint Hamiltonian paths, with optional treatment-replacement extensions (Cases 1 to 3).

Usage

method1_prep(v, case = 0, f = 1, g = 1, seed = NULL)

Arguments

Details

Each Hamiltonian path is assigned to one location, so every treatment occurs once or twice in every location. In Cases 2 and 3 the split blocks are formed with a linked (twisted) matching: the smallest-label treatment of each block takes the next member of its group, the others take member m. This links the copies of the design and makes it connected. The function stops with an error if a constructed design is not connected, or if replication is not as expected.

Value

A list with one element, Design1, which is a list with components

design

data frame with columns Location, Block, BaseBlock and Treatment1, Treatment2, ...

Design_parameters

list with method, case, f, g, v, b, r, k, L, lambda_is_constant, pairwise_concurrence_values and concurrence_frequency.

randomized_layout

data frame with columns Location, Block, Plot, Treatment.

location_replication

matrix (locations by treatments) of within-location replication.

Efficiency_Factors

list with CEF (canonical efficiency factor) and AVF (average variance factor).

Estimability

list with rank, n_components, connected, n_pairs, n_estimable_pairs and n_nonestimable_pairs.

See Also

method2_prep, method3_prep, design_summary

Examples

## Base design (Illustration 1): v = 6, b = 15, r = 5, k = 2, L = 3
x <- method1_prep(6)
d <- x$Design1
d$design                        # blocks, grouped by location
d$Design_parameters             # parameters and concurrence distribution
d$location_replication          # each treatment occurs once or twice per location
d$Efficiency_Factors            # CEF = 0.6, AVF = 0.6667
head(d$randomized_layout, 10)   # randomized field layout

## Reproducible randomization (the caller's random numbers are untouched)
method1_prep(6, seed = 123)$Design1$randomized_layout[1:6, ]

## Case 1: replacement with block enlargement (v = 4, f = 2 gives v' = 8)
c1 <- method1_prep(4, case = 1, f = 2)$Design1
c1$Design_parameters[c("v", "b", "r", "k", "L")]
c1$Efficiency_Factors           # CEF = 0.8235, AVF = 0.8095

## Case 2: replacement with block splitting (linked matching, connected)
c2 <- method1_prep(4, case = 2, f = 2)$Design1
c2$design[c2$design$BaseBlock == 1, ]   # base block (1, 2) -> (1, 4) and (2, 3)
c2$Estimability$connected               # TRUE
c2$Efficiency_Factors                   # CEF = 0.4828, AVF = 1.381

## Case 3: replacement (f) followed by column-wise splitting (g)
c3 <- method1_prep(4, case = 3, f = 2, g = 2, seed = 123)$Design1
c3$Design_parameters$pairwise_concurrence_values
c3$Efficiency_Factors                   # CEF = 0.6634, AVF = 1.0048

## One-row summary of several designs
design_summary(method1_prep(6))

Method II: Cyclic Blocks from a Hamiltonian Cycle

Description

Constructs p-rep designs from the v cyclic blocks B_i = \{i, i+1, \ldots, i+k-1\} (labels modulo v), one design for each feasible number of locations, with optional treatment-replacement extensions (Cases 1 to 3).

Usage

method2_prep(v, k, case = 0, f = 1, g = 1, L = NULL, seed = NULL)

Arguments

Details

Block B_i is placed in location ((i - 1) mod L) + 1. Within a location each treatment occurs q or q + 1 times, where q = floor(k / L); overall replication is r = k. Pairwise concurrence is not necessarily constant. Cases 2 and 3 use the linked matching described in method1_prep. The function stops with an error if a design is not connected.

Value

A list Design1, Design2, ..., one element per feasible (or requested) L. Each element is a list with components

design

data frame with columns Location, Block, BaseBlock and Treatment1, Treatment2, ...

Design_parameters

list with method, case, f, g, v, b, r, k, L, lambda_is_constant, pairwise_concurrence_values and concurrence_frequency.

randomized_layout

data frame with columns Location, Block, Plot, Treatment.

location_replication

matrix (locations by treatments) of within-location replication.

Efficiency_Factors

list with CEF (canonical efficiency factor) and AVF (average variance factor).

Estimability

list with rank, n_components, connected, n_pairs, n_estimable_pairs and n_nonestimable_pairs.

See Also

method1_prep, method3_prep, design_summary

Examples

## Base designs (Illustration 2): v = 6, k = 5 has two feasible L
y <- method2_prep(6, 5)
names(y)                                  # Design1 (L = 2), Design2 (L = 3)
y$Design1$design                          # blocks grouped by location
y$Design1$location_replication            # each treatment 2 or 3 times per location
y$Design2$Design_parameters               # every pair occurs together in 4 blocks
y$Design1$Efficiency_Factors              # CEF = 0.96, AVF = 0.4167

## Request one number of locations only
method2_prep(6, 5, L = 3)

## Case 1: replacement with block enlargement
c1 <- method2_prep(10, 7, case = 1, f = 2)$Design1
c1$Efficiency_Factors                     # CEF = 0.9753, AVF = 0.2929

## Case 2: replacement with block splitting (connected)
c2 <- method2_prep(6, 5, case = 2, f = 2)$Design1
c2$Estimability$connected                 # TRUE
c2$Efficiency_Factors                     # CEF = 0.5198, AVF = 0.7695

## Case 3: replacement followed by column-wise splitting
c3 <- method2_prep(10, 7, case = 3, f = 2, g = 2, seed = 1)$Design1
c3$Efficiency_Factors                     # CEF = 0.7323, AVF = 0.3902

## One row per design (here L = 2 and L = 4)
design_summary(method2_prep(8, 5))
## Invalid input: no feasible number of locations
try(method2_prep(8, 4))

Method III: Mutually Orthogonal Latin Squares

Description

Constructs a p-rep design on v = s^2 treatments from the s + 1 parallel classes given by the rows, the columns and the s - 1 mutually orthogonal Latin squares L_m(i, j) = i + mj over the Galois field GF(s).

Usage

method3_prep(s, augmented_class = NULL, seed = NULL)

Arguments

Details

Every treatment occurs once in every location and once more in the block of the augmented class, so within-location replication is one or two and overall replication is r = s + 1. The base design has b = s(s+1), k = L = s and lambda = 1; the value of lambda is reported from the computed concurrence distribution rather than assumed. For non-prime s finite-field arithmetic is used.

Value

A list with one element, Design1, structured as in method1_prep; its Design_parameters also contain s and blocks_per_location.

See Also

method1_prep, method2_prep, design_summary

Examples

## Illustration 3: s = 3 gives v = 9, b = 12, r = 4, k = 3, L = 3
z <- method3_prep(3)
z$Design1$design                          # four blocks per location
z$Design1$Design_parameters               # lambda = 1
z$Design1$location_replication            # each treatment once or twice per location
z$Design1$Efficiency_Factors              # CEF = 0.75, AVF = 0.6667

## Use a different parallel class for the extra block in each location
method3_prep(3, augmented_class = 2)$Design1$design

## Prime power s: GF(4) arithmetic
g4 <- method3_prep(4)$Design1
g4$Design_parameters$pairwise_concurrence_values   # 1
g4$Efficiency_Factors                              # CEF = 4/5, AVF = 0.5

## GF(8), with a reproducible randomized layout
method3_prep(8, seed = 123)$Design1$Efficiency_Factors   # CEF = 8/9

## Invalid input: 6 is not a prime power
try(method3_prep(6))