---
title: "Partially Replicated (p-rep) Design"
output: rmarkdown::html_vignette
bibliography: references.bib
vignette: >
  %\VignetteIndexEntry{Partially Replicated (p-rep) Design}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r, include = FALSE}
options(rmarkdown.html_vignette.check_title = FALSE)
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = NA,
  warning = FALSE, 
  message = FALSE
)
```

This vignette shows how to generate a **partially replicated (p-rep) design** 
using both the FielDHub Shiny App and the scripting function `partially_replicated()` 
from the `FielDHub` R package.

## Overview

Partially replicated designs are commonly employed in early generation field trials. This type 
of design is characterized by replication of a portion of the entries, with the remaining 
entries only appearing once in the experiment. Commonly, the part of treatments with reps 
is due to an arbitrary decision by the research, also in some cases, it is due to technical 
reasons. The replication ratio is typically 1:4 [@Cullis2006-pREP], which means that the portion of treatment 
repeated twice is p = 25%. However, the design can be adapted to meet specific needs by adjusting 
the values of $p$ and the level of replication. For example, standard varieties (checks) may be 
included with higher levels of replication than test lines.

In `FielDHub`, users can set the number of entries that will have reps, as well as the number of 
entries that will only appear once. You can also choose to run the same experiment over 
multiple locations. 

## Optimization

Each partially replicated (p-rep) design location undergoes an optimization process that involves 
the following procedure:

Given a matrix $X$ of integers (p-rep design within location), we want to ensure that the distance 
between any two occurrences of the same treatment is at least a distance $d$. More specifically, 
we want to modify $X$ to ensure that no treatments appear twice within a distance less than $d$ in the resulting 
matrix.

The goal of the optimization process is to find a modified matrix that satisfies this constraint 
while maximizing some measure of deviation from the original matrix $X$. In this case, the 
measure of deviation is the pairwise Euclidean distance between occurrences of the same treatment. 
The process is done by the function `swap_pairs()` that uses a heuristic algorithm that starts 
with a distance of $d = 3$ between pairs of occurrences of the same treatment, and 
increases this distance by $1$ and repeats the process until either the algorithm no 
longer converges or the maximum number of iterations is reached.

The algorithm works by first identifying all pairs of occurrences of the same treatment that 
are closer than $d$. For each such pair, the function selects a random occurrence of a different 
integer that is at least $d$ away, and swaps the two occurrences. This process is repeated until 
no further swaps can be made that increase the pairwise Euclidean distances between occurrences 
of the same treatment. 

#### Toy Example

Consider a p-rep design where ten treatments are replicated twice and forty only once. 
The matrix (field layout) for this experiment has 6 rows and 10 columns.

$X =$

```{r, echo=FALSE, eval=TRUE}
set.seed(123)
X <- matrix(sample(c(rep(1:10, 2), 11:50), replace = FALSE), ncol = 10)
X[2,2] <- 5
X[2,3] <- 33
print(X)
```

In this initial p-rep design, we notice that the two instances of treatment **5** are positioned 
next to each other. Additionally, treatments **7** and **9** are also situated in adjacent cells. 
These suboptimal allocations could lead to issues or inaccurate results when analyzing the data 
from this experiment due to the short distance between replicated treatments and the likely 
spatial correlation between them.

The following table shows the pairwise distances for the replicated treatments

```{r, echo=FALSE, eval=TRUE}
dist_X <- FielDHub:::pairs_distance(X = X)
print(dist_X)
```

#### Swap pairs

We can improve the efficiency of the design by swapping  the treatments that are close and 
next to each other by using the function `swap_pairs()` from `FielDHub` R package.

```{r}
library(FielDHub)
B <- swap_pairs(X, starting_dist = 3)
```

The new matrix or the optimized p-rep design is,

```{r}
print(B$optim_design)
```

The distances for each pairwise of treatments are,

```{r}
print(B$pairwise_distance)
```

As we can see, the minimum distance that the algorithm reached is `r B$min_distance`. This 
means no treatments appear twice within a distance less than `r B$min_distance` in the 
resulting prep design. It is a considerable improvement from the first version of the 
p-rep design

The `FielDHub` function `partially_replicated()` does internally all the optimization process 
and uses the function `swap_pairs()` to maximize the distance between replicated treatments.

### Acknowledge

We would like to acknowledge Mr. Jean-Marc Montpetit for contributing code and ideas for the `swap_pairs()` and `pairs_distance()` functions. His contributions have had a 
significant impact on improving the partially replicated (p-rep) design in the R 
package `FielDHub`. We thank him for his valuable contributions.

## Use case

Consider a plant breeding field trial with 300 plots containing 75 entries appearing 
two times each, and 150 entries only appearing once. This field trial is arranged in 
a field of 15 rows by 20 columns. In this case, the breeder decided to replicate the 
genotypes that do not share significant generic information with each other (75), as 
well as leave with just one copy the genotypes that are siblings (150).

## Running the Shiny App

To launch the app you need to run either

```{r, eval=FALSE}
FielDHub::run_app()
```

or

```{r, eval=FALSE}
library(FielDHub)
run_app()
```

## 1. Using the FielDHub Shiny App

Once the app is running, click the tab **Partially Replicated Design** and select **Single and Multi-Location p-rep** from the dropdown. 

Then, follow the following steps where we will show how to generate a partially replicated design.

## Inputs

1. **Import entries' list?** Choose whether to import a list with entry numbers and names for genotypes or treatments.
    * If the selection is `No`, that means the app is going to generate synthetic data for entries and names of the treatment/genotypes based on the user inputs.

    * If the selection is `Yes`, the entries list must fulfill a specific format and must be a `.csv` file. The file must have the columns `ENTRY`, `NAME`, and `REPS`. The `ENTRY` column must have a unique entry integer number for each treatment/genotype. The column `NAME` must have a unique name that identifies each treatment/genotype. The `REPS` column must have an integer number for the replications of the groups. Both ENTRY and NAME must be unique, duplicates are not allowed. In the following table, we show an example of the entries list format. This example has an entry list with four treatments/genotypes that will appear twice and 8 that appear just once. 
    
```{r, include=FALSE}
ENTRY <- 1:12
NAME <- c(paste0("Genotype", LETTERS[1:12]))
REPS <- c(rep(2,4),rep(1,8))
df <- data.frame(ENTRY,NAME,REPS)
```

```{r, echo = FALSE, results='asis'}
library(knitr)
kable(df)
```

2. Enter the number of entries per replicate group in the **# of Entries per Rep Group** box as a comma separated list. In our example we will have 2 groups with 85 and 130 entries. So, we enter `75, 150` in the box for our sample experiment. 

3. Enter the number of replications per group in the **# of Rep per Group** box. In our example we will have 2 and 1 replications for the 2 groups, so we enter `2, 1` in this box. 

4. Enter the number of locations in **Input # of Locations**. We will run this experiment over a single location, so set **Input # of Locations** to `1`.

5. Select `serpentine` or `cartesian` in the **Plot Order Layout**. For this example we will use the default `serpentine` layout.

6. To ensure that randomizations are consistent across sessions, we can set a random seed in the box labeled **random seed**. In this example, we will set it to `1245`. 

7. Enter the starting plot number in the **Starting Plot Number** box. If the experiment has multiple locations, you must enter a comma separated list of numbers the length of the number of locations for the input to be valid. 

8. Once we have entered the information for our experiment on the left side panel, click the **Run!** button to run the design. 

9. You will then be prompted to select the dimensions of the field from the list of options in the drop down in the middle of the screen with the box labeled **Select dimensions of field**. In our case, we will select `15 x 20`. 

10. Click the **Randomize!** button to randomize the experiment with the set field dimensions and to see the output plots. If you change the dimensions again, you must re-randomize.

If you change any of the inputs on the left side panel after running an experiment initially, you have to click the Run and Randomize buttons again, to re-run with the new inputs.

## Outputs

After you run a single diagonal arrangement in FielDHub and set the dimensions of the field, there are several ways to display the information contained in the field book. The first tab, **Get Random**, shows the option to change the dimensions of the field and re-randomize, as well as a reference guide for experiment design. 

### Data Input

On the second tab, **Data Input**, you can see all the entries in the randomization in a list, as well as a table of the checks with the number of times they appear in the field. In the list of entries, the reps for each check is included as well.


### Randomized Field

The **Randomized Field** tab displays a graphical representation of the randomization of the entries in a field of the specified dimensions. The checks are the green colored cells, with the  The display includes numbered labels for the rows and columns. You can copy the field as a table or save it directly as an Excel file with the _Copy_ and _Excel_ buttons at the top. 

### Plot Number Field

On the **Plot Number Field** tab, there is a table display of the field with the plots numbered according to the Plot Order Layout specified, either _serpentine_ or _cartesian_. You can see the corresponding entries for each plot number in the field book. Like the Randomized Field tab, you can copy the table or save it as an Excel file with the _Copy_ and _Excel_ buttons. 

### Field Book

The **Field Book** displays all the information on the experimental design in a table format. It contains the specific plot number and the row and column address of each entry, as well as the corresponding treatment on that plot. This table is searchable, and we can filter the data in relevant columns. 

## 2. Using the `FielDHub` function: `partially_replicated()`.

You can run the same design with the function `partially_replicated()` in the `FielDHub` package.

First, you need to load the `FielDHub` package typing,

```{r, echo = TRUE}
library(FielDHub)
```

Then, you can enter the information describing the above design like this:

```{r, echo = TRUE}
prep <- partially_replicated(
  nrows = 15,
  ncols = 20, 
  repGens = c(75,150),
  repUnits = c(2,1), 
  planter = "serpentine", 
  plotNumber = 101,
  l = 1, 
  exptName = "Expt1",
  locationNames = "PALMIRA",
  seed = 1245, 
)
```

#### Details on the inputs entered in `optimized_arrangement()` above

The description for the inputs that we used to generate the design,

*   `nrows = 15` is the number of rows in the field.
*   `ncols = 20` is the number of columns in the field.
*   `repGens = c(75,150)` are the values for the groups to replicate
*   `repUnits = c(2,1)` are the values for representing respective replicates of each group.
*   `planter = "serpentine"` is the layout order. 
*   `plotNumber = 101` is the starting plot number for the experiment.
*   `l = 1` is the number of locations.
*   `exptName = "Expt1"` is an optional name for experiment.
*   `locationNames = "PALMIRA"` is the optional name for the locations.
*   `seed = 1245` is the random seed to replicate identical randomizations.

### Print `prep` object

To print a summary of the information that is in the object `prep`, we can use the generic function `print()`.

```{r, echo=TRUE, eval=FALSE}
print(prep)
```

```{r, echo=FALSE, eval=TRUE}
print(prep)
```

### Access to `prep` output

The `partially_replicated()` function returns a list consisting of all the information displayed in the output tabs in the FielDHub app: design information, plot layout, plot numbering, entries list, and field book. These are Accessible by the `$` operator, i.e. `prep$layoutRandom` or `prep$fieldBook`. 

`prep$fieldBook` is a list containing information about every plot in the field, with information about the location of the plot and the treatment in each plot. As seen in the output below, the field book has columns for `ID`, `EXPT`, `LOCATION`, `YEAR`, `PLOT`, `ROW`, `COLUMN`, `CHECKS`, `ENTRY`, and `TREATMENT`.

Let us see the first 10 rows of the field book for this experiment.

```{r, echo=TRUE, eval=FALSE}
field_book <- prep$fieldBook
head(field_book, 10)
```

```{r, echo=FALSE, eval=TRUE}
field_book <- prep$fieldBook
head(field_book, 10)
```

### Plot field layout

For plotting the layout in function of the coordinates `ROW` and `COLUMN` in the field book object we can use the generic function `plot()` as follow,


```{r, fig.align='center', fig.width=7.2, fig.height=5.5}
plot(prep)
```

In the figure above, green plots contain replicated entries, and gray plots contain entries that only appear once.

# References