Fx_blocks: Matrix of candidate regressors for a block size-two model
In OptimalDesign: A Toolbox for Computing Efficient Designs of Experiments

Description Usage Arguments Details Value Note Author(s) References See Also Examples

Creates the matrix of all candidate regressors of a linear regression model corresponding to the problem of the optimal block size-two design.

1	Fx_blocks(n.treats, blocks=NULL, echo=TRUE)

`n.treats`	the number of "treatments" in the block experiment.
`blocks`	the `2` times `n` matrix of all permissible blocks (that is, permissible pairings of treatments). If `blocks=NULL`, `blocks` is set to `combn(n.treats, 2)`, which means that all treatment pairings are permissible.
`echo`	Print the call of the function?

Creates the matrix Fx of artificial regressors, such that the D- and A-optimal designs for the corresponding artificial LRM are are the same as what is called the D- and A-optimal design in the original block model with blocks of size two.

the n times m matrix of all candidate regressors of an auxiliary linear regression model corresponding to the problem of the optimal block size-two design (n is ncol(blocks), m is n.treats-1).

This optimal design problem is equivalent to various optimum-subgraph problems, depending on the criterion.

Radoslav Harman, Lenka Filova

Harman R, Filova, L: Computing efficient exact designs of experiments using integer quadratic programming, Computational Statistics and Data Analysis 71 (2014) 1159-1167.

Sagnol G, Harman R: Computing Exact D-optimal designs by mixed integer second-order cone programming, The Annals of Statistics 43 (2015), 2198-2224.

Fx_cube, Fx_simplex, Fx_glm, Fx_dose, Fx_survival

## Not run: 
# Compute a D-efficient block size-two design
# with 15 treatments and 10 blocks of size two

Fx <- Fx_blocks(10)
w <- od_KL(Fx, 15, t.max = 5)$w.best
des <- combn(10, 2)[, as.logical(w)]
print(des)


# We can visualize the design as a graph
library(igraph)
grp <- graph_(t(des), from_edgelist(directed = FALSE))
plot(grp, layout=layout_with_graphopt)

## End(Not run)

[1] Call of the function:
Fx_blocks(n.treats = 10)
[1] Call of the function:
od_KL(Fx = Fx, N = 15, t.max = 5)
[1] Call of the function:
od_REX(Fx = Fx, crit = "D", track = FALSE)
[1] Running od_D_KL for cca 5 seconds starting at 2021-03-25 20:44:51.
[1] The problem size is n=45, m=9, N=15
[1] Setting K=10, L=10
[1] od_D_KL Time: 0 Value: 2.578583 Efficiency: 0.773575
[1] od_D_KL Time: 1 Value: 3.00533 Efficiency: 0.901599
[1] od_D_KL Time: 2 Value: 3.00533 Efficiency: 0.901599
[1] od_D_KL Time: 3 Value: 3.00533 Efficiency: 0.901599
[1] od_D_KL Time: 4 Value: 3.00533 Efficiency: 0.901599
[1] od_D_KL finished after 5 seconds at 2021-03-25 20:44:56
[1] with 1025 restarts and 5312 exchanges.
     [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] [,14]
[1,]    1    1    1    2    2    2    3    3    4     4     5     5     6     7
[2,]    3    4    6    6    7    9    5    7    8     9     9    10    10     8
     [,15]
[1,]     8
[2,]    10

Attaching package: ‘igraph’

The following objects are masked from ‘package:stats’:

    decompose, spectrum

The following object is masked from ‘package:base’:

    union