Rbounds can generate uniformly sampled correlation matrices with
user-defined bounds on the correlation coefficients via differential
evolution (DE). Unconstrained \(R\) matrices (i.e., with no constraints placed
on the \(r_{ij}\)) computed from 12 or fewer variables can be generated relatively
quickly on a personal computer. Larger matrices may require
very long execution times. Rbounds can
generate larger matrices when the correlations are tightly
bounded (e.g., \(0 < r_{ij} < .5\) for all \(i \neq j\)). To generate
uniformly sampled \(R\) matrices, users should leave
NPopFactor and crAdaption at
their default values.
Rbounds(
Nvar = 3,
NMatrices = 1,
Minr = -1,
Maxr = 1,
MinEig = 0,
MaxIter = 200,
NPopFactor = 10,
crAdaption = 0,
delta = 1e-08,
PRINT = FALSE,
Seed = NULL
)Rbounds returns the following objects:
R (matrix) A list of generated correlation matrices.
converged: (logical) a logical that indicates the convergence status of the optimization for each matrix.
iter (integer) The number of cycles needed to reach a converged solution for each matrix.
(integer) The order of the generated correlation matrices.
(integer) Generate NMatrices
correlation matrices.
(numeric > -1 and < Maxr) The lower bound for all \(r_{ij}\) in
the generated R matrices. Default Minr = -1.
(numeric > Minr and <= 1). The upper bound for all \(r_{ij}\) in the
generated \(R\) matrices. Default Maxr = 1.
(numeric). Minimum size of the last eigenvalue of R. Default
MinEig = 0. By setting MinEig to a value slightly greater than
0 (e.g., 1E-3), all generated matrices will be positive definite.
(integer) The maximum number of iterations
(i.e., generations) for the DE optimizer. Default MaxIter = 200.
(numeric > 0). If \(R\) is an \(n \times n\) matrix, then each generation
will contain NPopFactor \(\times n(n-1)/2\) members. Default NPOP = 10.
(numeric (0,1]). Controls the speed of the crossover adaption.
This parameter is called `c' in the DEoptim.control help page.
Default crAdaption = 0.
(numeric > 0) A number that controls the convergence. See the DEoptim.control
accuracy of the differential evolution algorithm. Default delta = 1E-8.
(logical) When PRINT = TRUE the algorithm convergence status is printed.
Default PRINT = FALSE.
(integer) Initial random number seed. Default (Seed = NULL).
Niels G. Waller
Ardia, D., Boudt, K., Carl, P., Mullen, K.M., Peterson, B.G. (2011) Differential Evolution with DEoptim. An Application to Non-Convex Portfolio Optimization. URL The R Journal, 3(1), 27-34. URL https://journal.r-project.org/archive/2011-1/RJournal_2011-1_Ardia~et~al.pdf.
Georgescu, D. I., Higham, N. J., and Peters, G. W. (2018). Explicit solutions to correlation matrix completion problems, with an application to risk management and insurance. Royal Society Open Science, 5(3), 172348.
Mishra, S. K. (2007). Completing correlation matrices of arbitrary order by differential evolution method of global optimization: a Fortran program. Available at SSRN 968373.
Mullen, K.M, Ardia, D., Gil, D., Windover, D., Cline, J. (2011). DEoptim: An R Package for Global Optimization by Differential Evolution. Journal of Statistical Software, 40, 1-26. URL http://www.jstatsoft.org/v40/i06/.
Price, K.V., Storn, R.M., Lampinen J.A. (2005) Differential Evolution - A Practical Approach to Global Optimization. Berlin Heidelberg: Springer-Verlag. ISBN 3540209506.
Zhang, J. and Sanderson, A. (2009) Adaptive Differential Evolution. Springer-Verlag. ISBN 978-3-642-01526-7
## Example 1: Generate random 4 x 4 Correlation matrices with all rij >= 0.
out <- Rbounds(Nvar = 4,
NMatrices = 4,
Minr = 0,
Maxr = 1,
PRINT = TRUE,
Seed = 1)
# Check convergence status of matrices
print( table(out$converged) )
print( round( out$R[[1]] , 3) )
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