fungible (version 2.4.4)

RGen: Generate random R matrices with various user-defined properties via differential evolution (DE).

Description

Generate random R matrices with various user-defined properties via differential evolution (DE).

Usage

RGen(
  Nvar = 3,
  NMatrices = 1,
  Minr = -1,
  Maxr = 1,
  MinEig = 0,
  MaxIter = 200,
  delta = 1e-08,
  PRINT = FALSE,
  Seed = NULL
)

Value

RGen 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.

Arguments

Nvar

(integer) The order of the generated correlation matrices.

NMatrices

(integer) Generate NMatrices correlation matrices.

Minr

(numeric > -1 and < Maxr) The minimum rij in the generated R matrices. Default Minr = -1.

Maxr

(numeric > Minr and <= 1). The maximum rij in the generated R matrices. Default Maxr = 1.

MinEig

(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.

MaxIter

(integer) The maximum number of iterations (i.e., generations) for the DE optimizer. Default MaxIter = 200.

delta

(numeric > 0) A number that controls the convergence accuracy of the differential evolution algorithm. Default delta = 1E-8.

PRINT

(logical) When PRINT = TRUE the algorithm convergence status is printed. Default PRINT = FALSE.

Seed

(integer) Initial random number seed. Default (Seed = NULL).

Author

Niels G. Waller

References

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(6), 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

Examples

## Example 1: Generate random 4 x 4 Correlation matrices.

  out <- RGen(Nvar = 4,
              NMatrices = 4,
              PRINT = TRUE,
              Seed = 1)
                      
  # Check convergence status of all matrices                     
  print( table(out$converged) )                     

  print( round( out$R[[1]] , 3) )