Evaluate numerical properties square matrix

Function that evaluates various numerical properties of a square input matrix. The intended use is to evaluate the various numerical properties of what is assumed to be a covariance matrix. Another use is to evaluate the various numerical properties of a (regularized) precision matrix.

evaluateS(S, verbose = TRUE)

Arguments

S

Covariance or (regularized) precision matrix.

verbose

A logical indicating if output should be printed on screen.

Value

symm

A logical indicating if the matrix is symmetric.

realEigen

A logical indicating if the eigenvalues are real.

posEigen

A logical indicating if the eigenvalues are strictly positive.

dd

A logical indicating if the matrix is diagonally dominant.

trace

A numerical giving the value of the trace.

det

A numerical giving the value of the determinant.

condNumber

A numerical giving the value of the spectral condition number.

Details

The function evaluates various numerical properties of a covariance or precision input matrix. The function assesses if the input matrix is symmetric, if all its eigenvalues are real, if all its eigenvalues are strictly positive, and if it is a diagonally dominant matrix. In addition, the function calculates the trace, the determinant, and the spectral condition number of the input matrix. See, e.g., Harville (1997) for more details on the mentioned (numerical) matrix properties.

References

Harville, D.A.(1997). Matrix algebra from a statistician's perspective. New York: Springer-Verlag.

See also

covML, ridgeP

Author

Wessel N. van Wieringen, Carel F.W. Peeters <carel.peeters@wur.nl>

Examples

## Obtain some (high-dimensional) data
p = 25
n = 10
set.seed(333)
X = matrix(rnorm(n*p), nrow = n, ncol = p)
colnames(X)[1:25] = letters[1:25]
Cx <- covML(X)

## Evaluate numerical properties covariance matrix
## Obtain, e.g., value trace
Seval <- evaluateS(Cx); Seval
#> Properties of input matrix:
#> ----------------------------------------
#>        symmetric : TRUE
#> eigenvalues real : TRUE
#>  eigenvalues > 0 : FALSE
#>   diag. dominant : TRUE
#> 
#>            trace : 21.55145
#>      determinant : 0
#>  l2 cond. number : 2.694993e+16
#> ----------------------------------------
#> $symm
#> [1] TRUE
#> 
#> $realEigen
#> [1] TRUE
#> 
#> $posEigen
#> [1] FALSE
#> 
#> $diagDom
#> [1] TRUE
#> 
#> $trace
#> [1] 21.55145
#> 
#> $det
#> [1] -2.78594e-255
#> 
#> $condNumber
#> [1] 2.694993e+16
#> 
Seval$trace
#> [1] 21.55145

## Evaluate numerical properties precision matrix after regularization
P <- ridgeP(Cx, lambda = 10, type = 'Alt')
Peval <- evaluateS(P); Peval
#> Properties of input matrix:
#> ----------------------------------------
#>        symmetric : TRUE
#> eigenvalues real : TRUE
#>  eigenvalues > 0 : TRUE
#>   diag. dominant : TRUE
#> 
#>            trace : 19.8448
#>      determinant : 0.00211
#>  l2 cond. number : 1.95384
#> ----------------------------------------
#> $symm
#> [1] TRUE
#> 
#> $realEigen
#> [1] TRUE
#> 
#> $posEigen
#> [1] TRUE
#> 
#> $diagDom
#> [1] TRUE
#> 
#> $trace
#> [1] 19.8448
#> 
#> $det
#> [1] 0.002113186
#> 
#> $condNumber
#> [1] 1.953842
#>