Weighted Bending of a Matrix

Source: R/MakePD.R

This function implements the algorithm described in Jorjani2003. Without specifying a weight matrix, it corresponds to the unweighted bending where each eigenvalue is set to a lower limit which is given by the parameter pn_eps. The advantage of this bending method is that it is possible to specify a weight matrix where matrix elements with a high weight do not get changed as much as elements with a small weight. The number of observations used to estimate each variance component can be used as a weighting factor.

make_pd_weight(
  A,
  pmat_weight = matrix(1, nrow = nrow(A), ncol = ncol(A)),
  pn_eps = 1e-04,
  pn_max_iter = 1e+06,
  pn_digits = NULL
)

Arguments

A

input matrix
pmat_weight

weight matrix
pn_eps

smallest accepted eigenvalue
number

of digits to be rounded to

Value

mat_result bended matrix

Examples

# reading input matrix from paper by Jorjani et al 2003
sinput_file <- system.file('extdata', 'mat_test_jorjani2003.dat', package = 'rvcetools')
mat_test_jorjani <- as.matrix(readr::read_delim(file = sinput_file, delim = ' ', col_names = FALSE))

#> Rows: 5 Columns: 5
#> ── Column specification ────────────────────────────────────────────────────────
#> Delimiter: " "
#> dbl (5): X1, X2, X3, X4, X5
#> 
#> ℹ Use `spec()` to retrieve the full column specification for this data.
#> ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.
make_pd_weight(mat_test_jorjani)

#>             X1        X2        X3        X4        X5
#> [1,] 103.16918  90.83313  79.47122  44.53731  37.07254
#> [2,]  90.83313 106.49734  94.18961  74.07039  44.53731
#> [3,]  79.47122  94.18961 102.31355  94.18961  79.47122
#> [4,]  44.53731  74.07039  94.18961 106.49734  90.83313
#> [5,]  37.07254  44.53731  79.47122  90.83313 103.16918