Compute Single Value of the Diagonal of a Symmetric Matrix's Inverse

Via the eigen package's conjugate gradient descent algorithm.

Usage

eigen_compute_single_entry_of_diagonal_matrix(M, j, num_cores = 1)

Arguments

M

The symmetric matrix which to invert (and then extract one element of its diagonal)

j

The diagonal entry of M's inverse

num_cores

The number of cores to use. Default is 1.

Value

The \((j, j)\) entry of \(M^{-1}\).

Author

Adam Kapelner

Examples

  n = 500
  X = matrix(rnorm(n^2), nrow = n, ncol = n)
  M = t(X) %*% X
  j = 137
  eigen_compute_single_entry_of_diagonal_matrix(M, j)
#> [1] 3.185037
  solve(M)[j, j] #to ensure it's the same value
#> [1] 3.185037