generate_sparse_cov_matrix {Glarmadillo}

Generate Sparse Covariance Matrix

Description

Generates a sparse covariance matrix with specified dimension and rank. The generated matrix can be scaled or standardized, and further sparsified based on a given threshold.

Usage

generate_sparse_cov_matrix(
  n,
  p,
  standardize = TRUE,
  sparse_rho = 0,
  scale_power = 0
)

Arguments

n

The dimension of the covariance matrix (number of rows and columns).

p

The rank of the covariance matrix (number of non-zero eigenvalues). Must be less than or equal to n.

standardize

Logical indicating whether to standardize the matrix, setting this to TRUE overrides scale_power and sparse_rho.

sparse_rho

Numeric threshold for enforcing sparsity. Elements with absolute values below sparse_rho are set to zero.

scale_power

The exponent used to scale the matrix elements. Only used if standardize is FALSE.

Value

A n by n covariance matrix with rank p. If sparse_rho is greater than zero and standardize is FALSE, elements with absolute values below sparse_rho are set to zero to increase sparsity, while ensuring that the matrix is at least semi-definite.

Examples

# Generate a 10x10 sparse covariance matrix with rank 5
sparse_cov_matrix <- generate_sparse_cov_matrix(n = 10, p = 5)

# Generate a sparser matrix with elements below 0.3 set to zero
sparser_cov_matrix <- generate_sparse_cov_matrix(n = 100, p = 50,
                                                sparse_rho = 0.3,
                                              standardize = FALSE)

# Generate a standardized matrix
standardized_cov_matrix <- generate_sparse_cov_matrix(n = 100, p = 50, standardize = TRUE)