sample_spiked_wishart_and_jac: Efficiently sample the singular values corresponding to a...

In dependentsimr: Simulate Omics-Scale Data with Dependency

Efficiently sample the singular values corresponding to a random Wishart matrix with spiked eigenvalues and the Jacobian I.e., these are the singular values of G if GG^T is Wishart. The square of these give the eigenvalues of the random Wishart matrix.

Description

Efficiently sample the singular values corresponding to a random Wishart matrix with spiked eigenvalues and the Jacobian I.e., these are the singular values of G if GG^T is Wishart. The square of these give the eigenvalues of the random Wishart matrix.

Usage

sample_spiked_wishart_and_jac(
  spiked_sd,
  num_observations,
  num_variables,
  population_sd = 1,
  num_eigs = 0
)

Arguments

spiked_sd	The spiked standard deviations
num_observations	The number of observations (aka samples or columns)
num_variables	The number of variables (aka features or rows)
population_sd	the standard deviation of all non-spiked components (num_variables - length(spiked_sd) of them)
num_eigs	The number of eigenvalues to compute. If 0 compute all of them using dense matrix routines. If greater than zero, use sparse matrices and compute that many top eigenvalues.

Value

List with a vector of random singular values of G where G is a random num_variables x num_observations matrix with iid columns from N(0, Sigma) where Sigma is diagonal with entries spiked_sd^2 and all the remaining are population_sd^2. and also the Jacobian, where ⁠\[i,j\]⁠ is the derivative of the ith singular value with respect to the jth spiked SD and the gradient of the population_sd variable

Examples

set.seed(0)
# Sample eigenvalues of a covariance matrix of a 10 sample study with 1000 variables such that
# the top two (underlying true distribution of the data, not sample) principal components
# have SDs of 100 and 10 and the remaining 98 have 1
res = sample_spiked_wishart_and_jac(
  spiked_sd = c(500, 100),
  num_variables = 1000,
  num_observations = 10-1,
  num_eigs = 3
)
res$singular_vals # singular values of G, (i.e., square roots of the eigenvalues of W = G G^T)
res$jacobian # jacobian of the singular values with respect to the spiked_sd's
res$pop_sd_grad # gradient of population_sd parameter

dependentsimr documentation built on Aug. 8, 2025, 6:23 p.m.