spectralG.cpp: Perform spectral decomposition (inplemented by Rcpp)

Description

Perform spectral decomposition for $G = ZKZ'$ or $SGS$ where $S = I - X(X'X)^{-1}X$.

Usage

spectralG.cpp(
  ZETA,
  ZWs = NULL,
  X = NULL,
  weights = 1,
  return.G = TRUE,
  return.SGS = FALSE,
  spectral.method = NULL,
  tol = NULL,
  df.H = NULL
)

Value

$spectral.G: The spectral decomposition results of G.

Eigen vectors of G.

$delta

Eigen values of G.

$spectral.SGS

Estimator for $\sigma^2_e$

Eigen vectors of SGS.

$theta

Eigen values of SGS.

Arguments

ZETA: A list of variance (relationship) matrix (K; $m \times m$) and its design matrix (Z; $n \times m$) of random effects. You can use only one kernel matrix. For example, ZETA = list(A = list(Z = Z, K = K)) Please set names of list "Z" and "K"!
ZWs: A list of additional linear kernels other than genomic relationship matrix (GRM). We utilize this argument in RGWAS.multisnp function, so you can ignore this.
X: $n \times p$ matrix. You should assign mean vector (rep(1, n)) and covariates. NA is not allowed.
weights: If the length of ZETA >= 2, you should assign the ratio of variance components to this argument.
return.G: If thie argument is TRUE, spectral decomposition results of G will be returned. ($G = ZKZ'$)
return.SGS: If this argument is TRUE, spectral decomposition results of SGS will be returned. ($S = I - X(X'X)^{-1}X$, $G = ZKZ'$)
spectral.method: The method of spectral decomposition. In this function, "eigen" : eigen decomposition and "cholesky" : cholesky and singular value decomposition are offered. If this argument is NULL, either method will be chosen accorsing to the dimension of Z and X.
tol: The tolerance for detecting linear dependencies in the columns of G = ZKZ'. Eigen vectors whose eigen values are less than "tol" argument will be omitted from results. If tol is NULL, top 'n' eigen values will be effective.
df.H: The degree of freedom of K matrix. If this argument is NULL, min(n, sum(nrow(K1), nrow(K2), ...)) will be assigned.