spectralG.cpp: Perform spectral decomposition (inplemented by Rcpp)
In KosukeHamazaki/RAINBOW: Genome-Wide Association Study with SNP-Set Methods

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

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

`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.

$spectral.G: The spectral decomposition results of G.
$U: Eigen vectors of G.
$delta: Eigen values of G.
$spectral.SGS: Estimator for σ^2_e
$Q: Eigen vectors of SGS.
$theta: Eigen values of SGS.