CV_ADMMc: CV ADMM penalized precision matrix estimation (c++)
In MGallow/SCPME: Shrinking Characteristics of Precision Matrix Estimators

Cross validation function for ADMMsigma.

CV_ADMMc(X, S, Y, A, B, C, lam, alpha = 1, path = FALSE, tau = 10,
  rho = 2, mu = 10, tau_rho = 2, iter_rho = 10L, crit = "ADMM",
  tol_abs = 1e-04, tol_rel = 1e-04, maxit = 10000L, adjmaxit = 10000L,
  K = 5L, crit_cv = "MSE", start = "warm", trace = "progress")

`X`	option to provide a nxp matrix. Each row corresponds to a single observation and each column contains n observations of a single feature/variable.
`S`	option to provide a pxp sample covariance matrix (denominator n). If argument is `NULL` and `X` is provided instead then `S` will be computed automatically.
`Y`	option to provide nxr response matrix. Each row corresponds to a single response and each column contains n response of a single feature/response.
`A`	option to provide user-specified matrix for penalty term. This matrix must have p columns. Defaults to identity matrix.
`B`	option to provide user-specified matrix for penalty term. This matrix must have p rows. Defaults to identity matrix.
`C`	option to provide user-specified matrix for penalty term. This matrix must have nrow(A) rows and ncol(B) columns. Defaults to identity matrix.
`lam`	positive tuning parameters for elastic net penalty. If a vector of parameters is provided, they should be in increasing order.
`alpha`	elastic net mixing parameter contained in [0, 1]. `0 = ridge, 1 = lasso`. Alpha must be a single value (cross validation across alpha not supported).
`path`	option to return the regularization path. This option should be used with extreme care if the dimension is large. If set to TRUE, cores will be set to 1 and errors and optimal tuning parameters will based on the full sample. Defaults to FALSE.
`tau`	optional constant used to ensure positive definiteness in Q matrix in algorithm
`rho`	initial step size for ADMM algorithm.
`mu`	factor for primal and residual norms in the ADMM algorithm. This will be used to adjust the step size `rho` after each iteration.
`tau_rho`	factor in which to increase/decrease step size `rho`
`iter_rho`	step size `rho` will be updated every `iter.rho` steps
`crit`	criterion for convergence (`ADMM` or `loglik`). If `crit = loglik` then iterations will stop when the relative change in log-likelihood is less than `tol.abs`. Default is `ADMM` and follows the procedure outlined in Boyd, et al.
`tol_rel`	relative convergence tolerance. Defaults to 1e-4.
`maxit`	maximum number of iterations. Defaults to 1e4.
`adjmaxit`	adjusted maximum number of iterations. During cross validation this option allows the user to adjust the maximum number of iterations after the first `lam` tuning parameter has converged. This option is intended to be paired with `warm` starts and allows for 'one-step' estimators. Defaults to 1e4.
`K`	specify the number of folds for cross validation.
`crit_cv`	cross validation criterion (`loglik`, `penloglik`, `AIC`, or `BIC`). Defaults to `loglik`.
`start`	specify `warm` or `cold` start for cross validation. Default is `warm`.
`trace`	option to display progress of CV. Choose one of `progress` to print a progress bar, `print` to print completed tuning parameters, or `none`.

list of returns includes:

`lam`	optimal tuning parameter.
`path`	array containing the solution path. Solutions will be ordered in ascending lambda values.
`min.error`	minimum average cross validation error (cv_crit) for optimal parameters.
`avg.error`	average cross validation error (cv_crit) across all folds.
`cv.error`	cross validation errors (cv_crit).