CVP_ADMM: Parallel CV (uses CVP_ADMMc)
In MGallow/shrink: Shrinking Characteristics of Precision Matrix Estimators

Parallel implementation of cross validation.

CVP_ADMM(X, Y = NULL, A = diag(ncol(X)), B = diag(ncol(X)),
  C = diag(ncol(X)), lam = 10^seq(-2, 2, 0.2), alpha = 1, tau = 10,
  rho = 2, mu = 10, tau.rho = 2, iter.rho = 10, crit = c("ADMM",
  "loglik"), tol.abs = 1e-04, tol.rel = 1e-04, maxit = 1000,
  adjmaxit = NULL, K = 5, crit.cv = c("MSE", "loglik", "penloglik", "AIC",
  "BIC"), start = c("warm", "cold"), cores = 1, trace = c("progress",
  "print", "none"))

`X`	nxp data matrix. Each row corresponds to a single observation and each column contains n observations of a single feature/variable.
`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. Defaults to grid of values `10^seq(-2, 2, 0.2)`.
`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).
`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.abs`	absolute convergence tolerance. Defaults to 1e-4.
`tol.rel`	relative convergence tolerance. Defaults to 1e-4.
`maxit`	maximum number of iterations. Defaults to 1e3.
`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 NULL.
`K`	specify the number of folds for cross validation.
`crit.cv`	cross validation criterion (`MSE`, `loglik`, `penloglik`, `AIC`, or `BIC`). Defaults to `MSE`.
`start`	specify `warm` or `cold` start for cross validation. Default is `warm`.
`cores`	option to run CV in parallel. Defaults to `cores = 1`.
`trace`	option to display progress of CV. Choose one of `progress` to print a progress bar, `print` to print completed tuning parameters, or `none`.

returns list of returns which includes:

`lam`	optimal tuning parameter.
`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).