\name{choose_xenv}
\alias{choose_xenv}
\title{Choose u for the envelope based PLS.}
\description{
  Select the dimension of the envelope subspace using Bayesian information
  criterion, Akaike information criterion and Likelihood ratio testing. 
  }
\usage{
	   choose_xenv(X, Y)
}

\arguments{
  \item{X}{Predictors. An n by p matrix, p is the number of predictors. The predictors can be univariate or multivariate, discrete or continuous.}
  \item{Y}{Multivariate responses. An n by r matrix, r is the number of responses and n is number of observations. The responses must be continuous variables.}
\item{dims}{A vector. The dimensions to be chosen from. The default is  0 to p.}
  \item{maxiter}{Maximum number of iterations.  Default value: 100.}
  \item{ftol}{Tolerance parameter for F.  Default value: 1e-2. } 
  \item{verbose}{Flag for print out model fitting process, logical 0 or 1. Default value: 0.}  
}

\value{
  \item{result}{Dimensions of the envelope subspace chosen by BIC, AIC and LRT.}
  \item{detail}{-2*Loglik, BIC, AIC, degree of freedom and p-values for LRT test.}
}
  
\references{
The codes are implemented based on the algorithm in 4.5.1 of Cook et al (2012). 

Cook, R. Dennis, I. S. Helland, and Zhihua Su. "Envelopes and partial least squares regression." \emph{Journal of the Royal Statistical Society Series B} 20 (2012): 927-1010.
 
The Grassmann manifold optimization step implements the algorithm in sg_min 2.4.3 by Ross Lippert (http://web.mit.edu/~ripper/www.sgmin.html).

}

\author{Guangyu Zhu and Zhihua Su\cr Maintainer: Guangyu Zhu \email{gzhu22@ufl.edu}}



%\examples{
%# mussel
%data(AIS)
%choose_xenv(AIS$X,AIS$Y)
%}