fastclime: The main solver for fastclime package
In fastclime: A Fast Solver for Parameterized LP Problems, Constrained L1 Minimization Approach to Sparse Precision Matrix Estimation and Dantzig Selector

Description Usage Arguments Details Value Note Author(s) See Also Examples

A fast parametric simplex solver for constrainted l1 minimization approach to sparse precision matrix estimation

1	fastclime(x, lambda.min = 0.1, nlambda = 50)

`x`	There are 2 options: (1) `x` is an `n` by `d` data matrix (2) a `d` by `d` sample covariance matrix. The program automatically identifies the input matrix by checking the symmetry. (`n` is the sample size and `d` is the dimension)
`lambda.min`	This is the smallest value of lambda you would like the solver to explorer. The default value is `0.1`. If `nlambda` is large enough, the precision matrix selector function `fastclime.selector` will be able to find all precision matrix corresponding to all lambda values ranging from `1` to `lambda.min`.
`nlambda`	It is the number of the path length one would like to achieve. The default length is 50. Note if d is large and nlambda is also large, it is possible that the program will fail to allocate memory for the path.

This program uses parametric simplex linear programming method to solve CLIME (Constrained l1 Minimization Sparse Precision Matrix Estimation) problem. The solution path of the problem corresponds to the parameter in the parametric simplex method.

An object with S3 class "fastclime" is returned:

`data`	The `n` by `d` data matrix or `d` by `d` sample covariance matrix from the input
`cov.input`	An indicator of the sample covariance.
`sigmahat`	The empirical covariance of the data. If cov.inpu is TRUE, sigmahat = data
`maxnlambda`	The length of the path. If the program finds `lambda.min` in less than `nlambda` iterations for all columns, then the acutal maximum lenth for all columns will be returned. Otherwise it equals `nlambda`.
`lambdamtx`	The sequence of regularization parameters for each column, it is a `nlambda` by `d` matrix. It will be filled with 0 when the program finds the required `lambda.min` value for that column. This parameter is required for `fastclime.selector`.
`icovlist`	A `nlambda` list of `d` by `d` precision matrices as an alternative graph path (numerical path) corresponding to `lambdamtx`. This parameter is also required for `fastclime.selector`.

The program will stop when either the maximum number of iteration for each column nlambda is achieved or when the required lambda.min is achieved for each column. When the dimension is huge, make sure nlambda is small so that there are enough memory to allocate the solution path. lambdamtx and icovlist will be used in fastclime.selector.

Haotian Pang, Han Liu and Robert Vanderbei
Maintainer: Haotan Pang<hpang@princeton.edu>

fastclime.generator, fastclime.plot, fastclime.selector and fastclime-package.

#generate data
L = fastclime.generator(n = 100, d = 20)

#graph path estimation
out1 = fastclime(L$data,0.1)
out2 = fastclime.selector(out1$lambdamtx, out1$icovlist,0.2)
fastclime.plot(out2$adaj)

#graph path estimation using the sample covariance matrix as the input.
out1 = fastclime(cor(L$data),0.1)
out2 = fastclime.selector(out1$lambdamtx, out1$icovlist,0.2)
fastclime.plot(out2$adaj)

Loading required package: lattice
Loading required package: igraph

Attaching package: 'igraph'

The following objects are masked from 'package:stats':

    decompose, spectrum

The following object is masked from 'package:base':

    union

Loading required package: MASS
Loading required package: Matrix
Generating data from the multivariate normal distribution with the random graph structure....done.
Allocating memory 
start recovering 
preparing precision and path matrix list 
Done! 
Allocating memory 
start recovering 
preparing precision and path matrix list 
Done!