slm {SparseM}  R Documentation 
This is a function to illustrate the use of sparse linear algebra
to solve a linear least squares problem using Cholesky decomposition.
The syntax and output attempt to emulate lm()
but may
fail to do so fully satisfactorily. Ideally, this would eventually
become a method for lm
. The main obstacle to this step is
that it would be necessary to have a model.matrix function that
returned an object in sparse csr form. For the present, the objects
represented in the formula must be in dense form. If the user wishes
to specify fitting with a design matrix that is already in sparse form,
then the lower level function slm.fit()
should be used.
slm(formula, data, weights, na.action, method = "csr", contrasts = NULL, ...)
formula 
a formula object, with the response on the left of a ~ operator,
and the terms, separated by + operators, on the right. As in
lm() , the response variable in the formula can be matrix valued.

data 
a data.frame in which to interpret the variables named in the formula, or in the subset and the weights argument. If this is missing, then the variables in the formula should be on the search list. This may also be a single number to handle some special cases – see below for details. 
weights 
vector of observation weights; if supplied, the algorithm fits to minimize the sum of the weights multiplied into the absolute residuals. The length of weights must be the same as the number of observations. The weights must be nonnegative and it is strongly recommended that they be strictly positive, since zero weights are ambiguous. 
na.action 
a function to filter missing data.
This is applied to the model.frame after any subset argument has been used.
The default (with na.fail ) is to create an error if any missing
values are found. A possible alternative is na.omit , which
deletes observations that contain one or more missing values.

method 
there is only one method based on Cholesky factorization 
contrasts 
a list giving contrasts for some or all of the factors
default = NULL appearing in the model formula.
The elements of the list should have the same name as the variable
and should be either a contrast matrix (specifically, any fullrank
matrix with as many rows as there are levels in the factor),
or else a function to compute such a matrix given the number of levels.

... 
additional arguments for the fitting routines 
A list of class slm
consisting of:
coefficients 
estimated coefficients 
chol 
cholesky object from fitting 
residuals 
residuals 
fitted 
fitted values 
terms 
terms 
call 
call 
...
Roger Koenker
Koenker, R and Ng, P. (2002). SparseM: A Sparse Matrix Package for R,
http://www.econ.uiuc.edu/~roger/research
slm.methods
for methods summary
, print
, fitted
,
residuals
and coef
associated with class slm
,
and slm.fit
for lower level fitting functions. The latter functions
are of special interest if you would like to pass a sparse form of the
design matrix directly to the fitting process.
data(lsq) X < model.matrix(lsq) #extract the design matrix y < model.response(lsq) # extract the rhs X1 < as.matrix(X) slm.time < unix.time(slm(y~X11) > slm.o) # pretty fast lm.time < unix.time(lm(y~X11) > lm.o) # very slow cat("slm time =",slm.time,"\n") cat("slm Results: Reported Coefficients Truncated to 5 ","\n") sum.slm < summary(slm.o) sum.slm$coef < sum.slm$coef[1:5,] sum.slm cat("lm time =",lm.time,"\n") cat("lm Results: Reported Coefficients Truncated to 5 ","\n") sum.lm < summary(lm.o) sum.lm$coef < sum.lm$coef[1:5,] sum.lm