SparseM (version 0.57)

SparseM.solve: Linear Equation Solving for Sparse Matrices

Description

chol performs a Cholesky decomposition of a symmetric positive definite sparse matrix x of class matrix.csr. backsolve performs a triangular back-fitting to compute the solutions of a system of linear equations. solve combines chol and backsolve and will compute the inverse of a matrix if the right-hand-side is missing.

Usage

chol(x, ...)
backsolve(r, x, k, upper.tri, transpose)
solve(a, b, ...)

Arguments

a

symmetric positive definite matrix of class matrix.csr.

r

object of class matrix.csr.chol returned by the function chol.

x,b

vector(regular matrix) of right-hand-side(s) of a system of linear equations.

k

inherited from the generic; not used here.

pivot

inherited from the generic; not used here.

nsubmax,nnzlmax,tmpmax

dimensions of work arrays, in normal operation these are determined inside the algorithm.

upper.tri

inherited from the generic; not used here.

transpose

inherited from the generic; not used here.

...

further arguments passed to or from other methods.

Details

chol performs a Cholesky decomposition of a symmetric positive definite sparse matrix x of class matrix.csr using the block sparse Cholesky algorithm of Ng and Peyton (1993). backsolve does triangular back-fitting to compute the solutions of a system of linear equations. For systems of linear equations that only vary on the right-hand-side, the result from chol can be reused. solve combines chol and backsolve, and will compute the inverse of a matrix if the right-hand-side is missing. The determinant of the Cholesky factor is returned providing a means to efficiently compute the determinant of sparse positive definite symmetric matrices.

References

Koenker, R and Ng, P. (2002). SparseM: A Sparse Matrix Package for R, http://www.econ.uiuc.edu/~roger/research

Ng, E. G. and B. W. Peyton (1993), "Block sparse Cholesky algorithms on advanced uniprocessor computers", SIAM J. Sci. Comput., 14, pp. 1034-1056.

See Also

slm for sparse version of lm

Examples

data(lsq)
class(lsq) # -> [1] "matrix.csc.hb"
model.matrix(lsq)->design.o
class(design.o) # -> "matrix.csr"
dim(design.o) # -> [1] 1850  712
y <- model.response(lsq) # extract the rhs
length(y) # [1] 1850
t(design.o)%*%design.o -> XpX
t(design.o)%*%y -> Xpy
chol(XpX)->chol.o
backsolve(chol.o,Xpy)-> b1 # least squares solutions in two steps
solve(XpX,Xpy) -> b2 # least squares estimates in one step