complexity {spam}R Documentation

Complexity for Sparse Matrices

Description

A few results of computational complexities for selected sparse algoritms in spam

Details

chol performs a Cholesky decomposition of a symmetric positive definite sparse matrix x of class spam. Currently, there is only the block sparse Cholesky algorithm of Ng and Peyton (1993) implemented (method=NgPeyton).

To pivot/permute the matrix, you can choose between the multiple minimum degree (pivot=MMD) or reverse Cuthill-Mckee (pivot=RCM) from George and Lui (1981). It is also possible to furnish a specific permutation in which case pivot is a vector. For compatibility reasons, pivot can also take a logical in which for FALSE no permutation is done and for TRUE is equivalent to MMD.

Often the sparseness structure is fixed and does not change, but the entries do. In those cases, we can update the Cholesky factor with update.spam.chol.NgPeyton by suppling a Cholesky factor and the updated matrix.

The Cholesky decompositions requires parameters, linked to memory allocation. If the default values are too small the Fortran routine returns an error to R, which allocates more space and calls the Fortran routine again. The user can also pass better estimates of the allocation sizes to chol with the argument memory=list(nnzR=..., nnzcolindices=...). The minimal sizes for a fixed sparseness structure can be obtained from a summary call.

The output of chol can be used with forwardsolve and backsolve to solve a system of linear equations.

References

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

George, A. and Liu, J. (1981) Computer Solution of Large Sparse Positive Definite Systems, Prentice Hall.

See Also

det, solve, forwardsolve, backsolve and ordering.


[Package spam version 0.15-5 Index]