Currently, EPISCOPACY is being used in an application at NASA directed by J. A brief description is provided in the next section.
This module provides efficient implementations of all the basic linear algebra operations for sparse, symmetric, positive-definite matrices (as, for instance, commonly arise in least squares problems).
must have the same pattern of non-zeros as the matrix used to create this factor originally. The usual use for this is to factor AA’ when A has a large number of columns, or those columns become available incrementally.
Instead of loading all of A into memory, one can load in ‘strips’ of columns and pass them to this method one at a time.
Updated by @andreasnoack: I think qrupdate is the best package out there for this. Implementing this in Julia won't be a walk in the park; it's over 6000 lines of fortran (some of which is duplicated logic for different types of matrices).
I think qrupdate is the best package out there for this. Implementing this in Julia won't be a walk in the park; it's over 6000 lines of fortran (some of which is duplicated logic for different types of matrices).
Note that no fill-reduction analysis is done; whatever permutation was chosen by the initial call to Note This method uses an efficient implementation that extracts the diagonal D directly from CHOLMOD’s internal representation.
It never makes a copy of the factor matrices, or actually converts a full CHOLMOD itself supports matrices in CSC form with 32-bit integer indices and ‘double’ precision floats (64-bits, or 128-bits total for complex numbers).
DSCPACK is based on an efficient multifrontal implementation with fill-managing algorithms and implementation arising from earlier research by Raghavan and others.
If the matrix were dense, it would have O(N2) nonzeroes.
The most complicated part of such sparse Cholesky factorization relates to fill-in, i.e., zeroes in the original matrix that become nonzeroes in the factor L.
changes there are simple one-pass arrays that implement algorithms based on elimination and plane rotations.
In the case of negative rank-one changes, we do not feel that the standard algorithm  has a practical implementation.
LINPACK had these, but LAPACK left out the Cholesky update/downdate capabilities. f=2&t=2646 For the dense case, perhaps these should be implemented in julia.