# answers dating ariane - Updating cholesky

We should be able to add pure Julia Cholesky updates without too much effort. We should be able to add pure Julia Cholesky updates without too much effort. wrappers is conceptually not too bad, though CHOLMOD has a pretty confusing API at times.We already have the necessary components and the algorithm is fairly simple. We already have the necessary components and the algorithm is fairly simple. Some quality time with the API docs and/or headers along with and looking at the existing bindings in https://github.com/Julia Lang/julia/blob/master/base/sparse/should get you started.An efficient implementation depends to a large extent on complex data structures and on techniques from graph theory to reduce, identify, and manage fill.

Specifically, it exposes most of the capabilities of the CHOLMOD package, including: is any real scalar (usually 0 or 1).

(And denotes the identity matrix.) Note that if you are solving a conventional least-squares problem, you will need to transpose your matrix before calling this function, and therefore it will be somewhat more efficient to construct your matrix in CSR format (so that its transpose will be in CSC format).

I need to use rank 1 Cholesky updates for an adaptive algorithm I am working on, to bring down complexity from O(n^3) to O(n^2), and was a bit unclear from this open issue if there is some preliminary yet operational support (either built-in or by invoking QRupdate)?

I would also love being able to update a QR factorization by adding or deleting columns.

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.Sparse Cholesky factorization is typically a four step process: (1) ordering to compute a fill-reducing numbering, (2) symbolic factorization to determine the nonzero structure of L, (3) numeric factorization to compute L, and, (4) triangular solution to solve L(T)x = y and Ly = b.The first two steps are symbolic and are performed using the graph of the matrix.factor it (i.e., it performs a “symbolic Cholesky decomposition”).This function ignores the actual contents of the matrix A.for rank 1 updates and downdates to Cholesky factorizations.

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