# symbfact

## Purpose

Symbolic analysis of sparse Cholesky and LU factorization.

## Synopsis

    count = symbfact(A)
    count = symbfact(A,'f')
    [count,h,parent,post,R] = symbfact(...)

## Description

`count = symbfact(A)` returns the vector of row counts for the upper triangular Cholesky factor of a symmetric matrix whose upper triangle is that of `A`, assuming no cancellation during the factorization. This function is much faster than `chol(A)`.

`count = symbfact(A,'f')` lets you specify an option, where `f` can be

- `col` to analyze `A'`*`A` (without forming it explicitly).
- `sym` to obtain the same result as `symbfact(A)`.
  `[count,h,parent,post,R] = symbfact(...)` also returns

- the height of the elimination tree, `h`
- the elimination tree itself, `parent`
- a postordering permutation of the elimination tree, `post`
- a 0-1 matrix `R` whose structure is that of `chol(A)`

  ## See Also

      chol, etree

  (c) Copyright 1994 by The MathWorks, Inc.