# cholfact(A)

cholfact(A; shift=0, perm=Int[]) -> CHOLMOD.Factor

Compute the Cholesky factorization of a sparse positive definite matrix `A`

. A fill-reducing permutation is used. `F = cholfact(A)`

is most frequently used to solve systems of equations with `F\b`

, but also the methods `diag`

, `det`

, `logdet`

are defined for `F`

. You can also extract individual factors from `F`

, using `F[:L]`

. However, since pivoting is on by default, the factorization is internally represented as `A == P'*L*L'*P`

with a permutation matrix `P`

; using just `L`

without accounting for `P`

will give incorrect answers. To include the effects of permutation, it's typically preferable to extact "combined" factors like `PtL = F[:PtL]`

(the equivalent of `P'*L`

) and `LtP = F[:UP]`

(the equivalent of `L'*P`

).

Setting optional `shift`

keyword argument computes the factorization of `A+shift*I`

instead of `A`

. If the `perm`

argument is nonempty, it should be a permutation of `1:size(A,1)`

giving the ordering to use (instead of CHOLMOD's default AMD ordering).

The function calls the C library CHOLMOD and many other functions from the library are wrapped but not exported.

## Examples

## See Also

## User Contributed Notes

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