# ldl

Block LDL' factorization for Hermitian indefinite matrices

## Syntax

## Description

### Full Data

`[`

returns the permutation information in the form specified by
`L`

,`D`

,`P`

] = ldl(___,`outputForm`

)`outputForm`

. Specify `outputForm`

as
`"vector"`

to return the permutation information as a vector.

### Sparse Data

`[___] = ldl(___,`

,
where `triangle`

)`triangle`

is `"upper"`

, uses the upper triangle
of real sparse `S`

to compute the factorization. By default,
`triangle`

is `"lower"`

, which uses the lower
triangle of `S`

to compute the factorization. You can use any of the
input and output argument combinations in previous syntaxes for sparse matrices.

`[___] = ldl(___,`

returns the permutation information in the form specified by
`outputForm`

)`outputForm`

. Specify `outputForm`

as
`"vector"`

to return the permutation information as a vector.

## Examples

## Input Arguments

## Output Arguments

## More About

## References

[1] Ashcraft, Cleve, Roger G. Grimes,
and John G. Lewis. “Accurate Symmetric Indefinite Linear Equation Solvers.” *SIAM
Journal on Matrix Analysis and Applications* 20, no. 2 (January 1998): 513–61.
https://doi.org/10.1137/S0895479896296921.

[2] Anderson, E., Z. Bai, C. Bischof,
L. S. Blackford, J. Demmel, J. Dongarra, J. Du Croz, A. Greenbaum, S. Hammarling, A. McKenny,
and D. Sorensen. *LAPACK Users’ Guide*. Philadelphia:
Society for Industrial and Applied Mathematics, 1999. https://doi.org/10.1137/1.9780898719604.

[3] Duff, Iain S. “MA57---a Code for
the Solution of Sparse Symmetric Definite and Indefinite Systems.” *ACM Transactions
on Mathematical Software* 30, no. 2 (June 2004): 118–44. https://doi.org/10.1145/992200.992202.

## Extended Capabilities

## Version History

**Introduced before R2006a**

## See Also

`chol`

| `lu`

| `qr`

| `decomposition`