# Routines for Matrix Factorization

This section describes the LAPACK routines for matrix factorization. The following factorizations are supported:

- LU factorization

- Cholesky factorization of real symmetric positive-definite matrices

- Cholesky factorization of Hermitian positive-definite matrices

- Bunch-Kaufman factorization of real and complex symmetric matrices

- Bunch-Kaufman factorization of Hermitian matrices.

You can compute:

- the LU factorization using full and band storage of matrices

- the Cholesky factorization using full, packed, and band storage

- the Bunch-Kaufman factorization using full and packed storage.

- ?getrf
  Computes the LU factorization of a general m-by-n matrix.
- ?gbtrf
  Computes the LU factorization of a general m-by-n band matrix.
- ?gttrf
  Computes the LU factorization of a tridiagonal matrix.
- ?potrf
  Computes the Cholesky factorization of a symmetric (Hermitian) positive-definite matrix.
- ?pptrf
  Computes the Cholesky factorization of a symmetric (Hermitian) positive-definite matrix using packed storage.
- ?pbtrf
  Computes the Cholesky factorization of a symmetric (Hermitian) positive-definite band matrix.
- ?pttrf
  Computes the factorization of a symmetric (Hermitian) positive-definite tridiagonal matrix.
- ?sytrf
  Computes the Bunch-Kaufman factorization of a symmetric matrix.
- ?hetrf
  Computes the Bunch-Kaufman factorization of a complex Hermitian matrix.
- ?sptrf
  Computes the Bunch-Kaufman factorization of a symmetric matrix using packed storage.
- ?hptrf
  Computes the Bunch-Kaufman factorization of a complex Hermitian matrix using packed storage.

Parent topic: Computational Routines