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 real symmetric positive-definite matrices with pivoting

• Cholesky factorization of Hermitian positive-definite matrices

• Cholesky factorization of Hermitian positive-definite matrices with pivoting

• 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, RFP, 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.
• ?dttrfb
  Computes the factorization of a diagonally dominant tridiagonal matrix.
• ?potrf
  Computes the Cholesky factorization of a symmetric (Hermitian) positive-definite matrix.
• ?pstrf
  Computes the Cholesky factorization with complete pivoting of a real symmetric (complex Hermitian) positive semidefinite matrix.
• ?pftrf
  Computes the Cholesky factorization of a symmetric (Hermitian) positive-definite matrix using the Rectangular Full Packed (RFP) format .
• ?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.