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Matrix Factorization: LAPACK Computational Routines
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. - ?getrf_batch
Computes the LU factorization for 1 or more groups of general m-by-n matrices. - ?getrf_batch_strided
Computes the LU factorization of a group of general m-by-n matrices that are stored at a constant stride from each other in a contiguous block of memory. - mkl_?getrfnp
Computes the LU factorization of a general m-by-n matrix without pivoting. - ?getrfnp_batch_strided
Computes the LU factorization, without pivoting, of a group of general m-by-n matrices that are stored at a constant stride from each other in a contiguous block of memory. - mkl_?getrfnpi
Performs LU factorization (complete or incomplete) of a general matrix without pivoting. - ?getrf2
Computes LU factorization using partial pivoting with row interchanges. - ?getri_oop_batch
Computes the inverses for 1 or more groups of LU factored, n-by-n matrices. - ?getri_oop_batch_strided
Computes the inverses of a group of LU factored matrices that are stored at a constant stride from each other in a contiguous block of memory. - ?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. - ?potrf2
Computes Cholesky factorization using a recursive algorithm. - ?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. - ?sytrf_aa
Computes the factorization of a symmetric matrix using Aasen's algorithm. - ?sytrf_rook
Computes the bounded Bunch-Kaufman factorization of a symmetric matrix. - ?sytrf_rk
Computes the factorization of a real or complex symmetric indefinite matrix using the bounded Bunch-Kaufman (rook) diagonal pivoting method (BLAS3 blocked algorithm). - ?hetrf
Computes the Bunch-Kaufman factorization of a complex Hermitian matrix. - ?hetrf_aa
Computes the factorization of a complex hermitian matrix using Aasen's algorithm. - ?hetrf_rook
Computes the bounded Bunch-Kaufman factorization of a complex Hermitian matrix. - ?hetrf_rk
Computes the factorization of a complex Hermitian indefinite matrix using the bounded Bunch-Kaufman (rook) diagonal pivoting method (BLAS3 blocked algorithm). - ?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. - mkl_?spffrt2, mkl_?spffrtx
Computes the partial LDLT factorization of a symmetric matrix using packed storage.