Matrix Inversion: LAPACK Computational Routines

It is seldom necessary to compute an explicit inverse of a matrix. In particular, do not attempt to solve a system of equations Ax = b by first computing A^-1 and then forming the matrix-vector product x = A^-1b. Call a solver routine instead (see Routines for Solving Systems of Linear Equations); this is more efficient and more accurate.

However, matrix inversion routines are provided for the rare occasions when an explicit inverse matrix is needed.

?getri
Computes the inverse of an LU-factored general matrix.
mkl_?getrinp
Computes the inverse of an LU-factored general matrix without pivoting.
?potri
Computes the inverse of a symmetric (Hermitian) positive-definite matrix using the Cholesky factorization.
?pftri
Computes the inverse of a symmetric (Hermitian) positive-definite matrix in RFP format using the Cholesky factorization.
?pptri
Computes the inverse of a packed symmetric (Hermitian) positive-definite matrix using Cholesky factorization.
?sytri
Computes the inverse of a symmetric matrix using U*D*U^T or L*D*L^T Bunch-Kaufman factorization.
?hetri
Computes the inverse of a complex Hermitian matrix using U*D*U^H or L*D*L^H Bunch-Kaufman factorization.
?sytri2
Computes the inverse of a symmetric indefinite matrix through allocating memory and calling ?sytri2x.
?hetri2
Computes the inverse of a Hermitian indefinite matrix through allocating memory and calling ?hetri2x.
?sytri2x
Computes the inverse of a symmetric indefinite matrix after ?sytri2allocates memory.
?hetri2x
Computes the inverse of a Hermitian indefinite matrix after ?hetri2allocates memory.
?sytri_3
Computes the inverse of a real or complex symmetric matrix.
?hetri_3
Computes the inverse of a complex Hermitian matrix using the factorization computed by ?hetrf_rk.
?sptri
Computes the inverse of a symmetric matrix using U*D*U^T or L*D*L^T Bunch-Kaufman factorization of matrix in packed storage.
?hptri
Computes the inverse of a complex Hermitian matrix using U*D*U^H or L*D*L^H Bunch-Kaufman factorization of matrix in packed storage.
?trtri
Computes the inverse of a triangular matrix.
?tftri
Computes the inverse of a triangular matrix stored in the Rectangular Full Packed (RFP) format.
?tptri
Computes the inverse of a triangular matrix using packed storage.