Matrix Inversion: LAPACK Computational Routines

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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Date 7/13/2023

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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.

Parent topic: LAPACK Linear Equation Computational Routines

?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.
?sytri_rook
Computes the inverse of a symmetric matrix using U*D*U^T or L*D*L^T bounded 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.
?hetri_rook
Computes the inverse of a complex Hermitian matrix using U*D*U^H or L*D*L^H bounded Bunch-Kaufman factorization.
?sytri2
Computes the inverse of a symmetric indefinite matrix through setting the leading dimension of the workspace and calling ?sytri2x.
?hetri2
Computes the inverse of a Hermitian indefinite matrix through setting the leading dimension of the workspace and calling ?hetri2x.
?sytri2x
Computes the inverse of a symmetric indefinite matrix after ?sytri2sets the leading dimension of the workspace.
?hetri2x
Computes the inverse of a Hermitian indefinite matrix after ?hetri2sets the leading dimension of the workspace.
?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.

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

Matrix Inversion: LAPACK Computational Routines