Compute the inverse of a matrix using the LU factorization from dgetrf

Wolfram Language



This information is part of the Modelica Standard Library maintained by the Modelica Association.

Lapack documentation

    DGETRI computes the inverse of a matrix using the LU factorization
    computed by DGETRF.

    This method inverts U and then computes inv(A) by solving the system
    inv(A)*L = inv(U) for inv(A).


    N       (input) INTEGER
            The order of the matrix A.  N >= 0.

    A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)
            On entry, the factors L and U from the factorization
            A = P*L*U as computed by DGETRF.
            On exit, if INFO = 0, the inverse of the original matrix A.

    LDA     (input) INTEGER
            The leading dimension of the array A.  LDA >= max(1,N).

    IPIV    (input) INTEGER array, dimension (N)
            The pivot indices from DGETRF; for 1<=i<=N, row i of the
            matrix was interchanged with row IPIV(i).

    WORK    (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK))
            On exit, if INFO=0, then WORK(1) returns the optimal LWORK.

    LWORK   (input) INTEGER
            The dimension of the array WORK.  LWORK >= max(1,N).
            For optimal performance LWORK >= N*NB, where NB is
            the optimal blocksize returned by ILAENV.

            If LWORK = -1, then a workspace query is assumed; the routine
            only calculates the optimal size of the WORK array, returns
            this value as the first entry of the WORK array, and no error
            message related to LWORK is issued by XERBLA.

    INFO    (output) INTEGER
            = 0:  successful exit
            < 0:  if INFO = -i, the i-th argument had an illegal value
            > 0:  if INFO = i, U(i,i) is exactly zero; the matrix is
                  singular and its inverse could not be computed.


(inv, info) = dgetri(LU, pivots)

Inputs (2)


Type: Real[:,size(LU, 1)]

Description: LU factorization of dgetrf of a square matrix


Type: Integer[size(LU, 1)]

Description: Pivot vector of dgetrf

Outputs (2)


Default Value: LU

Type: Real[size(LU, 1),size(LU, 2)]

Description: Inverse of matrix P*L*U


Type: Integer