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       LAPACK-3 - computes the inverse of a matrix using the LU factorization computed by SGETRF



           INTEGER        INFO, LDA, LWORK, N

           INTEGER        IPIV( * )

           REAL           A( LDA, * ), WORK( * )


       SGETRI computes the inverse of a matrix using the LU factorization computed by SGETRF.
        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) REAL array, dimension (LDA,N)
                On entry, the factors L and U from the factorization
                A = P*L*U as computed by SGETRF.
                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 SGETRF; for 1<=i<=N, row i of the
                matrix was interchanged with row IPIV(i).

        WORK    (workspace/output) REAL 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.

 LAPACK routine (version 3.2)               April 2011                            SGETRI(3lapack)