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sgetri

 NAME
      SGETRI - compute the inverse of a matrix using the LU fac-
      torization computed by SGETRF

 SYNOPSIS
      SUBROUTINE SGETRI( N, A, LDA, IPIV, WORK, LWORK, INFO )

          INTEGER        INFO, LDA, LWORK, N

          INTEGER        IPIV( * )

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

 PURPOSE
      SGETRI computes the inverse of a matrix using the LU factor-
      ization computed by SGETRF.

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

 ARGUMENTS
      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) REAL array, dimension (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.

      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 com-
              puted.