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( * )


PURPOSE

       SGETRI computes the inverse of a matrix using the LU  fac­
       torization  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 factoriza­
               tion 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 (LWORK)
               On exit, if INFO=0, then WORK(1) returns the opti­
               mal 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.

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


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