ZGETRI - compute the inverse of a matrix using the LU fac­
       torization computed by ZGETRF


SYNOPSIS

       SUBROUTINE ZGETRI( N, A, LDA, IPIV, WORK, LWORK, INFO )

           INTEGER        INFO, LDA, LWORK, N

           INTEGER        IPIV( * )

           COMPLEX*16     A( LDA, * ), WORK( * )


PURPOSE

       ZGETRI computes the inverse of a matrix using the LU  fac­
       torization  computed by ZGETRF.  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) COMPLEX*16 array, dimension (LDA,N)
               On entry, the factors L and U from the  factoriza­
               tion A = P*L*U as computed by ZGETRF.  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 ZGETRF; for 1<=i<=N, row i
               of the matrix was interchanged with row IPIV(i).

       WORK    (workspace/output) COMPLEX*16 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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