DGETRI - compute the inverse of a matrix using the LU fac­
       torization computed by DGETRF


SYNOPSIS

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

           INTEGER        INFO, LDA, LWORK, N

           INTEGER        IPIV( * )

           DOUBLE         PRECISION A( LDA, * ), WORK( * )


PURPOSE

       DGETRI computes the inverse of a matrix using the LU  fac­
       torization  computed by DGETRF.  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) DOUBLE PRECISION array, dimension
               (LDA,N)
               On entry, the factors L and U from the  factoriza­
               tion 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 (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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