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DGETRI(l)			       )			     DGETRI(l)

NAME
       DGETRI  -  compute  the	inverse of a matrix using the LU factorization
       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 factorization com‐
       puted  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 factorization 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 optimal LWORK.

       LWORK   (input) INTEGER
	       The dimension of the array WORK.	 LWORK >= max(1,N).  For opti‐
	       mal performance LWORK >= N*NB, where NB is the  optimal	block‐
	       size 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 singu‐
	       lar and its inverse could not be computed.

LAPACK version 3.0		 15 June 2000			     DGETRI(l)
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