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LAPACK version 3.0
dgetri(3)

PURPOSE
  DGETRI - compute the inverse of a matrix using the LU factorization
  computed by DGETRF

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

      INTEGER	     INFO, LDA, LWORK, N

      INTEGER	     IPIV( * )

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

DESCRIPTION
  DGETRI computes the inverse of a matrix using the LU factorization 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 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 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.

  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 computed.