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# dgetri

NAME
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( LWORK )

PURPOSE
DGETRI computes the inverse of a matrix using the LU factor-
ization 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) 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.

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 com-
puted.