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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