NAME¶

DGETRI - computes 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 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 (MAX(1,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.