NAME¶

CGETRI - computes the inverse of a matrix using the LU factorization computed by CGETRF

SYNOPSIS¶

SUBROUTINE CGETRI(

N, A, LDA, IPIV, WORK, LWORK, INFO )

INTEGER INFO, LDA, LWORK, N INTEGER IPIV( * ) COMPLEX A( LDA, * ), WORK( * )

PURPOSE¶

CGETRI computes the inverse of a matrix using the LU factorization computed by CGETRF. 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) COMPLEX array, dimension (LDA,N)

On entry, the factors L and U from the factorization A = P*L*U as computed by CGETRF. 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 CGETRF; for 1<=i<=N, row i of the matrix was interchanged with row IPIV(i).

WORK (workspace/output) COMPLEX 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.