zgetri(3)

NAME

ZGETRI - compute the inverse of a matrix using the LU fac

torization computed by ZGETRF

SYNOPSIS

SUBROUTINE ZGETRI( N, A, LDA, IPIV, WORK, LWORK, INFO )
    INTEGER        INFO, LDA, LWORK, N
    INTEGER        IPIV( * )
    COMPLEX*16     A( LDA, * ), WORK( * )

PURPOSE

ZGETRI computes the inverse of a matrix using the LU fac

torization computed by ZGETRF. 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*16 array, dimension (LDA,N)

On entry, the factors L and U from the factoriza

tion A = P*L*U as computed by ZGETRF. 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 ZGETRF; for 1<=i<=N, row i

of the matrix was interchanged with row IPIV(i).

WORK (workspace/output) COMPLEX*16 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.

INFO (output) INTEGER

= 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 ma

trix is singular and its inverse could not be computed.

LAPACK version 3.0 15 June 2000

ZGETRI(3)