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## man page of LAPACK-3

### LAPACK-3: computes the inverse of a matrix using the LU factorization computed by ZGETRF

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## NAME

LAPACK-3 - computes the inverse of a matrix using the LU factorization 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 factorization 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 factorization 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 (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. LAPACK routine (version 3.2) March 2011 LAPACK-3(3)

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