CGETRI(1) LAPACK routine (version 3.2) CGETRI(1)[top]NAMECGETRI - computes the inverse of a matrix using the LU factorization computed by CGETRFSYNOPSISSUBROUTINE CGETRI( N, A, LDA, IPIV, WORK, LWORK, INFO ) INTEGER INFO, LDA, LWORK, N INTEGER IPIV( * ) COMPLEX A( LDA, * ), WORK( * )PURPOSECGETRI computes the inverse of a matrix using the LU factorization com‐ puted by CGETRF. This method inverts U and then computes inv(A) by solving the system inv(A)*L = inv(U) for inv(A).ARGUMENTSN (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 opti‐ mal performance LWORK >= N*NB, where NB is the optimal block‐ size returned by ILAENV. If LWORK =, 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 =-1, the i-th argument had an illegal value > 0: if INFO = i, U(i,i) is exactly zero; the matrix is singu‐ lar and its inverse could not be computed. LAPACK routine (version 3.2) November 2008 CGETRI(1)-i

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