Provided by: liblapack-doc_3.3.1-1_all

**NAME**

LAPACK-3 - computes the inverse of a COMPLEX*16 hermitian indefinite matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by ZSYTRF

**SYNOPSIS**

SUBROUTINE ZSYTRI2( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO ) CHARACTER UPLO INTEGER INFO, LDA, LWORK, N INTEGER IPIV( * ) COMPLEX*16 A( LDA, * ), WORK( * )

**PURPOSE**

ZSYTRI2 computes the inverse of a COMPLEX*16 hermitian indefinite matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by ZSYTRF. ZSYTRI2 sets the LEADING DIMENSION of the workspace before calling ZSYTRI2X that actually computes the inverse.

**ARGUMENTS**

UPLO (input) CHARACTER*1 Specifies whether the details of the factorization are stored as an upper or lower triangular matrix. = 'U': Upper triangular, form is A = U*D*U**T; = 'L': Lower triangular, form is A = L*D*L**T. N (input) INTEGER The order of the matrix A. N >= 0. A (input/output) COMPLEX*16 array, dimension (LDA,N) On entry, the NB diagonal matrix D and the multipliers used to obtain the factor U or L as computed by ZSYTRF. On exit, if INFO = 0, the (symmetric) inverse of the original matrix. If UPLO = 'U', the upper triangular part of the inverse is formed and the part of A below the diagonal is not referenced; if UPLO = 'L' the lower triangular part of the inverse is formed and the part of A above the diagonal is not referenced. LDA (input) INTEGER The leading dimension of the array A. LDA >= max(1,N). IPIV (input) INTEGER array, dimension (N) Details of the interchanges and the NB structure of D as determined by ZSYTRF. WORK (workspace) COMPLEX*16 array, dimension (N+NB+1)*(NB+3) LWORK (input) INTEGER The dimension of the array WORK. WORK is size >= (N+NB+1)*(NB+3) If LDWORK = -1, then a workspace query is assumed; the routine 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 LDWORK 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, D(i,i) = 0; the matrix is singular and its inverse could not be computed. LAPACK routine (version 3.3.1) April 2011 ZSYTRI2(3lapack)