# zsytri_3.f - Man Page

SRC/zsytri_3.f

## Synopsis

### Functions/Subroutines

subroutine **zsytri_3** (uplo, n, a, lda, e, ipiv, work, lwork, info)**ZSYTRI_3**

## Function/Subroutine Documentation

### subroutine zsytri_3 (character uplo, integer n, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) e, integer, dimension( * ) ipiv, complex*16, dimension( * ) work, integer lwork, integer info)

**ZSYTRI_3**

**Purpose:**

ZSYTRI_3 computes the inverse of a complex symmetric indefinite matrix A using the factorization computed by ZSYTRF_RK or ZSYTRF_BK: A = P*U*D*(U**T)*(P**T) or A = P*L*D*(L**T)*(P**T), where U (or L) is unit upper (or lower) triangular matrix, U**T (or L**T) is the transpose of U (or L), P is a permutation matrix, P**T is the transpose of P, and D is symmetric and block diagonal with 1-by-1 and 2-by-2 diagonal blocks. ZSYTRI_3 sets the leading dimension of the workspace before calling ZSYTRI_3X that actually computes the inverse. This is the blocked version of the algorithm, calling Level 3 BLAS.

**Parameters***UPLO*UPLO is CHARACTER*1 Specifies whether the details of the factorization are stored as an upper or lower triangular matrix. = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored.

*N*N is INTEGER The order of the matrix A. N >= 0.

*A*A is COMPLEX*16 array, dimension (LDA,N) On entry, diagonal of the block diagonal matrix D and factors U or L as computed by ZSYTRF_RK and ZSYTRF_BK: a) ONLY diagonal elements of the symmetric block diagonal matrix D on the diagonal of A, i.e. D(k,k) = A(k,k); (superdiagonal (or subdiagonal) elements of D should be provided on entry in array E), and b) If UPLO = 'U': factor U in the superdiagonal part of A. If UPLO = 'L': factor L in the subdiagonal part of A. 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*LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).

*E*E is COMPLEX*16 array, dimension (N) On entry, contains the superdiagonal (or subdiagonal) elements of the symmetric block diagonal matrix D with 1-by-1 or 2-by-2 diagonal blocks, where If UPLO = 'U': E(i) = D(i-1,i),i=2:N, E(1) not referenced; If UPLO = 'L': E(i) = D(i+1,i),i=1:N-1, E(N) not referenced. NOTE: For 1-by-1 diagonal block D(k), where 1 <= k <= N, the element E(k) is not referenced in both UPLO = 'U' or UPLO = 'L' cases.

*IPIV*IPIV is INTEGER array, dimension (N) Details of the interchanges and the block structure of D as determined by ZSYTRF_RK or ZSYTRF_BK.

*WORK*WORK is COMPLEX*16 array, dimension (N+NB+1)*(NB+3). On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

*LWORK*LWORK is INTEGER The length of WORK. LWORK >= (N+NB+1)*(NB+3). If LDWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of 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*INFO is 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.

**Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Contributors:**

November 2017, Igor Kozachenko, Computer Science Division, University of California, Berkeley

Definition at line **168** of file **zsytri_3.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page zsytri_3(3) is an alias of zsytri_3.f(3).

Tue Nov 28 2023 12:08:42 Version 3.12.0 LAPACK