# chetri_3x.f - Man Page

SRC/chetri_3x.f

## Synopsis

### Functions/Subroutines

subroutine **chetri_3x** (uplo, n, a, lda, e, ipiv, work, nb, info)**CHETRI_3X**

## Function/Subroutine Documentation

### subroutine chetri_3x (character uplo, integer n, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) e, integer, dimension( * ) ipiv, complex, dimension( n+nb+1, * ) work, integer nb, integer info)

**CHETRI_3X**

**Purpose:**

CHETRI_3X computes the inverse of a complex Hermitian indefinite matrix A using the factorization computed by CHETRF_RK or CHETRF_BK: A = P*U*D*(U**H)*(P**T) or A = P*L*D*(L**H)*(P**T), where U (or L) is unit upper (or lower) triangular matrix, U**H (or L**H) is the conjugate of U (or L), P is a permutation matrix, P**T is the transpose of P, and D is Hermitian and block diagonal with 1-by-1 and 2-by-2 diagonal blocks. 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 array, dimension (LDA,N) On entry, diagonal of the block diagonal matrix D and factors U or L as computed by CHETRF_RK and CHETRF_BK: a) ONLY diagonal elements of the Hermitian 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 Hermitian 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 array, dimension (N) On entry, contains the superdiagonal (or subdiagonal) elements of the Hermitian 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 CHETRF_RK or CHETRF_BK.

*WORK*WORK is COMPLEX array, dimension (N+NB+1,NB+3).

*NB*NB is INTEGER Block size.

*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:**

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

Definition at line **158** of file **chetri_3x.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page chetri_3x(3) is an alias of chetri_3x.f(3).

Tue Nov 28 2023 12:08:41 Version 3.12.0 LAPACK