?hetri2

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 3/31/2023

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?hetri2

Computes the inverse of a Hermitian indefinite matrix through setting the leading dimension of the workspace and calling ?hetri2x.

Syntax

call chetri2( uplo, n, a, lda, ipiv, work, lwork, info )

call zhetri2( uplo, n, a, lda, ipiv, work, lwork, info )

call hetri2( a,ipiv[,uplo][,info] )

Include Files

mkl.fi, lapack.f90

Description

The routine computes the inverse inv(A) of a Hermitian indefinite matrix A using the factorization A = U*D*U^H or A = L*D*L^H computed by ?hetrf.

The ?hetri2 routine sets the leading dimension of the workspace before calling ?hetri2x that actually computes the inverse.

Input Parameters

uplo	CHARACTER1. Must be 'U' or 'L'. Indicates how the input matrix `A` has been factored: If `uplo = 'U'`, the array `a` stores the factorization `A = UDU^H`. If `uplo = 'L'`, the array `a` stores the factorization `A = LD*L^H`.
n	INTEGER. The order of the matrix `A`; `n≥ 0`.
a, work	COMPLEX for chetri2 DOUBLE COMPLEX for zhetri2 Array a(size `lda` by ) contains the block diagonal matrix `D` and the multipliers used to obtain the factor U or L as returned by ?sytrf. The second dimension of a must be at least `max(1,n)`. work is a workspace array of `(n+nb+1)(nb+3)` dimension.
lda	INTEGER. The leading dimension of `a`; `lda≥ max(1, n)`.
ipiv	INTEGER. Array, size at least `max(1, n)`. Details of the interchanges and the block structure of `D` as returned by ?hetrf.
lwork	INTEGER. The dimension of the work array. `lwork≥ (n+nb+1)*(nb+3)` where `nb` is the block size parameter as returned by hetrf. 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.

Output Parameters

If info = 0, the 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.

info

INTEGER.

If info = 0, the execution is successful.

If info =-i, the i-th parameter had an illegal value.

If info = i, D(i,i) = 0; D is singular and its inversion could not be computed.

LAPACK 95 Interface Notes

Routines in Fortran 95 interface have fewer arguments in the calling sequence than their FORTRAN 77 counterparts. For general conventions applied to skip redundant or reconstructible arguments, see LAPACK 95 Interface Conventions.

Specific details for the routine hetri2 interface are as follows:

a	Holds the matrix `A` of size (`n,n`).
ipiv	Holds the vector of length `n`.
uplo	Indicates how the input matrix `A` has been factored. Must be 'U' or 'L'.

Parent topic: Matrix Inversion: LAPACK Computational Routines

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?hetri2

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