?hetri

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 4/28/2026

Version

Public

?hetri

Computes the inverse of a complex Hermitian matrix using U * D * U^H or L * D * L^H Bunch-Kaufman factorization.

Syntax

call chetri ( uplo , n , a , lda , ipiv , work , info )

call zhetri ( uplo , n , a , lda , ipiv , work , info )

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

Include Files

mkl.fi , mkl_lapack.f90

Description

chetri zhetri hetri

The routine computes the inverse inv(A) of a complex Hermitian matrix A . Before calling this routine, call ?hetrf (Computes the Bunch-Kaufman factorization of a complex Hermitian matrix.) to factorize A .

Input Parameters

uplo

CHARACTER*1 . Must be ‘U’ or ‘L’ .

Indicates how the input matrix A has been factored:

If uplo = 'U' , the array a stores the Bunch-Kaufman factorization A = U*D*U^{H} .

If uplo = 'L' , the array a stores the Bunch-Kaufman factorization A = L*D*L^{H} .

n

INTEGER . The order of the matrix A ; n≥ 0 .

a , work

COMPLEX for chetri

DOUBLE COMPLEX for zhetri .

Arrays:

a(lda,*) contains the factorization of the matrix A , as returned by ?hetrf (Computes the Bunch-Kaufman factorization of a complex Hermitian matrix.) .

The second dimension of a must be at least max(1,n) .

work(*) is a workspace array.

The dimension of work must be at least max(1,n) .

a ,

Array a (size lda by *) contains the factorization of the matrix A , as returned by GUID-D115CA2C-FB54-4605-9E0C-6152237D63D9.xml#GUID-D115CA2C-FB54-4605-9E0C-6152237D63D9 . The second dimension of a must be at least max(1,n) .

lda

INTEGER . The leading dimension of a ; lda≥ max(1, n) .

ipiv

INTEGER .

Array, size at least max(1, n) . The ipiv array, as returned by ?hetrf (Computes the Bunch-Kaufman factorization of a complex Hermitian matrix.) .

Output Parameters

a

Overwritten by the n -by- n matrix inv( A ).

info

INTEGER .

If info = 0 , the execution is successful.
If info = -i , the i -th parameter had an illegal value.
If info = i , the i -th diagonal element of D is zero, D is singular, and the inversion could not be completed.

Return Values

No return value, info is an Output Parameter.

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 hetri interface are as follows:

a

Holds the matrix A of size ( n,n ).

ipiv

Holds the vector of length n .

uplo

Must be ‘U’ or ‘L’ . The default value is ‘U’ .

Application Notes

The computed inverse \(X\) satisfies the following error bounds:

\[|D U^{H} P^{T} X P U - I| \leq c(n)\varepsilon(|D||U^{H}|P^{T}|X|P|U| + |D||D^{-1}|)\]

for uplo = ‘U’ , and

\[|D L^{H} P^{T} X P L - I| \leq c(n)\varepsilon(|D||L^{H}|P^{T}|X|P|L| + |D||D^{-1}|)\]

for uplo = 'L' . Here c(n) is a modest linear function of n , and \(\varepsilon\) is the machine precision; \(I\) denotes the identity matrix.

The total number of floating-point operations is approximately \((8/3)n^{3}\) for complex flavors.

The real counterpart of this routine is ?sytri (Computes the inverse of a symmetric matrix using U*D*UT or L*D*LT Bunch-Kaufman factorization.) .

NOTE:

Matrix Storage Schemes

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

?hetri

Syntax

Include Files

Description

Input Parameters

Output Parameters

Return Values

LAPACK 95 Interface Notes

Application Notes