Developer Reference for Intel® oneAPI Math Kernel Library for C

ID 766684
Date 3/22/2024
Public

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?hetri

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

Syntax

lapack_int LAPACKE_chetri (int matrix_layout , char uplo , lapack_int n , lapack_complex_float * a , lapack_int lda , const lapack_int * ipiv );

lapack_int LAPACKE_zhetri (int matrix_layout , char uplo , lapack_int n , lapack_complex_double * a , lapack_int lda , const lapack_int * ipiv );

Include Files

  • mkl.h

Description

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

Input Parameters

matrix_layout

Specifies whether matrix storage layout is row major (LAPACK_ROW_MAJOR) or column major (LAPACK_COL_MAJOR).

uplo

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*UH.

If uplo = 'L', the array a stores the Bunch-Kaufman factorization A = L*D*LH.

n

The order of the matrix A; n 0.

a,

Array a(size max(1, lda*n)) contains the factorization of the matrix A, as returned by ?hetrf. The second dimension of a must be at least max(1,n).

lda

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

ipiv

Array, size at least max(1, n). The ipiv array, as returned by ?hetrf.

Output Parameters

a

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

Return Values

This function returns a value info.

If info = 0, the execution is successful.

If info = -i, parameter i 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.

Application Notes

The computed inverse X satisfies the following error bounds:

|D*UH*PT*X*P*U - I|  c(n)ε(|D||UH|PT|X|P|U| + |D||D-1|)

for uplo = 'U', and

|D*LH*PT*X*P*L - I|  c(n)ε(|D||LH|PT|X|P|L| + |D||D-1|)

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

The total number of floating-point operations is approximately (8/3)n3 for complex flavors.

The real counterpart of this routine is ?sytri.