?hetri

Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 11/07/2023

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?hetri_3

Computes the inverse of a complex Hermitian matrix using the factorization computed by ?hetrf_rk.

lapack_int LAPACKE_chetri_3 (int matrix_layout, char uplo, lapack_int n, lapack_complex_float * A, lapack_int lda, const lapack_complex_float * e, const lapack_int * ipiv);

lapack_int LAPACKE_zhetri_3 (int matrix_layout, char uplo, lapack_int n, lapack_complex_double * A, lapack_int lda, const lapack_complex_double * e, const lapack_int * ipiv);

Description

?hetri_3 computes the inverse of a complex Hermitian matrix A using the factorization computed by ?hetrf_rk: A = P*U*D*(U^H)*(P^T) or A = P*L*D*(L^H)*(P^T), where U (or L) is a 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 a Hermitian and block diagonal with 1-by-1 and 2-by-2 diagonal blocks.

?hetri_3 sets the leading dimension of the workspace before calling ?hetri_3x, which actually computes the inverse.

This is the blocked version of the algorithm, calling Level-3 BLAS.

Input Parameters

matrix_layout

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

uplo

Specifies whether the details of the factorization are stored as an upper or lower triangular matrix.

= 'U': The upper triangle of A is stored.
= 'L': The lower triangle of A is stored.

n

The order of the matrix A. n ≥ 0.

A

Array of size max(1, lda*n). On entry, diagonal of the block diagonal matrix D and factor U or L as computed by ?hetrf_rk:

Only diagonal elements of the Hermitian block diagonal matrix D on the diagonal of A; that is, D(k,k) = A(k,k). Superdiagonal (or subdiagonal) elements of D should be provided on entry in array e.
If uplo = 'U', factor U in the superdiagonal part of A. If uplo = 'L', factor L is the subdiagonal part of A.

lda

The leading dimension of the array A.

e

Array of size 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. If uplo = 'U', e(i) = D(i-1,i), i=2:N, and e(1) is not referenced. If uplo = 'L', e(i) = D(i+1,i), i=1:N-1, and e(n) is not referenced.

NOTE:

For 1-by-1 diagonal block D(k), where 1 ≤ k ≤ n, the element e[k-1] is not referenced in both the uplo = 'U' and uplo = 'L' cases.

ipiv

Array of size n. Details of the interchanges and the block structure of D as determined by ?hetrf_rk.

Output Parameters

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.

Return Values

This function returns a value info.

= 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.

Parent topic: Matrix Inversion: LAPACK Computational Routines

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