SRC/zhetri_3x.f(3)

🦋 NAME 🦋

This page is from the Library Functions Manual, and the star of the show is SRC/zhetri_3x.f — yes bestie, that's the manual name, and we're about to get into it 💅

✨ SYNOPSIS ✨

🫶 Functions/Subroutines

subroutine zhetri_3x (uplo, n, a, lda, e, ipiv, work, nb, info)

ZHETRI_3X

💅 Function/Subroutine Documentation 💅

🌟 subroutine zhetri_3x 🌟

subroutine zhetri_3x (character uplo, integer n, complex*16, dimension( lda,
       * ) a, integer lda, complex*16, dimension( * ) e, integer, dimension( *
       ) ipiv, complex*16, dimension( n+nb+1, * ) work, integer nb, integer
       info)

ZHETRI_3X

🎯 Purpose

Okay so ZHETRI_3X computes the inverse of a complex Hermitian indefinite matrix A using the factorization computed by ZHETRF_RK or ZHETRF_BK, fr fr:

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. Slay 💅

🧸 Parameters

UPLO

UPLO is CHARACTER*1 — tells us whether the factorization details are stored as an upper or lower triangular matrix, bestie:

• = '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*16 array, dimension (LDA,N) — on entry, this carries the diagonal of the block diagonal matrix D and the factors U or L as computed by ZHETRF_RK and ZHETRF_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*16 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. Important, bestie 🫶

IPIV

IPIV is INTEGER array, dimension (N) — details of the interchanges and the block structure of D as determined by ZHETRF_RK or ZHETRF_BK.

WORK

WORK is COMPLEX*16 array, dimension (N+NB+1,NB+3).

NB

NB is INTEGER — Block size.

INFO

INFO is INTEGER — the vibe check on the exit:

• = 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 zhetri_3x.f.

🫶 Author 🫶

Generated automatically by Doxygen for LAPACK from the source code.

---

Okay bestie, that's the whole page: LAPACK Version 3.12.0, source SRC/zhetri_3x.f(3). The footer didn't give me a date, so I'm not inventing one — mwah 💋✨