SRC/chetri_3.f(3)

🌸 NAME 🌸

SRC/chetri_3.f — that's the page name, bestie. Short, iconic, done. 🎀

This is SRC/chetri_3.f(3) from the Library Functions Manual, and it's all about CHETRI_3. no cap. 💅

🦋 SYNOPSIS 🦋

✨ Functions/Subroutines ✨

okay so the call shape is:

subroutine chetri_3 (uplo, n, a, lda, e, ipiv, work, lwork, info)
       CHETRI_3

That CHETRI_3 label is the documented symbol. 🦋

💖 Function/Subroutine Documentation 💖

The documented signature, exactly:

subroutine chetri_3 (character uplo, integer n, complex, dimension( lda, * )
       a, integer lda, complex, dimension( * ) e, integer, dimension( * ) ipiv,
       complex, dimension( * ) work, integer lwork, integer info)
       CHETRI_3

🎯 Purpose 🎯

Bestie, CHETRI_3 computes the inverse of a complex Hermitian indefinite matrix A using the factorization computed by CHETRF_RK or CHETRF_BK:

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 Hermitian and block diagonal with 1-by-1 and 2-by-2 diagonal blocks. 💅

Before it calls CHETRI_3X — the routine that actually computes the inverse — CHETRI_3 sets the leading dimension of the workspace. This is the blocked version of the algorithm, and yes, it calls Level 3 BLAS. periodt. 🔥

🌟 Parameters 🌟

💅 UPLO 💅

UPLO is CHARACTER*1. It says whether the details of the factorization are stored as an upper or lower triangular matrix. = 'U': upper triangle of A is stored; = 'L': lower triangle of A is stored. slay. ✨

🫶 N 🫶

N is INTEGER. It's the order of the matrix A. Constraint: N >= 0. 🫶

😭 A 😭

A is COMPLEX array, dimension (LDA,N). On entry, it holds the diagonal of the block diagonal matrix D and factors U or L as computed by CHETRF_RK and CHETRF_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, you get 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. 😭 iconic.

💜 LDA 💜

LDA is INTEGER. It's the leading dimension of the array A. Constraint: LDA >= max(1,N). 💜

🧚 E 🧚

E is COMPLEX array, dimension (N). On entry, it 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. 🧚

🦋 IPIV 🦋

IPIV is INTEGER array, dimension (N). Details of the interchanges and the block structure of D as determined by CHETRF_RK or CHETRF_BK. 🦋

🎀 WORK 🎀

WORK is COMPLEX array, dimension (MAX(1,LWORK)). On exit, if INFO = 0, WORK(1) returns the optimal LWORK. 🎀

💀 LWORK 💀

LWORK is INTEGER. It's the length of WORK. If N = 0, then LWORK >= 1; else LWORK >= (N+NB+1)*(NB+3).

If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of 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. yes, that's the wording, bestie. 💀

💔 INFO 💔

INFO is INTEGER.

= 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: 🌈

• November 2017, Igor Kozachenko
• Computer Science Division, University of California, Berkeley

Definition at line 169 of file chetri_3.f. 🫶

👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code.

Footer moment, bestie: LAPACK Version 3.12.0, page SRC/chetri_3.f(3). The footer doesn't show a date, so I'm not inventing one — periodt. 💖✨