CHETRI_3(3)

💖 NAME 💖

okay bestie, welcome to chetri_3(3) — this is the Library Functions Manual page for it, and the file path is exactly:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/chetri_3.f

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🌟 SYNOPSIS 🌟

Functions/Subroutines

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

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🧚 Function/Subroutine Documentation 🧚

here's the full signature, bestie, copied 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 💫

okay so 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 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.

CHETRI_3 sets the leading dimension of the workspace before calling CHETRI_3X that actually computes the inverse. This is the blocked version of the algorithm, calling Level 3 BLAS. periodt.

🌈 Parameters 🌈

🌸 UPLO 🌸

UPLO is CHARACTER*1 — tells you whether the details of the factorization are stored as an upper or lower triangular matrix. iykyk.

• = '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 array, dimension (LDA,N)

On entry, diagonal of the block diagonal matrix D and factors U or L as computed by CHETRF_RK and CHETRF_BK:

1. 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
2. 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 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.

🔥 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 (N+NB+1)*(NB+3).

On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

💅 LWORK 💅

LWORK is INTEGER — the length of WORK. LWORK >= (N+NB+1)*(NB+3).

If LDWORK = -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.

💀 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 168 of file chetri_3.f.

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🦋 Author 🦋

Generated automatically by Doxygen for LAPACK from the source code.

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okay bestie, that's the whole iconic page 💖 footer sign-off: source/version vibes are LAPACK Version 3.12.0, and the path is /home/abui.../chetri_3.f(3) 🫶✨