/home/abui...hetri_3x.f(3)

💖 /home/abui...hetri_3x.f(3) — Library Functions Manual 💖

Okay bestie, this page is /home/abui...hetri_3x.f(3) from the Library Functions Manual, and it's serving pure LAPACK 3.12.0 energy ✨ The actual source file is /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/chetri_3x.f — yes, that whole path, no cap 🫶

🌸 NAME 🌸

The NAME is literally this source file path, bestie:

• /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/chetri_3x.f

✨ SYNOPSIS ✨

🦋 Functions/Subroutines 🦋

• subroutine CHETRI_3X (uplo, n, a, lda, e, ipiv, work, nb, info)
• CHETRI_3X

🎀 Function/Subroutine Documentation 🎀

subroutine CHETRI_3X (character uplo, integer n, complex, dimension( lda, *
       ) a, integer lda, complex, dimension( * ) e, integer, dimension( * )
       ipiv, complex, dimension( n+nb+1, * ) work, integer nb, integer info)

CHETRI_3X — the main character, the icon, the whole vibe 👑

💅 Purpose: 💅

CHETRI_3X 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.

This is the blocked version of the algorithm, calling Level 3 BLAS. It's giving blocked algorithm glam, periodt 💅🔥

🌸 Parameters 🌸

• UPLO — CHARACTER*1. Specifies 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.
• N — INTEGER. The order of the matrix A. N >= 0.
• A — 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:
    • 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 — INTEGER. The leading dimension of the array A. LDA >= max(1,N).
• E — 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 — INTEGER array, dimension (N). Details of the interchanges and the block structure of D as determined by CHETRF_RK or CHETRF_BK.
• WORK — COMPLEX array, dimension (N+NB+1,NB+3).
• NB — INTEGER. Block size.
• INFO — 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.

⚠️ That INFO > 0 case is the singular-matrix emergency: D(i,i) = 0, so the inverse could not be computed. Not the slay we wanted 💀

👑 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 chetri_3x.f.

🎀 Author 🎀

Generated automatically by Doxygen for LAPACK from the source code.

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