SRC/chetri_3x.f(3)

💖 SRC/chetri_3x.f(3) 💖

Welcome to the SRC/chetri_3x.f(3) page from the Library Functions Manual, bestie — this is the glow-up for chetri_3x, and yes, she's an icon. 💅✨

✨ NAME ✨

SRC/chetri_3x.f — that's the file, and the main character inside is the chetri_3x subroutine. 🫶

✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

• subroutine chetri_3x (uplo, n, a, lda, e, ipiv, work, nb, info) — CHETRI_3X

🛠️ Function/Subroutine Documentation 🛠️

Okay so here's the full signature, character-for-character, no cap:

   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 — iconic. 💅

💡 Purpose

Okay so 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. Periodt.

🎀 Parameters

UPLO — CHARACTER*1, and it 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.

👑 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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Cute sign-off: LAPACK Version 3.12.0, SRC/chetri_3x.f(3) — date: not listed in the footer, so no fake date energy here, bestie 💖🫶