/home/abui.../zhetri2.f(3)

✨ NAME ✨

Okay bestie, we are in the Library Functions Manual and the header is pointing at /home/abui.../zhetri2.f(3). The actual source file is /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/zhetri2.f — that’s the LAPACK page for ZHETRI2, no cap.

✨ SYNOPSIS ✨

🦋 Functions/Subroutines 🦋

• subroutine ZHETRI2 (uplo, n, a, lda, ipiv, work, lwork, info) — main character energy; the routine is ZHETRI2.

💖 Function/Subroutine Documentation 💖

🌸 subroutine ZHETRI2 (character uplo, integer n, complex*16, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, complex*16, dimension( * ) work, integer lwork, integer info) 🌸

ZHETRI2

🎀 Purpose 🎀

So ZHETRI2 computes the inverse of a COMPLEX*16 hermitian indefinite matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by ZHETRF. Also, ZHETRI2 set the LEADING DIMENSION of the workspace before calling ZHETRI2X, which actually computes the inverse. Obsessed with the division of labor, honestly. 💅

🌸 Parameters 🌸

• UPLO — CHARACTER*1. Specifies whether the details of the factorization are stored as an upper or lower triangular matrix.
  • = 'U': upper triangular, form is A = U*D*U**T;
  • = 'L': lower triangular, form is A = L*D*L**T.
• N — INTEGER. The order of matrix A. N >= 0.
• A — COMPLEX*16 array, dimension (LDA,N). On entry, the block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by ZHETRF. On exit, if INFO = 0, the (symmetric) 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).
• IPIV — INTEGER array, dimension (N). Details of the interchanges and the block structure of D as determined by ZHETRF.
• WORK — COMPLEX*16 array, dimension (N+NB+1)*(NB+3).
• LWORK — INTEGER. The dimension of the array WORK. WORK is size >= (N+NB+1)*(NB+3). If LWORK = -1, then a workspace query is assumed; the routine calculates:
  • 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 — 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.

Ngl, that INFO > 0 case is the dramatic one: singular matrix, inverse said “not today.” 😭

👑 Author 👑

• Univ. of Tennessee
• Univ. of California Berkeley
• Univ. of Colorado Denver
• NAG Ltd.

Definition at line 126 of file zhetri2.f.

👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code.

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Slay, that’s the whole page, bestie. The footer says LAPACK Version 3.12.0 and /home/abui.../zhetri2.f(3) — periodt. 🫶✨