SRC/chptri.f(3)

🌸 SRC/chptri.f — from the Library Functions Manual 💅

okay bestie, sit down, we're doing linear algebra today ✨ this is a page out of the Library Functions Manual, and honestly? she's iconic. it's SRC/chptri.f, and she inverts complex Hermitian indefinite matrices. yes, that kind. no cap, she ate. 🔥

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✨ SYNOPSIS ✨

Functions/Subroutines

subroutine chptri (uplo, n, ap, ipiv, work, info)

CHPTRI — that's the whole name, she's lowkey mysterious like that 🎀

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🦋 Function/Subroutine Documentation 🦋

subroutine chptri (character uplo, integer n, complex, dimension( * ) ap,
    integer, dimension( * ) ipiv, complex, dimension( * ) work, integer
    info)

CHPTRI — here's her whole deal 👑

💜 Purpose:

CHPTRI computes the inverse of a complex Hermitian indefinite matrix A in packed storage using the factorization A = U*D*U**H or A = L*D*L**H computed by CHPTRF.

so basically: CHPTRF did the hard part (the factorization), and CHPTRI comes in and flips it into an inverse. it's giving "I'll finish what you started" main character energy 💅

🎀 Parameters 🎀

• UPLO — UPLO is CHARACTER*1. tells us whether the factorization details are stored as an upper or lower triangular matrix, iykyk:
  • = 'U': upper triangular, form is A = U*D*U**H;
  • = 'L': lower triangular, form is A = L*D*L**H.
• N — N is INTEGER. the order of the matrix A. and the vibe check is N >= 0 (if N is negative, that's a no from her 🙈).
• AP — AP is COMPLEX array, dimension (N*(N+1)/2). okay so on entry, this holds the block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by CHPTRF, stored as a packed triangular matrix. on exit, if INFO = 0, you get the (Hermitian) inverse of the original matrix, stored as a packed triangular matrix. the j-th column of inv(A) is stored in the array AP like this:
  • if UPLO = 'U', AP(i + (j-1)*j/2) = inv(A)(i,j) for 1<=i<=j;
  • if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = inv(A)(i,j) for j<=i<=n.

literally copy those index formulas exactly, bestie, they are not vibes-based 🫶

• IPIV — IPIV is INTEGER array, dimension (N). the details of the interchanges and the block structure of D, as determined by CHPTRF. she got receipts 💀
• WORK — WORK is COMPLEX array, dimension (N). scratch space, she's just there to help 🌸
• INFO — INFO is INTEGER. the outcome, the moment of truth:
  • = 0: successful exit 🎉 slay;
  • < 0: if INFO = -i, the i-th argument had an illegal value (you gave her something cursed 😭);
  • > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its inverse could not be computed. she literally cannot, the math does not exist 💀

fr fr, if you see INFO > 0 don't come for her — the matrix was singular. it's not her fault. 🥲

👑 Author

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

⭐ Definition

Definition at line 108 of file chptri.f.

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🌈 Author (again, the meta one)

Generated automatically by Doxygen for LAPACK from the source code. yeah, she was born from a machine, and she's still iconic 🧚

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LAPACK · Version 3.12.0 · SRC/chptri.f(3)

and that's the whole page, bestie — go invert something Hermitian, drink some water, and remember: packed storage is just storage with ✨aura✨. mwah 💖🎀🦋