CHECON(3)

CHECON — LAPACK 💅✨

Okay so bestie, let me introduce you to CHECON — a whole icon from the LAPACK library. Fr fr, she's out here doing the math so you don't have to. 💖

✨ SYNOPSIS ✨

subroutine CHECON (uplo, n, a, lda, ipiv, anorm, rcond, work, info)

🫶 Functions/Subroutines

• subroutine CHECON (uplo, n, a, lda, ipiv, anorm, rcond, work, info) — the one and only, the main character herself.

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📖 Function/Subroutine Documentation 📖

🦋 Purpose 🦋

!> CHECON estimates the reciprocal of the condition number of a complex !> Hermitian matrix A using the factorization A = U*D*UH or !> A = L*D*LH computed by CHETRF. !> !> An estimate is obtained for norm(inv(A)), and the reciprocal of the !> condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).

No cap, this is the whole vibe: you give her a matrix that's already been factored by CHETRF, and she tells you how "sensitive" it is. It's giving numerical self-care. 🌸

🌈 Parameters 🌈

• UPLO — CHARACTER*1. Tells you whether the factorization details are stored as an upper or lower triangular matrix.
  • = 'U': Upper triangular, form is A = U*D*U**H;
  • = 'L': Lower triangular, form is A = L*D*L**H.

Like, pick your lane bestie. 💅

• N — INTEGER. The order of the matrix A. Condition: N >= 0. Zero is valid, don't come for her. ✨
• A — COMPLEX array, dimension (LDA,N). The block diagonal matrix D and the multipliers used to obtain the factor U or L, exactly as computed by CHETRF. She's not doing the factoring, she's just reading the receipts. 🧾
• LDA — INTEGER. The leading dimension of the array A. Condition: LDA >= max(1,N). Respect the dimensions or she will not be happy. 😭
• IPIV — INTEGER array, dimension (N). The details of the interchanges and the block structure of D, as determined by CHETRF. Think of it as the lore. 📜
• ANORM — REAL. The 1-norm of the original matrix A. It's giving OG matrix energy. 💚
• RCOND — REAL. The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an estimate of the 1-norm of inv(A) computed in this routine. The final boss output. 👑
• WORK — COMPLEX array, dimension (2*N). Workspace. She needs a little room to do her thing. 🎀
• INFO — INTEGER. The vibe check on the exit:
  • = 0: successful exit, slay 💅
  • < 0: if INFO = -i, the i-th argument had an illegal value. Not cute. 🚩

Warning bestie: If INFO comes back negative, one of your arguments is lowkey illegal. The exact value -i tells you which argument is the problem. Fix it and try again. 🙈

👑 Author 👑

Shoutout to the legends who made this possible:

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

Icons, every single one. 🌟

Definition at line 123 of file checon.f. Periodt. 💀

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This little beauty was auto-generated by Doxygen for LAPACK from the source code. Version 3.12.0, file checon.f(3). Stay nerdy, bestie. 💖🫶✨