TESTING/LIN/zhpt01.f(3)

🎀 TESTING/LIN/zhpt01.f(3) 🎀

okay bestie, this page is from the Library Functions Manual, and it's giving “LAPACK testing internals but make it cute” 💅✨

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✨ NAME ✨

TESTING/LIN/zhpt01.f

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🦋 SYNOPSIS 🦋

💖 Functions/Subroutines 💖

• subroutine zhpt01 (uplo, n, a, afac, ipiv, c, ldc, rwork, resid) — the ZHPT01 girl herself 🫶

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💖 Function/Subroutine Documentation 💖

subroutine zhpt01 (character uplo, integer n, complex*16, dimension( * ) a,
    complex*16, dimension( * ) afac, integer, dimension( * ) ipiv,
    complex*16, dimension( ldc, * ) c, integer ldc, double precision,
    dimension( * ) rwork, double precision resid)

ZHPT01 — iconic, honestly 👑

🧚 Purpose 🧚

okay so ZHPT01 reconstructs a Hermitian indefinite packed matrix A from its block L*D*L' or U*D*U' factorization and computes the residual

norm( C - A ) / ( N * norm(A) * EPS ),

where C is the reconstructed matrix, EPS is the machine epsilon, L' is the conjugate transpose of L, and U' is the conjugate transpose of U. no cap, that's the whole vibe 💫

🎀 Parameters 🎀

🌸 UPLO 🌸

• UPLO is CHARACTER*1 — specifies whether the upper or lower triangular part of the Hermitian matrix A is stored:
  • = 'U': Upper triangular
  • = 'L': Lower triangular

🍓 N 🍓

• N is INTEGER — the number of rows and columns of the matrix A. N >= 0. periodt 💅

🦋 A 🦋

• A is COMPLEX*16 array, dimension (N*(N+1)/2) — the original Hermitian matrix A, stored as a packed triangular matrix. literally packed with drama and data ✨

💜 AFAC 💜

• AFAC is COMPLEX*16 array, dimension (N*(N+1)/2) — the factored form of the matrix A, stored as a packed triangular matrix. AFAC contains the block diagonal matrix D and the multipliers used to obtain the factor L or U from the block L*D*L' or U*D*U' factorization as computed by ZHPTRF. she's got layers 🫶

🌈 IPIV 🌈

• IPIV is INTEGER array, dimension (N) — the pivot indices from ZHPTRF. pivot pivot slay 💅

⭐ C ⭐

• C is COMPLEX*16 array, dimension (LDC,N) — that's the reconstructed-matrix storage, bestie 💖

🎀 LDC 🎀

• LDC is INTEGER — the leading dimension of the array C. LDC >= max(1,N). don't skimp on the leading dimension, fr fr 🙈

🧚 RWORK 🧚

• RWORK is DOUBLE PRECISION array, dimension (N) — workspace for the real-number side of the operation ✨

🔥 RESID 🔥

• RESID is DOUBLE PRECISION — the residual, computed like this:
  • If UPLO = 'L', norm(L*D*L' - A) / ( N * norm(A) * EPS )
  • If UPLO = 'U', norm(U*D*U' - A) / ( N * norm(A) * EPS )

👑 Author 👑

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

📌 Definition at line 112 of file zhpt01.f. 📌

that's the exact line, bestie — 112 of zhpt01.f 🫶

🪄 Author 🪄

Generated automatically by Doxygen for LAPACK from the source code. yes, the docs wrote themselves, main character energy 😭💅

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signed off with love from LAPACK Version 3.12.0 and the source file TESTING/LIN/zhpt01.f — this cutie was generated automatically by Doxygen for LAPACK from the source code, and that's the tea 🎀🦋✨