TESTING/LIN/dgtt01.f(3)

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version 3.12.1 · 2 versions
, in arch rolling

✨ TESTING/LIN/dgtt01.f ✨

okay bestie, so this is like the manual page for TESTING/LIN/dgtt01.f and honestly it's giving "I test linear algebra so you don't have to" energy 💅

🌸 SYNOPSIS 🌸

Functions/Subroutines

subroutine dgtt01 (n, dl, d, du, dlf, df, duf, du2, ipiv, work, ldwork,
    rwork, resid)

DGTT01 — that's the name, no cap 🎀

💖 Function/Subroutine Documentation 💖

subroutine dgtt01 (integer n, double precision, dimension( * ) dl, double precision, dimension( * ) d, double precision, dimension( * ) du, double precision, dimension( * ) dlf, double precision, dimension( * ) df, double precision, dimension( * ) duf, double precision, dimension( * ) du2, integer, dimension( * ) ipiv, double precision, dimension( ldwork, * ) work, integer ldwork, double precision, dimension( * ) rwork, double precision resid)

DGTT01 — yes queen, say it again 👑

🦋 Purpose 🦋

so like, DGTT01 reconstructs a tridiagonal matrix A from its LU factorization, and then it computes the residual — and the formula is literally:

norm(L*U - A) / ( norm(A) * EPS ),

where EPS is the machine epsilon, bestie. that's the whole vibe ✨

🌈 Parameters 🌈

okay so here's every single parameter, no skipping, we're thorough in this house:

  • N — N is INTEGER. it's the order of the matrix A, and it's gotta be N >= 0. periodt 💅
  • DL — DL is DOUBLE PRECISION array, dimension (N-1). these are the (n-1) sub-diagonal elements of A. lowkey important 🎀
  • D — D is DOUBLE PRECISION array, dimension (N). the diagonal elements of A. main character energy honestly ⭐
  • DU — DU is DOUBLE PRECISION array, dimension (N-1). the (n-1) super-diagonal elements of A. slay 💜
  • DLF — DLF is DOUBLE PRECISION array, dimension (N-1). these are the (n-1) multipliers that define the matrix L from the LU factorization of A. iconic 🔥
  • DF — DF is DOUBLE PRECISION array, dimension (N). the n diagonal elements of the upper triangular matrix U from the LU factorization of A. we stan 🌸
  • DUF — DUF is DOUBLE PRECISION array, dimension (N-1). the (n-1) elements of the first super-diagonal of U. yes bestie 🦋
  • DU2 — DU2 is DOUBLE PRECISION array, dimension (N-2). the (n-2) elements of the second super-diagonal of U. look at her go 💖
  • IPIV — IPIV is INTEGER array, dimension (N). these are the pivot indices; for 1 <= i <= n, row i of the matrix was interchanged with row IPIV(i). and here's the tea: IPIV(i) will always be either i or i+1; if IPIV(i) = i that means a row interchange was not required. iykyk 🙈
  • WORK — WORK is DOUBLE PRECISION array, dimension (LDWORK,N). it's workspace, it works hard so you don't have to ✨
  • LDWORK — LDWORK is INTEGER. it's the leading dimension of the array WORK, and it needs LDWORK >= max(1,N). don't forget that constraint bestie 💀
  • RWORK — RWORK is DOUBLE PRECISION array, dimension (N). more workspace, we love to see it 🎀
  • RESID — RESID is DOUBLE PRECISION. it's the scaled residual: norm(L*U - A) / (norm(A) * EPS). this is the final answer, the payoff, the moment we've all been waiting for 👑

👑 Author 👑

like, the whole squad of institutions:

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

Definition at line 132 of file dgtt01.f. periodt 💅

Author

Generated automatically by Doxygen for LAPACK from the source code. not me being auto-generated 😭

this whole page is from LAPACK, Version 3.12.0, and the manual page date is just TESTING/LIN/dgtt01.f(3) — so like, that's the vibe check done and dusted ✨💖🦋

hope that helped bestie, now go reconstruct those tridiagonal matrices and slay 🎀👑💅

📦 where this page comes from