SDTTRF(l)

💖 SDTTRF(l) — the LAPACK routine, bestie edition 💖

okay so you're in section l of the manual and you found SDTTRF — that's a LAPACK routine, version 2.0, and she's here to do exactly one job and do it slayfully. no cap.

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✨ NAME ✨

SDTTRF — compute an LU factorization of a complex tridiagonal matrix A using elimination without partial pivoting. yes. no pivoting. we're rawdogging the elimination, bestie 🫶

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🌸 SYNOPSIS 🌸

SUBROUTINE SDTTRF( N, DL, D, DU, INFO )

    INTEGER        INFO, N

    REAL           D( * ), DL( * ), DU( * )

look at her. five arguments. she's not complicated, she's just precise 💅

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🦋 PURPOSE 🦋

SDTTRF computes an LU factorization of a complex tridiagonal matrix A using elimination without partial pivoting. (iykyk what that means for stability — she said what she said.)

the factorization has the form

A = L * U

where L is a product of unit lower bidiagonal matrices and U is upper triangular with nonzeros in only the main diagonal and first superdiagonal. it's giving "sparse but make it structured" ✨

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🎀 ARGUMENTS 🎀

• N (input) INTEGER — the order of the matrix A. and listen: N >= 0. that's the vibe check. negative N? not on her watch.
• DL (input/output) COMPLEX array, dimension (N-1) — on entry, DL must contain the (n-1) subdiagonal elements of A. on exit, DL is overwritten by the (n-1) multipliers that define the matrix L from the LU factorization of A. so like… she borrows your subdiagonal and gives you back multipliers instead. trade offer, honestly 🍓
• D (input/output) COMPLEX array, dimension (N) — on entry, D must contain the diagonal elements of A. on exit, D is overwritten by the n diagonal elements of the upper triangular matrix U from the LU factorization of A. in goes A's diagonal, out comes U's diagonal. glow-up complete 💖
• DU (input/output) COMPLEX array, dimension (N-1) — on entry, DU must contain the (n-1) superdiagonal elements of A. on exit, DU is overwritten by the (n-1) elements of the first superdiagonal of U. same energy, different superdiagonal 🧚
• INFO (output) INTEGER — the receipts. she tells you how it went:
  • = 0: successful exit. we love a clean run 👑
  • < 0: if INFO = -i, the i-th argument had an illegal value. bestie, you passed something cursed 🙈
  • > 0: if INFO = i, U(i,i) is exactly zero. the factorization has been completed, but the factor U is exactly singular, and division by zero will occur if it is used to solve a system of equations. so like — she finished the job, but the result is a 💀. do not go solving systems with that unless you want NaN flavored chaos.

⚠️ real talk: no partial pivoting means no safety net. INFO > 0 is not a warning, it's a prophecy. if U(i,i) is exactly zero, division by zero will happen when you solve. periodt.

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🌈 SEE ALSO 🌈

ngl bestie, this page didn't ship a SEE ALSO section, so there's nothing to cross-reference here. go ask the rest of LAPACK, she's around 💜

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and that's the whole page, no notes ✨

this was a modified LAPACK routine, dated 12 May 1997 — shoutout to the elders who wrote her, she's been serving since before some of us were born and she still eats 💅🫶 bye bestie, go pivot responsibly (or don't, that's literally the whole point) ⭐