ZDTTRF(l)

💖 ZDTTRF — bestie's guide to LU-ing a complex tridiagonal matrix 💖

okay so this is a LAPACK routine, and the whole vibe is: you hand it a complex tridiagonal matrix, it hands you back an LU factorization. no partial pivoting, no drama, just elimination. it's giving "I trust your matrix, bestie." ✨

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✨ NAME ✨

ZDTTRF — computes an LU factorization of a complex tridiagonal matrix A using elimination without partial pivoting. 🎀

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🦋 SYNOPSIS 🦋

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

    INTEGER        INFO, N

    COMPLEX*16     D( * ), DL( * ), DU( * )

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🌸 PURPOSE 🌸

ZDTTRF computes an LU factorization of a complex tridiagonal matrix A using elimination without partial pivoting. (say it with me: no pivoting. iykyk. 🙈)

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. so like… mostly zeros. queen of minimalism. 👑

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💅 ARGUMENTS 💅

• N (input) INTEGER — the order of the matrix A. must satisfy N >= 0. if it's negative, that's not slay, that's a bug. 💀
• DL (input/output) COMPLEX array, dimension (N-1) — on entry, DL must contain the (n-1) subdiagonal elements of A. on exit, DL gets overwritten by the (n-1) multipliers that define the matrix L from the LU factorization of A. glow-up achieved. ✨
• 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. main character energy, honestly. 👑
• 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. bye original values, you served well 🫶
• INFO (output) INTEGER — the receipts 📋:
  • = 0: successful exit. we ate. 🍓
  • < 0: if INFO = -i, the i-th argument had an illegal value. something you passed in was a mess, bestie 😭
  • > 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. 🚨

⚠️ fr fr, listen up: that INFO > 0 case is NOT a "everything's fine" situation. the routine did finish, but U is singular and any solve on top of it is gonna divide by zero. do not ignore this. it's giving haunted. 💀

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🌈 A LIL NOTE ON THE VIBE 🌈

• no partial pivoting means this is fast and simple, but it also means the routine trusts that your leading minors are fine. that's the trade, that's the deal, that's the tea. 🍵
• everything gets overwritten in place: DL, D, and DU all leave as something new. don't come looking for your original matrix, she's gone 💜

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modified LAPACK routine — 12 May 1997 🌸 this page is a LAPACK routine (version 2.0) situation, and that date is the original one, so shoutout to the 90s for this absolute icon. periodt. 💅✨