CDTTRF(l)

💖 CDTTRF(l) — the LAPACK girlies' guide to tridiagonal LU 💖

okay bestie, so this is CDTTRF from the LAPACK routine crew (version 2.0, she's a classic), and she's about to factor a complex tridiagonal matrix for you. no partial pivoting. we're doing this raw. let's GO 🦋

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✨ NAME ✨

CDTTRF — she computes an LU factorization of a complex tridiagonal matrix A using elimination without partial pivoting. that's the whole vibe. 💅

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🌸 SYNOPSIS 🌸

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

    INTEGER        INFO, N

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

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🎀 PURPOSE 🎀

so like, CDTTRF computes an LU factorization of a complex tridiagonal matrix A using elimination without partial pivoting. yes, without. we're brave. we're fearless. we're trusting the math. 😭

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. like, U is that girl who only shows up in two places and slays in both of them. ✨

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👑 ARGUMENTS 👑

• N (input) INTEGER — the order of the matrix A. the rule is N >= 0, no exceptions, we do not do negative dimensions in this house. 🚫
• 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 she comes in as one thing and leaves as another. glow-up energy. 💅
• 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 diagonal of A in, main diagonal of U out. iconic behavior. 👑
• 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. she's just out here living her best superdiagonal life. 🌈
• INFO (output) INTEGER — the vibe check report, and it goes like this:
  • = 0: successful exit. we ate. 🍽️
  • < 0: if INFO = -i, the i-th argument had an illegal value. somebody passed something cursed, and she's telling you exactly which one. 🙈
  • > 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. that's not a drill bestie, that's a 💀 moment. singular U means no solving for you.

⚠️ real talk: if you get INFO > 0 and then go solve a system anyway, you're dividing by zero. she warned you. she told you. U(i,i) is literally zero. do not pass go. 🛑

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💜 that's the whole page 💜

modified LAPACK routine, dated 12 May 1997 — yeah she's vintage, she's a classic, she's been serving tridiagonal LU since before you were born and she still hits. stan her. 🫶✨

no cap, go factor something. 💖