TESTING/EIG/dstt21.f(3)

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version 3.12.1 · 3 versions
, in arch rolling

💅 TESTING/EIG/dstt21.f 💅

okay so this is a page from the Library Functions Manual — yes, that's the actual manual name, it's giving very "official docs" energy — and it's all about one lil subroutine that does a vibe check on your matrix decomposition. no cap, she's a tester, and she's judging you (lovingly). 🫶

✨ NAME ✨

TESTING/EIG/dstt21.f — that's her, that's the whole name, iconic and to the point 💖

🦋 SYNOPSIS 🦋

Functions/Subroutines

subroutine dstt21 (n, kband, ad, ae, sd, se, u, ldu, work, result)

DSTT21 🎀 (that's literally all the synopsis says about her and honestly? mysterious queen behavior)

👑 Function/Subroutine Documentation 👑

subroutine dstt21 (integer n, integer kband, double precision, dimension( * )
ad, double precision, dimension( * ) ae, double precision, dimension( * ) sd,
double precision, dimension( * ) se, double precision, dimension( ldu, * ) u,
integer ldu, double precision, dimension( * ) work, double precision,
dimension( 2 ) result)

DSTT21 ✨

🌸 Purpose 🌸

bestie. listen. DSTT21 checks a decomposition of the form

A = U S U'

where ' means transpose, A is symmetric tridiagonal, U is orthogonal, and S is diagonal (if KBAND=0) or symmetric tridiagonal (if KBAND=1). she runs two tests, because one is never enough:

RESULT(1) = | A - U S U' | / ( |A| n ulp )

RESULT(2) = | I - UU' | / ( n ulp )

like, accuracy queen fr fr 😭🔥

🎀 Parameters 🎀

  • N — N is INTEGER. the size of the matrix. if it's zero, DSTT21 does nothing (respect honestly, she's not doing unpaid labor 💀). it must be at least zero.
  • KBAND — KBAND is INTEGER. the bandwidth of the matrix S. it may only be zero or one — no in-between, no chaos, we stay on the binary. if zero, then S is diagonal and SE is not referenced. if one, then S is symmetric tri-diagonal.
  • AD — AD is DOUBLE PRECISION array, dimension (N). the diagonal of the original (unfactored) matrix A. A is assumed to be symmetric tridiagonal. she's the main character 💅
  • AE — AE is DOUBLE PRECISION array, dimension (N-1). the off-diagonal of the original (unfactored) matrix A. A is assumed to be symmetric tridiagonal. AE(1) is the (1,2) and (2,1) element, AE(2) is the (2,3) and (3,2) element, etc. — yes she repeats herself because symmetry DID that 🌈
  • SD — SD is DOUBLE PRECISION array, dimension (N). the diagonal of the (symmetric tri-) diagonal matrix S. cute, simple, diagonal.
  • SE — SE is DOUBLE PRECISION array, dimension (N-1). the off-diagonal of the (symmetric tri-) diagonal matrix S. not referenced if KBSND=0 (yes, that's literally what it says — KBSND, not KBAND, that's not me, that's the source, iykyk 🙈). if KBAND=1, then AE(1) is the (1,2) and (2,1) element, SE(2) is the (2,3) and (3,2) element, etc. (also exactly what it says — AE(1) and SE(2), don't come for me 🍓)
  • U — U is DOUBLE PRECISION array, dimension (LDU, N). the orthogonal matrix in the decomposition. she's orthogonal, she's unbothered, she's at a right angle to your nonsense 💜
  • LDU — LDU is INTEGER. the leading dimension of U. LDU must be at least N. no shortcuts bestie.
  • WORK — WORK is DOUBLE PRECISION array, dimension (N*(N+1)). it's the workspace, she's just there to hold stuff 🧚
  • RESULT — RESULT is DOUBLE PRECISION array, dimension (2). the values computed by the two tests described above. the values are currently limited to 1/ulp, to avoid overflow — yes, capped, we don't do overflow in this house 🔥. RESULT(1) is always modified.
⚠️ quick reality check: RESULT(1) being always modified is stated as fact, and the 1/ulp limit is a real constraint, not a suggestion. don't assume anything else about these fields beyond what's written above, okay? 💀

💖 Author 💖

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

all of them. a whole collab. a group project that actually worked 😭👑

Definition at line 125 of file dstt21.f.

⭐ Author (yes, again) ⭐

Generated automatically by Doxygen for LAPACK from the source code. so technically the author of this page is a robot 🤖 she's doing her best.

and that's the whole page, bestie! 💅💖

sign-off: this gorgeous lil doc is LAPACK, Version 3.12.0, and it lives at TESTING/EIG/dstt21.f(3) — go off, queen 🌸✨🦋

📦 where this page comes from