TESTING/EIG/dstech.f(3)

💅 TESTING/EIG/dstech.f ✨

okay so bestie, welcome to the dstech page from the LAPACK manual (that's the Library Functions Manual situation we're in 🎀). This is one of those auto-generated function pages, and it's honestly giving "short but mighty." Let's get into it 🫶

---

🌸 SYNOPSIS 🌸

Functions/Subroutines

• subroutine dstech (n, a, b, eig, tol, work, info) — literally just DSTECH, that's the whole vibe 💅

---

🦋 Function/Subroutine Documentation 🦋

subroutine dstech (integer n, double precision, dimension( * ) a, double precision, dimension( * ) b, double precision, dimension( * ) eig, double precision tol, double precision, dimension( * ) work, integer info)

DSTECH — bestie. the name. iconic. 💖

✨ Purpose: ✨

!> !> Let T be the tridiagonal matrix with diagonal entries A(1) ,..., !> A(N) and offdiagonal entries B(1) ,..., B(N-1)). DSTECH checks to !> see if EIG(1) ,..., EIG(N) are indeed accurate eigenvalues of T. !> It does this by expanding each EIG(I) into an interval !> [SVD(I) - EPS, SVD(I) + EPS], merging overlapping intervals if !> any, and using Sturm sequences to count and verify whether each !> resulting interval has the correct number of eigenvalues (using !> DSTECT). Here EPS = TOL*MAZHEPS*MAXEIG, where MACHEPS is the !> machine precision and MAXEIG is the absolute value of the largest !> eigenvalue. If each interval contains the correct number of !> eigenvalues, INFO = 0 is returned, otherwise INFO is the index of !> the first eigenvalue in the first bad interval. !>

so like, translation for the girlies 👑: take your tridiagonal matrix T — diagonals from A(1) … A(N), off-diagonals from B(1) … B(N-1). Then it's a whole vibe check on EIG(1) … EIG(N) to see if those are actually accurate eigenvalues. The way it does that is lowkey clever: it expands every EIG(I) into an interval [SVD(I) - EPS, SVD(I) + EPS], merges any overlapping intervals (slay, dedupe), and then uses Sturm sequences to count and verify that each resulting interval has the correct number of eigenvalues — that part runs through DSTECT. And EPS = TOL*MAZHEPS*MAXEIG, where MACHEPS is the machine precision and MAXEIG is the absolute value of the largest eigenvalue. If every interval has the right number of eigenvalues, you get INFO = 0. If not, INFO is the index of the first eigenvalue in the first bad interval 😭 (yes, it's snitching on you, fr fr).

---

💜 Parameters 💜

• N

!> N is INTEGER !> The dimension of the tridiagonal matrix T. !>

it's an INTEGER, and it's the dimension of the tridiagonal matrix T. that's the whole job. no notes 💅

• A

!> A is DOUBLE PRECISION array, dimension (N) !> The diagonal entries of the tridiagonal matrix T. !>

DOUBLE PRECISION array, dimension (N). These are the diagonal entries of T — the main character energy of the matrix ngl ⭐

• B

!> B is DOUBLE PRECISION array, dimension (N-1) !> The offdiagonal entries of the tridiagonal matrix T. !>

DOUBLE PRECISION array, dimension (N-1) — note the N-1, bestie, it's off-diagonal so there's one fewer, that's just how tridiagonal works 🎀 These are the offdiagonal entries of T.

• EIG

!> EIG is DOUBLE PRECISION array, dimension (N) !> The purported eigenvalues to be checked. !>

DOUBLE PRECISION array, dimension (N). "Purported" eigenvalues 😭 — like the eigenvalues are claiming to be eigenvalues and DSTECH is the vibe check. 💀

• TOL

!> TOL is DOUBLE PRECISION !> Error tolerance for checking, a multiple of the !> machine precision. !>

a plain DOUBLE PRECISION. It's the error tolerance for the checking, expressed as a multiple of the machine precision. dial it up or down, you're the main character ✨

• WORK

!> WORK is DOUBLE PRECISION array, dimension (N) !>

DOUBLE PRECISION array, dimension (N). It works. that's it. that's the parameter. 🙈

• INFO

!> INFO is INTEGER !> 0 if the eigenvalues are all correct (to within !> 1 +- TOL*MAZHEPS*MAXEIG) !> >0 if the interval containing the INFO-th eigenvalue !> contains the incorrect number of eigenvalues. !>

an INTEGER, and it's the tea ☕:

• 0 — the eigenvalues are all correct (to within 1 +- TOL*MAZHEPS*MAXEIG) 🎉
• >0 — the interval containing the INFO-th eigenvalue contains the incorrect number of eigenvalues 😭 (this is the bad interval situation, the one from the Purpose section, no cap)

heads up bestie: MAZHEPS shows up exactly like that in the original text (and MACHEPS shows up in the prose part) — I'm not touching it, I'm just the messenger 🫶

---

🌈 Author 🌈

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

Definition at line 100 of file dstech.f. 🦋

---

💖 Author 💖

Generated automatically by Doxygen for LAPACK from the source code. (yes, two Author sections, that's just how the page is laid out, we don't question the auto-generator's choices 😌)

---

okay that's the whole page bestie, every flag, every array, every dimension, every !> — nothing skipped, periodt 💅

LAPACK · Version 3.12.0 · TESTING/EIG/dstech.f(3) — mwah, go check those eigenvalues, you're gonna slay 🎀✨🔥