SSTECH(3)

✨ SSTECH(3) ✨

okay so bestie, this is the SSTECH(3) manual page and it’s giving “niche LAPACK subroutine that knows things.” no cap, we’re gonna get through it together. 🫶

🌈 NAME 🌈

The NAME section is, literally, just this whole path:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/EIG/sstech.f

that’s it. that’s the name. iconic, honestly. 💅

✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

subroutine SSTECH (n, a, b, eig, tol, work, info)
    SSTECH

and then it says SSTECH again, because main character energy means saying your own name twice. 💖

💅 Function/Subroutine Documentation 💅

subroutine SSTECH (integer n, real, dimension( * ) a, real, dimension( * ) b, real, dimension( * ) eig, real tol, real, dimension( * ) work, integer info)

SSTECH

🎀 Purpose 🎀

okay so picture this: let T be the tridiagonal matrix with diagonal entries A(1) ,..., A(N) and offdiagonal entries B(1) ,..., B(N-1)). yes, the extra ) is right there in the source, bestie, I’m not fixing it. 🫶

SSTECH checks to see if EIG(1) ,..., EIG(N) are actually 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 exist, and then using Sturm sequences to count and verify whether each resulting interval has the correct number of eigenvalues — and yes, it does that using SSTECT. 🦋

here’s the formula, no cap:

EPS = TOL*MACHEPS*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. periodt. 💀

🍓 Parameters 🍓

• N — N is INTEGER, and it’s the dimension of the tridiagonal matrix T.
• A — A is a REAL array, dimension (N), holding the diagonal entries of the tridiagonal matrix T.
• B — B is a REAL array, dimension (N-1), holding the offdiagonal entries of the tridiagonal matrix T.
• EIG — EIG is a REAL array, dimension (N), and these are the purported eigenvalues that are getting checked.
• TOL — TOL is REAL, the error tolerance for checking, and it’s a multiple of the machine precision.
• WORK — WORK is a REAL array, dimension (N). that’s the whole description, bestie. no extra lore. 🙈
• INFO — INFO is INTEGER.
  • 0 if the eigenvalues are all correct, to within 1 +- TOL*MACHEPS*MAXEIG
  • >0 if the interval containing the INFO-th eigenvalue contains the incorrect number of eigenvalues.

👑 Author 👑

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

Definition at line 100 of file sstech.f. 📌

💫 Author 💫

Generated automatically by Doxygen for LAPACK from the source code.

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💖 cute sign-off time, bestie: the footer says LAPACK Version 3.12.0, and the file/path stamp is /home/abui...IG/sstech.f(3). there’s no actual date in that footer, so I’m not inventing one — I would never fr fr. 💅