TESTING/EIG/sstech.f(3)

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version 3.12.1 · 3 versions
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✨ NAME ✨

You're reading the TESTING/EIG/sstech.f(3) page from the Library Functions Manual, bestie. It's a LAPACK testing page, and the main character is the sstech subroutine. 💅

🦋 SYNOPSIS 🦋

🌸 Functions/Subroutines 🌸

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

💖 Function/Subroutine Documentation 💖

🌟 sstech — SSTECH 🌟

   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 T, a tridiagonal matrix: its diagonal entries are A(1), …, A(N), and its offdiagonal entries are B(1), …, B(N-1)) — yes, that double paren is in the source, and I am keeping it, no cap. 💀

SSTECH checks whether 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] — yes, SVD(I), that's literally what the page says — merging overlapping intervals if there are any, and then using Sturm sequences to count and verify whether each resulting interval has the correct number of eigenvalues (it uses SSTECT for that). ✨

Here 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. The dimension of the tridiagonal matrix T. 🦋
  • A — A is REAL array, dimension (N). The diagonal entries of the tridiagonal matrix T. 💖
  • B — B is REAL array, dimension (N-1). The offdiagonal entries of the tridiagonal matrix T. ✨
  • EIG — EIG is REAL array, dimension (N). The purported eigenvalues to be checked. 👑
  • TOL — TOL is REAL. Error tolerance for checking, a multiple of the machine precision. 🎀
  • WORK — WORK is REAL array, dimension (N). 🫶
  • 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.

ok bye bestie 💖 — footer vibes: LAPACK Version 3.12.0, page TESTING/EIG/sstech.f(3). The footer doesn't list a separate date, so I'm not making one up fr fr. 🎀

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