SSVDCH(3)

💅 SSVDCH(3) 💅

Okay bestie, welcome to the Library Functions Manual corner of the internet — this page is all about SSVDCH, and we're gonna make it make sense. 💖

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✨ NAME ✨

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

That's the exact path this page is filed under, and yes it's long enough to need its own vibe check. 🫶

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🌸 SYNOPSIS 🌸

🌟 Functions/Subroutines 🌟

subroutine SSVDCH (n, s, e, svd, tol, info)
    SSVDCH

Short, iconic, to the point.

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🦋 Function/Subroutine Documentation 🦋

subroutine SSVDCH (integer n, real, dimension( * ) s, real, dimension( * )
    e, real, dimension( * ) svd, real tol, integer info)
    SSVDCH

🎯 Purpose 🎯

Okay so the whole point, no cap: SSVDCH checks whether SVD(1) ,..., SVD(N) are accurate singular values of the bidiagonal matrix B with diagonal entries S(1) ,..., S(N) and superdiagonal entries E(1) ,..., E(N-1)).

It does this by expanding each SVD(I) into the interval [SVD(I) * (1-EPS) , SVD(I) * (1+EPS)], merging overlapping intervals if any, and using Sturm sequences to count and verify whether each resulting interval has the correct number of singular values (using SSVDCT).

Here's the formula tea: EPS=TOL*MAX(N/10,1)*MACHEP, where MACHEP is the machine precision. Write that down bestie, it's important. 💅

The routine assumes the singular values are sorted with SVD(1) the largest and SVD(N) smallest.

If each interval contains the correct number of singular values, INFO = 0 is returned. Otherwise INFO is the index of the first singular value in the first bad interval. So INFO is literally pointing at the first spot that failed the vibe check. 😭

🌈 Parameters 🌈

• N — N is INTEGER. The dimension of the bidiagonal matrix B.
• S — S is REAL array, dimension (N). The diagonal entries of the bidiagonal matrix B.
• E — E is REAL array, dimension (N-1). The superdiagonal entries of the bidiagonal matrix B.
• SVD — SVD is REAL array, dimension (N). The computed singular values to be checked.
• TOL — TOL is REAL. Error tolerance for checking, a multiplier of the machine precision.
• INFO — INFO is INTEGER.
  • =0 if the singular values are all correct (to within 1 +- TOL*MACHEPS).
  • >0 if the interval containing the INFO-th singular value contains the incorrect number of singular values.

That MACHEPS spelling in the INFO bit is exactly what the page says, so we're keeping it, iykyk. ✨

👑 Author 👑

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

Definition at line 96 of file ssvdch.f.

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🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code.

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Okay that's the whole page, bestie — every parameter, formula, author credit, and tiny detail accounted for. 💖

Cutest possible sign-off: this footer is serving LAPACK Version 3.12.0, path /home/abui...IG/ssvdch.f(3), and that's the whole footer vibe — signed, sealed, slayed. 🫶