TESTING/EIG/ssvdch.f(3)

💅 TESTING/EIG/ssvdch.f

okay BESTIE, this is a page from the Library Functions Manual and it's serving TESTING/EIG/ssvdch.f realness. The subroutine in the spotlight is ssvdch, aka SSVDCH, and it's here to vibe-check whether your computed singular values are accurate. 💖✨

🎀 NAME 🎀

TESTING/EIG/ssvdch.f

🌸 SYNOPSIS 🌸

✨ Functions/Subroutines ✨

• subroutine ssvdch (n, s, e, svd, tol, info) — SSVDCH

🦋 Function/Subroutine Documentation 🦋

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

SSVDCH

🎯 Purpose:

okay so SSVDCH checks to see if 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 an 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 EPS=TOL*MAX(N/10,1)*MACHEP, where MACHEP is the machine precision. 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. 🔥

📦 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. 💅

👑 Author

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

📍 Definition at line 96 of file ssvdch.f.

👑 Author

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okay that's the whole page, bestie! 🌈 Source/version sign-off: this is LAPACK, Version 3.12.0, with page tag TESTING/EIG/ssvdch.f(3) — and the original footer has no date slot filled in, so no date to report. 💅✨