CBDT05(3)

💅 CBDT05(3) — like, the Library Functions Manual page, bestie 🎀

okay so first things first: this is a page out of the Library Functions Manual, and the star of the show lives at this exact address, no cap:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/EIG/cbdt05.f

that's the whole NAME situation. she's a Fortran file. she's in the TESTING/EIG folder. iconic behavior honestly.

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✨ SYNOPSIS ✨

Functions/Subroutines 🦋

so there's literally one (1) subroutine here and she's the main character:

subroutine CBDT05 (m, n, a, lda, s, ns, u, ldu, vt, ldvt, work, resid)

yep. that's her. CBDT05. go off queen 👑

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🌸 Function/Subroutine Documentation 🌸

subroutine CBDT05 — the full signature, spelled out 💖

subroutine CBDT05 (integer m, integer n, complex, dimension( lda, * ) a,
    integer lda, real, dimension( * ) s, integer ns, complex, dimension( * )
    u, integer ldu, complex, dimension( ldvt, * ) vt, integer ldvt, complex,
    dimension( * ) work, real resid)

CBDT05. that's the name. that's the vibe.

🧚 Purpose 🧚

okay so here's what she actually does:

CBDT05 reconstructs a bidiagonal matrix B from its (partial) SVD:

S = U' * B * V

where U and V are orthogonal matrices and S is diagonal. slay.

and the test ratio used to check the singular value decomposition is:

RESID = norm( S - U' * B * V ) / ( n * norm(B) * EPS )

where VT = V' and EPS is the machine precision. periodt. 💅

🎀 Parameters 🎀

every single one, in order, no skipping, i'm obsessed with being thorough:

• M — INTEGER. the number of rows of the matrices A and U. that's it, that's her job.
• N — INTEGER. the number of columns of the matrices A and VT. same energy, different axis, we love to see it.
• A — COMPLEX array, dimension (LDA,N). it's the m by n matrix A. your actual data bestie 💜
• LDA — INTEGER. the leading dimension of the array A. and listen: LDA >= max(1,M). that's a requirement, not a suggestion 🙈
• S — REAL array, dimension (NS). the singular values from the (partial) SVD of B, sorted in decreasing order. organized queen 🌈
• NS — INTEGER. the number of singular values/vectors from the (partial) SVD of B. not all of them? that's fine, partial is valid ✨
• U — COMPLEX array, dimension (LDU,NS). the n by ns orthogonal matrix U in S = U' * B * V. go girl 🫶
• LDU — INTEGER. the leading dimension of the array U, and LDU >= max(1,N). respect the constraint or perish 😭
• VT — COMPLEX array, dimension (LDVT,N). the n by ns orthogonal matrix V in S = U' * B * V. yes she's stored transposed, that's just her thing 💀
• LDVT — INTEGER. the leading dimension of the array VT. no inequality given, just vibes. ⭐
• WORK — COMPLEX array, dimension (M,N). scratch space. the backstage crew who never get credit but honestly carry the whole show 🍓
• RESID — REAL. the test ratio: norm(S - U' * A * V) / ( n * norm(A) * EPS ). the moment of truth, the final grade, the vibe check 🔥

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👑 Author 👑

the legends behind this:

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

a whole squad. we stan an academic-industrial collab 💖

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⭐ Definition ⭐

found her at line 123 of file cbdt05.f. go look, she's right there.

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🌈 Author (yes, again) 🌈

Generated automatically by Doxygen for LAPACK from the source code.

so nobody hand-wrote this one, a robot did it. and honestly? the robot ate. 💅✨

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okay bestie that's the whole page!! mwah 💖 this was LAPACK, version 3.12.0, and the whole thing came out of that same /home/abui...IG/cbdt05.f situation — 3️⃣ sections, 1️⃣2️⃣ parameters, 0️⃣ notes left behind 🎀🦋🌸