DBDT05(3)

okay so bestie, you just opened DBDT05(3) from the Library Functions Manual — and yes, the LAPACK girlies are at it again 💅✨. This page is lowkey about checking a (partial) SVD by rebuilding the bidiagonal matrix B, and the math is giving main-character energy 🫶.

🌸 NAME 🌸

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/EIG/dbdt05.f

that’s the source file, periodt 💖.

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✨ SYNOPSIS ✨

🧩 Functions/Subroutines 🧩

       subroutine DBDT05 (m, n, a, lda, s, ns, u, ldu, vt, ldvt, work, resid)
           DBDT05

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🎀 Function/Subroutine Documentation 🎀

here’s the full signature, wrapped exactly like the source page, because we respect the formatting 🫶:

   subroutine DBDT05 (integer m, integer n, double precision, dimension( lda, *
       ) a, integer lda, double precision, dimension( * ) s, integer ns, double
       precision, dimension( ldu, * ) u, integer ldu, double precision,
       dimension( ldvt, * ) vt, integer ldvt, double precision, dimension( * )
       work, double precision resid)
       DBDT05

🎯 Purpose: 🎯

okay so the whole point: DBDT05 reconstructs a bidiagonal matrix B from its (partial) SVD:

S = U' * B * V

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

the test ratio to test the singular value decomposition is:

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

where VT = V' and EPS is the machine precision. no cap, that’s the whole vibe check 😭.

📝 Parameters 📝

💜 M

M is INTEGER — the number of rows of the matrices A and U. slay.

💜 N

N is INTEGER — the number of columns of the matrices A and VT. periodt.

💜 A

A is DOUBLE PRECISION array, dimension (LDA,N) — the m by n matrix A 🎀.

💜 LDA

LDA is INTEGER — the leading dimension of the array A. LDA >= max(1,M). bestie, respect the leading dimension 💅.

💜 S

S is DOUBLE PRECISION array, dimension (NS) — the singular values from the (partial) SVD of B, sorted in decreasing order. iconic ⭐.

💜 NS

NS is INTEGER — the number of singular values/vectors from the (partial) SVD of B 🦋.

💜 U

U is DOUBLE PRECISION array, dimension (LDU,NS) — the n by ns orthogonal matrix U in S = U' * B * V 👑.

💜 LDU

LDU is INTEGER — the leading dimension of the array U. LDU >= max(1,N). yes, keep it valid ✨.

💜 VT

VT is DOUBLE PRECISION array, dimension (LDVT,N) — the n by ns orthogonal matrix V in S = U' * B * V 🌸.

💜 LDVT

LDVT is INTEGER — the leading dimension of the array VT 🎀.

💜 WORK

WORK is DOUBLE PRECISION array, dimension (M,N). that’s the workspace, bestie 🧚.

💜 RESID

RESID is DOUBLE PRECISION — the test ratio: norm(S - U' * A * V) / ( n * norm(A) * EPS ). this is the number you’re side-eyeing 💀.

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👑 Author 👑

shoutout to the institutions that brought you this page:

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

Definition at line 125 of file dbdt05.f. — yes, exact line, we don’t guess 🔥.

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🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code. — the robots did this one, and they ate 🤖💅.

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mwah 💋 — source/version vibes: LAPACK, Version 3.12.0, page path /home/abui...IG/dbdt05.f(3). bye bestie, go check those singular values 🫶✨.