DBDT03(3)

💜 DBDT03(3) — like, the bidiagonal SVD reconstruction test, bestie

okay so before we even get into it — this page lives at /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/EIG/dbdt03.f, it's a Library Functions Manual entry, and honestly? it's giving "quiet little workhorse that keeps your SVD honest." 🫶

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✨ SYNOPSIS ✨

Functions/Subroutines

• subroutine DBDT03 (uplo, n, kd, d, e, u, ldu, s, vt, ldvt, work, resid) — that's the one, that's our girl. DBDT03. 💅

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🎀 Function/Subroutine Documentation 🎀

subroutine DBDT03 (character uplo, integer n, integer kd, double precision,
    dimension( * ) d, double precision, dimension( * ) e, double precision,
    dimension( ldu, * ) u, integer ldu, double precision, dimension( * ) s,
    double precision, dimension( ldvt, * ) vt, integer ldvt, double
    precision, dimension( * ) work, double precision resid)

DBDT03. no notes. 😌

🌸 Purpose 🌸

!> !> DBDT03 reconstructs a bidiagonal matrix B from its 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( B - U * S * VT ) / ( n * norm(B) * EPS ) !> where VT = V' and EPS is the machine precision. !>

so like. it takes your SVD apart, rebuilds B, and then checks how badly you fumbled it. the ratio is literally "how far off are you, scaled by matrix size and machine precision" — and lower is better, periodt. 🔥

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💖 Parameters 💖

• UPLO — UPLO is CHARACTER*1. it tells us whether the matrix B is upper or lower bidiagonal:

!> = 'U': Upper bidiagonal !> = 'L': Lower bidiagonal

pick one, bestie, there is no third option. 🙈

• N — N is INTEGER. the order of the matrix B. iykyk. ⭐
• KD — KD is INTEGER. the bandwidth of the bidiagonal matrix B. okay so this one has rules:

!> If KD = 1, the matrix B is bidiagonal, and if KD = 0, B is diagonal and E is !> not referenced. If KD is greater than 1, it is assumed to be !> 1, and if KD is less than 0, it is assumed to be 0.

so like… it lowkey clamps itself. KD > 1 → treated as 1, KD < 0 → treated as 0. no cap. 🦋

• D — D is DOUBLE PRECISION array, dimension (N). the n diagonal elements of the bidiagonal matrix B. the main characters, honestly. 👑
• E — E is DOUBLE PRECISION array, dimension (N-1). the (n-1) superdiagonal elements of B if UPLO = 'U', or the (n-1) subdiagonal elements of B if UPLO = 'L'. know the difference, it matters. ✨
• U — U is DOUBLE PRECISION array, dimension (LDU,N). the n by n orthogonal matrix U in the reduction B = U'*A*P. (yes it says A and P in there, that's what the page says, we don't fix, we report 💀)
• LDU — LDU is INTEGER. the leading dimension of the array U. LDU >= max(1,N). respect the bound or perish. 🫶
• S — S is DOUBLE PRECISION array, dimension (N). the singular values from the SVD of B, sorted in decreasing order. biggest first, always. 📉
• VT — VT is DOUBLE PRECISION array, dimension (LDVT,N). the n by n orthogonal matrix V' in the reduction B = U * S * V'. note the transpose energy 🎀
• LDVT — LDVT is INTEGER. the leading dimension of the array VT.
• WORK — WORK is DOUBLE PRECISION array, dimension (2*N). scratch space. it's not doing anything glamorous, it's just holding the vibes. 💜
• RESID — RESID is DOUBLE PRECISION. the test ratio:

!> The test ratio: norm(B - U * S * V') / ( n * norm(A) * EPS )

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⭐ Author ⭐

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

(academic royalty, fr fr 👑)

Definition at line 133 of file dbdt03.f.

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🌈 Author (the meta one) 🌈

Generated automatically by Doxygen for LAPACK from the source code. it did not write itself, it was generated, and it ate. 💅

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okay that's the whole page, no skips, no summaries — and a cute little sign-off: this was LAPACK, Version 3.12.0, documented at /home/abui...IG/dbdt03.f(3). go test your SVDs, bestie, and may your RESID stay tiny 🦋✨🎀