TESTING/EIG/sbdt04.f(3)

💅 TESTING/EIG/sbdt04.f — the bidiagonal SVD vibe check

okay so bestie, welcome to TESTING/EIG/sbdt04.f, a manual page from the LAPACK library (yes, that LAPACK, the linear algebra icon herself ✨). It's real, it's here, and it's lowkey giving "quality control for your singular value decomposition."

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🌸 SYNOPSIS — functions & subroutines

• subroutine sbdt04 (uplo, n, d, e, s, ns, u, ldu, vt, ldvt, work, resid) — the one and only, SBDT04 itself 🎀

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✨ Function/Subroutine Documentation ✨

subroutine sbdt04 (character uplo, integer n, real, dimension( * ) d, real, dimension( * ) e, real, dimension( * ) s, integer ns, real, dimension( ldu, * ) u, integer ldu, real, dimension( ldvt, * ) vt, integer ldvt, real, dimension( * ) work, real resid)

SBDT04 — say it with me 🫶

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🎯 Purpose

fortran !> SBDT04 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. >

So basically: it takes a bidiagonal matrix B, rebuilds it from its (possibly partial) singular value decomposition, and then checks how badly reality diverged from the math. That ratio? That's the receipts 🔥. EPS is the machine precision, VT is V', and norm is doing its thing.

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🧸 Parameters

• UPLO

fortran !> UPLO is CHARACTER*1 !> Specifies whether the matrix B is upper or lower bidiagonal. !> = 'U': Upper bidiagonal !> = 'L': Lower bidiagonal

Pick your fighter: 'U' for upper bidiagonal, 'L' for lower. That's it, that's the whole choice 💅

• N

fortran !> N is INTEGER !> The order of the matrix B.

How big is B? This many. The order, the main character energy of the whole operation 👑

• D

fortran !> D is REAL array, dimension (N) !> The n diagonal elements of the bidiagonal matrix B.

The N diagonal elements of B. The main diagonal, the backbone, the moment ✨

• E

fortran !> E is REAL array, dimension (N-1) !> The (n-1) superdiagonal elements of the bidiagonal matrix B !> if UPLO = 'U', or the (n-1) subdiagonal elements of B if !> UPLO = 'L'.

The off-diagonal bestie: (n-1) superdiagonals when UPLO = 'U', or (n-1) subdiagonals when UPLO = 'L'. It literally does both depending on the vibe check 🦋

• S

fortran !> S is REAL array, dimension (NS) !> The singular values from the (partial) SVD of B, sorted in !> decreasing order.

The singular values from the (partial) SVD of B, sorted in decreasing order. Big to small, no exceptions, we love a sorted queen 🌈

• NS

fortran !> NS is INTEGER !> The number of singular values/vectors from the (partial) !> SVD of B.

How many singular values/vectors we actually kept from the (partial) SVD. It's giving "we don't always need all of them" 🙈

• U

fortran !> U is REAL array, dimension (LDU,NS) !> The n by ns orthogonal matrix U in S = U' * B * V.

The n by ns orthogonal matrix U in S = U' * B * V. Orthogonal legend 💖

• LDU

fortran !> LDU is INTEGER !> The leading dimension of the array U. LDU >= max(1,N)

The leading dimension of U. And it better be LDU >= max(1,N) — no cap, respect the bound 😤

• VT

fortran !> VT is REAL array, dimension (LDVT,N) !> The n by ns orthogonal matrix V in S = U' * B * V.

The n by ns orthogonal matrix V in S = U' * B * V. Note the plot twist: it arrives as VT, i.e. V'. Transposed and thriving 🧚

• LDVT

fortran !> LDVT is INTEGER !> The leading dimension of the array VT.

The leading dimension of VT, plain and simple 🎀

• WORK

fortran !> WORK is REAL array, dimension (2*N)

Scratch workspace, dimension (2*N). Our behind-the-scenes icon ⭐

• RESID

fortran !> RESID is REAL !> The test ratio: norm(S - U' * B * V) / ( n * norm(B) * EPS )

The final verdict fr fr: norm(S - U' * B * V) / ( n * norm(B) * EPS ). Low number = slay. High number = 💀

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👑 Author

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

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Definition at line 129 of file sbdt04.f.

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tiny print bestie: this page was Generated automatically by Doxygen for LAPACK from the source code — so if it looks a little typed-by-a-robot, that's because it was 🫶

okay that's the whole page, no notes. LAPACK, Version 3.12.0 💖 thanks for reading, mwah 🎀