DBDT04(3)

🎀 DBDT04(3) · Library Functions Manual

Hi bestie! This page is dbdt04.f(3) from the Library Functions Manual — the header path gets shortened to /home/abui...IG/dbdt04.f(3) — and it's all about the LAPACK test routine DBDT04. 💖

🌸 NAME

The NAME is literally this whole path, no cap:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/EIG/dbdt04.f

✨ SYNOPSIS

Functions/Subroutines

       subroutine DBDT04 (uplo, n, d, e, s, ns, u, ldu, vt, ldvt, work, resid)
           DBDT04

🫶 Function/Subroutine Documentation

Okay so here's the full signature, exactly as this test routine declares it — no edits, periodt:

   subroutine DBDT04 (character uplo, integer n, double precision, dimension( *
       ) d, double precision, dimension( * ) e, 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)
       DBDT04

🌟 Purpose

DBDT04 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 that checks the singular value decomposition is:

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

where VT = V' and EPS is the machine precision. That's the whole vibe: compare S against U' * B * V, then scale by n, norm(B), and EPS. 💅

🔍 Parameters

Every argument, bestie — in order, no skipping:

• UPLO — CHARACTER*1. Says whether the matrix B is upper or lower bidiagonal. = 'U': upper bidiagonal. = 'L': lower bidiagonal.
• N — INTEGER. The order of the matrix B.
• D — DOUBLE PRECISION array, dimension (N). The n diagonal elements of the bidiagonal matrix B.
• E — 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'.
• S — DOUBLE PRECISION array, dimension (NS). The singular values from the (partial) SVD of B, sorted in decreasing order.
• NS — INTEGER. The number of singular values/vectors from the (partial) SVD of B.
• U — DOUBLE PRECISION array, dimension (LDU,NS). The n by ns orthogonal matrix U in S = U' * B * V.
• LDU — INTEGER. The leading dimension of the array U. LDU >= max(1,N).
• VT — DOUBLE PRECISION array, dimension (LDVT,N). The n by ns orthogonal matrix V in S = U' * B * V.
• LDVT — INTEGER. The leading dimension of the array VT.
• WORK — DOUBLE PRECISION array, dimension (2*N).
• RESID — DOUBLE PRECISION. The test ratio: norm(S - U' * B * V) / ( n * norm(B) * EPS ).

👑 Author

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

📍 Definition at line 129 of file dbdt04.f.

Yep, that's where this icon lives: line 129 of dbdt04.f. 🦋

🤖 Author

Generated automatically by Doxygen for LAPACK from the source code.

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Bye bestie 💖 This page is from LAPACK Version 3.12.0, source/page path /home/abui...IG/dbdt04.f(3). The footer doesn't give a separate date, so I'm not making one up — periodt. 🎀✨