SBDT04(3)

💖 SBDT04(3)

Okay bestie, welcome to SBDT04(3) from the Library Functions Manual — it’s giving LAPACK test-ratio main character energy, and we’re gonna get through it together. 💅✨

🌸 NAME

This whole page is about this file, no cap:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/EIG/sbdt04.f

✨ SYNOPSIS

Functions/Subroutines

• subroutine SBDT04 (uplo, n, d, e, s, ns, u, ldu, vt, ldvt, work, resid) — SBDT04

💫 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

🎯 Purpose

So 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. 🫶

🧸 Parameters

UPLO

UPLO is CHARACTER*1 — it specifies whether the matrix B is upper or lower bidiagonal, bestie:

• = 'U': Upper bidiagonal
• = 'L': Lower bidiagonal

N

N is INTEGER — the order of the matrix B. 🔢

D

D is REAL array, dimension (N) — the n diagonal elements of the bidiagonal matrix B. 💖

E

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'. 🌈

S

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

NS

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

U

U is REAL 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). 🎀

VT

VT is REAL 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 REAL array, dimension (2*N). 🧚

RESID

RESID is REAL — 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 sbdt04.f.

🤖 Author

Generated automatically by Doxygen for LAPACK from the source code.

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okay that’s the whole page, bestie — final footer flex: LAPACK, Version 3.12.0, and the path vibe /home/abui...IG/sbdt04.f(3). Byeee 🫶✨