ZBDT03(3)

👑 ZBDT03(3) — Library Functions Manual energy 👑

okay so bestie, this is the zbdt03.f(3) page from the Library Functions Manual. It's all about ZBDT03, a subroutine that's lowkey doing SVD reconstruction math and highkey serving. 💅

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✨ NAME ✨

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/EIG/zbdt03.f

💅 SYNOPSIS 💅

🌸 Functions/Subroutines 🌸

subroutine ZBDT03 (uplo, n, kd, d, e, u, ldu, s, vt, ldvt, work, resid)
    ZBDT03

🦋 Function/Subroutine Documentation 🦋

subroutine ZBDT03 (character uplo, integer n, integer kd, double precision,
    dimension( * ) d, double precision, dimension( * ) e, complex*16,
    dimension( ldu, * ) u, integer ldu, double precision, dimension( * ) s,
    complex*16, dimension( ldvt, * ) vt, integer ldvt, complex*16,
    dimension( * ) work, double precision resid)
    ZBDT03

🎀 Purpose 🎀

ZBDT03 reconstructs a bidiagonal matrix B from its SVD:

S = U' * B * V

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

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. That's the whole vibe check. ✨

💖 Parameters 💖

• UPLO — CHARACTER*1. Specifies whether the matrix B is upper or lower bidiagonal. = 'U': Upper bidiagonal. = 'L': Lower bidiagonal.
• N — INTEGER. The order of the matrix B.
• KD — INTEGER. The bandwidth of the bidiagonal matrix B. 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.
• 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 the bidiagonal matrix B if UPLO = 'U', or the (n-1) subdiagonal elements of B if UPLO = 'L'.
• U — COMPLEX*16 array, dimension (LDU,N). The n by n orthogonal matrix U in the reduction B = U'*A*P.
• LDU — INTEGER. The leading dimension of the array U. LDU >= max(1,N).
• S — DOUBLE PRECISION array, dimension (N). The singular values from the SVD of B, sorted in decreasing order.
• VT — COMPLEX*16 array, dimension (LDVT,N). The n by n orthogonal matrix V' in the reduction B = U * S * V'.
• LDVT — INTEGER. The leading dimension of the array VT.
• WORK — COMPLEX*16 array, dimension (2*N).
• RESID — DOUBLE PRECISION. The test ratio: norm(B - U * S * V') / ( n * norm(A) * EPS ). Yep, it says norm(A) in the parameter text — I'm not touching it, bestie. 💅

🌈 Author 🌈

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

Definition at line 133 of file zbdt03.f.

🫶 Author 🫶

Generated automatically by Doxygen for LAPACK from the source code.

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okay that's the whole page, bestie 💖 — signed off by LAPACK Version 3.12.0 and the footer path /home/abui...IG/zbdt03.f(3). That's the source/version and date line, periodt. 🎀