SBDT03(3)

💅 SBDT03(3) 💅

okay so bestie, this is the Library Functions Manual page for SBDT03(3), and the manual name it's filed under near the top is literally the path to the source file. The vibe is very "LAPACK test routine, but make it cute." No cap. ✨

🌸 NAME 🌸

The NAME line is this exact source path:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/EIG/sbdt03.f

That's it — that's the name. Iconic file path energy. 🎀

🦋 SYNOPSIS 🦋

   Functions/Subroutines
       subroutine SBDT03 (uplo, n, kd, d, e, u, ldu, s, vt, ldvt, work, resid)
           SBDT03

🦋 Function/Subroutine Documentation 🦋

Here's the full signature, copied exactly because bestie we do not mess with Fortran:

   subroutine SBDT03 (character uplo, integer n, integer kd, real, dimension( *
       ) d, real, dimension( * ) e, real, dimension( ldu, * ) u, integer ldu,
       real, dimension( * ) s, real, dimension( ldvt, * ) vt, integer ldvt,
       real, dimension( * ) work, real resid)
       SBDT03

✨ Purpose ✨

SBDT03 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 that checks 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 purpose, and it ate. 💅

🎀 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 — REAL array, dimension (N). The n diagonal elements of the bidiagonal matrix B.
• E — 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'.
• U — REAL 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 — REAL array, dimension (N). The singular values from the SVD of B, sorted in decreasing order.
• VT — REAL 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 — REAL array, dimension (2*N).
• RESID — REAL. The test ratio: norm(B - U * S * V') / ( n * norm(A) * EPS ).

👑 Author 👑

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

Definition at line 133 of file sbdt03.f.

🌟 Author 🌟

Generated automatically by Doxygen for LAPACK from the source code.

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💖 cute sign-off: the footer is giving LAPACK version 3.12.0 and the path /home/abui...IG/sbdt03.f(3) — no date listed, just version-and-path energy. mwah 💋