TESTING/EIG/sbdt03.f(3)

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version 3.12.1 · 3 versions
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✨ NAME ✨

Okay bestie, this is the page for TESTING/EIG/sbdt03.f in the Library Functions Manual — yes, the whole TESTING/EIG/sbdt03.f(3) situation. It’s giving “LAPACK testing routine with main character energy,” lowkey. 💅

✨ SYNOPSIS ✨

✨ Functions/Subroutines ✨

  • subroutine sbdt03 (uplo, n, kd, d, e, u, ldu, s, vt, ldvt, work, resid) — SBDT03

Also, here’s the exact signature from the docs, no cap:

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 — that’s the routine name, periodt. ✨

✨ Function/Subroutine Documentation ✨

✨ Purpose ✨

Bestie, here’s the whole point: 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 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. Literally the whole vibe check. 🌸

✨ Parameters ✨

  • UPLO — UPLO is CHARACTER*1. Specifies whether the matrix B is upper or lower bidiagonal. = 'U': Upper bidiagonal. = 'L': Lower bidiagonal. 👑
  • N — N is INTEGER. The order of the matrix B. 💖
  • KD — KD is 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. That’s the rule, fr fr. ✨
  • 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'. 🦋
  • U — U is REAL array, dimension (LDU,N). The n by n orthogonal matrix U in the reduction B = U'*A*P. 💜
  • LDU — LDU is INTEGER. The leading dimension of the array U. LDU >= max(1,N). 🌟
  • S — S is REAL array, dimension (N). The singular values from the SVD of B, sorted in decreasing order. Obsessed with a sorted list ngl. 🔥
  • VT — VT is REAL array, dimension (LDVT,N). The n by n orthogonal matrix V' in the reduction B = U * S * 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(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. 🤖✨

Cute sign-off time: this page is from LAPACK Version 3.12.0 and it’s labeled TESTING/EIG/sbdt03.f(3). No date on this footer, so we’re not inventing one — we’re just saying byeee bestie! 💖🦋

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