TESTING/EIG/dbdt03.f(3)

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version 3.12.1 · 3 versions
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🎀 NAME 🎀

okay bestie, this is the manual page for TESTING/EIG/dbdt03.f(3) from the Library Functions Manual — and the star of the show is TESTING/EIG/dbdt03.f itself. 💅✨

🦋 SYNOPSIS 🦋

🧚 Functions/Subroutines 🧚

subroutine dbdt03 (uplo, n, kd, d, e, u, ldu, s, vt, ldvt, work, resid)
    DBDT03

💖 Function/Subroutine Documentation 💖

subroutine dbdt03 (character uplo, integer n, integer kd, double precision, dimension( * ) d, double precision, dimension( * ) e, double precision, dimension( ldu, * ) u, integer ldu, double precision, dimension( * ) s, double precision, dimension( ldvt, * ) vt, integer ldvt, double precision, dimension( * ) work, double precision resid)

DBDT03 — that’s the label, no cap. 🫶

🌸 Purpose 🌸

DBDT03 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. 💖

🍓 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 — DOUBLE PRECISION 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 — DOUBLE PRECISION 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 — DOUBLE PRECISION array, dimension (2*N). 🧰
  • RESID — DOUBLE PRECISION. 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 dbdt03.f. 📌

🧚 Author 🧚

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okay that’s the whole page, bestie! This was LAPACK Version 3.12.0, on the TESTING/EIG/dbdt03.f(3) page — mwah! 💋💖

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