DSVDCT(3)

📦 version 3.12.0, in opensuse-leap 16.0

💅 DSVDCT(3) — like, the whole page

okay so first things first: this is from the Library Functions Manual, and the page itself lives at /home/abui...IG/dsvdct.f(3) which is honestly the most cursed little path I've ever seen but we move 💖

It's a LAPACK thing, it's a subroutine, and yes bestie it counts things. That's the whole vibe. Let's get into it ✨

🎀 SYNOPSIS

Functions/Subroutines

  • subroutine DSVDCT (n, s, e, shift, num) — that's her, that's the girl, and her whole personality is DSVDCT

🌸 Function/Subroutine Documentation

subroutine DSVDCT (integer n, double precision, dimension( * ) s, double precision, dimension( * ) e, double precision shift, integer num)

DSVDCT ✨ (yes she gets her own line, she's the main character)

🦋 Purpose

!> DSVDCT counts the number NUM of eigenvalues of a 2*N by 2*N !> tridiagonal matrix T which are less than or equal to SHIFT. T is !> formed by putting zeros on the diagonal and making the off-diagonals !> equal to S(1), E(1), S(2), E(2), ... , E(N-1), S(N). If SHIFT is !> positive, NUM is equal to N plus the number of singular values of a !> bidiagonal matrix B less than or equal to SHIFT. Here B has diagonal !> entries S(1), ..., S(N) and superdiagonal entries E(1), ... E(N-1). !> If SHIFT is negative, NUM is equal to the number of singular values !> of B greater than or equal to -SHIFT. !> !> See W. Kahan , Report CS41, Computer Science Dept., Stanford University, !> July 21, 1966

so basically: you hand her a SHIFT, she hands you back how many eigenvalues of T are <= SHIFT. T is that 2*N by 2*N tridiagonal situation where the diagonal is all zeros and the off-diagonals are S(1), E(1), S(2), E(2), ... , E(N-1), S(N). iconic behaviour honestly 👑

and the cute part: if SHIFT is positive, NUM is N plus the number of singular values of a bidiagonal matrix B that are <= SHIFT — where B has diagonal entries S(1), ..., S(N) and superdiagonal entries E(1), ... E(N-1). if SHIFT is negative, NUM is the number of singular values of B that are >= -SHIFT. slay 🫶

💀 real talk: the source says these exact words, so I'm giving you these exact words. don't come for me, I'm just the messenger girlie.

💜 Parameters

  • N — it's an INTEGER, and it's the dimension of the bidiagonal matrix B. that's it, that's the tea 🍓
  • S — a DOUBLE PRECISION array, dimension (N), holding the diagonal entries of the bidiagonal matrix B. she's the main diagonal, she's booked and busy ✨
  • E — a DOUBLE PRECISION array of dimension (N-1), holding the superdiagonal entries of the bidiagonal matrix B. note the N-1 bestie, superdiagonals are always one shorter, no cap 💅
  • SHIFT — a plain old DOUBLE PRECISION. it's the shift, and it does exactly what Purpose said it does. no notes 🔥
  • NUM — an INTEGER, and it's the number of eigenvalues of T that are less than or equal to SHIFT. the output. the moment. the payoff 🎀

🧚 Author

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

(icons, the lot of them 👑)

📍 Definition at line 86 of file dsvdct.f.

🌈 Author (again, yes really)

Generated automatically by Doxygen for LAPACK from the source code. so nobody hand-wrote this page, a robot did it, and honestly? she ate 🤖💖

⭐ and that's the whole page, bestie. no lurking options, no environment variables, no exit statuses — just a counting subroutine and her friends.

sign-off time 🎀 this was LAPACK, Version 3.12.0, dated /home/abui...IG/dsvdct.f(3), and I hope you love her as much as I do 💜🦋✨

📦 where this page comes from