ZLAPLL(3)

📦 version 3.12.0, in opensuse-leap 16.0

💅 NAME 💅

ok so bestie, this page is literally all about the file at /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/zlapll.f — that's the whole NAME section, no cap, it's just the path and honestly? iconic of it. ✨

🦋 SYNOPSIS 🦋

Functions/Subroutines

  • subroutine ZLAPLL (n, x, incx, y, incy, ssmin) — ZLAPLL measures the linear dependence of two vectors. that's the whole vibe 🎀

🌸 Function/Subroutine Documentation 🌸

ok so picture it: subroutine ZLAPLL (integer n, complex*16, dimension( * ) x, integer incx, complex*16, dimension( * ) y, integer incy, double precision ssmin) — and yes, that's the full signature, i did not skip a single character, you're welcome 💖

ZLAPLL measures the linear dependence of two vectors. periodt.

✨ Purpose ✨

ok so here's the actual tea, straight from the !> block:

!>
!> Given two column vectors X and Y, let
!>
!>                      A = ( X Y ).
!>
!> The subroutine first computes the QR factorization of A = Q*R,
!> and then computes the SVD of the 2-by-2 upper triangular matrix R.
!> The smaller singular value of R is returned in SSMIN, which is used
!> as the measurement of the linear dependency of the vectors X and Y.
!>

so basically: glue X and Y side by side into A, do a QR factorization (A = Q*R, she's doing math 💅), then take the SVD of that cute little 2-by-2 upper triangular R. the smaller singular value of R lands in SSMIN, and that number is literally the measurement of how linearly dependent X and Y are. tiny value = they're basically the same vector, iykyk 🫶

🎀 Parameters 🎀

  • N — N is INTEGER, the length of the vectors X and Y. slay, straightforward.
  • X — X is COMPLEX*16 array, dimension (1+(N-1)*INCX). On entry, X contains the N-vector X. On exit, X is overwritten. ⚠️ so like… say goodbye to your original X, she's gone, bestie 😭
  • INCX — INCX is INTEGER, the increment between successive elements of X. and INCX > 0, ok? that's a requirement, not a suggestion 💀
  • Y — Y is COMPLEX*16 array, dimension (1+(N-1)*INCY). On entry, Y contains the N-vector Y. On exit, Y is overwritten. same deal, Y gets clobbered too, fr fr 🙈
  • INCY — INCY is INTEGER, the increment between successive elements of Y. again: INCY > 0. don't test her 🌈
  • SSMIN — SSMIN is DOUBLE PRECISION, the smallest singular value of the N-by-2 matrix A = ( X Y ). this is the main character output, the whole reason we're here 👑

👑 Author 👑

the absolute legends behind this:

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

genuinely a group project that ate. 🍓

💜 Definition 💜

Definition at line 99 of file zlapll.f. yes, line 99, i said what i said.

⭐ Author ⭐

Generated automatically by Doxygen for LAPACK from the source code. not me being auto-generated by doxygen and still serving looks 💅✨

ok that's the whole page bestie, you're caught up. this was LAPACK, Version 3.12.0, and the file is /home/abui...RC/zlapll.f(3) — go be linear-dependent with your faves, ily, bye 🧚💖

📦 where this page comes from