CLAPLL(3)

💖 CLAPLL(3) 💖

Welcome to the Library Functions Manual page for CLAPLL, bestie — this is the LAPACK linear-dependence detector and it's lowkey iconic. ✨

💖 NAME 💖

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/clapll.f

That's the source file this page is serving up. 🫶

✨ SYNOPSIS ✨

🧸 Functions/Subroutines 🧸

• subroutine CLAPLL (n, x, incx, y, incy, ssmin) — CLAPLL measures the linear dependence of two vectors. 💅

🎀 Function/Subroutine Documentation 🎀

🦋 subroutine CLAPLL 🦋

subroutine CLAPLL (integer n, complex, dimension( * ) x, integer incx,
    complex, dimension( * ) y, integer incy, real ssmin)

CLAPLL measures the linear dependence of two vectors. No cap, that's the whole gig. 🌸

💖 Purpose 💖

Given two column vectors X and Y, let:

!>
!> 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 yeah: it first computes the QR factorization of A = Q*R, then computes the SVD of the 2-by-2 upper triangular matrix R. The smaller singular value of R comes back in SSMIN, and that's the measurement of the linear dependency of X and Y. Slay. 🔥

🌸 Parameters 🌸

• N — N is INTEGER; it's the length of the vectors X and Y. 🎀
• X — X is COMPLEX array, dimension (1+(N-1)*INCX). On entry, X contains the N-vector X; on exit, X is overwritten. 🙈
• INCX — INCX is INTEGER; the increment between successive elements of X. INCX > 0. 💅
• Y — Y is COMPLEX array, dimension (1+(N-1)*INCY). On entry, Y contains the N-vector Y; on exit, Y is overwritten. 🦋
• INCY — INCY is INTEGER; the increment between successive elements of Y. INCY > 0. ✨
• SSMIN — SSMIN is REAL; the smallest singular value of the N-by-2 matrix A = ( X Y ). 👑

👑 Author 👑

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

📌 Definition 📌

Definition at line 99 of file clapll.f. 🫶

🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code. 💖

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And we're out, bestie: the footer's date isn't listed, but it does say LAPACK, Version 3.12.0, and the source/version path /home/abui...RC/clapll.f(3). Periodt. 💅✨