CGELQ2(3)

✨ NAME ✨

okay bestie, this is the CGELQ2(3) page from the Library Functions Manual, and the literal source file it points at is:

/home/abuild/rpmbuild/BUILD/lapack-
static-3.12.0-build/lapack-3.12.0/SRC/cgelq2.f

That hyphen line break is just how the manpage wrapped it — the vibes are immaculate, the path is still the path. 💅

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🎀 SYNOPSIS 🎀

🧚 Functions/Subroutines 🧚

subroutine CGELQ2 (m, n, a, lda, tau, work, info)

CGELQ2 computes the LQ factorization of a general rectangular matrix using an unblocked algorithm. slay. ✨

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💖 FUNCTION/SUBROUTINE DOCUMENTATION 💖

subroutine CGELQ2 (integer m, integer n, complex, dimension( lda, * ) a,
    integer lda, complex, dimension( * ) tau, complex, dimension( * ) work,
    integer info)

CGELQ2 computes the LQ factorization of a general rectangular matrix using an unblocked algorithm. periodt. 🫶

🌸 Purpose 🌸

the actual !> comment says:

!>
!> CGELQ2 computes an LQ factorization of a complex m-by-n matrix A:
!>
!>    A = ( L 0 ) *  Q
!>
!> where:
!>
!>    Q is a n-by-n orthogonal matrix;
!>    L is a lower-triangular m-by-m matrix;
!>    0 is a m-by-(n-m) zero matrix, if m < n.
!>
!>

💅 Parameters 💅

• M — M is INTEGER The number of rows of the matrix A. M >= 0. no cap.
• N — N is INTEGER The number of columns of the matrix A. N >= 0. 🌈
• A — A is COMPLEX array, dimension (LDA,N) On entry, the m by n matrix A. On exit, the elements on and below the diagonal of the array contain the m by min(m,n) lower trapezoidal matrix L (L is lower triangular if m <= n); the elements above the diagonal, with the array TAU, represent the unitary matrix Q as a product of elementary reflectors (see Further Details). 🔥
• LDA — LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).
• TAU — TAU is COMPLEX array, dimension (min(M,N)) The scalar factors of the elementary reflectors (see Further Details). 💜
• WORK — WORK is COMPLEX array, dimension (M)
• INFO — INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value 😭

👑 Author 👑

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

🦋 Further Details 🦋

!>
!>  The matrix Q is represented as a product of elementary reflectors
!>
!>     Q = H(k)**H . . . H(2)**H H(1)**H, where k = min(m,n).
!>
!>  Each H(i) has the form
!>
!>     H(i) = I - tau * v * v**H
!>
!>  where tau is a complex scalar, and v is a complex vector with
!>  v(1:i-1) = 0 and v(i) = 1; conjg(v(i+1:n)) is stored on exit in
!>  A(i,i+1:n), and tau in TAU(i).
!>

Definition at line 128 of file cgelq2.f. 📌

✨ Author ✨ (the auto-generated one)

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

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cute little sign-off: this page is serving LAPACK Version 3.12.0 energy, with the footer file /home/abui...RC/cgelq2.f(3) — and ngl, there’s no extra date listed on this page, so I’m not inventing one. 🫶💖🎀