DGELQ2(3)

💅 DGELQ2(3) — Library Functions Manual ✨

okay bestie, this page is from the Library Functions Manual and it's giving "unblocked LQ factorization realness." No cap, every flag, equation, path, and author is staying exactly where it belongs. 🫶

🎀 NAME 🎀

The NAME section is literally this path, line-wrapped exactly like the original (yes, the whole NAME is a file path, iconic):

/home/abuild/rpmbuild/BUILD/lapack-
static-3.12.0-build/lapack-3.12.0/SRC/dgelq2.f

🌸 SYNOPSIS 🌸

✨ Functions/Subroutines ✨

• subroutine DGELQ2 (m, n, a, lda, tau, work, info) — DGELQ2 computes the LQ factorization of a general rectangular matrix using an unblocked algorithm.

🦋 Function/Subroutine Documentation 🦋

Here's the full signature, bestie, with every type and dimension exactly as given:

subroutine DGELQ2 (integer m, integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) tau, double precision, dimension( * ) work, integer info)

DGELQ2 computes the LQ factorization of a general rectangular matrix using an unblocked algorithm.

💖 Purpose 💖

The original purpose block has those Doxygen !> comment markers, so here's the exact code-comment tea:

!>
!> DGELQ2 computes an LQ factorization of a real 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.
!>
!>

Translation, bestie: it factors a real m-by-n matrix A as A = ( L 0 ) * Q. Q is n-by-n orthogonal, L is lower-triangular m-by-m, and 0 is the m-by-(n-m) zero matrix when m < n. Slay. 💅

🌈 Parameters 🌈

• M — M is INTEGER. The number of rows of the matrix A. M >= 0.
• N — N is INTEGER. The number of columns of the matrix A. N >= 0.
• A — A is DOUBLE PRECISION 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 orthogonal 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 DOUBLE PRECISION array, dimension (min(M,N)). The scalar factors of the elementary reflectors (see Further Details).
• WORK — WORK is DOUBLE PRECISION 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(2) H(1), where k = min(m,n).

Each H(i) has the form:

H(i) = I - tau * v * v**T

where tau is a real scalar, and v is a real vector with v(1:i-1) = 0 and v(i) = 1; 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 dgelq2.f.

📜 Author (the generated one) 📜

Generated automatically by Doxygen for LAPACK from the source code.

---

okay that's the whole page, bestie. The footer energy is LAPACK Version 3.12.0 and /home/abui...RC/dgelq2.f(3); no date line in the footer, so that's the full sign-off 💖✨🫶