SRC/sgeql2.f(3)

💅 SRC/sgeql2.f(3) — Library Functions Manual 💅

okay so welcome to the SRC/sgeql2.f(3) page from the Library Functions Manual, bestie. This is the manual entry for the sgeql2 subroutine, and yes, we're gonna get into the QL factorization tea. ✨

🌸 NAME 🌸

SRC/sgeql2.f — that's the page name, no cap. 🫶

🎀 SYNOPSIS 🎀

✨ Functions/Subroutines ✨

• subroutine sgeql2 (m, n, a, lda, tau, work, info) — SGEQL2 computes the QL factorization of a general rectangular matrix using an unblocked algorithm. 🔥

🦋 Function/Subroutine Documentation 🦋

🌟 subroutine sgeql2 (integer m, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( * ) tau, real, dimension( * ) work, integer info) 🌟

SGEQL2 computes the QL factorization of a general rectangular matrix using an unblocked algorithm. That's the whole vibe of this routine. 💖

🧚 Purpose 🧚

The source comment says it plain: SGEQL2 computes a QL factorization of a real m by n matrix A:

!>
!> SGEQL2 computes a QL factorization of a real m by n matrix A:
!> A = Q * L.
!>

🍓 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 REAL array, dimension (LDA,N). On entry, the m by n matrix A. On exit, if m >= n, the lower triangle of the subarray A(m-n+1:m,1:n) contains the n by n lower triangular matrix L; if m <= n, the elements on and below the (n-m)-th superdiagonal contain the m by n lower trapezoidal matrix L; the remaining elements, 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 REAL array, dimension (min(M,N)). The scalar factors of the elementary reflectors (see Further Details). 🎀
• WORK — WORK is REAL array, dimension (N). 🛠️
• 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 🌈

Here's the exact source-comment block for the reflector math, because we do not paraphrase equations in this group chat:

!>
!>  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(m-k+i+1:m) = 0 and v(m-k+i) = 1; v(1:m-k+i-1) is stored on exit in
!>  A(1:m-k+i-1,n-k+i), and tau in TAU(i).
!>

Definition at line 122 of file sgeql2.f. 📍

🌟 Author 🌟

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

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Cute sign-off, bestie: source/version is LAPACK Version 3.12.0, the page is SRC/sgeql2.f(3), and the footer shows no date, so I'm not inventing one — periodt. 💅✨