SGELQ2(3)

💅 SGELQ2(3) 💅

okay bestie, welcome to the Library Functions Manual page for SGELQ2(3) — yes, the header has that title and manual name folded in, and the abbreviated path up top is /home/abui...RC/sgelq2.f(3). We're about to get into an LQ factorization, and it's lowkey iconic. 🦋

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✨ NAME ✨

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/sgelq2.f — that's it, that's the NAME section. The full source path is doing main character energy, and this page is for the SGELQ2 routine, which computes the LQ factorization of a general rectangular matrix using an unblocked algorithm. Slay. 💅

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🌸 SYNOPSIS 🌸

Functions/Subroutines

subroutine SGELQ2 (m, n, a, lda, tau, work, info)

SGELQ2 computes the LQ factorization of a general rectangular matrix using an unblocked algorithm. Periodt. ✨

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🦋 Function/Subroutine Documentation 🦋

subroutine SGELQ2 (integer m, integer n, real, dimension( lda, * ) a,
       integer lda, real, dimension( * ) tau, real, dimension( * ) work,
       integer info)

SGELQ2 computes the LQ factorization of a general rectangular matrix using an unblocked algorithm. Okay so now we're in the actual documentation, and it's giving very precise. 🎀

🎀 Purpose 🎀

SGELQ2 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.

💖 Parameters 💖

The parameter lineup, in order, no skipping bestie:

• 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, 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 REAL array, dimension (min(M,N)); the scalar factors of the elementary reflectors (see Further Details). 💖
• WORK — WORK is REAL array, dimension (M). 🎀
• INFO — INFO is INTEGER; = 0: successful exit; < 0: if INFO = -i, the i-th argument had an illegal value. 💀

👑 Author 👑

Shoutout to the author squad:

• 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 sgelq2.f. 📌

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👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code.

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okay bestie, that's the whole page. The footer/source vibes are: LAPACK, Version 3.12.0, and the path /home/abui...RC/sgelq2.f(3) — date/version slot included, no cap. Mwah 💋✨