SRC/sgelq2.f(3)

🌸 NAME 🌸

SRC/sgelq2.f — okay bestie, this is the page for SRC/sgelq2.f(3) from the Library Functions Manual, and it's all about one very specific LAPACK subroutine. 💖

✨ 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. 🔥

🛠️ 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. 💅

💫 Purpose: 💫

Okay so 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 📋

• 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 👑

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

🔍 Further Details 🔍

Here's the tea: 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.

🌈 Author 🌈

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

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Bye bestie 💜 — that's the whole page. The footer vibe is LAPACK Version 3.12.0 and SRC/sgelq2.f(3); no separate date is shown, so I'm not inventing one. 🫶✨