SGEQL2(3)

✨ SGEQL2(3) — Library Functions Manual ✨

okay so bestie, this is the page for SGEQL2: the unblocked-algorithm girlie who computes a QL factorization of a real m by n matrix. She’s giving linear algebra main character energy, and I’m obsessed. 💅

🌸 NAME 🌸

The exact source file path is:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/sgeql2.f

✨ 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 💖

Full signature, copied exactly:

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. no cap.

🦋 Purpose 🦋

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 🌈

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 footer sign-off: LAPACK, Version 3.12.0, source path /home/abui...RC/sgeql2.f(3). Date? The footer is not giving one, so I’m not inventing it — periodt. 🫶