DGEQL2(3)

💖 DGEQL2(3) 💖

okay bestie, welcome to DGEQL2(3) from the LAPACK manual — yes, the QL factorization one, and we're keeping every detail, no cap. 🫶 This is the group chat where linear algebra finally gets main character energy. 💅

🎀 NAME 🎀

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/dgeql2.f

🦋 SYNOPSIS 🦋

Functions/Subroutines

       subroutine DGEQL2 (m, n, a, lda, tau, work, info)
           DGEQL2 computes the QL factorization of a general rectangular matrix
           using an unblocked algorithm.

💜 Function/Subroutine Documentation 💜

Here's the full signature, copied exactly so nothing gets lost in the group chat:

   subroutine DGEQL2 (integer m, integer n, double precision, dimension( lda, *
       ) a, integer lda, double precision, dimension( * ) tau, double
       precision, dimension( * ) work, integer info)

And the energy of it? DGEQL2 computes the QL factorization of a general rectangular matrix using an unblocked algorithm. ✨

🌸 Purpose 🌸

DGEQL2 computes a QL factorization of a real m by n matrix A:

A = Q * L.

That's the vibe: A gets factored into Q and L, with the unblocked algorithm doing its thing. 💫

🍓 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, 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 DOUBLE PRECISION array, dimension (min(M,N)). The scalar factors of the elementary reflectors (see Further Details).

WORK

WORK is DOUBLE PRECISION 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 dgeql2.f.

🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code.

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LAPACK Version 3.12.0 — source: /home/abui...RC/dgeql2.f(3). Stay slay, bestie 💖