ZGEQL2(3)

📦 version 3.12.0, in opensuse-leap 16.0

okay so bestie, welcome to zgeql2.f(3) from the Library Functions Manual. it's giving LAPACK core, it's giving unblocked QL factorization, and we're keeping every single detail. no cap. 💅

🌸 NAME 🌸

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/zgeql2.f

✨ SYNOPSIS ✨

🦋 Functions/Subroutines 🦋

  • subroutine ZGEQL2 (m, n, a, lda, tau, work, info) — ZGEQL2 computes the QL factorization of a general rectangular matrix using an unblocked algorithm.

💖 Function/Subroutine Documentation 💖

subroutine ZGEQL2 (integer m, integer n, complex*16, dimension( lda, * ) a,
    integer lda, complex*16, dimension( * ) tau, complex*16, dimension( * )
    work, integer info)

ZGEQL2 computes the QL factorization of a general rectangular matrix using an unblocked algorithm.

✨ Purpose: ✨

ZGEQL2 computes a QL factorization of a complex 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 COMPLEX*16 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 unitary 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 COMPLEX*16 array, dimension (min(M,N)).

The scalar factors of the elementary reflectors (see Further Details).

🍓 WORK

WORK is COMPLEX*16 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**H

where tau is a complex scalar, and v is a complex 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 zgeql2.f.

📜 Author 📜

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okay bestie, that's the whole page 💖 the source/version sign-off is LAPACK Version 3.12.0 and the path /home/abui...RC/zgeql2.f(3). periodt 🫶

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