SRC/cgeql2.f(3)

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💖 SRC/cgeql2.f(3) 💖 — Library Functions Manual 🌈

🌸 NAME 🌸

SRC/cgeql2.f — bestie, this is the page for the cgeql2 subroutine, and it’s all about computing the QL factorization of a general rectangular matrix using an unblocked algorithm. Slay. 💅

✨ SYNOPSIS ✨

🎀 Functions/Subroutines 🎀

  • subroutine cgeql2 (m, n, a, lda, tau, work, info) — CGEQL2 computes the QL factorization of a general rectangular matrix using an unblocked algorithm. 💖

💖 Function/Subroutine Documentation 💖

subroutine cgeql2 (integer m, integer n, complex, dimension( lda, * ) a,
       integer lda, complex, dimension( * ) tau, complex, dimension( * ) work,
       integer info)

CGEQL2 computes the QL factorization of a general rectangular matrix using an unblocked algorithm.

🦋 Purpose 🦋

okay so here’s the main character moment: CGEQL2 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 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 array, dimension (min(M,N)); the scalar factors of the elementary reflectors (see Further Details). 🎀
  • WORK — WORK is COMPLEX 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 cgeql2.f.

👑 Author 👑

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