CGEQL2(3)

🌸 NAME 🌸

This is CGEQL2(3) — page title cgeql2.f(3) — from the Library Functions Manual, bestie. 💅 The file path is literally:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/cgeql2.f

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💫 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. ✨

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🛠️ 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. No cap. 💖

✨ Purpose ✨

CGEQL2 computes a QL factorization of a complex m by n matrix A:

!>
!> CGEQL2 computes a QL factorization of a complex m by n matrix A:
!> A = Q * L.
!>

🌈 Parameters 🌈

• M — M is INTEGER. It’s the number of rows of the matrix A, and M >= 0. 🫶
• N — N is INTEGER. It’s the number of columns of the matrix A, and N >= 0. 🦋
• A — A is COMPLEX array, dimension (LDA,N). On entry, it’s 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). Iconic behavior, honestly. 👑
• LDA — LDA is INTEGER. It’s the leading dimension of the array A, and LDA >= max(1,M). 💅
• TAU — TAU is COMPLEX array, dimension (min(M,N)). These are the scalar factors of the elementary reflectors (see Further Details). 🎀
• WORK — WORK is COMPLEX array, dimension (N). That’s the whole work vibe. 🍓
• 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 (generated) 🤖

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

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Sign-off bestie: this footer says LAPACK Version 3.12.0 and the page path is /home/abui...RC/cgeql2.f(3). No separate date is printed in this footer, so no invented date — just the source/version vibe check. Periodt. 💅✨