ZGEQLF(3)

💅 zgeqlf.f(3) — Library Functions Manual 🌸

okay bestie, this is the page for the Fortran subroutine ZGEQLF, and the manual name is literally Library Functions Manual. The header path is /home/abui...RC/zgeqlf.f(3), so you already know she's a little extra. 💖

💖 NAME 💖

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

✨ SYNOPSIS ✨

🌟 Functions/Subroutines

• subroutine ZGEQLF (m, n, a, lda, tau, work, lwork, info) — ZGEQLF

🦋 Function/Subroutine Documentation 🦋

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

And the routine name is ZGEQLF — main character energy, obviously. 💅

🎯 Purpose

!>
!> ZGEQLF 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 (MAX(1,LWORK)). On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
• LWORK — LWORK is INTEGER. The dimension of the array WORK. LWORK >= max(1,N). For optimum performance LWORK >= N*NB, where NB is the optimal blocksize.
  • If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA.
• 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 137

Definition at line 137 of file zgeqlf.f.

🤖 Author

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and that's the vibe check, bestie 💖 this page comes from LAPACK Version 3.12.0 and points at /home/abui...RC/zgeqlf.f(3) in the footer. auto-generated, but still iconic. periodt. 🎀✨