/home/abui.../zgelqt3.f(3)

okay so bestie, you're on the <pink>/home/abui.../zgelqt3.f(3)</pink> page from the Library Functions Manual — and it's giving recursive LQ-factorization main character energy. ZGELQT3 is here to slay. 💅

🎀 NAME 🎀

The NAME section is literally just this source path, no cap:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/zgelqt3.f

✨ SYNOPSIS ✨

🫶 Functions/Subroutines 🫶

• recursive subroutine ZGELQT3 (m, n, a, lda, t, ldt, info) — ZGELQT3 recursively computes a LQ factorization of a general real or complex matrix using the compact WY representation of Q. 🦋

💅 Function/Subroutine Documentation 💅

🌸 recursive subroutine ZGELQT3 🌸

recursive subroutine ZGELQT3 (integer m, integer n, complex*16, dimension(
     lda, * ) a, integer lda, complex*16, dimension( ldt, * ) t, integer ldt,
     integer info)

ZGELQT3 recursively computes a LQ factorization of a general real or complex matrix using the compact WY representation of Q. 🫶

🦋 Purpose 🦋

!>
!> ZGELQT3 recursively computes a LQ factorization of a complex M-by-N
!> matrix A, using the compact WY representation of Q.
!>
!> Based on the algorithm of Elmroth and Gustavson,
!> IBM J. Res. Develop. Vol 44 No. 4 July 2000.
!>

🍓 Parameters 🍓

• M — M is INTEGER; it's the number of rows of the matrix A, and the condition is M =< N. 🌈
• N — N is INTEGER; it's the number of columns of the matrix A, and N >= 0. ✨
• A — A is COMPLEX*16 array, dimension (LDA,N). On entry, it's the complex M-by-N matrix A. On exit, the elements on and below the diagonal contain the N-by-N lower triangular matrix L; the elements above the diagonal are the rows of V. See below for further details. 💖
• LDA — LDA is INTEGER; it's the leading dimension of the array A, with LDA >= max(1,M). 🎀
• T — T is COMPLEX*16 array, dimension (LDT,N). It's the N-by-N upper triangular factor of the block reflector. The elements on and above the diagonal contain the block reflector T; the elements below the diagonal are not used. See below for further details. 🦋
• LDT — LDT is INTEGER; it's the leading dimension of the array T, with LDT >= max(1,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 V stores the elementary reflectors H(i) in the i-th row
!>  above the diagonal. For example, if M=5 and N=3, the matrix V is
!>
!>               V = (  1  v1 v1 v1 v1 )
!>                   (     1  v2 v2 v2 )
!>                   (     1  v3 v3 v3 )
!>
!>
!>  where the vi's represent the vectors which define H(i), which are returned
!>  in the matrix A.  The 1's along the diagonal of V are not stored in A.  The
!>  block reflector H is then given by
!>
!>               H = I - V * T * V**T
!>
!>  where V**T is the transpose of V.
!>
!>  For details of the algorithm, see Elmroth and Gustavson (cited above).
!>

Definition at line 130 of file zgelqt3.f.

🌟 Author 🌟

Generated automatically by Doxygen for LAPACK from the source code.

---

okay bestie, that's the whole page 💖✨ — the footer says LAPACK Version 3.12.0, and the page path is /home/abui.../zgelqt3.f(3). Slay and bye! 🎀🦋💅