/home/abui.../dgelqt3.f(3)

💅 dgelqt3.f(3) 💅

okay so this page is from the Library Functions Manual, and it’s literally all about /home/abui.../dgelqt3.f(3). bestie, we’re diving into a Fortran subroutine that does LQ factorization, and yes it’s giving main-character linear algebra energy. ✨

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🌸 NAME 🌸

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/dgelqt3.f — that’s the file, no cap. 🫶

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✨ SYNOPSIS ✨

🎀 Functions/Subroutines 🎀

• recursive subroutine DGELQT3 (m, n, a, lda, t, ldt, info) — DGELQT3 recursively computes a LQ factorization of a general real or complex matrix using the compact WY representation of Q. 💖

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🌟 Function/Subroutine Documentation 🌟

🦋 recursive subroutine DGELQT3 🦋

recursive subroutine DGELQT3 (integer m, integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( ldt, * ) t, integer ldt, integer info)

DGELQT3 recursively computes a LQ factorization of a general real or complex matrix using the compact WY representation of Q. periodt. 💅

🔥 Purpose 🔥

!>
!> DGELQT3 recursively computes a LQ factorization of a real 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. The number of rows of the matrix A. M =< N. 💖
• N — N is INTEGER. The number of columns of the matrix A. N >= 0. ✨
• A — A is DOUBLE PRECISION array, dimension (LDA,N). On entry, the real 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. The leading dimension of the array A. LDA >= max(1,M). 💅
• T — T is DOUBLE PRECISION array, dimension (LDT,N). 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. The leading dimension of the array T. 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 dgelqt3.f. 📌

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💀 Author 💀

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

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okay bestie, that’s the whole page 💖✨ the source/version vibe at the very end is LAPACK, Version 3.12.0, and the page is /home/abui.../dgelqt3.f(3). slay, go forth and factorize responsibly. 🎀🦋💅