TESTING/LIN/dlqt02.f(3)

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version 3.12.1 · 2 versions
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okay so you clicked into TESTING/LIN/dlqt02.f(3), and yes bestie, that's the whole manual-page title vibe. The manual is the Library Functions Manual, and this is a LAPACK test-routine page. Buckle up — it's giving Fortran cutie with a very specific job. 🦋

🌸 NAME 🌸

TESTING/LIN/dlqt02.f

✨ SYNOPSIS ✨

Functions/Subroutines

subroutine dlqt02 (m, n, k, a, af, q, l, lda, tau, work, lwork, rwork,
    result)
    DLQT02

💖 Function/Subroutine Documentation 💖

subroutine dlqt02

subroutine dlqt02 (integer m, integer n, integer k, double precision,
    dimension( lda, * ) a, double precision, dimension( lda, * ) af, double
    precision, dimension( lda, * ) q, double precision, dimension( lda, * )
    l, integer lda, double precision, dimension( * ) tau, double precision,
    dimension( lwork ) work, integer lwork, double precision, dimension( * )
    rwork, double precision, dimension( * ) result)
    DLQT02

Purpose

okay so this routine is basically a vibe check for DORGLQ, which generates an m-by-n matrix Q with orthonormal rows and is defined as the product of k elementary reflectors. 🫶

Given the LQ factorization of an m-by-n matrix A, DLQT02 generates the orthogonal matrix Q defined by the factorization of the first k rows of A; it compares L(1:k,1:m) with A(1:k,1:n)*Q(1:m,1:n)', and checks that the rows of Q are orthonormal. No cap, that's the whole purpose. 💅

Parameters

Here's the whole cast, bestie — every single one stays:

  • M — INTEGER. The number of rows of the matrix Q to be generated. M >= 0. ✨
  • N — INTEGER. The number of columns of the matrix Q to be generated. N >= M >= 0. 💖
  • K — INTEGER. The number of elementary reflectors whose product defines the matrix Q. M >= K >= 0. 🎀
  • A — DOUBLE PRECISION array, dimension (LDA,N). The m-by-n matrix A which was factorized by DLQT01. 🌸
  • AF — DOUBLE PRECISION array, dimension (LDA,N). Details of the LQ factorization of A, as returned by DGELQF. See DGELQF for further details. 🦋
  • Q — DOUBLE PRECISION array, dimension (LDA,N). That's the array — no extra lore in this line. 💅
  • L — DOUBLE PRECISION array, dimension (LDA,M). Same energy: type and dimensions, and that's it. 💜
  • LDA — INTEGER. The leading dimension of the arrays A, AF, Q and L. LDA >= N. 🔥
  • TAU — DOUBLE PRECISION array, dimension (M). The scalar factors of the elementary reflectors corresponding to the LQ factorization in AF. 🌈
  • WORK — DOUBLE PRECISION array, dimension (LWORK). Literally the work array, doing its thing. ⭐
  • LWORK — INTEGER. The dimension of the array WORK. 🧚
  • RWORK — DOUBLE PRECISION array, dimension (M). Another array, another slay. 💀
  • RESULT — DOUBLE PRECISION array, dimension (2). The test ratios:
    • RESULT(1) = norm( L - A*Q' ) / ( N * norm(A) * EPS )
    • RESULT(2) = norm( I - Q*Q' ) / ( N * EPS )

👑 Author 👑

  • Univ. of Tennessee
  • Univ. of California Berkeley
  • Univ. of Colorado Denver
  • NAG Ltd.

Definition at line 133 of file dlqt02.f.

👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code.

okay that's the whole page, bestie 🫶 — source/version: LAPACK Version 3.12.0; date: the footer doesn't hand one over, so no fake date from me, periodt. 💅✨

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