TESTING/LIN/sqrt11.f(3)

🌸 NAME 🌸

Ok so this page is for TESTING/LIN/sqrt11.f, and it lives in the Library Functions Manual. The page title is TESTING/LIN/sqrt11.f(3) if you're keeping track, bestie. 💅

✨ SYNOPSIS ✨

Functions/Subroutines

• real function sqrt11 (m, k, a, lda, tau, work, lwork) — SQRT11 — that's the whole vibe, no extra notes, just the function and its name.

🧚 Function/Subroutine Documentation 🧚

real function sqrt11 (integer m, integer k, real, dimension( lda, * ) a,
    integer lda, real, dimension( * ) tau, real, dimension( lwork ) work,
    integer lwork)

SQRT11 — iconic, lowkey the main character here.

🎀 Purpose:

!>
!> SQRT11 computes the test ratio
!>
!>       || Q'*Q - I || / (eps * m)
!>
!> where the orthogonal matrix Q is represented as a product of
!> elementary transformations.  Each transformation has the form
!>
!>    H(k) = I - tau(k) v(k) v(k)'
!>
!> where tau(k) is stored in TAU(k) and v(k) is an m-vector of the form
!> [ 0 ... 0 1 x(k) ]', where x(k) is a vector of length m-k stored
!> in A(k+1:m,k).
!>

🦋 Parameters 🦋

• M — M is INTEGER. The number of rows of the matrix A.
• K — K is INTEGER. The number of columns of A whose subdiagonal entries contain information about orthogonal transformations.
• A — A is REAL array, dimension (LDA,K). The (possibly partial) output of a QR reduction routine.
• LDA — LDA is INTEGER. The leading dimension of the array A.
• TAU — TAU is REAL array, dimension (K). The scaling factors tau for the elementary transformations as computed by the QR factorization routine.
• WORK — WORK is REAL array, dimension (LWORK).
• LWORK — LWORK is INTEGER. The length of the array WORK. LWORK >= M*M + M.

👑 Author 👑

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

Definition at line 97 of file sqrt11.f.

👑 Author (the auto-generated encore) 👑

Generated automatically by Doxygen for LAPACK from the source code.

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That's it, bestie! Footer vibes: LAPACK, Version 3.12.0, page TESTING/LIN/sqrt11.f(3). The footer doesn't show a date, so no invented date here — just pure version energy. 🫶💖