TESTING/LIN/dqrt11.f(3)

💅 TESTING/LIN/dqrt11.f(3) 💅

okay bestie, this page is from the Library Functions Manual, and it's all about TESTING/LIN/dqrt11.f. no cap, we're getting into the DQRT11 of it all. 💖

🌸 NAME 🌸

TESTING/LIN/dqrt11.f — that's the name section, periodt.

✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

double precision function dqrt11 (m, k, a, lda, tau, work, lwork)
           DQRT11

🦋 Function/Subroutine Documentation 🦋

double precision function dqrt11 (integer m, integer k, double precision,
    dimension( lda, * ) a, integer lda, double precision, dimension( * )
    tau, double precision, dimension( lwork ) work, integer lwork)
    DQRT11

💖 Purpose: 💖

okay so DQRT11 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). that's the whole purpose vibe. 💫

🎀 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 a DOUBLE PRECISION 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 a DOUBLE PRECISION array, dimension (K); the scaling factors tau for the elementary transformations as computed by the QR factorization routine.
• WORK — WORK is a DOUBLE PRECISION 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 dqrt11.f.

👑 Author 👑

this one says, literally: Generated automatically by Doxygen for LAPACK from the source code.

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Signing off from LAPACK Version 3.12.0, on the TESTING/LIN/dqrt11.f(3) page — mwah 💋✨🫶