TESTING/LIN/zqrt11.f(3)

🌸 NAME 🌸

TESTING/LIN/zqrt11.f — okay bestie, you found the Library Functions Manual page for TESTING/LIN/zqrt11.f, and it’s giving “Doxygen made a whole little shrine for ZQRT11” energy 💅✨

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✨ SYNOPSIS ✨

🎀 Functions/Subroutines 🎀

• double precision function zqrt11 (m, k, a, lda, tau, work, lwork) — ZQRT11

💖 Function/Subroutine Documentation 💖

double precision function zqrt11 (integer m, integer k, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) tau, complex*16, dimension( lwork ) work, integer lwork)

ZQRT11

🔥 Purpose 🔥

okay so ZQRT11 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). Lowkey iconic math behavior 🧚💜

🫶 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 COMPLEX*16 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 COMPLEX*16 array, dimension (K); the scaling factors tau for the elementary transformations as computed by the QR factorization routine.
• WORK — WORK is COMPLEX*16 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 zqrt11.f.

🦋 Author 🦋

Generated automatically by Doxygen for LAPACK from the source code.

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and that’s the whole vibe, bestie: TESTING/LIN/zqrt11.f(3) from LAPACK Version 3.12.0 — no cap, that’s the footer sign-off 💅💖