TESTING/LIN/cqrt11.f(3)

💅 TESTING/LIN/cqrt11.f 💅

Okay so this page is from the Library Functions Manual, and it’s all about cqrt11 — yes, bestie, lowercase because that’s how Fortran rolls. 💖 This is the TESTING/LIN corner of LAPACK, and this routine is here to compute a test ratio. Slay.

✨ SYNOPSIS ✨

🛠️ Functions/Subroutines 🛠️

• real function cqrt11 (m, k, a, lda, tau, work, lwork) — CQRT11

💖 Function/Subroutine Documentation 💖

   real function cqrt11 (integer m, integer k, complex, dimension( lda, * ) a,
       integer lda, complex, dimension( * ) tau, complex, dimension( lwork )
       work, integer lwork)

CQRT11

🎯 Purpose

CQRT11 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 COMPLEX 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 array, dimension (K); the scaling factors tau for the elementary transformations as computed by the QR factorization routine.
• WORK — WORK is COMPLEX 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 cqrt11.f.

💖 Author 💖

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💖 Sign-off, bestie: LAPACK Version 3.12.0, page TESTING/LIN/cqrt11.f(3), auto-generated by Doxygen for LAPACK from the source code. Mwah! 💖