TESTING/LIN/drqt02.f(3)

💖 NAME 💖

This is the TESTING/LIN/drqt02.f(3) page, straight out of the Library Functions Manual — and yes bestie, we're looking at the Fortran test routine drqt02. It's giving deep-LAPACK-testing main character energy, no cap. 💅

✨ SYNOPSIS ✨

🎀 Functions/Subroutines 🎀

subroutine drqt02 (m, n, k, a, af, q, r, lda, tau, work, lwork, rwork, result)

The function is DRQT02. Periodt.

🌸 Function/Subroutine Documentation 🌸

subroutine drqt02 (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, * ) r, integer lda, double precision, dimension( * ) tau, double precision, dimension( lwork ) work, integer lwork, double precision, dimension( * ) rwork, double precision, dimension( * ) result)

DRQT02, iconic. ✨

🦋 Purpose: 🦋

Okay so DRQT02 tests DORGRQ, which generates an m-by-n matrix Q with orthonormal rows that is defined as the product of k elementary reflectors.

Given the RQ factorization of an m-by-n matrix A, DRQT02 generates the orthogonal matrix Q defined by the factorization of the last k rows of A; it compares R(m-k+1:m,n-m+1:n) with A(m-k+1:m,1:n)*Q(n-m+1:n,1:n)', and checks that the rows of Q are orthonormal. Lowkey a whole vibe check for Q. 🦋

💅 Parameters 💅

• M — M is INTEGER; the number of rows of the matrix Q to be generated. M >= 0.
• N — N is INTEGER; the number of columns of the matrix Q to be generated. N >= M >= 0.
• K — K is INTEGER; the number of elementary reflectors whose product defines the matrix Q. M >= K >= 0.
• A — A is DOUBLE PRECISION array, dimension (LDA,N); the m-by-n matrix A which was factorized by DRQT01.
• AF — AF is DOUBLE PRECISION array, dimension (LDA,N); details of the RQ factorization of A, as returned by DGERQF. See DGERQF for further details.
• Q — Q is DOUBLE PRECISION array, dimension (LDA,N).
• R — R is DOUBLE PRECISION array, dimension (LDA,M).
• LDA — LDA is INTEGER; the leading dimension of the arrays A, AF, Q and L. LDA >= N.
• TAU — TAU is DOUBLE PRECISION array, dimension (M); the scalar factors of the elementary reflectors corresponding to the RQ factorization in AF.
• WORK — WORK is DOUBLE PRECISION array, dimension (LWORK).
• LWORK — LWORK is INTEGER; the dimension of the array WORK.
• RWORK — RWORK is DOUBLE PRECISION array, dimension (M).
• RESULT — RESULT is DOUBLE PRECISION array, dimension (2); the test ratios:
  • RESULT(1) = norm( R - 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 134 of file drqt02.f.

🌈 Author 🌈

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Footer flex: LAPACK Version 3.12.0, page TESTING/LIN/drqt02.f(3), no date listed — just version info and immaculate test-routine energy. Mwah 💋✨