TESTING/LIN/dqrt02.f(3)

okay so bestie, welcome to TESTING/LIN/dqrt02.f(3) — this is the Library Functions Manual moment, and we're getting into the Fortran test-subroutine of it all. 💖✨

🎀 NAME 🎀

TESTING/LIN/dqrt02.f — literally the page name, periodt. 👑

🌸 SYNOPSIS 🌸

💅 Functions/Subroutines

subroutine dqrt02 (m, n, k, a, af, q, r, lda, tau, work, lwork, rwork, result)

DQRT02

🦋 Function/Subroutine Documentation 🦋

Here's the exact signature, bestie, no cap:

subroutine dqrt02 (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)

DQRT02

✨ Purpose ✨

DQRT02 tests DORGQR, which generates an m-by-n matrix Q with orthonormal columns that is defined as the product of k elementary reflectors. 🫶

Given the QR factorization of an m-by-n matrix A, DQRT02 generates the orthogonal matrix Q defined by the factorization of the first k columns of A; it compares R(1:n,1:k) with Q(1:m,1:n)'*A(1:m,1:k), and checks that the columns of Q are orthonormal. the way that whole sentence is doing the most but it's correct, okay? 💅

💖 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. M >= N >= 0. 🌸
• K — K is INTEGER. The number of elementary reflectors whose product defines the matrix Q. N >= K >= 0. ⭐
• A — A is DOUBLE PRECISION array, dimension (LDA,N). The m-by-n matrix A which was factorized by DQRT01. 🦋
• AF — AF is DOUBLE PRECISION array, dimension (LDA,N). Details of the QR factorization of A, as returned by DGEQRF. See DGEQRF for further details. 👑
• Q — Q is DOUBLE PRECISION array, dimension (LDA,N). 🎀
• R — R is DOUBLE PRECISION array, dimension (LDA,N). 🌈
• LDA — LDA is INTEGER. The leading dimension of the arrays A, AF, Q and R. LDA >= M. 💜
• TAU — TAU is DOUBLE PRECISION array, dimension (N). The scalar factors of the elementary reflectors corresponding to the QR 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 - Q'*A ) / ( M * norm(A) * EPS )
  • RESULT(2) = norm( I - Q'*Q ) / ( M * EPS )

👑 Author 👑

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 133 of file dqrt02.f. 📍

🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code. 🤖💖

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