TESTING/LIN/srqt02.f(3)

💖 NAME 💖

Okay so this is TESTING/LIN/srqt02.f(3) — the manual name is the Library Functions Manual, and the page itself is all about TESTING/LIN/srqt02.f. It’s giving very specific “test the linear algebra routine” energy, and honestly? Iconic. 💅

✨ SYNOPSIS ✨

Functions/Subroutines

       subroutine srqt02 (m, n, k, a, af, q, r, lda, tau, work, lwork, rwork,
           result)
           SRQT02

🧚 Function/Subroutine Documentation 🧚

Meet the full signature, bestie — every type and dimension exactly as written:

   subroutine srqt02 (integer m, integer n, integer k, real, dimension( lda, *
       ) a, real, dimension( lda, * ) af, real, dimension( lda, * ) q, real,
       dimension( lda, * ) r, integer lda, real, dimension( * ) tau, real,
       dimension( lwork ) work, integer lwork, real, dimension( * ) rwork,
       real, dimension( * ) result)

The routine’s name is SRQT02, periodt. 🫶

🎯 Purpose 🎯

SRQT02 tests SORGRQ, 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, SRQT02 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. ✨

📝 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 REAL array, dimension (LDA,N). The m-by-n matrix A which was factorized by SRQT01.
• AF — AF is REAL array, dimension (LDA,N). Details of the RQ factorization of A, as returned by SGERQF. See SGERQF for further details.
• Q — Q is REAL array, dimension (LDA,N).
• R — R is REAL array, dimension (LDA,M).
• LDA — LDA is INTEGER. The leading dimension of the arrays A, AF, Q and L. LDA >= N.
• TAU — TAU is REAL array, dimension (M). The scalar factors of the elementary reflectors corresponding to the RQ factorization in AF.
• WORK — WORK is REAL array, dimension (LWORK).
• LWORK — LWORK is INTEGER. The dimension of the array WORK.
• RWORK — RWORK is REAL array, dimension (M).
• RESULT — RESULT is REAL 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 srqt02.f.

🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code.

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Bye bestie! Footer vibes: source/version is LAPACK Version 3.12.0, page is TESTING/LIN/srqt02.f(3) — and there’s no date printed in this footer, so I’m not inventing one 🌸💅