TESTING/LIN/slqt02.f(3)

okay bestie, this is the TESTING/LIN/slqt02.f(3) page from the Library Functions Manual, and the source file is TESTING/LIN/slqt02.f. it's giving Fortran test-ratio realness, and we're gonna read every single line together 💖

🌸 NAME 🌸

TESTING/LIN/slqt02.f

💫 SYNOPSIS 💫

🧚 Functions/Subroutines 🧚

       subroutine slqt02 (m, n, k, a, af, q, l, lda, tau, work, lwork, rwork,
           result)
           SLQT02

🦋 Function/Subroutine Documentation 🦋

here's the full signature, no cap:

   subroutine slqt02 (integer m, integer n, integer k, real, dimension( lda, *
       ) a, real, dimension( lda, * ) af, real, dimension( lda, * ) q, real,
       dimension( lda, * ) l, integer lda, real, dimension( * ) tau, real,
       dimension( lwork ) work, integer lwork, real, dimension( * ) rwork,
       real, dimension( * ) result)
       SLQT02

🎯 Purpose 🎯

SLQT02 tests SORGLQ, which generates an m-by-n matrix Q with orthonormal rows that is defined as the product of k elementary reflectors. ✨

Given the LQ factorization of an m-by-n matrix A, SLQT02 generates the orthogonal matrix Q defined by the factorization of the first k rows of A; it compares L(1:k,1:m) with A(1:k,1:n)*Q(1:m,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 SLQT01.
• AF — AF is REAL array, dimension (LDA,N). Details of the LQ factorization of A, as returned by SGELQF. See SGELQF for further details.
• Q — Q is REAL array, dimension (LDA,N).
• L — L 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 LQ 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( L - A*Q' ) / ( N * norm(A) * EPS ) and 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 133 of file slqt02.f.

🫶 Author 🫶

Generated automatically by Doxygen for LAPACK from the source code.

---

💖 okay that's the whole page, bestie — it's LAPACK Version 3.12.0, page TESTING/LIN/slqt02.f(3). periodt 💅