TESTING/LIN/zrqt01.f(3)

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💅 TESTING/LIN/zrqt01.f(3) — Library Functions Manual energy 💅

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✨ NAME ✨

TESTING/LIN/zrqt01.f

🌸 SYNOPSIS 🌸

🫶 Functions/Subroutines 🫶

  • subroutine zrqt01 — the main character. Signature incoming, bestie:
       subroutine zrqt01 (m, n, a, af, q, r, lda, tau, work, lwork, rwork,
           result)
           ZRQT01

💖 Function/Subroutine Documentation 💖

🌟 subroutine zrqt01 🌟

Full signature, character-for-character, no cap:

   subroutine zrqt01 (integer m, integer n, complex*16, dimension( lda, * ) a,
       complex*16, dimension( lda, * ) af, complex*16, dimension( lda, * ) q,
       complex*16, dimension( lda, * ) r, integer lda, complex*16, dimension( *
       ) tau, complex*16, dimension( lwork ) work, integer lwork, double
       precision, dimension( * ) rwork, double precision, dimension( * )
       result)
       ZRQT01

🎀 Purpose 🎀

ZRQT01 tests ZGERQF, which computes the RQ factorization of an m-by-n matrix A, and partially tests ZUNGRQ which forms the n-by-n orthogonal matrix Q.

ZRQT01 compares R with A*Q', and checks that Q is orthogonal. That's the whole assignment, and it ate. 💅

💅 Parameters 💅

  • M — M is INTEGER; the number of rows of the matrix A. M >= 0.
  • N — N is INTEGER; the number of columns of the matrix A. N >= 0.
  • A — A is COMPLEX*16 array, dimension (LDA,N); the m-by-n matrix A.
  • AF — AF is COMPLEX*16 array, dimension (LDA,N); details of the RQ factorization of A, as returned by ZGERQF. See ZGERQF for further details.
  • Q — Q is COMPLEX*16 array, dimension (LDA,N); the n-by-n orthogonal matrix Q.
  • R — R is COMPLEX*16 array, dimension (LDA,max(M,N)).
  • LDA — LDA is INTEGER; the leading dimension of the arrays A, AF, Q and L. LDA >= max(M,N).
  • TAU — TAU is COMPLEX*16 array, dimension (min(M,N)); the scalar factors of the elementary reflectors, as returned by ZGERQF.
  • WORK — WORK is COMPLEX*16 array, dimension (LWORK).
  • LWORK — LWORK is INTEGER; the dimension of the array WORK.
  • RWORK — RWORK is DOUBLE PRECISION array, dimension (max(M,N)).
  • 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 124 of file zrqt01.f.

👑 Author 👑

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