TESTING/LIN/zrqt02.f(3)

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version 3.12.1 · 3 versions
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💅 TESTING/LIN/zrqt02.f — zrqt02 💅

Hii bestie! Welcome to the Library Functions Manual page for TESTING/LIN/zrqt02.f. This is zrqt02, and she is literally here to test ZUNGRQ. No cap, it's giving Fortran realness. ✨

🎀 NAME 🎀

TESTING/LIN/zrqt02.f

That's the name, bestie — just the file path, no extra lore. 💖

✨ SYNOPSIS ✨

Functions/Subroutines

       subroutine zrqt02 (m, n, k, a, af, q, r, lda, tau, work, lwork, rwork,
           result)
           ZRQT02

💖 Function/Subroutine Documentation 💖

   subroutine zrqt02 (integer m, integer n, integer k, 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)
       ZRQT02

🌸 Purpose 🌸

Okay so ZRQT02 tests ZUNGRQ, which generates an m-by-n matrix Q with orthonormal rows that is defined as the product of k elementary reflectors. That's the whole assignment, and she ate. 💅

Given the RQ factorization of an m-by-n matrix A, ZRQT02 generates the orthogonal matrix Q defined by the factorization of the last k rows of A. Then 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. Vibe check: passed? 👑

🦋 Parameters 🦋

M

M is INTEGER. The number of rows of the matrix Q to be generated. Constraint: M >= 0.

N

N is INTEGER. The number of columns of the matrix Q to be generated. Constraint: N >= M >= 0.

K

K is INTEGER. The number of elementary reflectors whose product defines the matrix Q. Constraint: M >= K >= 0.

A

A is COMPLEX*16 array, dimension (LDA,N). The m-by-n matrix A which was factorized by ZRQT01.

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). No extra notes on this one, bestie.

R

R is COMPLEX*16 array, dimension (LDA,M). No extra notes here either.

LDA

LDA is INTEGER. The leading dimension of the arrays A, AF, Q and L. Constraint: LDA >= N.

TAU

TAU is COMPLEX*16 array, dimension (M). The scalar factors of the elementary reflectors corresponding to the RQ factorization in AF.

WORK

WORK is COMPLEX*16 array, dimension (LWORK). No extra notes.

LWORK

LWORK is INTEGER. The dimension of the array WORK.

RWORK

RWORK is DOUBLE PRECISION array, dimension (M). No extra notes.

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 zrqt02.f.

🌈 Author 🌈

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