/home/abui...hr_col01.f(3)

📦 version 3.12.0, in opensuse-leap 16.0

💅 NAME

ok so bestie, this page is for /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/zunhr_col01.f — yes that entire path is literally the name, she has a long government name and we respect it 💖. It lives in the Library Functions Manual, and honestly? iconic placement.

✨ SYNOPSIS

🎀 Functions/Subroutines

  • subroutine ZUNHR_COL01 (m, n, mb1, nb1, nb2, result) — the whole vibe of this page, it's the one and only routine we're talking about, no cap.

🦋 Function/Subroutine Documentation

subroutine ZUNHR_COL01 (integer m, integer n, integer mb1, integer nb1,
    integer nb2, double precision, dimension(6) result)

💜 Purpose

!> ZUNHR_COL01 tests ZUNGTSQR and ZUNHR_COL using ZLATSQR, ZGEMQRT. !> Therefore, ZLATSQR (part of ZGEQR), ZGEMQRT (part of ZGEMQR) !> have to be tested before this test. !>

so yeah — this is a test routine, and it's lowkey dependent on other stuff being tested first. Order matters, periodt 🫶

🌸 Parameters

  • M — M is INTEGER, and it's the number of rows in the test matrix. row queen 👑
  • N — N is INTEGER, the number of columns in the test matrix. slay.
  • MB1 — MB1 is INTEGER, the number of rows in a row block of an input test matrix. (yeah, the original says "row", we're keeping that energy ✨)
  • NB1 — NB1 is INTEGER, the number of columns in a column block of an input test matrix.
  • NB2 — NB2 is INTEGER, the number of columns in a column block of an output test matrix. different matrix, different block, keep up bestie 💅
  • RESULT — RESULT is a DOUBLE PRECISION array, dimension (6). It holds the results of each of the six tests below, and this is where it gets good:
!> RESULT is DOUBLE PRECISION array, dimension (6) !> Results of each of the six tests below. !> !> A is a m-by-n test input matrix to be factored. !> so that A = Q_gr * ( R ) !> ( 0 ), !> !> Q_qr is an implicit m-by-m unitary Q matrix, the result !> of factorization in blocked WY-representation, !> stored in ZGEQRT output format. !> !> R is a n-by-n upper-triangular matrix, !> !> 0 is a (m-n)-by-n zero matrix, !> !> Q is an explicit m-by-m unitary matrix Q = Q_gr * I !> !> C is an m-by-n random matrix, !> !> D is an n-by-m random matrix. !> !> The six tests are:

and here are the six tests, fr fr, exactly as written:

  1. RESULT(1) = |R - (Q**H) * A| / ( eps * m * |A| ) which is equivalent to testing for | A - Q * R | / (eps * m * |A|),
  2. RESULT(2) = |I - (Q**H) * Q| / ( eps * m ),
  3. RESULT(3) = | Q_qr * C - Q * C | / (eps * m * |C|),
  4. RESULT(4) = | (Q_gr**H) * C - (Q**H) * C | / (eps * m * |C|)
  5. RESULT(5) = | D * Q_qr - D * Q | / (eps * m * |D|)
  6. RESULT(6) = | D * (Q_qr**H) - D * (Q**H) | / (eps * m * |D|),
!> where: !> Q_qr * C, (Q_grH) * C, D * Q_qr, D * (Q_qrH) are !> computed using ZGEMQRT, !> !> Q * C, (QH) * C, D * Q, D * (QH) are !> computed using ZGEMM. !>

so half the products go through ZGEMQRT and the other half through ZGEMM — that's the whole point of the comparison, iykyk 🔥

👑 Author

  • Univ. of Tennessee
  • Univ. of California Berkeley
  • Univ. of Colorado Denver
  • NAG Ltd.

Definition at line 118 of file zunhr_col01.f. 🎯

🌈 Sign-off

This page was generated automatically by Doxygen for LAPACK from the source code, and it's serving LAPACK, Version 3.12.0 💖 — the page itself is /home/abui...hr_col01.f(3). bye bestie, go test some matrices 🦋✨

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