ZUNHR_COL01(3)

📦
version 3.12.1 · 2 versions
, in arch rolling

💅 NAME

TESTING/LIN/zunhr_col01.f

Okay bestie, we're in the Library Functions Manual and this is the page for that LAPACK testing file. It's giving “I verify the factorization girls” energy, and honestly? Iconic. ✨

🌸 SYNOPSIS

Functions/Subroutines

subroutine zunhr_col01 (m, n, mb1, nb1, nb2, result)
    ZUNHR_COL01

💖 FUNCTION/SUBROUTINE DOCUMENTATION

subroutine zunhr_col01 (integer m, integer n, integer mb1, integer nb1,
    integer nb2, double precision, dimension(6) result)
    ZUNHR_COL01

🎯 Purpose

ZUNHR_COL01 tests ZUNGTSQR and ZUNHR_COL using ZLATSQR, ZGEMQRT. Therefore, ZLATSQR (part of ZGEQR) and ZGEMQRT (part of ZGEMQR) have to be tested before this test. Yes, bestie, it's a prerequisite chain — do the earlier tests first, no skipping. 💅

🌟 Parameters

  • M — M is INTEGER. Number of rows in test matrix. 📏
  • N — N is INTEGER. Number of columns in test matrix. 📐
  • MB1 — MB1 is INTEGER. Number of row in row block in an input test matrix. (That's literally what it says, bestie.)
  • NB1 — NB1 is INTEGER. Number of columns in column block an input test matrix.
  • NB2 — NB2 is INTEGER. Number of columns in column block in an output test matrix.
  • RESULT — RESULT is DOUBLE PRECISION array, dimension (6). Results of each of the six tests below. 👑

RESULT details, because this cast is long and we love a full ensemble:

  • 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:

  1. RESULT(1) = |R - (Q**H) * A| / ( eps * m * |A| ) — is equivalent to test 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_gr**H) * C, D * Q_qr, D * (Q_qr**H) are computed using ZGEMQRT,
  • Q * C, (Q**H) * C, D * Q, D * (Q**H) are computed using ZGEMM.

👑 Author

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

Definition at line 118 of file zunhr_col01.f.

🪄 AUTHOR

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💖 Cute little sign-off: this page lives in the Library Functions Manual, and the footer tea is LAPACK Version 3.12.0, with page tag TESTING/LI...nhr_col01.f(3). Slay, and good luck with your tests. 🎀

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