SORHR_COL02(3)

💖 NAME 💖

TESTING/LIN/sorhr_col02.f — okay bestie, this is the page from the Library Functions Manual (page tag: TESTING/LI...rhr_col02.f(3)), and it's all about the sorhr_col02 test subroutine. 💅

✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

• subroutine sorhr_col02 (m, n, mb1, nb1, nb2, result)
  • SORHR_COL02

🌸 Function/Subroutine Documentation 🌸

subroutine sorhr_col02 (integer m, integer n, integer mb1, integer nb1,
    integer nb2, real, dimension(6) result)

SORHR_COL02

🎀 Purpose 🎀

SORHR_COL02 tests SORGTSQR_ROW and SORHR_COL inside SGETSQRHRT (which calls SLATSQR, SORGTSQR_ROW and SORHR_COL) using SGEMQRT.

so yeah, SLATSQR (part of SGEQR) and SGEMQRT (part of SGEMQR) have to be tested before this test, bestie. no skipping the prerequisites, periodt.

💖 Parameters 💖

• M — M is INTEGER. number of rows in the test matrix. 🌈
• N — N is INTEGER. number of columns in the test matrix. 🦋
• MB1 — MB1 is INTEGER. number of row in a row block in an input test matrix. yep, “row,” that's the original wording, iykyk. 🎀
• NB1 — NB1 is INTEGER. number of columns in a column block of an input test matrix. 🌸
• NB2 — NB2 is INTEGER. number of columns in a column block in an output test matrix. 💜
• RESULT — RESULT is REAL 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 orthogonal Q matrix, the result
of factorization in blocked WY-representation,
stored in SGEQRT 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 orthogonal 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:

RESULT(1) = |R - (Q**H) * A| / ( eps * m * |A| )
  is equivalent to test for | A - Q * R | / (eps * m * |A|),

RESULT(2) = |I - (Q**H) * Q| / ( eps * m ),

RESULT(3) = | Q_qr * C - Q * C | / (eps * m * |C|),

RESULT(4) = | (Q_gr**H) * C - (Q**H) * C | / (eps * m * |C|)

RESULT(5) = | D * Q_qr - D * Q | / (eps * m * |D|)

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 SGEMQRT,

  Q * C, (Q**H) * C, D * Q, D * (Q**H)  are
  computed using SGEMM.

💜 Author 💜

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

Definition at line 119 of file sorhr_col02.f.

👑 Author (the generated-by one) 👑

Generated automatically by Doxygen for LAPACK from the source code.

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okay that's the whole page, bestie. source/version: LAPACK Version 3.12.0. date: the footer didn't show one, so I'm not inventing one, fr fr. footer tag: TESTING/LI...rhr_col02.f(3). bye bestie, slay responsibly 💅🫶✨