/home/abui...hr_col02.f(3)

💅 DORHR_COL02 💅

okay so bestie, this is a Library Functions Manual page for /home/abui...hr_col02.f(3) — and it's all about the DORHR_COL02 subroutine. It's giving "LAPACK test routine that checks the checkers," and honestly? iconic. 💖

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💖 NAME 💖

The name is literally this whole path, no edits:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/dorhr_col02.f

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✨ SYNOPSIS ✨

🦋 Functions/Subroutines

       subroutine DORHR_COL02 (m, n, mb1, nb1, nb2, result)
           DORHR_COL02

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🌸 Function/Subroutine Documentation 🌸

The signature, preserved exactly:

   subroutine DORHR_COL02 (integer m, integer n, integer mb1, integer nb1,
       integer nb2, double precision, dimension(6) result)
       DORHR_COL02

🎀 Purpose

DORHR_COL02 tests DORGTSQR_ROW and DORHR_COL inside DGETSQRHRT (which calls DLATSQR, DORGTSQR_ROW, and DORHR_COL) using DGEMQRT. So yeah — DLATSQR (part of DGEQR) and DGEMQRT (part of DGEMQR) have to be tested before this test. No skipping the prerequisites, bestie. 💅

🌈 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.

💜 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.

Okay so the setup is giving a whole little matrix cinematic universe:

• 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 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 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 DGEMQRT.
• Q * C, (Q**H) * C, D * Q, D * (Q**H) are computed using DGEMM.

👑 Author

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

Definition at line 119 of file dorhr_col02.f.

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👑 Author

Generated automatically by Doxygen for LAPACK from the source code.

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and that's the whole page, bestie! This one is from LAPACK Version 3.12.0, with footer path /home/abui...hr_col02.f(3). No date printed on it, so I'm not inventing one — just pure LAPACK version energy. bye! 💅✨🦋