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

okay so this is the Library Functions Manual page for /home/abui...hr_col01.f(3), and it’s giving “LAPACK test doc but make it cute” energy. 💅✨

💖 NAME 💖

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/dorhr_col01.f

✨ SYNOPSIS ✨

🎀 Functions/Subroutines 🎀

subroutine DORHR_COL01 (m, n, mb1, nb1, nb2, result)
    DORHR_COL01

🦋 Function/Subroutine Documentation 🦋

subroutine DORHR_COL01 (integer m, integer n, integer mb1, integer nb1,
       integer nb2, double precision, dimension(6) result)
       DORHR_COL01

🎀 Purpose 🎀

okay so DORHR_COL01 tests DORGTSQR and DORHR_COL using DLATSQR, DGEMQRT. Therefore, DLATSQR (part of DGEQR), DGEMQRT (part of DGEMQR) have to be tested before this test. No cap, that’s literally the whole vibe. 💅

🌸 Parameters 🌸

• M — INTEGER. Number of rows in test matrix. 💖
• N — INTEGER. Number of columns in test matrix. ✨
• MB1 — INTEGER. Number of row in row block in an input test matrix. 🎀
• NB1 — INTEGER. Number of columns in column block an input test matrix. 🦋
• NB2 — INTEGER. Number of columns in column block in an output test matrix. 🌸
• RESULT — DOUBLE PRECISION array, dimension (6). Results of each of the six tests below. 👑

bestie, here are the main characters in this little math drama: 💅

• 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 118 of file dorhr_col01.f.

💖 Author (Doxygen’s auto-generated era) 💖

Generated automatically by Doxygen for LAPACK from the source code. ✨

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okay that’s the whole page, bestie. Source/version check: LAPACK, Version 3.12.0, page dated /home/abui...hr_col01.f(3). mwah 💋💅