CUNHR_COL01(3)

💅 CUNHR_COL01(3) 💅

okay so this is a Library Functions Manual page, and yes bestie, the manual name is folded right here near the top: Library Functions Manual. The header title vibe is TESTING/LI...nhr_col01.f(3), and the actual file star of the show is TESTING/LIN/cunhr_col01.f. We're about to get into some Fortran testing, and it's lowkey iconic. 🦋

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✨ NAME ✨

TESTING/LIN/cunhr_col01.f — that's the whole name. This page is the Library Functions Manual entry for it. 💖

🌸 SYNOPSIS 🌸

Functions/Subroutines

subroutine cunhr_col01 (m, n, mb1, nb1, nb2, result)
    CUNHR_COL01

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🎀 Function/Subroutine Documentation 🎀

subroutine cunhr_col01

subroutine cunhr_col01 (integer m, integer n, integer mb1, integer nb1,
    integer nb2, real, dimension(6) result)
    CUNHR_COL01

🧚 Purpose 🧚

okay so CUNHR_COL01 tests CUNGTSQR and CUNHR_COL using CLATSQR and CGEMQRT. That means CLATSQR (part of CGEQR) and CGEMQRT (part of CGEMQR) have to be tested before this test. No cap — that's the order, bestie. ✨

Dependency tea: CLATSQR lives in CGEQR, CGEMQRT lives in CGEMQR, and both need their tests run first. 💅

🍓 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 rows in a row block in an input test matrix. 🎀

🍓 NB1

NB1 is INTEGER. Number of columns in a column block in an input test matrix. 💜

🍓 NB2

NB2 is INTEGER. Number of columns in a column block in an output test matrix. 🫶

🍓 RESULT

RESULT is a REAL array, dimension (6). It holds the 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 CGEQRT 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:

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 CGEMQRT.
• Q * C, (Q**H) * C, D * Q, D * (Q**H) are computed using CGEMM.

👑 Author 👑

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

Definition at line 118 of file cunhr_col01.f. 🫶

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🌈 Author 🌈

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

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Cute sign-off, bestie: this footer is giving LAPACK, Version 3.12.0, and TESTING/LI...nhr_col01.f(3). It doesn't list a separate date here, so I'm not making one up — periodt. Stay shiny and slay your tests. 💖✨