ZUNHR_COL02.F(3)

💖 ZUNHR_COL02(3) 💖

Okay bestie, this is the Library Functions Manual page for ZUNHR_COL02(3), and the file path is TESTING/LIN/zunhr_col02.f. The page tag vibe is TESTING/LI...nhr_col02.f(3). Buckle up, we're getting into the whole subroutine tea. ✨

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🌸 NAME 🌸

TESTING/LIN/zunhr_col02.f

✨ SYNOPSIS ✨

Functions/Subroutines

• subroutine zunhr_col02 (m, n, mb1, nb1, nb2, result)
  • ZUNHR_COL02

🎀 Function/Subroutine Documentation 🎀

subroutine zunhr_col02 (integer m, integer n, integer mb1, integer nb1,
    integer nb2, double precision, dimension(6) result)

ZUNHR_COL02

🦋 Purpose 🦋

So ZUNHR_COL02 tests ZUNGTSQR_ROW and ZUNHR_COL inside ZGETSQRHRT — and ZGETSQRHRT is the one calling ZLATSQR, ZUNGTSQR_ROW, and ZUNHR_COL — using ZGEMQRT. Therefore, ZLATSQR (part of ZGEQR) and ZGEMQRT (part of ZGEMQR) have to be tested before this test. Periodt. 💅

🍓 Parameters 🍓

• M — M is INTEGER and it's the number of rows in the test matrix. Rows, bestie. 📏
• N — N is INTEGER and it's the number of columns in the test matrix. Columns. 🌈
• MB1 — MB1 is INTEGER and it's the number of row in row block in an input test matrix. (Yes, that's the original wording — “row,” singular, iconic.) 🎀
• NB1 — NB1 is INTEGER and it's the number of columns in column block an input test matrix. 🦋
• NB2 — NB2 is INTEGER and it's the number of columns in column block in an output test matrix. ✨
• RESULT — RESULT is DOUBLE PRECISION array, dimension (6). It holds the results of each of the six tests below. 👑

Then the setup goes like this:

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.

And 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 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 119 of file zunhr_col02.f.

💫 Author 💫

Generated automatically by Doxygen for LAPACK from the source code.

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