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

💖 /home/abui...hr_col02.f(3) — Library Functions Manual 💖

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✨ NAME ✨

The NAME section points at:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/sorhr_col02.f

🦋 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 🌸

okay so SORHR_COL02 tests SORGTSQR_ROW and SORHR_COL inside SGETSQRHRT (which calls SLATSQR, SORGTSQR_ROW and SORHR_COL) using SGEMQRT. Therefore, SLATSQR (part of SGEQR), SGEMQRT (part of SGEMQR) have to be tested before this test. periodt. 💅

🎀 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 — REAL array, dimension (6); results of each of the six tests below.

Here's the matrix lore, bestie:

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 🌈

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