DORHR_COL01(3)

okay so bestie, this page is TESTING/LI...rhr_col01.f(3) from the Library Functions Manual — and we're about to get into some LAPACK test-subroutine business. 💖

🎀 NAME 🎀

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 🌸

DORHR_COL01 tests DORGTSQR and DORHR_COL using DLATSQR, DGEMQRT.

So yes: DLATSQR (part of DGEQR) and DGEMQRT (part of DGEMQR) have to be tested before this test. Order matters, bestie — this test is not doing the whole warm-up by itself. 🫶

🧚 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.

The whole RESULT vibe is this little cast of matrices and factors:

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 👑

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