# cunhr_col01.f - Man Page

TESTING/LIN/cunhr_col01.f

## Synopsis

### Functions/Subroutines

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

## Function/Subroutine Documentation

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

CUNHR_COL01

Purpose:

``` CUNHR_COL01 tests CUNGTSQR and CUNHR_COL using CLATSQR, CGEMQRT.
Therefore, CLATSQR (part of CGEQR), CGEMQRT (part of CGEMQR)
have to be tested before this test.```
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 REAL array, dimension (6)
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

NAG Ltd.

Definition at line 118 of file cunhr_col01.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page cunhr_col01(3) is an alias of cunhr_col01.f(3).

Tue Nov 28 2023 12:08:42 Version 3.12.0 LAPACK