# sqrt03.f - Man Page

TESTING/LIN/sqrt03.f

## Synopsis

### Functions/Subroutines

subroutine sqrt03 (m, n, k, af, c, cc, q, lda, tau, work, lwork, rwork, result)
SQRT03

## Function/Subroutine Documentation

### subroutine sqrt03 (integer m, integer n, integer k, real, dimension( lda, * ) af, real, dimension( lda, * ) c, real, dimension( lda, * ) cc, real, dimension( lda, * ) q, integer lda, real, dimension( * ) tau, real, dimension( lwork ) work, integer lwork, real, dimension( * ) rwork, real, dimension( * ) result)

SQRT03

Purpose:

``` SQRT03 tests SORMQR, which computes Q*C, Q'*C, C*Q or C*Q'.

SQRT03 compares the results of a call to SORMQR with the results of
forming Q explicitly by a call to SORGQR and then performing matrix
multiplication by a call to SGEMM.```
Parameters

M

```          M is INTEGER
The order of the orthogonal matrix Q.  M >= 0.```

N

```          N is INTEGER
The number of rows or columns of the matrix C; C is m-by-n if
Q is applied from the left, or n-by-m if Q is applied from
the right.  N >= 0.```

K

```          K is INTEGER
The number of elementary reflectors whose product defines the
orthogonal matrix Q.  M >= K >= 0.```

AF

```          AF is REAL array, dimension (LDA,N)
Details of the QR factorization of an m-by-n matrix, as
returned by SGEQRF. See SGEQRF for further details.```

C

`          C is REAL array, dimension (LDA,N)`

CC

`          CC is REAL array, dimension (LDA,N)`

Q

`          Q is REAL array, dimension (LDA,M)`

LDA

```          LDA is INTEGER
The leading dimension of the arrays AF, C, CC, and Q.```

TAU

```          TAU is REAL array, dimension (min(M,N))
The scalar factors of the elementary reflectors corresponding
to the QR factorization in AF.```

WORK

`          WORK is REAL array, dimension (LWORK)`

LWORK

```          LWORK is INTEGER
The length of WORK.  LWORK must be at least M, and should be
M*NB, where NB is the blocksize for this environment.```

RWORK

`          RWORK is REAL array, dimension (M)`

RESULT

```          RESULT is REAL array, dimension (4)
The test ratios compare two techniques for multiplying a
random matrix C by an m-by-m orthogonal matrix Q.
RESULT(1) = norm( Q*C - Q*C )  / ( M * norm(C) * EPS )
RESULT(2) = norm( C*Q - C*Q )  / ( M * norm(C) * EPS )
RESULT(3) = norm( Q'*C - Q'*C )/ ( M * norm(C) * EPS )
RESULT(4) = norm( C*Q' - C*Q' )/ ( M * norm(C) * EPS )```
Author

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Definition at line 134 of file sqrt03.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page sqrt03(3) is an alias of sqrt03.f(3).

Tue Nov 28 2023 12:08:43 Version 3.12.0 LAPACK