# sqrt11.f - Man Page

TESTING/LIN/sqrt11.f

## Synopsis

### Functions/Subroutines

real function sqrt11 (m, k, a, lda, tau, work, lwork)
SQRT11

## Function/Subroutine Documentation

### real function sqrt11 (integer m, integer k, real, dimension( lda, * ) a, integer lda, real, dimension( * ) tau, real, dimension( lwork ) work, integer lwork)

SQRT11

Purpose:

``` SQRT11 computes the test ratio

|| Q'*Q - I || / (eps * m)

where the orthogonal matrix Q is represented as a product of
elementary transformations.  Each transformation has the form

H(k) = I - tau(k) v(k) v(k)'

where tau(k) is stored in TAU(k) and v(k) is an m-vector of the form
[ 0 ... 0 1 x(k) ]', where x(k) is a vector of length m-k stored
in A(k+1:m,k).```
Parameters

M

```          M is INTEGER
The number of rows of the matrix A.```

K

```          K is INTEGER
The number of columns of A whose subdiagonal entries

A

```          A is REAL array, dimension (LDA,K)
The (possibly partial) output of a QR reduction routine.```

LDA

```          LDA is INTEGER
The leading dimension of the array A.```

TAU

```          TAU is REAL array, dimension (K)
The scaling factors tau for the elementary transformations as
computed by the QR factorization routine.```

WORK

`          WORK is REAL array, dimension (LWORK)`

LWORK

```          LWORK is INTEGER
The length of the array WORK.  LWORK >= M*M + M.```
Author

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Definition at line 97 of file sqrt11.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page sqrt11(3) is an alias of sqrt11.f(3).

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