---
name: "sqrt11.f"
section: "3"
platform: "linux"
package: "lapack-doc"
version: "3.12.1-2"
release: "Arch Linux 2026-11-01"
platforms: ["linux"]
url: "https://new.carta.tech/sqrt11.f"
---

# sqrt11.f(3)

## NAME

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
!>          contain information about orthogonal transformations.
!>
```

*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

Univ. of Colorado Denver

NAG Ltd.

Definition at line **97** of file **sqrt11.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.