---
name: "sqrt14.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/sqrt14.f"
---

# sqrt14.f(3)

## NAME

TESTING/LIN/sqrt14.f

## SYNOPSIS

### Functions/Subroutines

real function **sqrt14** (trans, m, n, nrhs, a, lda, x, ldx, work, lwork)\
 **SQRT14**

## Function/Subroutine Documentation

### real function sqrt14 (character trans, integer m, integer n, integer nrhs, real, dimension( lda, \* ) a, integer lda, real, dimension( ldx, \* ) x, integer ldx, real, dimension( lwork ) work, integer lwork)

**SQRT14**

**Purpose:**

```
!>
!> SQRT14 checks whether X is in the row space of A or A'.  It does so
!> by scaling both X and A such that their norms are in the range
!> [sqrt(eps), 1/sqrt(eps)], then computing a QR factorization of [A,X]
!> (if TRANS = 'T') or an LQ factorization of [A',X]' (if TRANS = 'N'),
!> and returning the norm of the trailing triangle, scaled by
!> MAX(M,N,NRHS)*eps.
!>
```

**Parameters**

*TRANS*

```
!>          TRANS is CHARACTER*1
!>          = 'N':  No transpose, check for X in the row space of A
!>          = 'T':  Transpose, check for X in the row space of A'.
!>
```

*M*

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

*N*

```
!>          N is INTEGER
!>          The number of columns of the matrix A.
!>
```

*NRHS*

```
!>          NRHS is INTEGER
!>          The number of right hand sides, i.e., the number of columns
!>          of X.
!>
```

*A*

```
!>          A is REAL array, dimension (LDA,N)
!>          The M-by-N matrix A.
!>
```

*LDA*

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

*X*

```
!>          X is REAL array, dimension (LDX,NRHS)
!>          If TRANS = 'N', the N-by-NRHS matrix X.
!>          IF TRANS = 'T', the M-by-NRHS matrix X.
!>
```

*LDX*

```
!>          LDX is INTEGER
!>          The leading dimension of the array X.
!>
```

*WORK*

```
!>          WORK is REAL array dimension (LWORK)
!>
```

*LWORK*

```
!>          LWORK is INTEGER
!>          length of workspace array required
!>          If TRANS = 'N', LWORK >= (M+NRHS)*(N+2);
!>          if TRANS = 'T', LWORK >= (N+NRHS)*(M+2).
!>
```

**Author**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **114** of file **sqrt14.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.