# cqrt14.f - Man Page

TESTING/LIN/cqrt14.f

## Synopsis

### Functions/Subroutines

real function cqrt14 (trans, m, n, nrhs, a, lda, x, ldx, work, lwork)
CQRT14

## Function/Subroutine Documentation

### real function cqrt14 (character trans, integer m, integer n, integer nrhs, complex, dimension( lda, * ) a, integer lda, complex, dimension( ldx, * ) x, integer ldx, complex, dimension( lwork ) work, integer lwork)

CQRT14

Purpose:

``` CQRT14 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 = 'C') 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
= 'C':  Conjugate transpose, check for X in 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 COMPLEX array, dimension (LDA,N)
The M-by-N matrix A.```

LDA

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

X

```          X is COMPLEX array, dimension (LDX,NRHS)
If TRANS = 'N', the N-by-NRHS matrix X.
IF TRANS = 'C', the M-by-NRHS matrix X.```

LDX

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

WORK

`          WORK is COMPLEX array dimension (LWORK)`

LWORK

```          LWORK is INTEGER
length of workspace array required
If TRANS = 'N', LWORK >= (M+NRHS)*(N+2);
if TRANS = 'C', LWORK >= (N+NRHS)*(M+2).```
Author

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Definition at line 114 of file cqrt14.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page cqrt14(3) is an alias of cqrt14.f(3).

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