# 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

Univ. of Colorado Denver

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