dqrt14()

double precision function dqrt14	(	character	TRANS,
		integer	M,
		integer	N,
		integer	NRHS,
		double precision, dimension( lda, * )	A,
		integer	LDA,
		double precision, dimension( ldx, * )	X,
		integer	LDX,
		double precision, dimension( lwork )	WORK,
		integer	LWORK
	)

DQRT14

Purpose:

 DQRT14 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

[in]	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'.
[in]	M	M is INTEGER The number of rows of the matrix A.
[in]	N	N is INTEGER The number of columns of the matrix A.
[in]	NRHS	NRHS is INTEGER The number of right hand sides, i.e., the number of columns of X.
[in]	A	A is DOUBLE PRECISION array, dimension (LDA,N) The M-by-N matrix A.
[in]	LDA	LDA is INTEGER The leading dimension of the array A.
[in]	X	X is DOUBLE PRECISION array, dimension (LDX,NRHS) If TRANS = 'N', the N-by-NRHS matrix X. IF TRANS = 'T', the M-by-NRHS matrix X.
[in]	LDX	LDX is INTEGER The leading dimension of the array X.
[out]	WORK	WORK is DOUBLE PRECISION array dimension (LWORK)
[in]	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.