DQRT14
Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
November 2006
November 2006
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.
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.
Arguments
| TRANS |
(input) 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 |
(input) INTEGER
The number of rows of the matrix A.
|
| N |
(input) INTEGER
The number of columns of the matrix A.
|
| NRHS |
(input) INTEGER
The number of right hand sides, i.e., the number of columns
of X. |
| A |
(input) DOUBLE PRECISION array, dimension (LDA,N)
The M-by-N matrix A.
|
| LDA |
(input) INTEGER
The leading dimension of the array A.
|
| X |
(input) DOUBLE PRECISION array, dimension (LDX,NRHS)
If TRANS = 'N', the N-by-NRHS matrix X.
IF TRANS = 'T', the M-by-NRHS matrix X. |
| LDX |
(input) INTEGER
The leading dimension of the array X.
|
| WORK |
(workspace) DOUBLE PRECISION array dimension (LWORK)
|
| LWORK |
(input) INTEGER
length of workspace array required
If TRANS = 'N', LWORK >= (M+NRHS)*(N+2); if TRANS = 'T', LWORK >= (N+NRHS)*(M+2). |