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.

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 DOUBLE PRECISION array, dimension (LDA,N)


          The M-by-N matrix A.

LDA

          LDA is INTEGER


          The leading dimension of the array A.

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.

LDX

          LDX is INTEGER


          The leading dimension of the array X.

WORK

          WORK is DOUBLE PRECISION 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).

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