DGRQTS tests DGGRQF, which computes the GRQ factorization of an
 M-by-N matrix A and a P-by-N matrix B: A = R*Q and B = Z*T*Q.

M

          M is INTEGER
          The number of rows of the matrix A.  M >= 0.

P

          P is INTEGER
          The number of rows of the matrix B.  P >= 0.

N

          N is INTEGER
          The number of columns of the matrices A and B.  N >= 0.

A

          A is DOUBLE PRECISION array, dimension (LDA,N)
          The M-by-N matrix A.

AF

          AF is DOUBLE PRECISION array, dimension (LDA,N)
          Details of the GRQ factorization of A and B, as returned
          by DGGRQF, see SGGRQF for further details.

Q

          Q is DOUBLE PRECISION array, dimension (LDA,N)
          The N-by-N orthogonal matrix Q.

R

          R is DOUBLE PRECISION array, dimension (LDA,MAX(M,N))

LDA

          LDA is INTEGER
          The leading dimension of the arrays A, AF, R and Q.
          LDA >= max(M,N).

TAUA

          TAUA is DOUBLE PRECISION array, dimension (min(M,N))
          The scalar factors of the elementary reflectors, as returned
          by DGGQRC.

B

          B is DOUBLE PRECISION array, dimension (LDB,N)
          On entry, the P-by-N matrix A.

BF

          BF is DOUBLE PRECISION array, dimension (LDB,N)
          Details of the GQR factorization of A and B, as returned
          by DGGRQF, see SGGRQF for further details.

Z

          Z is DOUBLE PRECISION array, dimension (LDB,P)
          The P-by-P orthogonal matrix Z.

T

          T is DOUBLE PRECISION array, dimension (LDB,max(P,N))

BWK

          BWK is DOUBLE PRECISION array, dimension (LDB,N)

LDB

          LDB is INTEGER
          The leading dimension of the arrays B, BF, Z and T.
          LDB >= max(P,N).

TAUB

          TAUB is DOUBLE PRECISION array, dimension (min(P,N))
          The scalar factors of the elementary reflectors, as returned
          by DGGRQF.

WORK

          WORK is DOUBLE PRECISION array, dimension (LWORK)

LWORK

          LWORK is INTEGER
          The dimension of the array WORK, LWORK >= max(M,P,N)**2.

RWORK

          RWORK is DOUBLE PRECISION array, dimension (M)

RESULT

          RESULT is DOUBLE PRECISION array, dimension (4)
          The test ratios:
            RESULT(1) = norm( R - A*Q' ) / ( MAX(M,N)*norm(A)*ULP)
            RESULT(2) = norm( T*Q - Z'*B ) / (MAX(P,N)*norm(B)*ULP)
            RESULT(3) = norm( I - Q'*Q ) / ( N*ULP )
            RESULT(4) = norm( I - Z'*Z ) / ( P*ULP )

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