ZGRQTS tests ZGGRQF, 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 COMPLEX*16 array, dimension (LDA,N)


          The M-by-N matrix A.

AF

          AF is COMPLEX*16 array, dimension (LDA,N)


          Details of the GRQ factorization of A and B, as returned


          by ZGGRQF, see CGGRQF for further details.

Q

          Q is COMPLEX*16 array, dimension (LDA,N)


          The N-by-N unitary matrix Q.

R

          R is COMPLEX*16 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 COMPLEX*16 array, dimension (min(M,N))


          The scalar factors of the elementary reflectors, as returned


          by DGGQRC.

B

          B is COMPLEX*16 array, dimension (LDB,N)


          On entry, the P-by-N matrix A.

BF

          BF is COMPLEX*16 array, dimension (LDB,N)


          Details of the GQR factorization of A and B, as returned


          by ZGGRQF, see CGGRQF for further details.

Z

          Z is DOUBLE PRECISION array, dimension (LDB,P)


          The P-by-P unitary matrix Z.

T

          T is COMPLEX*16 array, dimension (LDB,max(P,N))

BWK

          BWK is COMPLEX*16 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 COMPLEX*16 array, dimension (min(P,N))


          The scalar factors of the elementary reflectors, as returned


          by DGGRQF.

WORK

          WORK is COMPLEX*16 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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