CGQRTS tests CGGQRF, which computes the GQR factorization of an


 N-by-M matrix A and a N-by-P matrix B: A = Q*R and B = Q*T*Z.

N

          N is INTEGER


          The number of rows of the matrices A and B.  N >= 0.

M

          M is INTEGER


          The number of columns of the matrix A.  M >= 0.

P

          P is INTEGER


          The number of columns of the matrix B.  P >= 0.

A

          A is COMPLEX array, dimension (LDA,M)


          The N-by-M matrix A.

AF

          AF is COMPLEX array, dimension (LDA,N)


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


          by CGGQRF, see CGGQRF for further details.

Q

          Q is COMPLEX array, dimension (LDA,N)


          The M-by-M unitary matrix Q.

R

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


          The scalar factors of the elementary reflectors, as returned


          by CGGQRF.

B

          B is COMPLEX array, dimension (LDB,P)


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

BF

          BF is COMPLEX array, dimension (LDB,N)


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


          by CGGQRF, see CGGQRF for further details.

Z

          Z is COMPLEX array, dimension (LDB,P)


          The P-by-P unitary matrix Z.

T

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

BWK

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


          The scalar factors of the elementary reflectors, as returned


          by SGGRQF.

WORK

          WORK is COMPLEX array, dimension (LWORK)

LWORK

          LWORK is INTEGER


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

RWORK

          RWORK is REAL array, dimension (max(N,M,P))

RESULT

          RESULT is REAL array, dimension (4)


          The test ratios:


            RESULT(1) = norm( R - Q'*A ) / ( MAX(M,N)*norm(A)*ULP)


            RESULT(2) = norm( T*Z - Q'*B ) / (MAX(P,N)*norm(B)*ULP)


            RESULT(3) = norm( I - Q'*Q ) / ( M*ULP )


            RESULT(4) = norm( I - Z'*Z ) / ( P*ULP )

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