cgrqts.f3

!>
!> CGRQTS tests CGGRQF, 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 array, dimension (LDA,N)
!>          The M-by-N matrix A.
!> 

AF

!>          AF is COMPLEX array, dimension (LDA,N)
!>          Details of the GRQ factorization of A and B, as returned
!>          by CGGRQF, see CGGRQF for further details.
!> 

Q

!>          Q is COMPLEX array, dimension (LDA,N)
!>          The N-by-N 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 SGGQRC.
!> 

B

!>          B is COMPLEX array, dimension (LDB,N)
!>          On entry, the P-by-N matrix A.
!> 

BF

!>          BF is COMPLEX array, dimension (LDB,N)
!>          Details of the GQR factorization of A and B, as returned
!>          by CGGRQF, see CGGRQF for further details.
!> 

Z

!>          Z is REAL 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(M,P,N)**2.
!> 

RWORK

!>          RWORK is REAL array, dimension (M)
!> 

RESULT

!>          RESULT is REAL 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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