cqrt023

!>
!> CQRT02 tests CUNGQR, which generates an m-by-n matrix Q with
!> orthonormal columns that is defined as the product of k elementary
!> reflectors.
!>
!> Given the QR factorization of an m-by-n matrix A, CQRT02 generates
!> the orthogonal matrix Q defined by the factorization of the first k
!> columns of A; it compares R(1:n,1:k) with Q(1:m,1:n)'*A(1:m,1:k),
!> and checks that the columns of Q are orthonormal.
!> 

M

!>          M is INTEGER
!>          The number of rows of the matrix Q to be generated.  M >= 0.
!> 

N

!>          N is INTEGER
!>          The number of columns of the matrix Q to be generated.
!>          M >= N >= 0.
!> 

K

!>          K is INTEGER
!>          The number of elementary reflectors whose product defines the
!>          matrix Q. N >= K >= 0.
!> 

A

!>          A is COMPLEX array, dimension (LDA,N)
!>          The m-by-n matrix A which was factorized by CQRT01.
!> 

AF

!>          AF is COMPLEX array, dimension (LDA,N)
!>          Details of the QR factorization of A, as returned by CGEQRF.
!>          See CGEQRF for further details.
!> 

Q

!>          Q is COMPLEX array, dimension (LDA,N)
!> 

R

!>          R is COMPLEX array, dimension (LDA,N)
!> 

LDA

!>          LDA is INTEGER
!>          The leading dimension of the arrays A, AF, Q and R. LDA >= M.
!> 

TAU

!>          TAU is COMPLEX array, dimension (N)
!>          The scalar factors of the elementary reflectors corresponding
!>          to the QR factorization in AF.
!> 

WORK

!>          WORK is COMPLEX array, dimension (LWORK)
!> 

LWORK

!>          LWORK is INTEGER
!>          The dimension of the array WORK.
!> 

RWORK

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

RESULT

!>          RESULT is REAL array, dimension (2)
!>          The test ratios:
!>          RESULT(1) = norm( R - Q'*A ) / ( M * norm(A) * EPS )
!>          RESULT(2) = norm( I - Q'*Q ) / ( M * EPS )
!> 

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