ZQRT02 tests ZUNGQR, 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, ZQRT02 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*16 array, dimension (LDA,N)


          The m-by-n matrix A which was factorized by ZQRT01.

AF

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


          Details of the QR factorization of A, as returned by ZGEQRF.


          See ZGEQRF for further details.

Q

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

R

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


          The scalar factors of the elementary reflectors corresponding


          to the QR factorization in AF.

WORK

          WORK is COMPLEX*16 array, dimension (LWORK)

LWORK

          LWORK is INTEGER


          The dimension of the array WORK.

RWORK

          RWORK is DOUBLE PRECISION array, dimension (M)

RESULT

          RESULT is DOUBLE PRECISION 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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