DQRT02 tests DORGQR, 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, DQRT02 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 DOUBLE PRECISION array, dimension (LDA,N)


          The m-by-n matrix A which was factorized by DQRT01.

AF

          AF is DOUBLE PRECISION array, dimension (LDA,N)


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


          See DGEQRF for further details.

Q

          Q is DOUBLE PRECISION array, dimension (LDA,N)

R

          R is DOUBLE PRECISION array, dimension (LDA,N)

LDA

          LDA is INTEGER


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

TAU

          TAU is DOUBLE PRECISION array, dimension (N)


          The scalar factors of the elementary reflectors corresponding


          to the QR factorization in AF.

WORK

          WORK is DOUBLE PRECISION 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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