SQRT02 tests SORGQR, 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, SQRT02 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 REAL array, dimension (LDA,N)


          The m-by-n matrix A which was factorized by SQRT01.

AF

          AF is REAL array, dimension (LDA,N)


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


          See SGEQRF for further details.

Q

          Q is REAL array, dimension (LDA,N)

R

          R is REAL array, dimension (LDA,N)

LDA

          LDA is INTEGER


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

TAU

          TAU is REAL array, dimension (N)


          The scalar factors of the elementary reflectors corresponding


          to the QR factorization in AF.

WORK

          WORK is REAL 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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