TESTING/LIN/dqrt02.f(3)    Library Functions Manual    TESTING/LIN/dqrt02.f(3)

NAME
       TESTING/LIN/dqrt02.f

SYNOPSIS
   Functions/Subroutines
       subroutine dqrt02 (m, n, k, a, af, q, r, lda, tau, work, lwork, rwork,
           result)
           DQRT02

Function/Subroutine Documentation
   subroutine dqrt02 (integer m, integer n, integer k, double precision,
       dimension( lda, * ) a, double precision, dimension( lda, * ) af, double
       precision, dimension( lda, * ) q, double precision, dimension( lda, * )
       r, integer lda, double precision, dimension( * ) tau, double precision,
       dimension( lwork ) work, integer lwork, double precision, dimension( *
       ) rwork, double precision, dimension( * ) result)
       DQRT02

       Purpose:


            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.

       Parameters
           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 )

       Author
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Definition at line 133 of file dqrt02.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

LAPACK                          Version 3.12.0         TESTING/LIN/dqrt02.f(3)