TESTING/LIN/cqrt02.f(3)    Library Functions Manual    TESTING/LIN/cqrt02.f(3)

NAME
       TESTING/LIN/cqrt02.f

SYNOPSIS
   Functions/Subroutines
       subroutine cqrt02 (m, n, k, a, af, q, r, lda, tau, work, lwork, rwork,
           result)
           CQRT02

Function/Subroutine Documentation
   subroutine cqrt02 (integer m, integer n, integer k, complex, dimension(
       lda, * ) a, complex, dimension( lda, * ) af, complex, dimension( lda, *
       ) q, complex, dimension( lda, * ) r, integer lda, complex, dimension( *
       ) tau, complex, dimension( lwork ) work, integer lwork, real,
       dimension( * ) rwork, real, dimension( * ) result)
       CQRT02

       Purpose:


            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.

       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 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 )

       Author
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Definition at line 133 of file cqrt02.f.

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

LAPACK                          Version 3.12.0         TESTING/LIN/cqrt02.f(3)