TESTING/LIN/sqrt02.f(3)    Library Functions Manual    TESTING/LIN/sqrt02.f(3)

NAME
       TESTING/LIN/sqrt02.f

SYNOPSIS
   Functions/Subroutines
       subroutine sqrt02 (m, n, k, a, af, q, r, lda, tau, work, lwork, rwork,
           result)
           SQRT02

Function/Subroutine Documentation
   subroutine sqrt02 (integer m, integer n, integer k, real, dimension( lda, *
       ) a, real, dimension( lda, * ) af, real, dimension( lda, * ) q, real,
       dimension( lda, * ) r, integer lda, real, dimension( * ) tau, real,
       dimension( lwork ) work, integer lwork, real, dimension( * ) rwork,
       real, dimension( * ) result)
       SQRT02

       Purpose:


            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.

       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 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 )

       Author
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Definition at line 133 of file sqrt02.f.

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

LAPACK                          Version 3.12.0         TESTING/LIN/sqrt02.f(3)