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

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