TESTING/LIN/zqrt02.f(3)

NAME
TESTING/LIN/zqrt02.f

SYNOPSIS

  Functions/Subroutines
subroutine zqrt02 (m, n, k, a, af, q, r, lda, tau, work, lwork, rwork, result)
ZQRT02

Function/Subroutine Documentation

  subroutine zqrt02 (integer m, integer n, integer k, complex*16, dimension( lda, * ) a, complex*16, dimension( lda, * ) af, complex*16, dimension( lda, * ) q, complex*16, dimension( lda, * ) r, integer lda, complex*16, dimension( * ) tau, complex*16, dimension( lwork ) work, integer lwork, double precision, dimension( * ) rwork, double precision, dimension( * ) result)

ZQRT02

Purpose:

     ZQRT02 tests ZUNGQR, 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, ZQRT02 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*16 array, dimension (LDA,N)
              The m-by-n matrix A which was factorized by ZQRT01.

    AF

              AF is COMPLEX*16 array, dimension (LDA,N)
              Details of the QR factorization of A, as returned by ZGEQRF.
              See ZGEQRF for further details.

    Q

              Q is COMPLEX*16 array, dimension (LDA,N)

    R

              R is COMPLEX*16 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*16 array, dimension (N)
              The scalar factors of the elementary reflectors corresponding
              to the QR factorization in AF.

    WORK

              WORK is COMPLEX*16 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 zqrt02.f.

Author

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