TESTING/LIN/zrqt02.f(3)

NAME
TESTING/LIN/zrqt02.f

SYNOPSIS

  Functions/Subroutines
subroutine zrqt02 (m, n, k, a, af, q, r, lda, tau, work, lwork, rwork, result)
ZRQT02

Function/Subroutine Documentation

  subroutine zrqt02 (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)

ZRQT02

Purpose:

    !>
    !> ZRQT02 tests ZUNGRQ, which generates an m-by-n matrix Q with
    !> orthonormal rows that is defined as the product of k elementary
    !> reflectors.
    !>
    !> Given the RQ factorization of an m-by-n matrix A, ZRQT02 generates
    !> the orthogonal matrix Q defined by the factorization of the last k
    !> rows of A; it compares R(m-k+1:m,n-m+1:n) with
    !> A(m-k+1:m,1:n)*Q(n-m+1:n,1:n)', and checks that the rows 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.
    !>          N >= M >= 0.
    !>

    K

    !>          K is INTEGER
    !>          The number of elementary reflectors whose product defines the
    !>          matrix Q. M >= K >= 0.
    !>

    A

    !>          A is COMPLEX*16 array, dimension (LDA,N)
    !>          The m-by-n matrix A which was factorized by ZRQT01.
    !>

    AF

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

    Q

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

    R

    !>          R is COMPLEX*16 array, dimension (LDA,M)
    !>

    LDA

    !>          LDA is INTEGER
    !>          The leading dimension of the arrays A, AF, Q and L. LDA >= N.
    !>

    TAU

    !>          TAU is COMPLEX*16 array, dimension (M)
    !>          The scalar factors of the elementary reflectors corresponding
    !>          to the RQ 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 - A*Q' ) / ( N * norm(A) * EPS )
    !>          RESULT(2) = norm( I - Q*Q' ) / ( N * EPS )
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 134 of file zrqt02.f.

Author

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