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

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