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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