dqrt02.f - Man Page

subroutine dqrt02 (m, n, k, a, af, q, r, lda, tau, work, lwork, rwork, result)
DQRT02

DQRT02

Purpose:

 DQRT02 tests DORGQR, 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, DQRT02 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 DOUBLE PRECISION array, dimension (LDA,N)
          The m-by-n matrix A which was factorized by DQRT01.

AF

          AF is DOUBLE PRECISION array, dimension (LDA,N)
          Details of the QR factorization of A, as returned by DGEQRF.
          See DGEQRF for further details.

Q

          Q is DOUBLE PRECISION array, dimension (LDA,N)

R

          R is DOUBLE PRECISION array, dimension (LDA,N)

LDA

          LDA is INTEGER
          The leading dimension of the arrays A, AF, Q and R. LDA >= M.

TAU

          TAU is DOUBLE PRECISION array, dimension (N)
          The scalar factors of the elementary reflectors corresponding
          to the QR factorization in AF.

WORK

          WORK is DOUBLE PRECISION 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 dqrt02.f.