dlqt02.f - Man Page

subroutine dlqt02 (m, n, k, a, af, q, l, lda, tau, work, lwork, rwork, result)
DLQT02

DLQT02

Purpose:

 DLQT02 tests DORGLQ, which generates an m-by-n matrix Q with
 orthonormal rows that is defined as the product of k elementary
 reflectors.

 Given the LQ factorization of an m-by-n matrix A, DLQT02 generates
 the orthogonal matrix Q defined by the factorization of the first k
 rows of A; it compares L(1:k,1:m) with A(1:k,1:n)*Q(1:m,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 DOUBLE PRECISION array, dimension (LDA,N)
          The m-by-n matrix A which was factorized by DLQT01.

AF

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

Q

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

L

          L is DOUBLE PRECISION array, dimension (LDA,M)

LDA

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

TAU

          TAU is DOUBLE PRECISION array, dimension (M)
          The scalar factors of the elementary reflectors corresponding
          to the LQ 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( L - 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 133 of file dlqt02.f.