zlqt02.f - Man Page

subroutine zlqt02 (m, n, k, a, af, q, l, lda, tau, work, lwork, rwork, result)
ZLQT02

ZLQT02

Purpose:

 ZLQT02 tests ZUNGLQ, 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, ZLQT02 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 COMPLEX*16 array, dimension (LDA,N)
          The m-by-n matrix A which was factorized by ZLQT01.

AF

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

Q

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

L

          L 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 LQ 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( 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 zlqt02.f.