zqlt02.f - Man Page

subroutine zqlt02 (m, n, k, a, af, q, l, lda, tau, work, lwork, rwork, result)
ZQLT02

ZQLT02

Purpose:

 ZQLT02 tests ZUNGQL, which generates an m-by-n matrix Q with
 orthonormal columns that is defined as the product of k elementary
 reflectors.

 Given the QL factorization of an m-by-n matrix A, ZQLT02 generates
 the orthogonal matrix Q defined by the factorization of the last k
 columns of A; it compares L(m-n+1:m,n-k+1:n) with
 Q(1:m,m-n+1:m)'*A(1:m,n-k+1:n), 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 COMPLEX*16 array, dimension (LDA,N)
          The m-by-n matrix A which was factorized by ZQLT01.

AF

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

Q

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

L

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

LDA

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

TAU

          TAU is COMPLEX*16 array, dimension (N)
          The scalar factors of the elementary reflectors corresponding
          to the QL 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 - 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 134 of file zqlt02.f.