zqrt02.f - Man Page

subroutine zqrt02 (m, n, k, a, af, q, r, lda, tau, work, lwork, rwork, result)
ZQRT02

ZQRT02

Purpose:

 ZQRT02 tests ZUNGQR, 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, ZQRT02 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 COMPLEX*16 array, dimension (LDA,N)
          The m-by-n matrix A which was factorized by ZQRT01.

AF

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

Q

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

R

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

LDA

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

TAU

          TAU is COMPLEX*16 array, dimension (N)
          The scalar factors of the elementary reflectors corresponding
          to the QR 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( 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 zqrt02.f.