cqrt02.f - Man Page

subroutine cqrt02 (m, n, k, a, af, q, r, lda, tau, work, lwork, rwork, result)
CQRT02

CQRT02

Purpose:

 CQRT02 tests CUNGQR, 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, CQRT02 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 array, dimension (LDA,N)
          The m-by-n matrix A which was factorized by CQRT01.

AF

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

Q

          Q is COMPLEX array, dimension (LDA,N)

R

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

WORK

          WORK is COMPLEX array, dimension (LWORK)

LWORK

          LWORK is INTEGER
          The dimension of the array WORK.

RWORK

          RWORK is REAL array, dimension (M)

RESULT

          RESULT is REAL 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 cqrt02.f.