crqt02.f - Man Page

subroutine crqt02 (m, n, k, a, af, q, r, lda, tau, work, lwork, rwork, result)
CRQT02

CRQT02

Purpose:

 CRQT02 tests CUNGRQ, which generates an m-by-n matrix Q with
 orthonormal rows that is defined as the product of k elementary
 reflectors.

 Given the RQ factorization of an m-by-n matrix A, CRQT02 generates
 the orthogonal matrix Q defined by the factorization of the last k
 rows of A; it compares R(m-k+1:m,n-m+1:n) with
 A(m-k+1:m,1:n)*Q(n-m+1:n,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 array, dimension (LDA,N)
          The m-by-n matrix A which was factorized by CRQT01.

AF

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

Q

          Q is COMPLEX array, dimension (LDA,N)

R

          R is COMPLEX 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 array, dimension (M)
          The scalar factors of the elementary reflectors corresponding
          to the RQ 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 - 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 134 of file crqt02.f.