zrqt02.f - Man Page

subroutine zrqt02 (m, n, k, a, af, q, r, lda, tau, work, lwork, rwork, result)
ZRQT02

ZRQT02

Purpose:

 ZRQT02 tests ZUNGRQ, 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, ZRQT02 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*16 array, dimension (LDA,N)
          The m-by-n matrix A which was factorized by ZRQT01.

AF

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

Q

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

R

          R 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 RQ 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 - 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 zrqt02.f.