crqt02.f3

!>
!> 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.
!> 

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 )
!> 

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.