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.

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 )

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