ZQRT01 tests ZGEQRF, which computes the QR factorization of an m-by-n


 matrix A, and partially tests ZUNGQR which forms the m-by-m


 orthogonal matrix Q.


 ZQRT01 compares R with Q'*A, and checks that Q is orthogonal.

M

          M is INTEGER


          The number of rows of the matrix A.  M >= 0.

N

          N is INTEGER


          The number of columns of the matrix A.  N >= 0.

A

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


          The m-by-n matrix A.

AF

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


          Details of the QR factorization of A, as returned by ZGEQRF.


          See ZGEQRF for further details.

Q

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


          The m-by-m orthogonal matrix Q.

R

          R is COMPLEX*16 array, dimension (LDA,max(M,N))

LDA

          LDA is INTEGER


          The leading dimension of the arrays A, AF, Q and R.


          LDA >= max(M,N).

TAU

          TAU is COMPLEX*16 array, dimension (min(M,N))


          The scalar factors of the elementary reflectors, as returned


          by ZGEQRF.

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 - Q'*A ) / ( M * norm(A) * EPS )


          RESULT(2) = norm( I - Q'*Q ) / ( M * EPS )

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.