ZRQT02
Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
November 2006
November 2006
Purpose
ZRQT02 tests ZUNGRQ, which generates an m-by-n matrix Q with
orthonornmal 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.
orthonornmal 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.
Arguments
| M |
(input) INTEGER
The number of rows of the matrix Q to be generated. M >= 0.
|
| N |
(input) INTEGER
The number of columns of the matrix Q to be generated.
N >= M >= 0. |
| K |
(input) INTEGER
The number of elementary reflectors whose product defines the
matrix Q. M >= K >= 0. |
| A |
(input) COMPLEX*16 array, dimension (LDA,N)
The m-by-n matrix A which was factorized by ZRQT01.
|
| AF |
(input) COMPLEX*16 array, dimension (LDA,N)
Details of the RQ factorization of A, as returned by ZGERQF.
See ZGERQF for further details. |
| Q |
(workspace) COMPLEX*16 array, dimension (LDA,N)
|
| R |
(workspace) COMPLEX*16 array, dimension (LDA,M)
|
| LDA |
(input) INTEGER
The leading dimension of the arrays A, AF, Q and L. LDA >= N.
|
| TAU |
(input) COMPLEX*16 array, dimension (M)
The scalar factors of the elementary reflectors corresponding
to the RQ factorization in AF. |
| WORK |
(workspace) COMPLEX*16 array, dimension (LWORK)
|
| LWORK |
(input) INTEGER
The dimension of the array WORK.
|
| RWORK |
(workspace) DOUBLE PRECISION array, dimension (M)
|
| RESULT |
(output) 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 ) |