SQRT02
Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
November 2006
November 2006
Purpose
SQRT02 tests SORGQR, which generates an m-by-n matrix Q with
orthonornmal columns that is defined as the product of k elementary
reflectors.
Given the QR factorization of an m-by-n matrix A, SQRT02 generates
the orthogonal matrix Q defined by the factorization of the first k
columns of A; it compares R(1:n,1:k) with Q(1:m,1:n)'*A(1:m,1:k),
and checks that the columns of Q are orthonormal.
orthonornmal columns that is defined as the product of k elementary
reflectors.
Given the QR factorization of an m-by-n matrix A, SQRT02 generates
the orthogonal matrix Q defined by the factorization of the first k
columns of A; it compares R(1:n,1:k) with Q(1:m,1:n)'*A(1:m,1:k),
and checks that the columns 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.
M >= N >= 0. |
| K |
(input) INTEGER
The number of elementary reflectors whose product defines the
matrix Q. N >= K >= 0. |
| A |
(input) REAL array, dimension (LDA,N)
The m-by-n matrix A which was factorized by SQRT01.
|
| AF |
(input) REAL array, dimension (LDA,N)
Details of the QR factorization of A, as returned by SGEQRF.
See SGEQRF for further details. |
| Q |
(workspace) REAL array, dimension (LDA,N)
|
| R |
(workspace) REAL array, dimension (LDA,N)
|
| LDA |
(input) INTEGER
The leading dimension of the arrays A, AF, Q and R. LDA >= M.
|
| TAU |
(input) REAL array, dimension (N)
The scalar factors of the elementary reflectors corresponding
to the QR factorization in AF. |
| WORK |
(workspace) REAL array, dimension (LWORK)
|
| LWORK |
(input) INTEGER
The dimension of the array WORK.
|
| RWORK |
(workspace) REAL array, dimension (M)
|
| RESULT |
(output) REAL array, dimension (2)
The test ratios:
RESULT(1) = norm( R - Q'*A ) / ( M * norm(A) * EPS ) RESULT(2) = norm( I - Q'*Q ) / ( M * EPS ) |