ZHST01
Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
November 2006
November 2006
Purpose
ZHST01 tests the reduction of a general matrix A to upper Hessenberg
form: A = Q*H*Q'. Two test ratios are computed;
RESULT(1) = norm( A - Q*H*Q' ) / ( norm(A) * N * EPS )
RESULT(2) = norm( I - Q'*Q ) / ( N * EPS )
The matrix Q is assumed to be given explicitly as it would be
following ZGEHRD + ZUNGHR.
In this version, ILO and IHI are not used, but they could be used
to save some work if this is desired.
form: A = Q*H*Q'. Two test ratios are computed;
RESULT(1) = norm( A - Q*H*Q' ) / ( norm(A) * N * EPS )
RESULT(2) = norm( I - Q'*Q ) / ( N * EPS )
The matrix Q is assumed to be given explicitly as it would be
following ZGEHRD + ZUNGHR.
In this version, ILO and IHI are not used, but they could be used
to save some work if this is desired.
Arguments
| N |
(input) INTEGER
The order of the matrix A. N >= 0.
|
| ILO |
(input) INTEGER
|
| IHI |
(input) INTEGER
A is assumed to be upper triangular in rows and columns
1:ILO-1 and IHI+1:N, so Q differs from the identity only in rows and columns ILO+1:IHI. |
| A |
(input) COMPLEX*16 array, dimension (LDA,N)
The original n by n matrix A.
|
| LDA |
(input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
|
| H |
(input) COMPLEX*16 array, dimension (LDH,N)
The upper Hessenberg matrix H from the reduction A = Q*H*Q'
as computed by ZGEHRD. H is assumed to be zero below the first subdiagonal. |
| LDH |
(input) INTEGER
The leading dimension of the array H. LDH >= max(1,N).
|
| Q |
(input) COMPLEX*16 array, dimension (LDQ,N)
The orthogonal matrix Q from the reduction A = Q*H*Q' as
computed by ZGEHRD + ZUNGHR. |
| LDQ |
(input) INTEGER
The leading dimension of the array Q. LDQ >= max(1,N).
|
| WORK |
(workspace) COMPLEX*16 array, dimension (LWORK)
|
| LWORK |
(input) INTEGER
The length of the array WORK. LWORK >= 2*N*N.
|
| RWORK |
(workspace) DOUBLE PRECISION array, dimension (N)
|
| RESULT |
(output) DOUBLE PRECISION array, dimension (2)
RESULT(1) = norm( A - Q*H*Q' ) / ( norm(A) * N * EPS )
RESULT(2) = norm( I - Q'*Q ) / ( N * EPS ) |