SORT01
Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
November 2006
November 2006
Purpose
SORT01 checks that the matrix U is orthogonal by computing the ratio
RESID = norm( I - U*U' ) / ( n * EPS ), if ROWCOL = 'R',
or
RESID = norm( I - U'*U ) / ( m * EPS ), if ROWCOL = 'C'.
Alternatively, if there isn't sufficient workspace to form
I - U*U' or I - U'*U, the ratio is computed as
RESID = abs( I - U*U' ) / ( n * EPS ), if ROWCOL = 'R',
or
RESID = abs( I - U'*U ) / ( m * EPS ), if ROWCOL = 'C'.
where EPS is the machine precision. ROWCOL is used only if m = n;
if m > n, ROWCOL is assumed to be 'C', and if m < n, ROWCOL is
assumed to be 'R'.
RESID = norm( I - U*U' ) / ( n * EPS ), if ROWCOL = 'R',
or
RESID = norm( I - U'*U ) / ( m * EPS ), if ROWCOL = 'C'.
Alternatively, if there isn't sufficient workspace to form
I - U*U' or I - U'*U, the ratio is computed as
RESID = abs( I - U*U' ) / ( n * EPS ), if ROWCOL = 'R',
or
RESID = abs( I - U'*U ) / ( m * EPS ), if ROWCOL = 'C'.
where EPS is the machine precision. ROWCOL is used only if m = n;
if m > n, ROWCOL is assumed to be 'C', and if m < n, ROWCOL is
assumed to be 'R'.
Arguments
| ROWCOL |
(input) CHARACTER
Specifies whether the rows or columns of U should be checked
for orthogonality. Used only if M = N. = 'R': Check for orthogonal rows of U = 'C': Check for orthogonal columns of U |
| M |
(input) INTEGER
The number of rows of the matrix U.
|
| N |
(input) INTEGER
The number of columns of the matrix U.
|
| U |
(input) REAL array, dimension (LDU,N)
The orthogonal matrix U. U is checked for orthogonal columns
if m > n or if m = n and ROWCOL = 'C'. U is checked for orthogonal rows if m < n or if m = n and ROWCOL = 'R'. |
| LDU |
(input) INTEGER
The leading dimension of the array U. LDU >= max(1,M).
|
| WORK |
(workspace) REAL array, dimension (LWORK)
|
| LWORK |
(input) INTEGER
The length of the array WORK. For best performance, LWORK
should be at least N*(N+1) if ROWCOL = 'C' or M*(M+1) if ROWCOL = 'R', but the test will be done even if LWORK is 0. |
| RESID |
(output) REAL
RESID = norm( I - U * U' ) / ( n * EPS ), if ROWCOL = 'R', or
RESID = norm( I - U' * U ) / ( m * EPS ), if ROWCOL = 'C'. |