SLATM6
Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
November 2006
November 2006
Purpose
SLATM6 generates test matrices for the generalized eigenvalue
problem, their corresponding right and left eigenvector matrices,
and also reciprocal condition numbers for all eigenvalues and
the reciprocal condition numbers of eigenvectors corresponding to
the 1th and 5th eigenvalues.
problem, their corresponding right and left eigenvector matrices,
and also reciprocal condition numbers for all eigenvalues and
the reciprocal condition numbers of eigenvectors corresponding to
the 1th and 5th eigenvalues.
Test Matrices
Two kinds of test matrix pairs
(A, B) = inverse(YH) * (Da, Db) * inverse(X)
are used in the tests:
Type 1:
Da = 1+a 0 0 0 0 Db = 1 0 0 0 0
0 2+a 0 0 0 0 1 0 0 0
0 0 3+a 0 0 0 0 1 0 0
0 0 0 4+a 0 0 0 0 1 0
0 0 0 0 5+a , 0 0 0 0 1 , and
Type 2:
Da = 1 -1 0 0 0 Db = 1 0 0 0 0
1 1 0 0 0 0 1 0 0 0
0 0 1 0 0 0 0 1 0 0
0 0 0 1+a 1+b 0 0 0 1 0
0 0 0 -1-b 1+a , 0 0 0 0 1 .
In both cases the same inverse(YH) and inverse(X) are used to compute
(A, B), giving the exact eigenvectors to (A,B) as (YH, X):
YH: = 1 0 -y y -y X = 1 0 -x -x x
0 1 -y y -y 0 1 x -x -x
0 0 1 0 0 0 0 1 0 0
0 0 0 1 0 0 0 0 1 0
0 0 0 0 1, 0 0 0 0 1 ,
where a, b, x and y will have all values independently of each other.
(A, B) = inverse(YH) * (Da, Db) * inverse(X)
are used in the tests:
Type 1:
Da = 1+a 0 0 0 0 Db = 1 0 0 0 0
0 2+a 0 0 0 0 1 0 0 0
0 0 3+a 0 0 0 0 1 0 0
0 0 0 4+a 0 0 0 0 1 0
0 0 0 0 5+a , 0 0 0 0 1 , and
Type 2:
Da = 1 -1 0 0 0 Db = 1 0 0 0 0
1 1 0 0 0 0 1 0 0 0
0 0 1 0 0 0 0 1 0 0
0 0 0 1+a 1+b 0 0 0 1 0
0 0 0 -1-b 1+a , 0 0 0 0 1 .
In both cases the same inverse(YH) and inverse(X) are used to compute
(A, B), giving the exact eigenvectors to (A,B) as (YH, X):
YH: = 1 0 -y y -y X = 1 0 -x -x x
0 1 -y y -y 0 1 x -x -x
0 0 1 0 0 0 0 1 0 0
0 0 0 1 0 0 0 0 1 0
0 0 0 0 1, 0 0 0 0 1 ,
where a, b, x and y will have all values independently of each other.
Arguments
| TYPE |
(input) INTEGER
Specifies the problem type (see futher details).
|
| N |
(input) INTEGER
Size of the matrices A and B.
|
| A |
(output) REAL array, dimension (LDA, N).
On exit A N-by-N is initialized according to TYPE.
|
| LDA |
(input) INTEGER
The leading dimension of A and of B.
|
| B |
(output) REAL array, dimension (LDA, N).
On exit B N-by-N is initialized according to TYPE.
|
| X |
(output) REAL array, dimension (LDX, N).
On exit X is the N-by-N matrix of right eigenvectors.
|
| LDX |
(input) INTEGER
The leading dimension of X.
|
| Y |
(output) REAL array, dimension (LDY, N).
On exit Y is the N-by-N matrix of left eigenvectors.
|
| LDY |
(input) INTEGER
The leading dimension of Y.
|
| ALPHA |
(input) REAL
|
| BETA |
(input) REAL
Weighting constants for matrix A.
|
| WX |
(input) REAL
Constant for right eigenvector matrix.
|
| WY |
(input) REAL
Constant for left eigenvector matrix.
|
| S |
(output) REAL array, dimension (N)
S(i) is the reciprocal condition number for eigenvalue i.
|
| DIF |
(output) REAL array, dimension (N)
DIF(i) is the reciprocal condition number for eigenvector i.
|