CLATM6
Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
June 2010
June 2010
Purpose
CLATM6 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+i 0 0 0 0 Db = 1 0 0 0 0
0 1-i 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)i 0 0 0 0 1 0
0 0 0 0 (1+a)-(1+b)i, 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+i 0 0 0 0 Db = 1 0 0 0 0
0 1-i 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)i 0 0 0 0 1 0
0 0 0 0 (1+a)-(1+b)i, 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) COMPLEX 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) COMPLEX array, dimension (LDA, N).
On exit B N-by-N is initialized according to TYPE.
|
| X |
(output) COMPLEX 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) COMPLEX 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) COMPLEX
|
| BETA |
(input) COMPLEX
Weighting constants for matrix A.
|
| WX |
(input) COMPLEX
Constant for right eigenvector matrix.
|
| WY |
(input) COMPLEX
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.
|