ZLATM6
Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
November 2006
November 2006
Purpose
ZLATM6 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*16 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*16 array, dimension (LDA, N).
On exit B N-by-N is initialized according to TYPE.
|
| X |
(output) COMPLEX*16 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*16 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*16
|
| BETA |
(input) COMPLEX*16
Weighting constants for matrix A.
|
| WX |
(input) COMPLEX*16
Constant for right eigenvector matrix.
|
| WY |
(input) COMPLEX*16
Constant for left eigenvector matrix.
|
| S |
(output) DOUBLE PRECISION array, dimension (N)
S(i) is the reciprocal condition number for eigenvalue i.
|
| DIF |
(output) DOUBLE PRECISION array, dimension (N)
DIF(i) is the reciprocal condition number for eigenvector i.
|