LAPACK
3.6.1
LAPACK: Linear Algebra PACKage
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subroutine zlatm6 | ( | integer | TYPE, |
integer | N, | ||
complex*16, dimension( lda, * ) | A, | ||
integer | LDA, | ||
complex*16, dimension( lda, * ) | B, | ||
complex*16, dimension( ldx, * ) | X, | ||
integer | LDX, | ||
complex*16, dimension( ldy, * ) | Y, | ||
integer | LDY, | ||
complex*16 | ALPHA, | ||
complex*16 | BETA, | ||
complex*16 | WX, | ||
complex*16 | WY, | ||
double precision, dimension( * ) | S, | ||
double precision, dimension( * ) | DIF | ||
) |
ZLATM6
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. 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.
[in] | TYPE | TYPE is INTEGER Specifies the problem type (see futher details). |
[in] | N | N is INTEGER Size of the matrices A and B. |
[out] | A | A is COMPLEX*16 array, dimension (LDA, N). On exit A N-by-N is initialized according to TYPE. |
[in] | LDA | LDA is INTEGER The leading dimension of A and of B. |
[out] | B | B is COMPLEX*16 array, dimension (LDA, N). On exit B N-by-N is initialized according to TYPE. |
[out] | X | X is COMPLEX*16 array, dimension (LDX, N). On exit X is the N-by-N matrix of right eigenvectors. |
[in] | LDX | LDX is INTEGER The leading dimension of X. |
[out] | Y | Y is COMPLEX*16 array, dimension (LDY, N). On exit Y is the N-by-N matrix of left eigenvectors. |
[in] | LDY | LDY is INTEGER The leading dimension of Y. |
[in] | ALPHA | ALPHA is COMPLEX*16 |
[in] | BETA | BETA is COMPLEX*16 \verbatim Weighting constants for matrix A. |
[in] | WX | WX is COMPLEX*16 Constant for right eigenvector matrix. |
[in] | WY | WY is COMPLEX*16 Constant for left eigenvector matrix. |
[out] | S | S is DOUBLE PRECISION array, dimension (N) S(i) is the reciprocal condition number for eigenvalue i. |
[out] | DIF | DIF is DOUBLE PRECISION array, dimension (N) DIF(i) is the reciprocal condition number for eigenvector i. |
Definition at line 176 of file zlatm6.f.