version 1.5, 2010/08/07 13:22:45
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version 1.8, 2011/07/22 07:38:21
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$ LDVL, VR, LDVR, S, DIF, MM, M, WORK, LWORK, |
$ LDVL, VR, LDVR, S, DIF, MM, M, WORK, LWORK, |
$ IWORK, INFO ) |
$ IWORK, INFO ) |
* |
* |
* -- LAPACK routine (version 3.2) -- |
* -- LAPACK routine (version 3.3.1) -- |
* -- LAPACK is a software package provided by Univ. of Tennessee, -- |
* -- LAPACK is a software package provided by Univ. of Tennessee, -- |
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
* November 2006 |
* -- April 2011 -- |
* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
CHARACTER HOWMNY, JOB |
CHARACTER HOWMNY, JOB |
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* The reciprocal of the condition number of the i-th generalized |
* The reciprocal of the condition number of the i-th generalized |
* eigenvalue w = (a, b) is defined as |
* eigenvalue w = (a, b) is defined as |
* |
* |
* S(I) = (|v'Au|**2 + |v'Bu|**2)**(1/2) / (norm(u)*norm(v)) |
* S(I) = (|v**HAu|**2 + |v**HBu|**2)**(1/2) / (norm(u)*norm(v)) |
* |
* |
* where u and v are the right and left eigenvectors of (A, B) |
* where u and v are the right and left eigenvectors of (A, B) |
* corresponding to w; |z| denotes the absolute value of the complex |
* corresponding to w; |z| denotes the absolute value of the complex |
* number, and norm(u) denotes the 2-norm of the vector u. The pair |
* number, and norm(u) denotes the 2-norm of the vector u. The pair |
* (a, b) corresponds to an eigenvalue w = a/b (= v'Au/v'Bu) of the |
* (a, b) corresponds to an eigenvalue w = a/b (= v**HAu/v**HBu) of the |
* matrix pair (A, B). If both a and b equal zero, then (A,B) is |
* matrix pair (A, B). If both a and b equal zero, then (A,B) is |
* singular and S(I) = -1 is returned. |
* singular and S(I) = -1 is returned. |
* |
* |
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* Zl = [ kron(a, In-1) -kron(1, A22) ] |
* Zl = [ kron(a, In-1) -kron(1, A22) ] |
* [ kron(b, In-1) -kron(1, B22) ]. |
* [ kron(b, In-1) -kron(1, B22) ]. |
* |
* |
* Here In-1 is the identity matrix of size n-1 and X' is the conjugate |
* Here In-1 is the identity matrix of size n-1 and X**H is the conjugate |
* transpose of X. kron(X, Y) is the Kronecker product between the |
* transpose of X. kron(X, Y) is the Kronecker product between the |
* matrices X and Y. |
* matrices X and Y. |
* |
* |