version 1.1.1.1, 2010/01/26 15:22:45
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version 1.8, 2011/07/22 07:38:12
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$ LDD, E, LDE, F, LDF, SCALE, DIF, WORK, LWORK, |
$ LDD, E, LDE, F, LDF, SCALE, DIF, 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 TRANS |
CHARACTER TRANS |
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* In matrix notation (1) is equivalent to solve Zx = scale b, where |
* In matrix notation (1) is equivalent to solve Zx = scale b, where |
* Z is defined as |
* Z is defined as |
* |
* |
* Z = [ kron(In, A) -kron(B', Im) ] (2) |
* Z = [ kron(In, A) -kron(B**T, Im) ] (2) |
* [ kron(In, D) -kron(E', Im) ]. |
* [ kron(In, D) -kron(E**T, Im) ]. |
* |
* |
* Here Ik is the identity matrix of size k and X' is the transpose of |
* Here Ik is the identity matrix of size k and X**T is the transpose of |
* X. kron(X, Y) is the Kronecker product between the matrices X and Y. |
* X. kron(X, Y) is the Kronecker product between the matrices X and Y. |
* |
* |
* If TRANS = 'T', DTGSYL solves the transposed system Z'*y = scale*b, |
* If TRANS = 'T', DTGSYL solves the transposed system Z**T*y = scale*b, |
* which is equivalent to solve for R and L in |
* which is equivalent to solve for R and L in |
* |
* |
* A' * R + D' * L = scale * C (3) |
* A**T * R + D**T * L = scale * C (3) |
* R * B' + L * E' = scale * (-F) |
* R * B**T + L * E**T = scale * -F |
* |
* |
* This case (TRANS = 'T') is used to compute an one-norm-based estimate |
* This case (TRANS = 'T') is used to compute an one-norm-based estimate |
* of Dif[(A,D), (B,E)], the separation between the matrix pairs (A,D) |
* of Dif[(A,D), (B,E)], the separation between the matrix pairs (A,D) |
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ELSE |
ELSE |
* |
* |
* Solve transposed (I, J)-subsystem |
* Solve transposed (I, J)-subsystem |
* A(I, I)' * R(I, J) + D(I, I)' * L(I, J) = C(I, J) |
* A(I, I)**T * R(I, J) + D(I, I)**T * L(I, J) = C(I, J) |
* R(I, J) * B(J, J)' + L(I, J) * E(J, J)' = -F(I, J) |
* R(I, J) * B(J, J)**T + L(I, J) * E(J, J)**T = -F(I, J) |
* for I = 1,2,..., P; J = Q, Q-1,..., 1 |
* for I = 1,2,..., P; J = Q, Q-1,..., 1 |
* |
* |
SCALE = ONE |
SCALE = ONE |