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Diff for /rpl/lapack/lapack/dtgsen.f between versions 1.8 and 1.9

version 1.8, 2010/12/21 13:53:40 version 1.9, 2011/07/22 07:38:12
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      $                   ALPHAR, ALPHAI, BETA, Q, LDQ, Z, LDZ, M, PL,       $                   ALPHAR, ALPHAI, BETA, Q, LDQ, Z, LDZ, M, PL,
      $                   PR, DIF, WORK, LWORK, IWORK, LIWORK, INFO )       $                   PR, DIF, WORK, LWORK, IWORK, LIWORK, INFO )
 *  *
 *  -- LAPACK routine (version 3.2.2) --  *  -- 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..--
 *     January 2007  *  -- April 2011                                                      --
 *  *
 *     Modified to call DLACN2 in place of DLACON, 5 Feb 03, SJH.  *     Modified to call DLACN2 in place of DLACON, 5 Feb 03, SJH.
 *  *
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 *  *
 *  DTGSEN reorders the generalized real Schur decomposition of a real  *  DTGSEN reorders the generalized real Schur decomposition of a real
 *  matrix pair (A, B) (in terms of an orthonormal equivalence trans-  *  matrix pair (A, B) (in terms of an orthonormal equivalence trans-
 *  formation Q' * (A, B) * Z), so that a selected cluster of eigenvalues  *  formation Q**T * (A, B) * Z), so that a selected cluster of eigenvalues
 *  appears in the leading diagonal blocks of the upper quasi-triangular  *  appears in the leading diagonal blocks of the upper quasi-triangular
 *  matrix A and the upper triangular B. The leading columns of Q and  *  matrix A and the upper triangular B. The leading columns of Q and
 *  Z form orthonormal bases of the corresponding left and right eigen-  *  Z form orthonormal bases of the corresponding left and right eigen-
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 *  In other words, the selected eigenvalues are the eigenvalues of  *  In other words, the selected eigenvalues are the eigenvalues of
 *  (A11, B11) in:  *  (A11, B11) in:
 *  *
 *                U'*(A, B)*W = (A11 A12) (B11 B12) n1  *              U**T*(A, B)*W = (A11 A12) (B11 B12) n1
 *                              ( 0  A22),( 0  B22) n2  *                              ( 0  A22),( 0  B22) n2
 *                                n1  n2    n1  n2  *                                n1  n2    n1  n2
 *  *
 *  where N = n1+n2 and U' means the transpose of U. The first n1 columns  *  where N = n1+n2 and U**T means the transpose of U. The first n1 columns
 *  of U and W span the specified pair of left and right eigenspaces  *  of U and W span the specified pair of left and right eigenspaces
 *  (deflating subspaces) of (A, B).  *  (deflating subspaces) of (A, B).
 *  *
 *  If (A, B) has been obtained from the generalized real Schur  *  If (A, B) has been obtained from the generalized real Schur
 *  decomposition of a matrix pair (C, D) = Q*(A, B)*Z', then the  *  decomposition of a matrix pair (C, D) = Q*(A, B)*Z**T, then the
 *  reordered generalized real Schur form of (C, D) is given by  *  reordered generalized real Schur form of (C, D) is given by
 *  *
 *           (C, D) = (Q*U)*(U'*(A, B)*W)*(Z*W)',  *           (C, D) = (Q*U)*(U**T*(A, B)*W)*(Z*W)**T,
 *  *
 *  and the first n1 columns of Q*U and Z*W span the corresponding  *  and the first n1 columns of Q*U and Z*W span the corresponding
 *  deflating subspaces of (C, D) (Q and Z store Q*U and Z*W, resp.).  *  deflating subspaces of (C, D) (Q and Z store Q*U and Z*W, resp.).
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 *  where sigma-min(Zu) is the smallest singular value of the  *  where sigma-min(Zu) is the smallest singular value of the
 *  (2*n1*n2)-by-(2*n1*n2) matrix  *  (2*n1*n2)-by-(2*n1*n2) matrix
 *  *
 *       Zu = [ kron(In2, A11)  -kron(A22', In1) ]  *       Zu = [ kron(In2, A11)  -kron(A22**T, In1) ]
 *            [ kron(In2, B11)  -kron(B22', In1) ].  *            [ kron(In2, B11)  -kron(B22**T, In1) ].
 *  *
 *  Here, Inx is the identity matrix of size nx and A22' is the  *  Here, Inx is the identity matrix of size nx and A22**T is the
 *  transpose of A22. kron(X, Y) is the Kronecker product between  *  transpose of A22. kron(X, Y) is the Kronecker product between
 *  the matrices X and Y.  *  the matrices X and Y.
 *  *
Removed from v.1.8  
changed lines
  Added in v.1.9

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