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SUBROUTINE <a name="ZTGEXC.1"></a><a href="ztgexc.f.html#ZTGEXC.1">ZTGEXC</a>( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z,
$ LDZ, IFST, ILST, INFO )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> -- LAPACK routine (version 3.1) --
</span><span class="comment">*</span><span class="comment"> Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
</span><span class="comment">*</span><span class="comment"> November 2006
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> .. Scalar Arguments ..
</span> LOGICAL WANTQ, WANTZ
INTEGER IFST, ILST, INFO, LDA, LDB, LDQ, LDZ, N
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Array Arguments ..
</span> COMPLEX*16 A( LDA, * ), B( LDB, * ), Q( LDQ, * ),
$ Z( LDZ, * )
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Purpose
</span><span class="comment">*</span><span class="comment"> =======
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> <a name="ZTGEXC.20"></a><a href="ztgexc.f.html#ZTGEXC.1">ZTGEXC</a> reorders the generalized Schur decomposition of a complex
</span><span class="comment">*</span><span class="comment"> matrix pair (A,B), using an unitary equivalence transformation
</span><span class="comment">*</span><span class="comment"> (A, B) := Q * (A, B) * Z', so that the diagonal block of (A, B) with
</span><span class="comment">*</span><span class="comment"> row index IFST is moved to row ILST.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> (A, B) must be in generalized Schur canonical form, that is, A and
</span><span class="comment">*</span><span class="comment"> B are both upper triangular.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Optionally, the matrices Q and Z of generalized Schur vectors are
</span><span class="comment">*</span><span class="comment"> updated.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Q(in) * A(in) * Z(in)' = Q(out) * A(out) * Z(out)'
</span><span class="comment">*</span><span class="comment"> Q(in) * B(in) * Z(in)' = Q(out) * B(out) * Z(out)'
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Arguments
</span><span class="comment">*</span><span class="comment"> =========
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> WANTQ (input) LOGICAL
</span><span class="comment">*</span><span class="comment"> .TRUE. : update the left transformation matrix Q;
</span><span class="comment">*</span><span class="comment"> .FALSE.: do not update Q.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> WANTZ (input) LOGICAL
</span><span class="comment">*</span><span class="comment"> .TRUE. : update the right transformation matrix Z;
</span><span class="comment">*</span><span class="comment"> .FALSE.: do not update Z.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> N (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The order of the matrices A and B. N >= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> A (input/output) COMPLEX*16 array, dimension (LDA,N)
</span><span class="comment">*</span><span class="comment"> On entry, the upper triangular matrix A in the pair (A, B).
</span><span class="comment">*</span><span class="comment"> On exit, the updated matrix A.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> LDA (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The leading dimension of the array A. LDA >= max(1,N).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> B (input/output) COMPLEX*16 array, dimension (LDB,N)
</span><span class="comment">*</span><span class="comment"> On entry, the upper triangular matrix B in the pair (A, B).
</span><span class="comment">*</span><span class="comment"> On exit, the updated matrix B.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> LDB (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The leading dimension of the array B. LDB >= max(1,N).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Q (input/output) COMPLEX*16 array, dimension (LDZ,N)
</span><span class="comment">*</span><span class="comment"> On entry, if WANTQ = .TRUE., the unitary matrix Q.
</span><span class="comment">*</span><span class="comment"> On exit, the updated matrix Q.
</span><span class="comment">*</span><span class="comment"> If WANTQ = .FALSE., Q is not referenced.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> LDQ (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The leading dimension of the array Q. LDQ >= 1;
</span><span class="comment">*</span><span class="comment"> If WANTQ = .TRUE., LDQ >= N.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Z (input/output) COMPLEX*16 array, dimension (LDZ,N)
</span><span class="comment">*</span><span class="comment"> On entry, if WANTZ = .TRUE., the unitary matrix Z.
</span><span class="comment">*</span><span class="comment"> On exit, the updated matrix Z.
</span><span class="comment">*</span><span class="comment"> If WANTZ = .FALSE., Z is not referenced.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> LDZ (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The leading dimension of the array Z. LDZ >= 1;
</span><span class="comment">*</span><span class="comment"> If WANTZ = .TRUE., LDZ >= N.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> IFST (input) INTEGER
</span><span class="comment">*</span><span class="comment"> ILST (input/output) INTEGER
</span><span class="comment">*</span><span class="comment"> Specify the reordering of the diagonal blocks of (A, B).
</span><span class="comment">*</span><span class="comment"> The block with row index IFST is moved to row ILST, by a
</span><span class="comment">*</span><span class="comment"> sequence of swapping between adjacent blocks.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> INFO (output) INTEGER
</span><span class="comment">*</span><span class="comment"> =0: Successful exit.
</span><span class="comment">*</span><span class="comment"> <0: if INFO = -i, the i-th argument had an illegal value.
</span><span class="comment">*</span><span class="comment"> =1: The transformed matrix pair (A, B) would be too far
</span><span class="comment">*</span><span class="comment"> from generalized Schur form; the problem is ill-
</span><span class="comment">*</span><span class="comment"> conditioned. (A, B) may have been partially reordered,
</span><span class="comment">*</span><span class="comment"> and ILST points to the first row of the current
</span><span class="comment">*</span><span class="comment"> position of the block being moved.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Further Details
</span><span class="comment">*</span><span class="comment"> ===============
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