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SUBROUTINE <a name="STRSEN.1"></a><a href="strsen.f.html#STRSEN.1">STRSEN</a>( JOB, COMPQ, SELECT, N, T, LDT, Q, LDQ, WR, WI,
$ M, S, SEP, WORK, LWORK, IWORK, LIWORK, 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"> Modified to call <a name="SLACN2.8"></a><a href="slacn2.f.html#SLACN2.1">SLACN2</a> in place of <a name="SLACON.8"></a><a href="slacon.f.html#SLACON.1">SLACON</a>, 7 Feb 03, SJH.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> .. Scalar Arguments ..
</span> CHARACTER COMPQ, JOB
INTEGER INFO, LDQ, LDT, LIWORK, LWORK, M, N
REAL S, SEP
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Array Arguments ..
</span> LOGICAL SELECT( * )
INTEGER IWORK( * )
REAL Q( LDQ, * ), T( LDT, * ), WI( * ), WORK( * ),
$ WR( * )
<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="STRSEN.25"></a><a href="strsen.f.html#STRSEN.1">STRSEN</a> reorders the real Schur factorization of a real matrix
</span><span class="comment">*</span><span class="comment"> A = Q*T*Q**T, so that a selected cluster of eigenvalues appears in
</span><span class="comment">*</span><span class="comment"> the leading diagonal blocks of the upper quasi-triangular matrix T,
</span><span class="comment">*</span><span class="comment"> and the leading columns of Q form an orthonormal basis of the
</span><span class="comment">*</span><span class="comment"> corresponding right invariant subspace.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Optionally the routine computes the reciprocal condition numbers of
</span><span class="comment">*</span><span class="comment"> the cluster of eigenvalues and/or the invariant subspace.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> T must be in Schur canonical form (as returned by <a name="SHSEQR.34"></a><a href="shseqr.f.html#SHSEQR.1">SHSEQR</a>), that is,
</span><span class="comment">*</span><span class="comment"> block upper triangular with 1-by-1 and 2-by-2 diagonal blocks; each
</span><span class="comment">*</span><span class="comment"> 2-by-2 diagonal block has its diagonal elemnts equal and its
</span><span class="comment">*</span><span class="comment"> off-diagonal elements of opposite sign.
</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"> JOB (input) CHARACTER*1
</span><span class="comment">*</span><span class="comment"> Specifies whether condition numbers are required for the
</span><span class="comment">*</span><span class="comment"> cluster of eigenvalues (S) or the invariant subspace (SEP):
</span><span class="comment">*</span><span class="comment"> = 'N': none;
</span><span class="comment">*</span><span class="comment"> = 'E': for eigenvalues only (S);
</span><span class="comment">*</span><span class="comment"> = 'V': for invariant subspace only (SEP);
</span><span class="comment">*</span><span class="comment"> = 'B': for both eigenvalues and invariant subspace (S and
</span><span class="comment">*</span><span class="comment"> SEP).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> COMPQ (input) CHARACTER*1
</span><span class="comment">*</span><span class="comment"> = 'V': update the matrix Q of Schur vectors;
</span><span class="comment">*</span><span class="comment"> = 'N': do not update Q.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> SELECT (input) LOGICAL array, dimension (N)
</span><span class="comment">*</span><span class="comment"> SELECT specifies the eigenvalues in the selected cluster. To
</span><span class="comment">*</span><span class="comment"> select a real eigenvalue w(j), SELECT(j) must be set to
</span><span class="comment">*</span><span class="comment"> .TRUE.. To select a complex conjugate pair of eigenvalues
</span><span class="comment">*</span><span class="comment"> w(j) and w(j+1), corresponding to a 2-by-2 diagonal block,
</span><span class="comment">*</span><span class="comment"> either SELECT(j) or SELECT(j+1) or both must be set to
</span><span class="comment">*</span><span class="comment"> .TRUE.; a complex conjugate pair of eigenvalues must be
</span><span class="comment">*</span><span class="comment"> either both included in the cluster or both excluded.
</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 matrix T. N >= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> T (input/output) REAL array, dimension (LDT,N)
</span><span class="comment">*</span><span class="comment"> On entry, the upper quasi-triangular matrix T, in Schur
</span><span class="comment">*</span><span class="comment"> canonical form.
</span><span class="comment">*</span><span class="comment"> On exit, T is overwritten by the reordered matrix T, again in
</span><span class="comment">*</span><span class="comment"> Schur canonical form, with the selected eigenvalues in the
</span><span class="comment">*</span><span class="comment"> leading diagonal blocks.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> LDT (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The leading dimension of the array T. LDT >= max(1,N).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Q (input/output) REAL array, dimension (LDQ,N)
</span><span class="comment">*</span><span class="comment"> On entry, if COMPQ = 'V', the matrix Q of Schur vectors.
</span><span class="comment">*</span><span class="comment"> On exit, if COMPQ = 'V', Q has been postmultiplied by the
</span><span class="comment">*</span><span class="comment"> orthogonal transformation matrix which reorders T; the
</span><span class="comment">*</span><span class="comment"> leading M columns of Q form an orthonormal basis for the
</span><span class="comment">*</span><span class="comment"> specified invariant subspace.
</span><span class="comment">*</span><span class="comment"> If COMPQ = 'N', 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.
</span><span class="comment">*</span><span class="comment"> LDQ >= 1; and if COMPQ = 'V', LDQ >= N.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> WR (output) REAL array, dimension (N)
</span><span class="comment">*</span><span class="comment"> WI (output) REAL array, dimension (N)
</span><span class="comment">*</span><span class="comment"> The real and imaginary parts, respectively, of the reordered
</span><span class="comment">*</span><span class="comment"> eigenvalues of T. The eigenvalues are stored in the same
</span><span class="comment">*</span><span class="comment"> order as on the diagonal of T, with WR(i) = T(i,i) and, if
</span><span class="comment">*</span><span class="comment"> T(i:i+1,i:i+1) is a 2-by-2 diagonal block, WI(i) > 0 and
</span><span class="comment">*</span><span class="comment"> WI(i+1) = -WI(i). Note that if a complex eigenvalue is
</span><span class="comment">*</span><span class="comment"> sufficiently ill-conditioned, then its value may differ
</span><span class="comment">*</span><span class="comment"> significantly from its value before reordering.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> M (output) INTEGER
</span><span class="comment">*</span><span class="comment"> The dimension of the specified invariant subspace.
</span><span class="comment">*</span><span class="comment"> 0 < = M <= N.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> S (output) REAL
</span><span class="comment">*</span><span class="comment"> If JOB = 'E' or 'B', S is a lower bound on the reciprocal
</span><span class="comment">*</span><span class="comment"> condition number for the selected cluster of eigenvalues.
</span><span class="comment">*</span><span class="comment"> S cannot underestimate the true reciprocal condition number
</span><span class="comment">*</span><span class="comment"> by more than a factor of sqrt(N). If M = 0 or N, S = 1.
</span><span class="comment">*</span><span class="comment"> If JOB = 'N' or 'V', S is not referenced.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> SEP (output) REAL
</span><span class="comment">*</span><span class="comment"> If JOB = 'V' or 'B', SEP is the estimated reciprocal
</span><span class="comment">*</span><span class="comment"> condition number of the specified invariant subspace. If
</span><span class="comment">*</span><span class="comment"> M = 0 or N, SEP = norm(T).
</span><span class="comment">*</span><span class="comment"> If JOB = 'N' or 'E', SEP is not referenced.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> WORK (workspace/output) REAL array, dimension (MAX(1,LWORK))
</span><span class="comment">*</span><span class="comment"> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> LWORK (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The dimension of the array WORK.
</span><span class="comment">*</span><span class="comment"> If JOB = 'N', LWORK >= max(1,N);
</span><span class="comment">*</span><span class="comment"> if JOB = 'E', LWORK >= max(1,M*(N-M));
</span><span class="comment">*</span><span class="comment"> if JOB = 'V' or 'B', LWORK >= max(1,2*M*(N-M)).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> If LWORK = -1, then a workspace query is assumed; the routine
</span><span class="comment">*</span><span class="comment"> only calculates the optimal size of the WORK array, returns
</span><span class="comment">*</span><span class="comment"> this value as the first entry of the WORK array, and no error
</span><span class="comment">*</span><span class="comment"> message related to LWORK is issued by <a name="XERBLA.128"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> IWORK (workspace) INTEGER array, dimension (MAX(1,LIWORK))
</span><span class="comment">*</span><span class="comment"> On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> LIWORK (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The dimension of the array IWORK.
</span><span class="comment">*</span><span class="comment"> If JOB = 'N' or 'E', LIWORK >= 1;
</span><span class="comment">*</span><span class="comment"> if JOB = 'V' or 'B', LIWORK >= max(1,M*(N-M)).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> If LIWORK = -1, then a workspace query is assumed; the
</span><span class="comment">*</span><span class="comment"> routine only calculates the optimal size of the IWORK array,
</span><span class="comment">*</span><span class="comment"> returns this value as the first entry of the IWORK array, and
</span><span class="comment">*</span><span class="comment"> no error message related to LIWORK is issued by <a name="XERBLA.141"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> INFO (output) INTEGER
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