!>
!> CTRSEN reorders the Schur factorization of a complex matrix
!> A = Q*T*Q**H, so that a selected cluster of eigenvalues appears in
!> the leading positions on the diagonal of the upper triangular matrix
!> T, and the leading columns of Q form an orthonormal basis of the
!> corresponding right invariant subspace.
!>
!> Optionally the routine computes the reciprocal condition numbers of
!> the cluster of eigenvalues and/or the invariant subspace.
!> 

JOB

!>          JOB is CHARACTER*1
!>          Specifies whether condition numbers are required for the
!>          cluster of eigenvalues (S) or the invariant subspace (SEP):
!>          = 'N': none;
!>          = 'E': for eigenvalues only (S);
!>          = 'V': for invariant subspace only (SEP);
!>          = 'B': for both eigenvalues and invariant subspace (S and
!>                 SEP).
!> 

COMPQ

!>          COMPQ is CHARACTER*1
!>          = 'V': update the matrix Q of Schur vectors;
!>          = 'N': do not update Q.
!> 

SELECT

!>          SELECT is LOGICAL array, dimension (N)
!>          SELECT specifies the eigenvalues in the selected cluster. To
!>          select the j-th eigenvalue, SELECT(j) must be set to .TRUE..
!> 

N

!>          N is INTEGER
!>          The order of the matrix T. N >= 0.
!> 

T

!>          T is COMPLEX array, dimension (LDT,N)
!>          On entry, the upper triangular matrix T.
!>          On exit, T is overwritten by the reordered matrix T, with the
!>          selected eigenvalues as the leading diagonal elements.
!> 

LDT

!>          LDT is INTEGER
!>          The leading dimension of the array T. LDT >= max(1,N).
!> 

Q

!>          Q is COMPLEX array, dimension (LDQ,N)
!>          On entry, if COMPQ = 'V', the matrix Q of Schur vectors.
!>          On exit, if COMPQ = 'V', Q has been postmultiplied by the
!>          unitary transformation matrix which reorders T; the leading M
!>          columns of Q form an orthonormal basis for the specified
!>          invariant subspace.
!>          If COMPQ = 'N', Q is not referenced.
!> 

LDQ

!>          LDQ is INTEGER
!>          The leading dimension of the array Q.
!>          LDQ >= 1; and if COMPQ = 'V', LDQ >= N.
!> 

W

!>          W is COMPLEX array, dimension (N)
!>          The reordered eigenvalues of T, in the same order as they
!>          appear on the diagonal of T.
!> 

M

!>          M is INTEGER
!>          The dimension of the specified invariant subspace.
!>          0 <= M <= N.
!> 

S

!>          S is REAL
!>          If JOB = 'E' or 'B', S is a lower bound on the reciprocal
!>          condition number for the selected cluster of eigenvalues.
!>          S cannot underestimate the true reciprocal condition number
!>          by more than a factor of sqrt(N). If M = 0 or N, S = 1.
!>          If JOB = 'N' or 'V', S is not referenced.
!> 

SEP

!>          SEP is REAL
!>          If JOB = 'V' or 'B', SEP is the estimated reciprocal
!>          condition number of the specified invariant subspace. If
!>          M = 0 or N, SEP = norm(T).
!>          If JOB = 'N' or 'E', SEP is not referenced.
!> 

WORK

!>          WORK is COMPLEX array, dimension (MAX(1,LWORK))
!>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
!> 

LWORK

!>          LWORK is INTEGER
!>          The dimension of the array WORK.
!>          If JOB = 'N', LWORK >= 1;
!>          if JOB = 'E', LWORK = max(1,M*(N-M));
!>          if JOB = 'V' or 'B', LWORK >= max(1,2*M*(N-M)).
!>
!>          If LWORK = -1, then a workspace query is assumed; the routine
!>          only calculates the optimal size of the WORK array, returns
!>          this value as the first entry of the WORK array, and no error
!>          message related to LWORK is issued by XERBLA.
!> 

INFO

!>          INFO is INTEGER
!>          = 0:  successful exit
!>          < 0:  if INFO = -i, the i-th argument had an illegal value
!> 

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!>
!>  CTRSEN first collects the selected eigenvalues by computing a unitary
!>  transformation Z to move them to the top left corner of T. In other
!>  words, the selected eigenvalues are the eigenvalues of T11 in:
!>
!>          Z**H * T * Z = ( T11 T12 ) n1
!>                         (  0  T22 ) n2
!>                            n1  n2
!>
!>  where N = n1+n2. The first
!>  n1 columns of Z span the specified invariant subspace of T.
!>
!>  If T has been obtained from the Schur factorization of a matrix
!>  A = Q*T*Q**H, then the reordered Schur factorization of A is given by
!>  A = (Q*Z)*(Z**H*T*Z)*(Q*Z)**H, and the first n1 columns of Q*Z span the
!>  corresponding invariant subspace of A.
!>
!>  The reciprocal condition number of the average of the eigenvalues of
!>  T11 may be returned in S. S lies between 0 (very badly conditioned)
!>  and 1 (very well conditioned). It is computed as follows. First we
!>  compute R so that
!>
!>                         P = ( I  R ) n1
!>                             ( 0  0 ) n2
!>                               n1 n2
!>
!>  is the projector on the invariant subspace associated with T11.
!>  R is the solution of the Sylvester equation:
!>
!>                        T11*R - R*T22 = T12.
!>
!>  Let F-norm(M) denote the Frobenius-norm of M and 2-norm(M) denote
!>  the two-norm of M. Then S is computed as the lower bound
!>
!>                      (1 + F-norm(R)**2)**(-1/2)
!>
!>  on the reciprocal of 2-norm(P), the true reciprocal condition number.
!>  S cannot underestimate 1 / 2-norm(P) by more than a factor of
!>  sqrt(N).
!>
!>  An approximate error bound for the computed average of the
!>  eigenvalues of T11 is
!>
!>                         EPS * norm(T) / S
!>
!>  where EPS is the machine precision.
!>
!>  The reciprocal condition number of the right invariant subspace
!>  spanned by the first n1 columns of Z (or of Q*Z) is returned in SEP.
!>  SEP is defined as the separation of T11 and T22:
!>
!>                     sep( T11, T22 ) = sigma-min( C )
!>
!>  where sigma-min(C) is the smallest singular value of the
!>  n1*n2-by-n1*n2 matrix
!>
!>     C  = kprod( I(n2), T11 ) - kprod( transpose(T22), I(n1) )
!>
!>  I(m) is an m by m identity matrix, and kprod denotes the Kronecker
!>  product. We estimate sigma-min(C) by the reciprocal of an estimate of
!>  the 1-norm of inverse(C). The true reciprocal 1-norm of inverse(C)
!>  cannot differ from sigma-min(C) by more than a factor of sqrt(n1*n2).
!>
!>  When SEP is small, small changes in T can cause large changes in
!>  the invariant subspace. An approximate bound on the maximum angular
!>  error in the computed right invariant subspace is
!>
!>                      EPS * norm(T) / SEP
!>