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SUBROUTINE <a name="CGEESX.1"></a><a href="cgeesx.f.html#CGEESX.1">CGEESX</a>( JOBVS, SORT, SELECT, SENSE, N, A, LDA, SDIM, W,
$ VS, LDVS, RCONDE, RCONDV, WORK, LWORK, RWORK,
$ BWORK, INFO )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> -- LAPACK driver 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> CHARACTER JOBVS, SENSE, SORT
INTEGER INFO, LDA, LDVS, LWORK, N, SDIM
REAL RCONDE, RCONDV
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Array Arguments ..
</span> LOGICAL BWORK( * )
REAL RWORK( * )
COMPLEX A( LDA, * ), VS( LDVS, * ), W( * ), WORK( * )
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Function Arguments ..
</span> LOGICAL SELECT
EXTERNAL SELECT
<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="CGEESX.27"></a><a href="cgeesx.f.html#CGEESX.1">CGEESX</a> computes for an N-by-N complex nonsymmetric matrix A, the
</span><span class="comment">*</span><span class="comment"> eigenvalues, the Schur form T, and, optionally, the matrix of Schur
</span><span class="comment">*</span><span class="comment"> vectors Z. This gives the Schur factorization A = Z*T*(Z**H).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Optionally, it also orders the eigenvalues on the diagonal of the
</span><span class="comment">*</span><span class="comment"> Schur form so that selected eigenvalues are at the top left;
</span><span class="comment">*</span><span class="comment"> computes a reciprocal condition number for the average of the
</span><span class="comment">*</span><span class="comment"> selected eigenvalues (RCONDE); and computes a reciprocal condition
</span><span class="comment">*</span><span class="comment"> number for the right invariant subspace corresponding to the
</span><span class="comment">*</span><span class="comment"> selected eigenvalues (RCONDV). The leading columns of Z form an
</span><span class="comment">*</span><span class="comment"> orthonormal basis for this invariant subspace.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> For further explanation of the reciprocal condition numbers RCONDE
</span><span class="comment">*</span><span class="comment"> and RCONDV, see Section 4.10 of the LAPACK Users' Guide (where
</span><span class="comment">*</span><span class="comment"> these quantities are called s and sep respectively).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> A complex matrix is in Schur form if it is upper triangular.
</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"> JOBVS (input) CHARACTER*1
</span><span class="comment">*</span><span class="comment"> = 'N': Schur vectors are not computed;
</span><span class="comment">*</span><span class="comment"> = 'V': Schur vectors are computed.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> SORT (input) CHARACTER*1
</span><span class="comment">*</span><span class="comment"> Specifies whether or not to order the eigenvalues on the
</span><span class="comment">*</span><span class="comment"> diagonal of the Schur form.
</span><span class="comment">*</span><span class="comment"> = 'N': Eigenvalues are not ordered;
</span><span class="comment">*</span><span class="comment"> = 'S': Eigenvalues are ordered (see SELECT).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> SELECT (external procedure) LOGICAL FUNCTION of one COMPLEX argument
</span><span class="comment">*</span><span class="comment"> SELECT must be declared EXTERNAL in the calling subroutine.
</span><span class="comment">*</span><span class="comment"> If SORT = 'S', SELECT is used to select eigenvalues to order
</span><span class="comment">*</span><span class="comment"> to the top left of the Schur form.
</span><span class="comment">*</span><span class="comment"> If SORT = 'N', SELECT is not referenced.
</span><span class="comment">*</span><span class="comment"> An eigenvalue W(j) is selected if SELECT(W(j)) is true.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> SENSE (input) CHARACTER*1
</span><span class="comment">*</span><span class="comment"> Determines which reciprocal condition numbers are computed.
</span><span class="comment">*</span><span class="comment"> = 'N': None are computed;
</span><span class="comment">*</span><span class="comment"> = 'E': Computed for average of selected eigenvalues only;
</span><span class="comment">*</span><span class="comment"> = 'V': Computed for selected right invariant subspace only;
</span><span class="comment">*</span><span class="comment"> = 'B': Computed for both.
</span><span class="comment">*</span><span class="comment"> If SENSE = 'E', 'V' or 'B', SORT must equal 'S'.
</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 A. N >= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> A (input/output) COMPLEX array, dimension (LDA, N)
</span><span class="comment">*</span><span class="comment"> On entry, the N-by-N matrix A.
</span><span class="comment">*</span><span class="comment"> On exit, A is overwritten by its Schur form T.
</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"> SDIM (output) INTEGER
</span><span class="comment">*</span><span class="comment"> If SORT = 'N', SDIM = 0.
</span><span class="comment">*</span><span class="comment"> If SORT = 'S', SDIM = number of eigenvalues for which
</span><span class="comment">*</span><span class="comment"> SELECT is true.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> W (output) COMPLEX array, dimension (N)
</span><span class="comment">*</span><span class="comment"> W contains the computed eigenvalues, in the same order
</span><span class="comment">*</span><span class="comment"> that they appear on the diagonal of the output Schur form T.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> VS (output) COMPLEX array, dimension (LDVS,N)
</span><span class="comment">*</span><span class="comment"> If JOBVS = 'V', VS contains the unitary matrix Z of Schur
</span><span class="comment">*</span><span class="comment"> vectors.
</span><span class="comment">*</span><span class="comment"> If JOBVS = 'N', VS is not referenced.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> LDVS (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The leading dimension of the array VS. LDVS >= 1, and if
</span><span class="comment">*</span><span class="comment"> JOBVS = 'V', LDVS >= N.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> RCONDE (output) REAL
</span><span class="comment">*</span><span class="comment"> If SENSE = 'E' or 'B', RCONDE contains the reciprocal
</span><span class="comment">*</span><span class="comment"> condition number for the average of the selected eigenvalues.
</span><span class="comment">*</span><span class="comment"> Not referenced if SENSE = 'N' or 'V'.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> RCONDV (output) REAL
</span><span class="comment">*</span><span class="comment"> If SENSE = 'V' or 'B', RCONDV contains the reciprocal
</span><span class="comment">*</span><span class="comment"> condition number for the selected right invariant subspace.
</span><span class="comment">*</span><span class="comment"> Not referenced if SENSE = 'N' or 'E'.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> WORK (workspace/output) COMPLEX 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. LWORK >= max(1,2*N).
</span><span class="comment">*</span><span class="comment"> Also, if SENSE = 'E' or 'V' or 'B', LWORK >= 2*SDIM*(N-SDIM),
</span><span class="comment">*</span><span class="comment"> where SDIM is the number of selected eigenvalues computed by
</span><span class="comment">*</span><span class="comment"> this routine. Note that 2*SDIM*(N-SDIM) <= N*N/2. Note also
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