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</span><span class="comment">*</span><span class="comment"> BWORK (workspace) LOGICAL array, dimension (N)
</span><span class="comment">*</span><span class="comment"> Not referenced if SORT = 'N'.
</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"> > 0: if INFO = i, and i is
</span><span class="comment">*</span><span class="comment"> <= N: the QR algorithm failed to compute all the
</span><span class="comment">*</span><span class="comment"> eigenvalues; elements 1:ILO-1 and i+1:N of WR and WI
</span><span class="comment">*</span><span class="comment"> contain those eigenvalues which have converged; if
</span><span class="comment">*</span><span class="comment"> JOBVS = 'V', VS contains the transformation which
</span><span class="comment">*</span><span class="comment"> reduces A to its partially converged Schur form.
</span><span class="comment">*</span><span class="comment"> = N+1: the eigenvalues could not be reordered because some
</span><span class="comment">*</span><span class="comment"> eigenvalues were too close to separate (the problem
</span><span class="comment">*</span><span class="comment"> is very ill-conditioned);
</span><span class="comment">*</span><span class="comment"> = N+2: after reordering, roundoff changed values of some
</span><span class="comment">*</span><span class="comment"> complex eigenvalues so that leading eigenvalues in
</span><span class="comment">*</span><span class="comment"> the Schur form no longer satisfy SELECT=.TRUE. This
</span><span class="comment">*</span><span class="comment"> could also be caused by underflow due to scaling.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> =====================================================================
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> .. Parameters ..
</span> REAL ZERO, ONE
PARAMETER ( ZERO = 0.0E0, ONE = 1.0E0 )
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Local Scalars ..
</span> LOGICAL CURSL, LASTSL, LQUERY, LST2SL, SCALEA, WANTSB,
$ WANTSE, WANTSN, WANTST, WANTSV, WANTVS
INTEGER HSWORK, I, I1, I2, IBAL, ICOND, IERR, IEVAL,
$ IHI, ILO, INXT, IP, ITAU, IWRK, LWRK, LIWRK,
$ MAXWRK, MINWRK
REAL ANRM, BIGNUM, CSCALE, EPS, SMLNUM
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Local Arrays ..
</span> REAL DUM( 1 )
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. External Subroutines ..
</span> EXTERNAL SCOPY, <a name="SGEBAK.204"></a><a href="sgebak.f.html#SGEBAK.1">SGEBAK</a>, <a name="SGEBAL.204"></a><a href="sgebal.f.html#SGEBAL.1">SGEBAL</a>, <a name="SGEHRD.204"></a><a href="sgehrd.f.html#SGEHRD.1">SGEHRD</a>, <a name="SHSEQR.204"></a><a href="shseqr.f.html#SHSEQR.1">SHSEQR</a>, <a name="SLABAD.204"></a><a href="slabad.f.html#SLABAD.1">SLABAD</a>,
$ <a name="SLACPY.205"></a><a href="slacpy.f.html#SLACPY.1">SLACPY</a>, <a name="SLASCL.205"></a><a href="slascl.f.html#SLASCL.1">SLASCL</a>, <a name="SORGHR.205"></a><a href="sorghr.f.html#SORGHR.1">SORGHR</a>, SSWAP, <a name="STRSEN.205"></a><a href="strsen.f.html#STRSEN.1">STRSEN</a>, <a name="XERBLA.205"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. External Functions ..
</span> LOGICAL <a name="LSAME.208"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
INTEGER <a name="ILAENV.209"></a><a href="hfy-index.html#ILAENV">ILAENV</a>
REAL <a name="SLAMCH.210"></a><a href="slamch.f.html#SLAMCH.1">SLAMCH</a>, <a name="SLANGE.210"></a><a href="slange.f.html#SLANGE.1">SLANGE</a>
EXTERNAL <a name="LSAME.211"></a><a href="lsame.f.html#LSAME.1">LSAME</a>, <a name="ILAENV.211"></a><a href="hfy-index.html#ILAENV">ILAENV</a>, <a name="SLAMCH.211"></a><a href="slamch.f.html#SLAMCH.1">SLAMCH</a>, <a name="SLANGE.211"></a><a href="slange.f.html#SLANGE.1">SLANGE</a>
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Intrinsic Functions ..
</span> INTRINSIC MAX, SQRT
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Executable Statements ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Test the input arguments
</span><span class="comment">*</span><span class="comment">
</span> INFO = 0
WANTVS = <a name="LSAME.221"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( JOBVS, <span class="string">'V'</span> )
WANTST = <a name="LSAME.222"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( SORT, <span class="string">'S'</span> )
WANTSN = <a name="LSAME.223"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( SENSE, <span class="string">'N'</span> )
WANTSE = <a name="LSAME.224"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( SENSE, <span class="string">'E'</span> )
WANTSV = <a name="LSAME.225"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( SENSE, <span class="string">'V'</span> )
WANTSB = <a name="LSAME.226"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( SENSE, <span class="string">'B'</span> )
LQUERY = ( LWORK.EQ.-1 .OR. LIWORK.EQ.-1 )
IF( ( .NOT.WANTVS ) .AND. ( .NOT.<a name="LSAME.228"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( JOBVS, <span class="string">'N'</span> ) ) ) THEN
INFO = -1
ELSE IF( ( .NOT.WANTST ) .AND. ( .NOT.<a name="LSAME.230"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( SORT, <span class="string">'N'</span> ) ) ) THEN
INFO = -2
ELSE IF( .NOT.( WANTSN .OR. WANTSE .OR. WANTSV .OR. WANTSB ) .OR.
$ ( .NOT.WANTST .AND. .NOT.WANTSN ) ) THEN
INFO = -4
ELSE IF( N.LT.0 ) THEN
INFO = -5
ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
INFO = -7
ELSE IF( LDVS.LT.1 .OR. ( WANTVS .AND. LDVS.LT.N ) ) THEN
INFO = -12
END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Compute workspace
</span><span class="comment">*</span><span class="comment"> (Note: Comments in the code beginning "RWorkspace:" describe the
</span><span class="comment">*</span><span class="comment"> minimal amount of real workspace needed at that point in the
</span><span class="comment">*</span><span class="comment"> code, as well as the preferred amount for good performance.
</span><span class="comment">*</span><span class="comment"> IWorkspace refers to integer workspace.
</span><span class="comment">*</span><span class="comment"> NB refers to the optimal block size for the immediately
</span><span class="comment">*</span><span class="comment"> following subroutine, as returned by <a name="ILAENV.249"></a><a href="hfy-index.html#ILAENV">ILAENV</a>.
</span><span class="comment">*</span><span class="comment"> HSWORK refers to the workspace preferred by <a name="SHSEQR.250"></a><a href="shseqr.f.html#SHSEQR.1">SHSEQR</a>, as
</span><span class="comment">*</span><span class="comment"> calculated below. HSWORK is computed assuming ILO=1 and IHI=N,
</span><span class="comment">*</span><span class="comment"> the worst case.
</span><span class="comment">*</span><span class="comment"> If SENSE = 'E', 'V' or 'B', then the amount of workspace needed
</span><span class="comment">*</span><span class="comment"> depends on SDIM, which is computed by the routine <a name="STRSEN.254"></a><a href="strsen.f.html#STRSEN.1">STRSEN</a> later
</span><span class="comment">*</span><span class="comment"> in the code.)
</span><span class="comment">*</span><span class="comment">
</span> IF( INFO.EQ.0 ) THEN
LIWRK = 1
IF( N.EQ.0 ) THEN
MINWRK = 1
LWRK = 1
ELSE
MAXWRK = 2*N + N*<a name="ILAENV.263"></a><a href="hfy-index.html#ILAENV">ILAENV</a>( 1, <span class="string">'<a name="SGEHRD.263"></a><a href="sgehrd.f.html#SGEHRD.1">SGEHRD</a>'</span>, <span class="string">' '</span>, N, 1, N, 0 )
MINWRK = 3*N
<span class="comment">*</span><span class="comment">
</span> CALL <a name="SHSEQR.266"></a><a href="shseqr.f.html#SHSEQR.1">SHSEQR</a>( <span class="string">'S'</span>, JOBVS, N, 1, N, A, LDA, WR, WI, VS, LDVS,
$ WORK, -1, IEVAL )
HSWORK = WORK( 1 )
<span class="comment">*</span><span class="comment">
</span> IF( .NOT.WANTVS ) THEN
MAXWRK = MAX( MAXWRK, N + HSWORK )
ELSE
MAXWRK = MAX( MAXWRK, 2*N + ( N - 1 )*<a name="ILAENV.273"></a><a href="hfy-index.html#ILAENV">ILAENV</a>( 1,
$ <span class="string">'<a name="SORGHR.274"></a><a href="sorghr.f.html#SORGHR.1">SORGHR</a>'</span>, <span class="string">' '</span>, N, 1, N, -1 ) )
MAXWRK = MAX( MAXWRK, N + HSWORK )
END IF
LWRK = MAXWRK
IF( .NOT.WANTSN )
$ LWRK = MAX( LWRK, N + ( N*N )/2 )
IF( WANTSV .OR. WANTSB )
$ LIWRK = ( N*N )/4
END IF
IWORK( 1 ) = LIWRK
WORK( 1 ) = LWRK
<span class="comment">*</span><span class="comment">
</span> IF( LWORK.LT.MINWRK .AND. .NOT.LQUERY ) THEN
INFO = -16
ELSE IF( LIWORK.LT.1 .AND. .NOT.LQUERY ) THEN
INFO = -18
END IF
END IF
<span class="comment">*</span><span class="comment">
</span> IF( INFO.NE.0 ) THEN
CALL <a name="XERBLA.294"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>( <span class="string">'<a name="SGEESX.294"></a><a href="sgeesx.f.html#SGEESX.1">SGEESX</a>'</span>, -INFO )
RETURN
END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Quick return if possible
</span><span class="comment">*</span><span class="comment">
</span> IF( N.EQ.0 ) THEN
SDIM = 0
RETURN
END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Get machine constants
</span><span class="comment">*</span><span class="comment">
</span> EPS = <a name="SLAMCH.307"></a><a href="slamch.f.html#SLAMCH.1">SLAMCH</a>( <span class="string">'P'</span> )
SMLNUM = <a name="SLAMCH.308"></a><a href="slamch.f.html#SLAMCH.1">SLAMCH</a>( <span class="string">'S'</span> )
BIGNUM = ONE / SMLNUM
CALL <a name="SLABAD.310"></a><a href="slabad.f.html#SLABAD.1">SLABAD</a>( SMLNUM, BIGNUM )
SMLNUM = SQRT( SMLNUM ) / EPS
BIGNUM = ONE / SMLNUM
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Scale A if max element outside range [SMLNUM,BIGNUM]
</span><span class="comment">*</span><span class="comment">
</span> ANRM = <a name="SLANGE.316"></a><a href="slange.f.html#SLANGE.1">SLANGE</a>( <span class="string">'M'</span>, N, N, A, LDA, DUM )
SCALEA = .FALSE.
IF( ANRM.GT.ZERO .AND. ANRM.LT.SMLNUM ) THEN
SCALEA = .TRUE.
CSCALE = SMLNUM
ELSE IF( ANRM.GT.BIGNUM ) THEN
SCALEA = .TRUE.
CSCALE = BIGNUM
END IF
IF( SCALEA )
$ CALL <a name="SLASCL.326"></a><a href="slascl.f.html#SLASCL.1">SLASCL</a>( <span class="string">'G'</span>, 0, 0, ANRM, CSCALE, N, N, A, LDA, IERR )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Permute the matrix to make it more nearly triangular
</span><span class="comment">*</span><span class="comment"> (RWorkspace: need N)
</span><span class="comment">*</span><span class="comment">
</span> IBAL = 1
CALL <a name="SGEBAL.332"></a><a href="sgebal.f.html#SGEBAL.1">SGEBAL</a>( <span class="string">'P'</span>, N, A, LDA, ILO, IHI, WORK( IBAL ), IERR )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Reduce to upper Hessenberg form
</span><span class="comment">*</span><span class="comment"> (RWorkspace: need 3*N, prefer 2*N+N*NB)
</span><span class="comment">*</span><span class="comment">
</span> ITAU = N + IBAL
IWRK = N + ITAU
CALL <a name="SGEHRD.339"></a><a href="sgehrd.f.html#SGEHRD.1">SGEHRD</a>( N, ILO, IHI, A, LDA, WORK( ITAU ), WORK( IWRK ),
$ LWORK-IWRK+1, IERR )
<span class="comment">*</span><span class="comment">
</span> IF( WANTVS ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Copy Householder vectors to VS
</span><span class="comment">*</span><span class="comment">
</span> CALL <a name="SLACPY.346"></a><a href="slacpy.f.html#SLACPY.1">SLACPY</a>( <span class="string">'L'</span>, N, N, A, LDA, VS, LDVS )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Generate orthogonal matrix in VS
</span><span class="comment">*</span><span class="comment"> (RWorkspace: need 3*N-1, prefer 2*N+(N-1)*NB)
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