Move LAPACK trunk into position.

1 files changed, 1243 insertions, 0 deletions

diff --git a/SRC/shgeqz.f b/SRC/shgeqz.f
new file mode 100644
index 00000000..2f02b6d8
--- /dev/null
+++ b/SRC/shgeqz.f
@@ -0,0 +1,1243 @@
+      SUBROUTINE SHGEQZ( JOB, COMPQ, COMPZ, N, ILO, IHI, H, LDH, T, LDT,
+     $                   ALPHAR, ALPHAI, BETA, Q, LDQ, Z, LDZ, WORK,
+     $                   LWORK, INFO )
+*
+*  -- LAPACK routine (version 3.1) --
+*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
+*     November 2006
+*
+*     .. Scalar Arguments ..
+      CHARACTER          COMPQ, COMPZ, JOB
+      INTEGER            IHI, ILO, INFO, LDH, LDQ, LDT, LDZ, LWORK, N
+*     ..
+*     .. Array Arguments ..
+      REAL               ALPHAI( * ), ALPHAR( * ), BETA( * ),
+     $                   H( LDH, * ), Q( LDQ, * ), T( LDT, * ),
+     $                   WORK( * ), Z( LDZ, * )
+*     ..
+*
+*  Purpose
+*  =======
+*
+*  SHGEQZ computes the eigenvalues of a real matrix pair (H,T),
+*  where H is an upper Hessenberg matrix and T is upper triangular,
+*  using the double-shift QZ method.
+*  Matrix pairs of this type are produced by the reduction to
+*  generalized upper Hessenberg form of a real matrix pair (A,B):
+*
+*     A = Q1*H*Z1**T,  B = Q1*T*Z1**T,
+*
+*  as computed by SGGHRD.
+*
+*  If JOB='S', then the Hessenberg-triangular pair (H,T) is
+*  also reduced to generalized Schur form,
+*  
+*     H = Q*S*Z**T,  T = Q*P*Z**T,
+*  
+*  where Q and Z are orthogonal matrices, P is an upper triangular
+*  matrix, and S is a quasi-triangular matrix with 1-by-1 and 2-by-2
+*  diagonal blocks.
+*
+*  The 1-by-1 blocks correspond to real eigenvalues of the matrix pair
+*  (H,T) and the 2-by-2 blocks correspond to complex conjugate pairs of
+*  eigenvalues.
+*
+*  Additionally, the 2-by-2 upper triangular diagonal blocks of P
+*  corresponding to 2-by-2 blocks of S are reduced to positive diagonal
+*  form, i.e., if S(j+1,j) is non-zero, then P(j+1,j) = P(j,j+1) = 0,
+*  P(j,j) > 0, and P(j+1,j+1) > 0.
+*
+*  Optionally, the orthogonal matrix Q from the generalized Schur
+*  factorization may be postmultiplied into an input matrix Q1, and the
+*  orthogonal matrix Z may be postmultiplied into an input matrix Z1.
+*  If Q1 and Z1 are the orthogonal matrices from SGGHRD that reduced
+*  the matrix pair (A,B) to generalized upper Hessenberg form, then the
+*  output matrices Q1*Q and Z1*Z are the orthogonal factors from the
+*  generalized Schur factorization of (A,B):
+*
+*     A = (Q1*Q)*S*(Z1*Z)**T,  B = (Q1*Q)*P*(Z1*Z)**T.
+*  
+*  To avoid overflow, eigenvalues of the matrix pair (H,T) (equivalently,
+*  of (A,B)) are computed as a pair of values (alpha,beta), where alpha is
+*  complex and beta real.
+*  If beta is nonzero, lambda = alpha / beta is an eigenvalue of the
+*  generalized nonsymmetric eigenvalue problem (GNEP)
+*     A*x = lambda*B*x
+*  and if alpha is nonzero, mu = beta / alpha is an eigenvalue of the
+*  alternate form of the GNEP
+*     mu*A*y = B*y.
+*  Real eigenvalues can be read directly from the generalized Schur
+*  form: 
+*    alpha = S(i,i), beta = P(i,i).
+*
+*  Ref: C.B. Moler & G.W. Stewart, "An Algorithm for Generalized Matrix
+*       Eigenvalue Problems", SIAM J. Numer. Anal., 10(1973),
+*       pp. 241--256.
+*
+*  Arguments
+*  =========
+*
+*  JOB     (input) CHARACTER*1
+*          = 'E': Compute eigenvalues only;
+*          = 'S': Compute eigenvalues and the Schur form. 
+*
+*  COMPQ   (input) CHARACTER*1
+*          = 'N': Left Schur vectors (Q) are not computed;
+*          = 'I': Q is initialized to the unit matrix and the matrix Q
+*                 of left Schur vectors of (H,T) is returned;
+*          = 'V': Q must contain an orthogonal matrix Q1 on entry and
+*                 the product Q1*Q is returned.
+*
+*  COMPZ   (input) CHARACTER*1
+*          = 'N': Right Schur vectors (Z) are not computed;
+*          = 'I': Z is initialized to the unit matrix and the matrix Z
+*                 of right Schur vectors of (H,T) is returned;
+*          = 'V': Z must contain an orthogonal matrix Z1 on entry and
+*                 the product Z1*Z is returned.
+*
+*  N       (input) INTEGER
+*          The order of the matrices H, T, Q, and Z.  N >= 0.
+*
+*  ILO     (input) INTEGER
+*  IHI     (input) INTEGER
+*          ILO and IHI mark the rows and columns of H which are in
+*          Hessenberg form.  It is assumed that A is already upper
+*          triangular in rows and columns 1:ILO-1 and IHI+1:N.
+*          If N > 0, 1 <= ILO <= IHI <= N; if N = 0, ILO=1 and IHI=0.
+*
+*  H       (input/output) REAL array, dimension (LDH, N)
+*          On entry, the N-by-N upper Hessenberg matrix H.
+*          On exit, if JOB = 'S', H contains the upper quasi-triangular
+*          matrix S from the generalized Schur factorization;
+*          2-by-2 diagonal blocks (corresponding to complex conjugate
+*          pairs of eigenvalues) are returned in standard form, with
+*          H(i,i) = H(i+1,i+1) and H(i+1,i)*H(i,i+1) < 0.
+*          If JOB = 'E', the diagonal blocks of H match those of S, but
+*          the rest of H is unspecified.
+*
+*  LDH     (input) INTEGER
+*          The leading dimension of the array H.  LDH >= max( 1, N ).
+*
+*  T       (input/output) REAL array, dimension (LDT, N)
+*          On entry, the N-by-N upper triangular matrix T.
+*          On exit, if JOB = 'S', T contains the upper triangular
+*          matrix P from the generalized Schur factorization;
+*          2-by-2 diagonal blocks of P corresponding to 2-by-2 blocks of S
+*          are reduced to positive diagonal form, i.e., if H(j+1,j) is
+*          non-zero, then T(j+1,j) = T(j,j+1) = 0, T(j,j) > 0, and
+*          T(j+1,j+1) > 0.
+*          If JOB = 'E', the diagonal blocks of T match those of P, but
+*          the rest of T is unspecified.
+*
+*  LDT     (input) INTEGER
+*          The leading dimension of the array T.  LDT >= max( 1, N ).
+*
+*  ALPHAR  (output) REAL array, dimension (N)
+*          The real parts of each scalar alpha defining an eigenvalue
+*          of GNEP.
+*
+*  ALPHAI  (output) REAL array, dimension (N)
+*          The imaginary parts of each scalar alpha defining an
+*          eigenvalue of GNEP.
+*          If ALPHAI(j) is zero, then the j-th eigenvalue is real; if
+*          positive, then the j-th and (j+1)-st eigenvalues are a
+*          complex conjugate pair, with ALPHAI(j+1) = -ALPHAI(j).
+*
+*  BETA    (output) REAL array, dimension (N)
+*          The scalars beta that define the eigenvalues of GNEP.
+*          Together, the quantities alpha = (ALPHAR(j),ALPHAI(j)) and
+*          beta = BETA(j) represent the j-th eigenvalue of the matrix
+*          pair (A,B), in one of the forms lambda = alpha/beta or
+*          mu = beta/alpha.  Since either lambda or mu may overflow,
+*          they should not, in general, be computed.
+*
+*  Q       (input/output) REAL array, dimension (LDQ, N)
+*          On entry, if COMPZ = 'V', the orthogonal matrix Q1 used in
+*          the reduction of (A,B) to generalized Hessenberg form.
+*          On exit, if COMPZ = 'I', the orthogonal matrix of left Schur
+*          vectors of (H,T), and if COMPZ = 'V', the orthogonal matrix
+*          of left Schur vectors of (A,B).
+*          Not referenced if COMPZ = 'N'.
+*
+*  LDQ     (input) INTEGER
+*          The leading dimension of the array Q.  LDQ >= 1.
+*          If COMPQ='V' or 'I', then LDQ >= N.
+*
+*  Z       (input/output) REAL array, dimension (LDZ, N)
+*          On entry, if COMPZ = 'V', the orthogonal matrix Z1 used in
+*          the reduction of (A,B) to generalized Hessenberg form.
+*          On exit, if COMPZ = 'I', the orthogonal matrix of
+*          right Schur vectors of (H,T), and if COMPZ = 'V', the
+*          orthogonal matrix of right Schur vectors of (A,B).
+*          Not referenced if COMPZ = 'N'.
+*
+*  LDZ     (input) INTEGER
+*          The leading dimension of the array Z.  LDZ >= 1.
+*          If COMPZ='V' or 'I', then LDZ >= N.
+*
+*  WORK    (workspace/output) REAL array, dimension (MAX(1,LWORK))
+*          On exit, if INFO >= 0, WORK(1) returns the optimal LWORK.
+*
+*  LWORK   (input) INTEGER
+*          The dimension of the array WORK.  LWORK >= max(1,N).
+*
+*          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    (output) INTEGER
+*          = 0: successful exit
+*          < 0: if INFO = -i, the i-th argument had an illegal value
+*          = 1,...,N: the QZ iteration did not converge.  (H,T) is not
+*                     in Schur form, but ALPHAR(i), ALPHAI(i), and
+*                     BETA(i), i=INFO+1,...,N should be correct.
+*          = N+1,...,2*N: the shift calculation failed.  (H,T) is not
+*                     in Schur form, but ALPHAR(i), ALPHAI(i), and
+*                     BETA(i), i=INFO-N+1,...,N should be correct.
+*
+*  Further Details
+*  ===============
+*
+*  Iteration counters:
+*
+*  JITER  -- counts iterations.
+*  IITER  -- counts iterations run since ILAST was last
+*            changed.  This is therefore reset only when a 1-by-1 or
+*            2-by-2 block deflates off the bottom.
+*
+*  =====================================================================
+*
+*     .. Parameters ..
+*    $                     SAFETY = 1.0E+0 )
+      REAL               HALF, ZERO, ONE, SAFETY
+      PARAMETER          ( HALF = 0.5E+0, ZERO = 0.0E+0, ONE = 1.0E+0,
+     $                   SAFETY = 1.0E+2 )
+*     ..
+*     .. Local Scalars ..
+      LOGICAL            ILAZR2, ILAZRO, ILPIVT, ILQ, ILSCHR, ILZ,
+     $                   LQUERY
+      INTEGER            ICOMPQ, ICOMPZ, IFIRST, IFRSTM, IITER, ILAST,
+     $                   ILASTM, IN, ISCHUR, ISTART, J, JC, JCH, JITER,
+     $                   JR, MAXIT
+      REAL               A11, A12, A1I, A1R, A21, A22, A2I, A2R, AD11,
+     $                   AD11L, AD12, AD12L, AD21, AD21L, AD22, AD22L,
+     $                   AD32L, AN, ANORM, ASCALE, ATOL, B11, B1A, B1I,
+     $                   B1R, B22, B2A, B2I, B2R, BN, BNORM, BSCALE,
+     $                   BTOL, C, C11I, C11R, C12, C21, C22I, C22R, CL,
+     $                   CQ, CR, CZ, ESHIFT, S, S1, S1INV, S2, SAFMAX,
+     $                   SAFMIN, SCALE, SL, SQI, SQR, SR, SZI, SZR, T1,
+     $                   TAU, TEMP, TEMP2, TEMPI, TEMPR, U1, U12, U12L,
+     $                   U2, ULP, VS, W11, W12, W21, W22, WABS, WI, WR,
+     $                   WR2
+*     ..
+*     .. Local Arrays ..
+      REAL               V( 3 )
+*     ..
+*     .. External Functions ..
+      LOGICAL            LSAME
+      REAL               SLAMCH, SLANHS, SLAPY2, SLAPY3
+      EXTERNAL           LSAME, SLAMCH, SLANHS, SLAPY2, SLAPY3
+*     ..
+*     .. External Subroutines ..
+      EXTERNAL           SLAG2, SLARFG, SLARTG, SLASET, SLASV2, SROT,
+     $                   XERBLA
+*     ..
+*     .. Intrinsic Functions ..
+      INTRINSIC          ABS, MAX, MIN, REAL, SQRT
+*     ..
+*     .. Executable Statements ..
+*
+*     Decode JOB, COMPQ, COMPZ
+*
+      IF( LSAME( JOB, 'E' ) ) THEN
+         ILSCHR = .FALSE.
+         ISCHUR = 1
+      ELSE IF( LSAME( JOB, 'S' ) ) THEN
+         ILSCHR = .TRUE.
+         ISCHUR = 2
+      ELSE
+         ISCHUR = 0
+      END IF
+*
+      IF( LSAME( COMPQ, 'N' ) ) THEN
+         ILQ = .FALSE.
+         ICOMPQ = 1
+      ELSE IF( LSAME( COMPQ, 'V' ) ) THEN
+         ILQ = .TRUE.
+         ICOMPQ = 2
+      ELSE IF( LSAME( COMPQ, 'I' ) ) THEN
+         ILQ = .TRUE.
+         ICOMPQ = 3
+      ELSE
+         ICOMPQ = 0
+      END IF
+*
+      IF( LSAME( COMPZ, 'N' ) ) THEN
+         ILZ = .FALSE.
+         ICOMPZ = 1
+      ELSE IF( LSAME( COMPZ, 'V' ) ) THEN
+         ILZ = .TRUE.
+         ICOMPZ = 2
+      ELSE IF( LSAME( COMPZ, 'I' ) ) THEN
+         ILZ = .TRUE.
+         ICOMPZ = 3
+      ELSE
+         ICOMPZ = 0
+      END IF
+*
+*     Check Argument Values
+*
+      INFO = 0
+      WORK( 1 ) = MAX( 1, N )
+      LQUERY = ( LWORK.EQ.-1 )
+      IF( ISCHUR.EQ.0 ) THEN
+         INFO = -1
+      ELSE IF( ICOMPQ.EQ.0 ) THEN
+         INFO = -2
+      ELSE IF( ICOMPZ.EQ.0 ) THEN
+         INFO = -3
+      ELSE IF( N.LT.0 ) THEN
+         INFO = -4
+      ELSE IF( ILO.LT.1 ) THEN
+         INFO = -5
+      ELSE IF( IHI.GT.N .OR. IHI.LT.ILO-1 ) THEN
+         INFO = -6
+      ELSE IF( LDH.LT.N ) THEN
+         INFO = -8
+      ELSE IF( LDT.LT.N ) THEN
+         INFO = -10
+      ELSE IF( LDQ.LT.1 .OR. ( ILQ .AND. LDQ.LT.N ) ) THEN
+         INFO = -15
+      ELSE IF( LDZ.LT.1 .OR. ( ILZ .AND. LDZ.LT.N ) ) THEN
+         INFO = -17
+      ELSE IF( LWORK.LT.MAX( 1, N ) .AND. .NOT.LQUERY ) THEN
+         INFO = -19
+      END IF
+      IF( INFO.NE.0 ) THEN
+         CALL XERBLA( 'SHGEQZ', -INFO )
+         RETURN
+      ELSE IF( LQUERY ) THEN
+         RETURN
+      END IF
+*
+*     Quick return if possible
+*
+      IF( N.LE.0 ) THEN
+         WORK( 1 ) = REAL( 1 )
+         RETURN
+      END IF
+*
+*     Initialize Q and Z
+*
+      IF( ICOMPQ.EQ.3 )
+     $   CALL SLASET( 'Full', N, N, ZERO, ONE, Q, LDQ )
+      IF( ICOMPZ.EQ.3 )
+     $   CALL SLASET( 'Full', N, N, ZERO, ONE, Z, LDZ )
+*
+*     Machine Constants
+*
+      IN = IHI + 1 - ILO
+      SAFMIN = SLAMCH( 'S' )
+      SAFMAX = ONE / SAFMIN
+      ULP = SLAMCH( 'E' )*SLAMCH( 'B' )
+      ANORM = SLANHS( 'F', IN, H( ILO, ILO ), LDH, WORK )
+      BNORM = SLANHS( 'F', IN, T( ILO, ILO ), LDT, WORK )
+      ATOL = MAX( SAFMIN, ULP*ANORM )
+      BTOL = MAX( SAFMIN, ULP*BNORM )
+      ASCALE = ONE / MAX( SAFMIN, ANORM )
+      BSCALE = ONE / MAX( SAFMIN, BNORM )
+*
+*     Set Eigenvalues IHI+1:N
+*
+      DO 30 J = IHI + 1, N
+         IF( T( J, J ).LT.ZERO ) THEN
+            IF( ILSCHR ) THEN
+               DO 10 JR = 1, J
+                  H( JR, J ) = -H( JR, J )
+                  T( JR, J ) = -T( JR, J )
+   10          CONTINUE
+            ELSE
+               H( J, J ) = -H( J, J )
+               T( J, J ) = -T( J, J )
+            END IF
+            IF( ILZ ) THEN
+               DO 20 JR = 1, N
+                  Z( JR, J ) = -Z( JR, J )
+   20          CONTINUE
+            END IF
+         END IF
+         ALPHAR( J ) = H( J, J )
+         ALPHAI( J ) = ZERO
+         BETA( J ) = T( J, J )
+   30 CONTINUE
+*
+*     If IHI < ILO, skip QZ steps
+*
+      IF( IHI.LT.ILO )
+     $   GO TO 380
+*
+*     MAIN QZ ITERATION LOOP
+*
+*     Initialize dynamic indices
+*
+*     Eigenvalues ILAST+1:N have been found.
+*        Column operations modify rows IFRSTM:whatever.
+*        Row operations modify columns whatever:ILASTM.
+*
+*     If only eigenvalues are being computed, then
+*        IFRSTM is the row of the last splitting row above row ILAST;
+*        this is always at least ILO.
+*     IITER counts iterations since the last eigenvalue was found,
+*        to tell when to use an extraordinary shift.
+*     MAXIT is the maximum number of QZ sweeps allowed.
+*
+      ILAST = IHI
+      IF( ILSCHR ) THEN
+         IFRSTM = 1
+         ILASTM = N
+      ELSE
+         IFRSTM = ILO
+         ILASTM = IHI
+      END IF
+      IITER = 0
+      ESHIFT = ZERO
+      MAXIT = 30*( IHI-ILO+1 )
+*
+      DO 360 JITER = 1, MAXIT
+*
+*        Split the matrix if possible.
+*
+*        Two tests:
+*           1: H(j,j-1)=0  or  j=ILO
+*           2: T(j,j)=0
+*
+         IF( ILAST.EQ.ILO ) THEN
+*
+*           Special case: j=ILAST
+*
+            GO TO 80
+         ELSE
+            IF( ABS( H( ILAST, ILAST-1 ) ).LE.ATOL ) THEN
+               H( ILAST, ILAST-1 ) = ZERO
+               GO TO 80
+            END IF
+         END IF
+*
+         IF( ABS( T( ILAST, ILAST ) ).LE.BTOL ) THEN
+            T( ILAST, ILAST ) = ZERO
+            GO TO 70
+         END IF
+*
+*        General case: j<ILAST
+*
+         DO 60 J = ILAST - 1, ILO, -1
+*
+*           Test 1: for H(j,j-1)=0 or j=ILO
+*
+            IF( J.EQ.ILO ) THEN
+               ILAZRO = .TRUE.
+            ELSE
+               IF( ABS( H( J, J-1 ) ).LE.ATOL ) THEN
+                  H( J, J-1 ) = ZERO
+                  ILAZRO = .TRUE.
+               ELSE
+                  ILAZRO = .FALSE.
+               END IF
+            END IF
+*
+*           Test 2: for T(j,j)=0
+*
+            IF( ABS( T( J, J ) ).LT.BTOL ) THEN
+               T( J, J ) = ZERO
+*
+*              Test 1a: Check for 2 consecutive small subdiagonals in A
+*
+               ILAZR2 = .FALSE.
+               IF( .NOT.ILAZRO ) THEN
+                  TEMP = ABS( H( J, J-1 ) )
+                  TEMP2 = ABS( H( J, J ) )
+                  TEMPR = MAX( TEMP, TEMP2 )
+                  IF( TEMPR.LT.ONE .AND. TEMPR.NE.ZERO ) THEN
+                     TEMP = TEMP / TEMPR
+                     TEMP2 = TEMP2 / TEMPR
+                  END IF
+                  IF( TEMP*( ASCALE*ABS( H( J+1, J ) ) ).LE.TEMP2*
+     $                ( ASCALE*ATOL ) )ILAZR2 = .TRUE.
+               END IF
+*
+*              If both tests pass (1 & 2), i.e., the leading diagonal
+*              element of B in the block is zero, split a 1x1 block off
+*              at the top. (I.e., at the J-th row/column) The leading
+*              diagonal element of the remainder can also be zero, so
+*              this may have to be done repeatedly.
+*
+               IF( ILAZRO .OR. ILAZR2 ) THEN
+                  DO 40 JCH = J, ILAST - 1
+                     TEMP = H( JCH, JCH )
+                     CALL SLARTG( TEMP, H( JCH+1, JCH ), C, S,
+     $                            H( JCH, JCH ) )
+                     H( JCH+1, JCH ) = ZERO
+                     CALL SROT( ILASTM-JCH, H( JCH, JCH+1 ), LDH,
+     $                          H( JCH+1, JCH+1 ), LDH, C, S )
+                     CALL SROT( ILASTM-JCH, T( JCH, JCH+1 ), LDT,
+     $                          T( JCH+1, JCH+1 ), LDT, C, S )
+                     IF( ILQ )
+     $                  CALL SROT( N, Q( 1, JCH ), 1, Q( 1, JCH+1 ), 1,
+     $                             C, S )
+                     IF( ILAZR2 )
+     $                  H( JCH, JCH-1 ) = H( JCH, JCH-1 )*C
+                     ILAZR2 = .FALSE.
+                     IF( ABS( T( JCH+1, JCH+1 ) ).GE.BTOL ) THEN
+                        IF( JCH+1.GE.ILAST ) THEN
+                           GO TO 80
+                        ELSE
+                           IFIRST = JCH + 1
+                           GO TO 110
+                        END IF
+                     END IF
+                     T( JCH+1, JCH+1 ) = ZERO
+   40             CONTINUE
+                  GO TO 70
+               ELSE
+*
+*                 Only test 2 passed -- chase the zero to T(ILAST,ILAST)
+*                 Then process as in the case T(ILAST,ILAST)=0
+*
+                  DO 50 JCH = J, ILAST - 1
+                     TEMP = T( JCH, JCH+1 )
+                     CALL SLARTG( TEMP, T( JCH+1, JCH+1 ), C, S,
+     $                            T( JCH, JCH+1 ) )
+                     T( JCH+1, JCH+1 ) = ZERO
+                     IF( JCH.LT.ILASTM-1 )
+     $                  CALL SROT( ILASTM-JCH-1, T( JCH, JCH+2 ), LDT,
+     $                             T( JCH+1, JCH+2 ), LDT, C, S )
+                     CALL SROT( ILASTM-JCH+2, H( JCH, JCH-1 ), LDH,
+     $                          H( JCH+1, JCH-1 ), LDH, C, S )
+                     IF( ILQ )
+     $                  CALL SROT( N, Q( 1, JCH ), 1, Q( 1, JCH+1 ), 1,
+     $                             C, S )
+                     TEMP = H( JCH+1, JCH )
+                     CALL SLARTG( TEMP, H( JCH+1, JCH-1 ), C, S,
+     $                            H( JCH+1, JCH ) )
+                     H( JCH+1, JCH-1 ) = ZERO
+                     CALL SROT( JCH+1-IFRSTM, H( IFRSTM, JCH ), 1,
+     $                          H( IFRSTM, JCH-1 ), 1, C, S )
+                     CALL SROT( JCH-IFRSTM, T( IFRSTM, JCH ), 1,
+     $                          T( IFRSTM, JCH-1 ), 1, C, S )
+                     IF( ILZ )
+     $                  CALL SROT( N, Z( 1, JCH ), 1, Z( 1, JCH-1 ), 1,
+     $                             C, S )
+   50             CONTINUE
+                  GO TO 70
+               END IF
+            ELSE IF( ILAZRO ) THEN
+*
+*              Only test 1 passed -- work on J:ILAST
+*
+               IFIRST = J
+               GO TO 110
+            END IF
+*
+*           Neither test passed -- try next J
+*
+   60    CONTINUE
+*
+*        (Drop-through is "impossible")
+*
+         INFO = N + 1
+         GO TO 420
+*
+*        T(ILAST,ILAST)=0 -- clear H(ILAST,ILAST-1) to split off a
+*        1x1 block.
+*
+   70    CONTINUE
+         TEMP = H( ILAST, ILAST )
+         CALL SLARTG( TEMP, H( ILAST, ILAST-1 ), C, S,
+     $                H( ILAST, ILAST ) )
+         H( ILAST, ILAST-1 ) = ZERO
+         CALL SROT( ILAST-IFRSTM, H( IFRSTM, ILAST ), 1,
+     $              H( IFRSTM, ILAST-1 ), 1, C, S )
+         CALL SROT( ILAST-IFRSTM, T( IFRSTM, ILAST ), 1,
+     $              T( IFRSTM, ILAST-1 ), 1, C, S )
+         IF( ILZ )
+     $      CALL SROT( N, Z( 1, ILAST ), 1, Z( 1, ILAST-1 ), 1, C, S )
+*
+*        H(ILAST,ILAST-1)=0 -- Standardize B, set ALPHAR, ALPHAI,
+*                              and BETA
+*
+   80    CONTINUE
+         IF( T( ILAST, ILAST ).LT.ZERO ) THEN
+            IF( ILSCHR ) THEN
+               DO 90 J = IFRSTM, ILAST
+                  H( J, ILAST ) = -H( J, ILAST )
+                  T( J, ILAST ) = -T( J, ILAST )
+   90          CONTINUE
+            ELSE
+               H( ILAST, ILAST ) = -H( ILAST, ILAST )
+               T( ILAST, ILAST ) = -T( ILAST, ILAST )
+            END IF
+            IF( ILZ ) THEN
+               DO 100 J = 1, N
+                  Z( J, ILAST ) = -Z( J, ILAST )
+  100          CONTINUE
+            END IF
+         END IF
+         ALPHAR( ILAST ) = H( ILAST, ILAST )
+         ALPHAI( ILAST ) = ZERO
+         BETA( ILAST ) = T( ILAST, ILAST )
+*
+*        Go to next block -- exit if finished.
+*
+         ILAST = ILAST - 1
+         IF( ILAST.LT.ILO )
+     $      GO TO 380
+*
+*        Reset counters
+*
+         IITER = 0
+         ESHIFT = ZERO
+         IF( .NOT.ILSCHR ) THEN
+            ILASTM = ILAST
+            IF( IFRSTM.GT.ILAST )
+     $         IFRSTM = ILO
+         END IF
+         GO TO 350
+*
+*        QZ step
+*
+*        This iteration only involves rows/columns IFIRST:ILAST. We
+*        assume IFIRST < ILAST, and that the diagonal of B is non-zero.
+*
+  110    CONTINUE
+         IITER = IITER + 1
+         IF( .NOT.ILSCHR ) THEN
+            IFRSTM = IFIRST
+         END IF
+*
+*        Compute single shifts.
+*
+*        At this point, IFIRST < ILAST, and the diagonal elements of
+*        T(IFIRST:ILAST,IFIRST,ILAST) are larger than BTOL (in
+*        magnitude)
+*
+         IF( ( IITER / 10 )*10.EQ.IITER ) THEN
+*
+*           Exceptional shift.  Chosen for no particularly good reason.
+*           (Single shift only.)
+*
+            IF( ( REAL( MAXIT )*SAFMIN )*ABS( H( ILAST-1, ILAST ) ).LT.
+     $          ABS( T( ILAST-1, ILAST-1 ) ) ) THEN
+               ESHIFT = ESHIFT + H( ILAST-1, ILAST ) /
+     $                  T( ILAST-1, ILAST-1 )
+            ELSE
+               ESHIFT = ESHIFT + ONE / ( SAFMIN*REAL( MAXIT ) )
+            END IF
+            S1 = ONE
+            WR = ESHIFT
+*
+         ELSE
+*
+*           Shifts based on the generalized eigenvalues of the
+*           bottom-right 2x2 block of A and B. The first eigenvalue
+*           returned by SLAG2 is the Wilkinson shift (AEP p.512),
+*
+            CALL SLAG2( H( ILAST-1, ILAST-1 ), LDH,
+     $                  T( ILAST-1, ILAST-1 ), LDT, SAFMIN*SAFETY, S1,
+     $                  S2, WR, WR2, WI )
+*
+            TEMP = MAX( S1, SAFMIN*MAX( ONE, ABS( WR ), ABS( WI ) ) )
+            IF( WI.NE.ZERO )
+     $         GO TO 200
+         END IF
+*
+*        Fiddle with shift to avoid overflow
+*
+         TEMP = MIN( ASCALE, ONE )*( HALF*SAFMAX )
+         IF( S1.GT.TEMP ) THEN
+            SCALE = TEMP / S1
+         ELSE
+            SCALE = ONE
+         END IF
+*
+         TEMP = MIN( BSCALE, ONE )*( HALF*SAFMAX )
+         IF( ABS( WR ).GT.TEMP )
+     $      SCALE = MIN( SCALE, TEMP / ABS( WR ) )
+         S1 = SCALE*S1
+         WR = SCALE*WR
+*
+*        Now check for two consecutive small subdiagonals.
+*
+         DO 120 J = ILAST - 1, IFIRST + 1, -1
+            ISTART = J
+            TEMP = ABS( S1*H( J, J-1 ) )
+            TEMP2 = ABS( S1*H( J, J )-WR*T( J, J ) )
+            TEMPR = MAX( TEMP, TEMP2 )
+            IF( TEMPR.LT.ONE .AND. TEMPR.NE.ZERO ) THEN
+               TEMP = TEMP / TEMPR
+               TEMP2 = TEMP2 / TEMPR
+            END IF
+            IF( ABS( ( ASCALE*H( J+1, J ) )*TEMP ).LE.( ASCALE*ATOL )*
+     $          TEMP2 )GO TO 130
+  120    CONTINUE
+*
+         ISTART = IFIRST
+  130    CONTINUE
+*
+*        Do an implicit single-shift QZ sweep.
+*
+*        Initial Q
+*
+         TEMP = S1*H( ISTART, ISTART ) - WR*T( ISTART, ISTART )
+         TEMP2 = S1*H( ISTART+1, ISTART )
+         CALL SLARTG( TEMP, TEMP2, C, S, TEMPR )
+*
+*        Sweep
+*
+         DO 190 J = ISTART, ILAST - 1
+            IF( J.GT.ISTART ) THEN
+               TEMP = H( J, J-1 )
+               CALL SLARTG( TEMP, H( J+1, J-1 ), C, S, H( J, J-1 ) )
+               H( J+1, J-1 ) = ZERO
+            END IF
+*
+            DO 140 JC = J, ILASTM
+               TEMP = C*H( J, JC ) + S*H( J+1, JC )
+               H( J+1, JC ) = -S*H( J, JC ) + C*H( J+1, JC )
+               H( J, JC ) = TEMP
+               TEMP2 = C*T( J, JC ) + S*T( J+1, JC )
+               T( J+1, JC ) = -S*T( J, JC ) + C*T( J+1, JC )
+               T( J, JC ) = TEMP2
+  140       CONTINUE
+            IF( ILQ ) THEN
+               DO 150 JR = 1, N
+                  TEMP = C*Q( JR, J ) + S*Q( JR, J+1 )
+                  Q( JR, J+1 ) = -S*Q( JR, J ) + C*Q( JR, J+1 )
+                  Q( JR, J ) = TEMP
+  150          CONTINUE
+            END IF
+*
+            TEMP = T( J+1, J+1 )
+            CALL SLARTG( TEMP, T( J+1, J ), C, S, T( J+1, J+1 ) )
+            T( J+1, J ) = ZERO
+*
+            DO 160 JR = IFRSTM, MIN( J+2, ILAST )
+               TEMP = C*H( JR, J+1 ) + S*H( JR, J )
+               H( JR, J ) = -S*H( JR, J+1 ) + C*H( JR, J )
+               H( JR, J+1 ) = TEMP
+  160       CONTINUE
+            DO 170 JR = IFRSTM, J
+               TEMP = C*T( JR, J+1 ) + S*T( JR, J )
+               T( JR, J ) = -S*T( JR, J+1 ) + C*T( JR, J )
+               T( JR, J+1 ) = TEMP
+  170       CONTINUE
+            IF( ILZ ) THEN
+               DO 180 JR = 1, N
+                  TEMP = C*Z( JR, J+1 ) + S*Z( JR, J )
+                  Z( JR, J ) = -S*Z( JR, J+1 ) + C*Z( JR, J )
+                  Z( JR, J+1 ) = TEMP
+  180          CONTINUE
+            END IF
+  190    CONTINUE
+*
+         GO TO 350
+*
+*        Use Francis double-shift
+*
+*        Note: the Francis double-shift should work with real shifts,
+*              but only if the block is at least 3x3.
+*              This code may break if this point is reached with
+*              a 2x2 block with real eigenvalues.
+*
+  200    CONTINUE
+         IF( IFIRST+1.EQ.ILAST ) THEN
+*
+*           Special case -- 2x2 block with complex eigenvectors
+*
+*           Step 1: Standardize, that is, rotate so that
+*
+*                       ( B11  0  )
+*                   B = (         )  with B11 non-negative.
+*                       (  0  B22 )
+*
+            CALL SLASV2( T( ILAST-1, ILAST-1 ), T( ILAST-1, ILAST ),
+     $                   T( ILAST, ILAST ), B22, B11, SR, CR, SL, CL )
+*
+            IF( B11.LT.ZERO ) THEN
+               CR = -CR
+               SR = -SR
+               B11 = -B11
+               B22 = -B22
+            END IF
+*
+            CALL SROT( ILASTM+1-IFIRST, H( ILAST-1, ILAST-1 ), LDH,
+     $                 H( ILAST, ILAST-1 ), LDH, CL, SL )
+            CALL SROT( ILAST+1-IFRSTM, H( IFRSTM, ILAST-1 ), 1,
+     $                 H( IFRSTM, ILAST ), 1, CR, SR )
+*
+            IF( ILAST.LT.ILASTM )
+     $         CALL SROT( ILASTM-ILAST, T( ILAST-1, ILAST+1 ), LDT,
+     $                    T( ILAST, ILAST+1 ), LDH, CL, SL )
+            IF( IFRSTM.LT.ILAST-1 )
+     $         CALL SROT( IFIRST-IFRSTM, T( IFRSTM, ILAST-1 ), 1,
+     $                    T( IFRSTM, ILAST ), 1, CR, SR )
+*
+            IF( ILQ )
+     $         CALL SROT( N, Q( 1, ILAST-1 ), 1, Q( 1, ILAST ), 1, CL,
+     $                    SL )
+            IF( ILZ )
+     $         CALL SROT( N, Z( 1, ILAST-1 ), 1, Z( 1, ILAST ), 1, CR,
+     $                    SR )
+*
+            T( ILAST-1, ILAST-1 ) = B11
+            T( ILAST-1, ILAST ) = ZERO
+            T( ILAST, ILAST-1 ) = ZERO
+            T( ILAST, ILAST ) = B22
+*
+*           If B22 is negative, negate column ILAST
+*
+            IF( B22.LT.ZERO ) THEN
+               DO 210 J = IFRSTM, ILAST
+                  H( J, ILAST ) = -H( J, ILAST )
+                  T( J, ILAST ) = -T( J, ILAST )
+  210          CONTINUE
+*
+               IF( ILZ ) THEN
+                  DO 220 J = 1, N
+                     Z( J, ILAST ) = -Z( J, ILAST )
+  220             CONTINUE
+               END IF
+            END IF
+*
+*           Step 2: Compute ALPHAR, ALPHAI, and BETA (see refs.)
+*
+*           Recompute shift
+*
+            CALL SLAG2( H( ILAST-1, ILAST-1 ), LDH,
+     $                  T( ILAST-1, ILAST-1 ), LDT, SAFMIN*SAFETY, S1,
+     $                  TEMP, WR, TEMP2, WI )
+*
+*           If standardization has perturbed the shift onto real line,
+*           do another (real single-shift) QR step.
+*
+            IF( WI.EQ.ZERO )
+     $         GO TO 350
+            S1INV = ONE / S1
+*
+*           Do EISPACK (QZVAL) computation of alpha and beta
+*
+            A11 = H( ILAST-1, ILAST-1 )
+            A21 = H( ILAST, ILAST-1 )
+            A12 = H( ILAST-1, ILAST )
+            A22 = H( ILAST, ILAST )
+*
+*           Compute complex Givens rotation on right
+*           (Assume some element of C = (sA - wB) > unfl )
+*                            __
+*           (sA - wB) ( CZ   -SZ )
+*                     ( SZ    CZ )
+*
+            C11R = S1*A11 - WR*B11
+            C11I = -WI*B11
+            C12 = S1*A12
+            C21 = S1*A21
+            C22R = S1*A22 - WR*B22
+            C22I = -WI*B22
+*
+            IF( ABS( C11R )+ABS( C11I )+ABS( C12 ).GT.ABS( C21 )+
+     $          ABS( C22R )+ABS( C22I ) ) THEN
+               T1 = SLAPY3( C12, C11R, C11I )
+               CZ = C12 / T1
+               SZR = -C11R / T1
+               SZI = -C11I / T1
+            ELSE
+               CZ = SLAPY2( C22R, C22I )
+               IF( CZ.LE.SAFMIN ) THEN
+                  CZ = ZERO
+                  SZR = ONE
+                  SZI = ZERO
+               ELSE
+                  TEMPR = C22R / CZ
+                  TEMPI = C22I / CZ
+                  T1 = SLAPY2( CZ, C21 )
+                  CZ = CZ / T1
+                  SZR = -C21*TEMPR / T1
+                  SZI = C21*TEMPI / T1
+               END IF
+            END IF
+*
+*           Compute Givens rotation on left
+*
+*           (  CQ   SQ )
+*           (  __      )  A or B
+*           ( -SQ   CQ )
+*
+            AN = ABS( A11 ) + ABS( A12 ) + ABS( A21 ) + ABS( A22 )
+            BN = ABS( B11 ) + ABS( B22 )
+            WABS = ABS( WR ) + ABS( WI )
+            IF( S1*AN.GT.WABS*BN ) THEN
+               CQ = CZ*B11
+               SQR = SZR*B22
+               SQI = -SZI*B22
+            ELSE
+               A1R = CZ*A11 + SZR*A12
+               A1I = SZI*A12
+               A2R = CZ*A21 + SZR*A22
+               A2I = SZI*A22
+               CQ = SLAPY2( A1R, A1I )
+               IF( CQ.LE.SAFMIN ) THEN
+                  CQ = ZERO
+                  SQR = ONE
+                  SQI = ZERO
+               ELSE
+                  TEMPR = A1R / CQ
+                  TEMPI = A1I / CQ
+                  SQR = TEMPR*A2R + TEMPI*A2I
+                  SQI = TEMPI*A2R - TEMPR*A2I
+               END IF
+            END IF
+            T1 = SLAPY3( CQ, SQR, SQI )
+            CQ = CQ / T1
+            SQR = SQR / T1
+            SQI = SQI / T1
+*
+*           Compute diagonal elements of QBZ
+*
+            TEMPR = SQR*SZR - SQI*SZI
+            TEMPI = SQR*SZI + SQI*SZR
+            B1R = CQ*CZ*B11 + TEMPR*B22
+            B1I = TEMPI*B22
+            B1A = SLAPY2( B1R, B1I )
+            B2R = CQ*CZ*B22 + TEMPR*B11
+            B2I = -TEMPI*B11
+            B2A = SLAPY2( B2R, B2I )
+*
+*           Normalize so beta > 0, and Im( alpha1 ) > 0
+*
+            BETA( ILAST-1 ) = B1A
+            BETA( ILAST ) = B2A
+            ALPHAR( ILAST-1 ) = ( WR*B1A )*S1INV
+            ALPHAI( ILAST-1 ) = ( WI*B1A )*S1INV
+            ALPHAR( ILAST ) = ( WR*B2A )*S1INV
+            ALPHAI( ILAST ) = -( WI*B2A )*S1INV
+*
+*           Step 3: Go to next block -- exit if finished.
+*
+            ILAST = IFIRST - 1
+            IF( ILAST.LT.ILO )
+     $         GO TO 380
+*
+*           Reset counters
+*
+            IITER = 0
+            ESHIFT = ZERO
+            IF( .NOT.ILSCHR ) THEN
+               ILASTM = ILAST
+               IF( IFRSTM.GT.ILAST )
+     $            IFRSTM = ILO
+            END IF
+            GO TO 350
+         ELSE
+*
+*           Usual case: 3x3 or larger block, using Francis implicit
+*                       double-shift
+*
+*                                    2
+*           Eigenvalue equation is  w  - c w + d = 0,
+*
+*                                         -1 2        -1
+*           so compute 1st column of  (A B  )  - c A B   + d
+*           using the formula in QZIT (from EISPACK)
+*
+*           We assume that the block is at least 3x3
+*
+            AD11 = ( ASCALE*H( ILAST-1, ILAST-1 ) ) /
+     $             ( BSCALE*T( ILAST-1, ILAST-1 ) )
+            AD21 = ( ASCALE*H( ILAST, ILAST-1 ) ) /
+     $             ( BSCALE*T( ILAST-1, ILAST-1 ) )
+            AD12 = ( ASCALE*H( ILAST-1, ILAST ) ) /
+     $             ( BSCALE*T( ILAST, ILAST ) )
+            AD22 = ( ASCALE*H( ILAST, ILAST ) ) /
+     $             ( BSCALE*T( ILAST, ILAST ) )
+            U12 = T( ILAST-1, ILAST ) / T( ILAST, ILAST )
+            AD11L = ( ASCALE*H( IFIRST, IFIRST ) ) /
+     $              ( BSCALE*T( IFIRST, IFIRST ) )
+            AD21L = ( ASCALE*H( IFIRST+1, IFIRST ) ) /
+     $              ( BSCALE*T( IFIRST, IFIRST ) )
+            AD12L = ( ASCALE*H( IFIRST, IFIRST+1 ) ) /
+     $              ( BSCALE*T( IFIRST+1, IFIRST+1 ) )
+            AD22L = ( ASCALE*H( IFIRST+1, IFIRST+1 ) ) /
+     $              ( BSCALE*T( IFIRST+1, IFIRST+1 ) )
+            AD32L = ( ASCALE*H( IFIRST+2, IFIRST+1 ) ) /
+     $              ( BSCALE*T( IFIRST+1, IFIRST+1 ) )
+            U12L = T( IFIRST, IFIRST+1 ) / T( IFIRST+1, IFIRST+1 )
+*
+            V( 1 ) = ( AD11-AD11L )*( AD22-AD11L ) - AD12*AD21 +
+     $               AD21*U12*AD11L + ( AD12L-AD11L*U12L )*AD21L
+            V( 2 ) = ( ( AD22L-AD11L )-AD21L*U12L-( AD11-AD11L )-
+     $               ( AD22-AD11L )+AD21*U12 )*AD21L
+            V( 3 ) = AD32L*AD21L
+*
+            ISTART = IFIRST
+*
+            CALL SLARFG( 3, V( 1 ), V( 2 ), 1, TAU )
+            V( 1 ) = ONE
+*
+*           Sweep
+*
+            DO 290 J = ISTART, ILAST - 2
+*
+*              All but last elements: use 3x3 Householder transforms.
+*
+*              Zero (j-1)st column of A
+*
+               IF( J.GT.ISTART ) THEN
+                  V( 1 ) = H( J, J-1 )
+                  V( 2 ) = H( J+1, J-1 )
+                  V( 3 ) = H( J+2, J-1 )
+*
+                  CALL SLARFG( 3, H( J, J-1 ), V( 2 ), 1, TAU )
+                  V( 1 ) = ONE
+                  H( J+1, J-1 ) = ZERO
+                  H( J+2, J-1 ) = ZERO
+               END IF
+*
+               DO 230 JC = J, ILASTM
+                  TEMP = TAU*( H( J, JC )+V( 2 )*H( J+1, JC )+V( 3 )*
+     $                   H( J+2, JC ) )
+                  H( J, JC ) = H( J, JC ) - TEMP
+                  H( J+1, JC ) = H( J+1, JC ) - TEMP*V( 2 )
+                  H( J+2, JC ) = H( J+2, JC ) - TEMP*V( 3 )
+                  TEMP2 = TAU*( T( J, JC )+V( 2 )*T( J+1, JC )+V( 3 )*
+     $                    T( J+2, JC ) )
+                  T( J, JC ) = T( J, JC ) - TEMP2
+                  T( J+1, JC ) = T( J+1, JC ) - TEMP2*V( 2 )
+                  T( J+2, JC ) = T( J+2, JC ) - TEMP2*V( 3 )
+  230          CONTINUE
+               IF( ILQ ) THEN
+                  DO 240 JR = 1, N
+                     TEMP = TAU*( Q( JR, J )+V( 2 )*Q( JR, J+1 )+V( 3 )*
+     $                      Q( JR, J+2 ) )
+                     Q( JR, J ) = Q( JR, J ) - TEMP
+                     Q( JR, J+1 ) = Q( JR, J+1 ) - TEMP*V( 2 )
+                     Q( JR, J+2 ) = Q( JR, J+2 ) - TEMP*V( 3 )
+  240             CONTINUE
+               END IF
+*
+*              Zero j-th column of B (see SLAGBC for details)
+*
+*              Swap rows to pivot
+*
+               ILPIVT = .FALSE.
+               TEMP = MAX( ABS( T( J+1, J+1 ) ), ABS( T( J+1, J+2 ) ) )
+               TEMP2 = MAX( ABS( T( J+2, J+1 ) ), ABS( T( J+2, J+2 ) ) )
+               IF( MAX( TEMP, TEMP2 ).LT.SAFMIN ) THEN
+                  SCALE = ZERO
+                  U1 = ONE
+                  U2 = ZERO
+                  GO TO 250
+               ELSE IF( TEMP.GE.TEMP2 ) THEN
+                  W11 = T( J+1, J+1 )
+                  W21 = T( J+2, J+1 )
+                  W12 = T( J+1, J+2 )
+                  W22 = T( J+2, J+2 )
+                  U1 = T( J+1, J )
+                  U2 = T( J+2, J )
+               ELSE
+                  W21 = T( J+1, J+1 )
+                  W11 = T( J+2, J+1 )
+                  W22 = T( J+1, J+2 )
+                  W12 = T( J+2, J+2 )
+                  U2 = T( J+1, J )
+                  U1 = T( J+2, J )
+               END IF
+*
+*              Swap columns if nec.
+*
+               IF( ABS( W12 ).GT.ABS( W11 ) ) THEN
+                  ILPIVT = .TRUE.
+                  TEMP = W12
+                  TEMP2 = W22
+                  W12 = W11
+                  W22 = W21
+                  W11 = TEMP
+                  W21 = TEMP2
+               END IF
+*
+*              LU-factor
+*
+               TEMP = W21 / W11
+               U2 = U2 - TEMP*U1
+               W22 = W22 - TEMP*W12
+               W21 = ZERO
+*
+*              Compute SCALE
+*
+               SCALE = ONE
+               IF( ABS( W22 ).LT.SAFMIN ) THEN
+                  SCALE = ZERO
+                  U2 = ONE
+                  U1 = -W12 / W11
+                  GO TO 250
+               END IF
+               IF( ABS( W22 ).LT.ABS( U2 ) )
+     $            SCALE = ABS( W22 / U2 )
+               IF( ABS( W11 ).LT.ABS( U1 ) )
+     $            SCALE = MIN( SCALE, ABS( W11 / U1 ) )
+*
+*              Solve
+*
+               U2 = ( SCALE*U2 ) / W22
+               U1 = ( SCALE*U1-W12*U2 ) / W11
+*
+  250          CONTINUE
+               IF( ILPIVT ) THEN
+                  TEMP = U2
+                  U2 = U1
+                  U1 = TEMP
+               END IF
+*
+*              Compute Householder Vector
+*
+               T1 = SQRT( SCALE**2+U1**2+U2**2 )
+               TAU = ONE + SCALE / T1
+               VS = -ONE / ( SCALE+T1 )
+               V( 1 ) = ONE
+               V( 2 ) = VS*U1
+               V( 3 ) = VS*U2
+*
+*              Apply transformations from the right.
+*
+               DO 260 JR = IFRSTM, MIN( J+3, ILAST )
+                  TEMP = TAU*( H( JR, J )+V( 2 )*H( JR, J+1 )+V( 3 )*
+     $                   H( JR, J+2 ) )
+                  H( JR, J ) = H( JR, J ) - TEMP
+                  H( JR, J+1 ) = H( JR, J+1 ) - TEMP*V( 2 )
+                  H( JR, J+2 ) = H( JR, J+2 ) - TEMP*V( 3 )
+  260          CONTINUE
+               DO 270 JR = IFRSTM, J + 2
+                  TEMP = TAU*( T( JR, J )+V( 2 )*T( JR, J+1 )+V( 3 )*
+     $                   T( JR, J+2 ) )
+                  T( JR, J ) = T( JR, J ) - TEMP
+                  T( JR, J+1 ) = T( JR, J+1 ) - TEMP*V( 2 )
+                  T( JR, J+2 ) = T( JR, J+2 ) - TEMP*V( 3 )
+  270          CONTINUE
+               IF( ILZ ) THEN
+                  DO 280 JR = 1, N
+                     TEMP = TAU*( Z( JR, J )+V( 2 )*Z( JR, J+1 )+V( 3 )*
+     $                      Z( JR, J+2 ) )
+                     Z( JR, J ) = Z( JR, J ) - TEMP
+                     Z( JR, J+1 ) = Z( JR, J+1 ) - TEMP*V( 2 )
+                     Z( JR, J+2 ) = Z( JR, J+2 ) - TEMP*V( 3 )
+  280             CONTINUE
+               END IF
+               T( J+1, J ) = ZERO
+               T( J+2, J ) = ZERO
+  290       CONTINUE
+*
+*           Last elements: Use Givens rotations
+*
+*           Rotations from the left
+*
+            J = ILAST - 1
+            TEMP = H( J, J-1 )
+            CALL SLARTG( TEMP, H( J+1, J-1 ), C, S, H( J, J-1 ) )
+            H( J+1, J-1 ) = ZERO
+*
+            DO 300 JC = J, ILASTM
+               TEMP = C*H( J, JC ) + S*H( J+1, JC )
+               H( J+1, JC ) = -S*H( J, JC ) + C*H( J+1, JC )
+               H( J, JC ) = TEMP
+               TEMP2 = C*T( J, JC ) + S*T( J+1, JC )
+               T( J+1, JC ) = -S*T( J, JC ) + C*T( J+1, JC )
+               T( J, JC ) = TEMP2
+  300       CONTINUE
+            IF( ILQ ) THEN
+               DO 310 JR = 1, N
+                  TEMP = C*Q( JR, J ) + S*Q( JR, J+1 )
+                  Q( JR, J+1 ) = -S*Q( JR, J ) + C*Q( JR, J+1 )
+                  Q( JR, J ) = TEMP
+  310          CONTINUE
+            END IF
+*
+*           Rotations from the right.
+*
+            TEMP = T( J+1, J+1 )
+            CALL SLARTG( TEMP, T( J+1, J ), C, S, T( J+1, J+1 ) )
+            T( J+1, J ) = ZERO
+*
+            DO 320 JR = IFRSTM, ILAST
+               TEMP = C*H( JR, J+1 ) + S*H( JR, J )
+               H( JR, J ) = -S*H( JR, J+1 ) + C*H( JR, J )
+               H( JR, J+1 ) = TEMP
+  320       CONTINUE
+            DO 330 JR = IFRSTM, ILAST - 1
+               TEMP = C*T( JR, J+1 ) + S*T( JR, J )
+               T( JR, J ) = -S*T( JR, J+1 ) + C*T( JR, J )
+               T( JR, J+1 ) = TEMP
+  330       CONTINUE
+            IF( ILZ ) THEN
+               DO 340 JR = 1, N
+                  TEMP = C*Z( JR, J+1 ) + S*Z( JR, J )
+                  Z( JR, J ) = -S*Z( JR, J+1 ) + C*Z( JR, J )
+                  Z( JR, J+1 ) = TEMP
+  340          CONTINUE
+            END IF
+*
+*           End of Double-Shift code
+*
+         END IF
+*
+         GO TO 350
+*
+*        End of iteration loop
+*
+  350    CONTINUE
+  360 CONTINUE
+*
+*     Drop-through = non-convergence
+*
+      INFO = ILAST
+      GO TO 420
+*
+*     Successful completion of all QZ steps
+*
+  380 CONTINUE
+*
+*     Set Eigenvalues 1:ILO-1
+*
+      DO 410 J = 1, ILO - 1
+         IF( T( J, J ).LT.ZERO ) THEN
+            IF( ILSCHR ) THEN
+               DO 390 JR = 1, J
+                  H( JR, J ) = -H( JR, J )
+                  T( JR, J ) = -T( JR, J )
+  390          CONTINUE
+            ELSE
+               H( J, J ) = -H( J, J )
+               T( J, J ) = -T( J, J )
+            END IF
+            IF( ILZ ) THEN
+               DO 400 JR = 1, N
+                  Z( JR, J ) = -Z( JR, J )
+  400          CONTINUE
+            END IF
+         END IF
+         ALPHAR( J ) = H( J, J )
+         ALPHAI( J ) = ZERO
+         BETA( J ) = T( J, J )
+  410 CONTINUE
+*
+*     Normal Termination
+*
+      INFO = 0
+*
+*     Exit (other than argument error) -- return optimal workspace size
+*
+  420 CONTINUE
+      WORK( 1 ) = REAL( N )
+      RETURN
+*
+*     End of SHGEQZ
+*
+      END