stgsy2.f

          SUBROUTINE STGSY2( TRANS, IJOB, M, N, A, LDA, B, LDB, C, LDC, D,
         $                   LDD, E, LDE, F, LDF, SCALE, RDSUM, RDSCAL,
         $                   IWORK, PQ, INFO )
    *
    *  -- LAPACK auxiliary routine (version 3.1.1) --
    *     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
    *     January 2007
    *
    *     .. Scalar Arguments ..
          CHARACTER          TRANS
          INTEGER            IJOB, INFO, LDA, LDB, LDC, LDD, LDE, LDF, M, N,
         $                   PQ
          REAL               RDSCAL, RDSUM, SCALE
    *     ..
    *     .. Array Arguments ..
          INTEGER            IWORK( * )
          REAL               A( LDA, * ), B( LDB, * ), C( LDC, * ),
         $                   D( LDD, * ), E( LDE, * ), F( LDF, * )
    *     ..
    *
    *  Purpose
    *  =======
    *
    *  STGSY2 solves the generalized Sylvester equation:
    *
    *              A * R - L * B = scale * C                (1)
    *              D * R - L * E = scale * F,
    *
    *  using Level 1 and 2 BLAS. where R and L are unknown M-by-N matrices,
    *  (A, D), (B, E) and (C, F) are given matrix pairs of size M-by-M,
    *  N-by-N and M-by-N, respectively, with real entries. (A, D) and (B, E)
    *  must be in generalized Schur canonical form, i.e. A, B are upper
    *  quasi triangular and D, E are upper triangular. The solution (R, L)
    *  overwrites (C, F). 0 <= SCALE <= 1 is an output scaling factor
    *  chosen to avoid overflow.
    *
    *  In matrix notation solving equation (1) corresponds to solve
    *  Z*x = scale*b, where Z is defined as
    *
    *         Z = [ kron(In, A)  -kron(B', Im) ]             (2)
    *             [ kron(In, D)  -kron(E', Im) ],
    *
    *  Ik is the identity matrix of size k and X' is the transpose of X.
    *  kron(X, Y) is the Kronecker product between the matrices X and Y.
    *  In the process of solving (1), we solve a number of such systems
    *  where Dim(In), Dim(In) = 1 or 2.
    *
    *  If TRANS = 'T', solve the transposed system Z'*y = scale*b for y,
    *  which is equivalent to solve for R and L in
    *
    *              A' * R  + D' * L   = scale *  C           (3)
    *              R  * B' + L  * E'  = scale * -F
    *
    *  This case is used to compute an estimate of Dif[(A, D), (B, E)] =
    *  sigma_min(Z) using reverse communicaton with SLACON.
    *
    *  STGSY2 also (IJOB >= 1) contributes to the computation in STGSYL
    *  of an upper bound on the separation between to matrix pairs. Then
    *  the input (A, D), (B, E) are sub-pencils of the matrix pair in
    *  STGSYL. See STGSYL for details.
    *
    *  Arguments
    *  =========
    *
    *  TRANS   (input) CHARACTER*1
    *          = 'N', solve the generalized Sylvester equation (1).
    *          = 'T': solve the 'transposed' system (3).
    *
    *  IJOB    (input) INTEGER
    *          Specifies what kind of functionality to be performed.
    *          = 0: solve (1) only.
    *          = 1: A contribution from this subsystem to a Frobenius
    *               norm-based estimate of the separation between two matrix
    *               pairs is computed. (look ahead strategy is used).
    *          = 2: A contribution from this subsystem to a Frobenius
    *               norm-based estimate of the separation between two matrix
    *               pairs is computed. (SGECON on sub-systems is used.)
    *          Not referenced if TRANS = 'T'.
    *
    *  M       (input) INTEGER
    *          On entry, M specifies the order of A and D, and the row
    *          dimension of C, F, R and L.
    *
    *  N       (input) INTEGER
    *          On entry, N specifies the order of B and E, and the column
    *          dimension of C, F, R and L.
    *
    *  A       (input) REAL array, dimension (LDA, M)
    *          On entry, A contains an upper quasi triangular matrix.
    *
    *  LDA     (input) INTEGER
    *          The leading dimension of the matrix A. LDA >= max(1, M).
    *
    *  B       (input) REAL array, dimension (LDB, N)
    *          On entry, B contains an upper quasi triangular matrix.
    *
    *  LDB     (input) INTEGER
    *          The leading dimension of the matrix B. LDB >= max(1, N).
    *
    *  C       (input/output) REAL array, dimension (LDC, N)
    *          On entry, C contains the right-hand-side of the first matrix
    *          equation in (1).
    *          On exit, if IJOB = 0, C has been overwritten by the
    *          solution R.
    *
    *  LDC     (input) INTEGER
    *          The leading dimension of the matrix C. LDC >= max(1, M).
    *
    *  D       (input) REAL array, dimension (LDD, M)
    *          On entry, D contains an upper triangular matrix.
    *
    *  LDD     (input) INTEGER
    *          The leading dimension of the matrix D. LDD >= max(1, M).
    *
    *  E       (input) REAL array, dimension (LDE, N)
    *          On entry, E contains an upper triangular matrix.
    *
    *  LDE     (input) INTEGER
    *          The leading dimension of the matrix E. LDE >= max(1, N).
    *
    *  F       (input/output) REAL array, dimension (LDF, N)
    *          On entry, F contains the right-hand-side of the second matrix
    *          equation in (1).
    *          On exit, if IJOB = 0, F has been overwritten by the
    *          solution L.
    *
    *  LDF     (input) INTEGER
    *          The leading dimension of the matrix F. LDF >= max(1, M).
    *
    *  SCALE   (output) REAL
    *          On exit, 0 <= SCALE <= 1. If 0 < SCALE < 1, the solutions
    *          R and L (C and F on entry) will hold the solutions to a
    *          slightly perturbed system but the input matrices A, B, D and
    *          E have not been changed. If SCALE = 0, R and L will hold the
    *          solutions to the homogeneous system with C = F = 0. Normally,
    *          SCALE = 1.
    *
    *  RDSUM   (input/output) REAL
    *          On entry, the sum of squares of computed contributions to
    *          the Dif-estimate under computation by STGSYL, where the
    *          scaling factor RDSCAL (see below) has been factored out.
    *          On exit, the corresponding sum of squares updated with the
    *          contributions from the current sub-system.
    *          If TRANS = 'T' RDSUM is not touched.
    *          NOTE: RDSUM only makes sense when STGSY2 is called by STGSYL.
    *
    *  RDSCAL  (input/output) REAL
    *          On entry, scaling factor used to prevent overflow in RDSUM.
    *          On exit, RDSCAL is updated w.r.t. the current contributions
    *          in RDSUM.
    *          If TRANS = 'T', RDSCAL is not touched.
    *          NOTE: RDSCAL only makes sense when STGSY2 is called by
    *                STGSYL.
    *
    *  IWORK   (workspace) INTEGER array, dimension (M+N+2)
    *
    *  PQ      (output) INTEGER
    *          On exit, the number of subsystems (of size 2-by-2, 4-by-4 and
    *          8-by-8) solved by this routine.
    *
    *  INFO    (output) INTEGER
    *          On exit, if INFO is set to
    *            =0: Successful exit
    *            <0: If INFO = -i, the i-th argument had an illegal value.
    *            >0: The matrix pairs (A, D) and (B, E) have common or very
    *                close eigenvalues.
    *
    *  Further Details
    *  ===============
    *
    *  Based on contributions by
    *     Bo Kagstrom and Peter Poromaa, Department of Computing Science,
    *     Umea University, S-901 87 Umea, Sweden.
    *
    *  =====================================================================
    *  Replaced various illegal calls to SCOPY by calls to SLASET.
    *  Sven Hammarling, 27/5/02.
    *
    *     .. Parameters ..
          INTEGER            LDZ
          PARAMETER          ( LDZ = 8 )
          REAL               ZERO, ONE
          PARAMETER          ( ZERO = 0.0E+0, ONE = 1.0E+0 )
    *     ..
    *     .. Local Scalars ..
          LOGICAL            NOTRAN
          INTEGER            I, IE, IERR, II, IS, ISP1, J, JE, JJ, JS, JSP1,
         $                   K, MB, NB, P, Q, ZDIM
          REAL               ALPHA, SCALOC
    *     ..
    *     .. Local Arrays ..
          INTEGER            IPIV( LDZ ), JPIV( LDZ )
          REAL               RHS( LDZ ), Z( LDZ, LDZ )
    *     ..
    *     .. External Functions ..
          LOGICAL            LSAME
          EXTERNAL           LSAME
    *     ..
    *     .. External Subroutines ..
          EXTERNAL           SAXPY, SCOPY, SGEMM, SGEMV, SGER, SGESC2,
         $                   SGETC2, SSCAL, SLASET, SLATDF, XERBLA
    *     ..
    *     .. Intrinsic Functions ..
          INTRINSIC          MAX
    *     ..
    *     .. Executable Statements ..
    *
    *     Decode and test input parameters
    *
          INFO = 0
          IERR = 0
          NOTRAN = LSAME( TRANS, 'N' )
          IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) ) THEN
             INFO = -1
          ELSE IF( NOTRAN ) THEN
             IF( ( IJOB.LT.0 ) .OR. ( IJOB.GT.2 ) ) THEN
                INFO = -2
             END IF
          END IF
          IF( INFO.EQ.0 ) THEN
             IF( M.LE.0 ) THEN
                INFO = -3
             ELSE IF( N.LE.0 ) THEN
                INFO = -4
             ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
                INFO = -5
             ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
                INFO = -8
             ELSE IF( LDC.LT.MAX( 1, M ) ) THEN
                INFO = -10
             ELSE IF( LDD.LT.MAX( 1, M ) ) THEN
                INFO = -12
             ELSE IF( LDE.LT.MAX( 1, N ) ) THEN
                INFO = -14
             ELSE IF( LDF.LT.MAX( 1, M ) ) THEN
                INFO = -16
             END IF
          END IF
          IF( INFO.NE.0 ) THEN
             CALL XERBLA( 'STGSY2', -INFO )
             RETURN
          END IF
    *
    *     Determine block structure of A
    *
          PQ = 0
          P = 0
          I = 1
       10 CONTINUE
          IF( I.GT.M )
         $   GO TO 20
          P = P + 1
          IWORK( P ) = I
          IF( I.EQ.M )
         $   GO TO 20
          IF( A( I+1, I ).NE.ZERO ) THEN
             I = I + 2
          ELSE
             I = I + 1
          END IF
          GO TO 10
       20 CONTINUE
          IWORK( P+1 ) = M + 1
    *
    *     Determine block structure of B
    *
          Q = P + 1
          J = 1
       30 CONTINUE
          IF( J.GT.N )
         $   GO TO 40
          Q = Q + 1
          IWORK( Q ) = J
          IF( J.EQ.N )
         $   GO TO 40
          IF( B( J+1, J ).NE.ZERO ) THEN
             J = J + 2
          ELSE
             J = J + 1
          END IF
          GO TO 30
       40 CONTINUE
          IWORK( Q+1 ) = N + 1
          PQ = P*( Q-P-1 )
    *
          IF( NOTRAN ) THEN
    *
    *        Solve (I, J) - subsystem
    *           A(I, I) * R(I, J) - L(I, J) * B(J, J) = C(I, J)
    *           D(I, I) * R(I, J) - L(I, J) * E(J, J) = F(I, J)
    *        for I = P, P - 1, ..., 1; J = 1, 2, ..., Q
    *
             SCALE = ONE
             SCALOC = ONE
             DO 120 J = P + 2, Q
                JS = IWORK( J )
                JSP1 = JS + 1
                JE = IWORK( J+1 ) - 1
                NB = JE - JS + 1
                DO 110 I = P, 1, -1
    *
                   IS = IWORK( I )
                   ISP1 = IS + 1
                   IE = IWORK( I+1 ) - 1
                   MB = IE - IS + 1
                   ZDIM = MB*NB*2
    *
                   IF( ( MB.EQ.1 ) .AND. ( NB.EQ.1 ) ) THEN
    *
    *                 Build a 2-by-2 system Z * x = RHS
    *
                      Z( 1, 1 ) = A( IS, IS )
                      Z( 2, 1 ) = D( IS, IS )
                      Z( 1, 2 ) = -B( JS, JS )
                      Z( 2, 2 ) = -E( JS, JS )
    *
    *                 Set up right hand side(s)
    *
                      RHS( 1 ) = C( IS, JS )
                      RHS( 2 ) = F( IS, JS )
    *
    *                 Solve Z * x = RHS
    *
                      CALL SGETC2( ZDIM, Z, LDZ, IPIV, JPIV, IERR )
                      IF( IERR.GT.0 )
         $               INFO = IERR
    *
                      IF( IJOB.EQ.0 ) THEN
                         CALL SGESC2( ZDIM, Z, LDZ, RHS, IPIV, JPIV,
         $                            SCALOC )
                         IF( SCALOC.NE.ONE ) THEN
                            DO 50 K = 1, N
                               CALL SSCAL( M, SCALOC, C( 1, K ), 1 )
                               CALL SSCAL( M, SCALOC, F( 1, K ), 1 )
       50                   CONTINUE
                            SCALE = SCALE*SCALOC
                         END IF
                      ELSE
                         CALL SLATDF( IJOB, ZDIM, Z, LDZ, RHS, RDSUM,
         $                            RDSCAL, IPIV, JPIV )
                      END IF
    *
    *                 Unpack solution vector(s)
    *
                      C( IS, JS ) = RHS( 1 )
                      F( IS, JS ) = RHS( 2 )
    *
    *                 Substitute R(I, J) and L(I, J) into remaining
    *                 equation.
    *
                      IF( I.GT.1 ) THEN
                         ALPHA = -RHS( 1 )
                         CALL SAXPY( IS-1, ALPHA, A( 1, IS ), 1, C( 1, JS ),
         $                           1 )
                         CALL SAXPY( IS-1, ALPHA, D( 1, IS ), 1, F( 1, JS ),
         $                           1 )
                      END IF
                      IF( J.LT.Q ) THEN
                         CALL SAXPY( N-JE, RHS( 2 ), B( JS, JE+1 ), LDB,
         $                           C( IS, JE+1 ), LDC )
                         CALL SAXPY( N-JE, RHS( 2 ), E( JS, JE+1 ), LDE,
         $                           F( IS, JE+1 ), LDF )
                      END IF
    *
                   ELSE IF( ( MB.EQ.1 ) .AND. ( NB.EQ.2 ) ) THEN
    *
    *                 Build a 4-by-4 system Z * x = RHS
    *
                      Z( 1, 1 ) = A( IS, IS )
                      Z( 2, 1 ) = ZERO
                      Z( 3, 1 ) = D( IS, IS )
                      Z( 4, 1 ) = ZERO
    *
                      Z( 1, 2 ) = ZERO
                      Z( 2, 2 ) = A( IS, IS )
                      Z( 3, 2 ) = ZERO
                      Z( 4, 2 ) = D( IS, IS )
    *
                      Z( 1, 3 ) = -B( JS, JS )
                      Z( 2, 3 ) = -B( JS, JSP1 )
                      Z( 3, 3 ) = -E( JS, JS )
                      Z( 4, 3 ) = -E( JS, JSP1 )
    *
                      Z( 1, 4 ) = -B( JSP1, JS )
                      Z( 2, 4 ) = -B( JSP1, JSP1 )
                      Z( 3, 4 ) = ZERO
                      Z( 4, 4 ) = -E( JSP1, JSP1 )
    *
    *                 Set up right hand side(s)
    *
                      RHS( 1 ) = C( IS, JS )
                      RHS( 2 ) = C( IS, JSP1 )
                      RHS( 3 ) = F( IS, JS )
                      RHS( 4 ) = F( IS, JSP1 )
    *
    *                 Solve Z * x = RHS
    *
                      CALL SGETC2( ZDIM, Z, LDZ, IPIV, JPIV, IERR )
                      IF( IERR.GT.0 )
         $               INFO = IERR
    *
                      IF( IJOB.EQ.0 ) THEN
                         CALL SGESC2( ZDIM, Z, LDZ, RHS, IPIV, JPIV,
         $                            SCALOC )
                         IF( SCALOC.NE.ONE ) THEN
                            DO 60 K = 1, N
                               CALL SSCAL( M, SCALOC, C( 1, K ), 1 )
                               CALL SSCAL( M, SCALOC, F( 1, K ), 1 )
       60                   CONTINUE
                            SCALE = SCALE*SCALOC
                         END IF
                      ELSE
                         CALL SLATDF( IJOB, ZDIM, Z, LDZ, RHS, RDSUM,
         $                            RDSCAL, IPIV, JPIV )
                      END IF
    *
    *                 Unpack solution vector(s)
    *
                      C( IS, JS ) = RHS( 1 )
                      C( IS, JSP1 ) = RHS( 2 )
                      F( IS, JS ) = RHS( 3 )
                      F( IS, JSP1 ) = RHS( 4 )
    *
    *                 Substitute R(I, J) and L(I, J) into remaining
    *                 equation.
    *
                      IF( I.GT.1 ) THEN
                         CALL SGER( IS-1, NB, -ONE, A( 1, IS ), 1, RHS( 1 ),
         $                          1, C( 1, JS ), LDC )
                         CALL SGER( IS-1, NB, -ONE, D( 1, IS ), 1, RHS( 1 ),
         $                          1, F( 1, JS ), LDF )
                      END IF
                      IF( J.LT.Q ) THEN
                         CALL SAXPY( N-JE, RHS( 3 ), B( JS, JE+1 ), LDB,
         $                           C( IS, JE+1 ), LDC )
                         CALL SAXPY( N-JE, RHS( 3 ), E( JS, JE+1 ), LDE,
         $                           F( IS, JE+1 ), LDF )
                         CALL SAXPY( N-JE, RHS( 4 ), B( JSP1, JE+1 ), LDB,
         $                           C( IS, JE+1 ), LDC )
                         CALL SAXPY( N-JE, RHS( 4 ), E( JSP1, JE+1 ), LDE,
         $                           F( IS, JE+1 ), LDF )
                      END IF
    *
                   ELSE IF( ( MB.EQ.2 ) .AND. ( NB.EQ.1 ) ) THEN
    *
    *                 Build a 4-by-4 system Z * x = RHS
    *
                      Z( 1, 1 ) = A( IS, IS )
                      Z( 2, 1 ) = A( ISP1, IS )
                      Z( 3, 1 ) = D( IS, IS )
                      Z( 4, 1 ) = ZERO
    *
                      Z( 1, 2 ) = A( IS, ISP1 )
                      Z( 2, 2 ) = A( ISP1, ISP1 )
                      Z( 3, 2 ) = D( IS, ISP1 )
                      Z( 4, 2 ) = D( ISP1, ISP1 )
    *
                      Z( 1, 3 ) = -B( JS, JS )
                      Z( 2, 3 ) = ZERO
                      Z( 3, 3 ) = -E( JS, JS )
                      Z( 4, 3 ) = ZERO
    *
                      Z( 1, 4 ) = ZERO
                      Z( 2, 4 ) = -B( JS, JS )
                      Z( 3, 4 ) = ZERO
                      Z( 4, 4 ) = -E( JS, JS )
    *
    *                 Set up right hand side(s)
    *
                      RHS( 1 ) = C( IS, JS )
                      RHS( 2 ) = C( ISP1, JS )
                      RHS( 3 ) = F( IS, JS )
                      RHS( 4 ) = F( ISP1, JS )
    *
    *                 Solve Z * x = RHS
    *
                      CALL SGETC2( ZDIM, Z, LDZ, IPIV, JPIV, IERR )
                      IF( IERR.GT.0 )
         $               INFO = IERR
                      IF( IJOB.EQ.0 ) THEN
                         CALL SGESC2( ZDIM, Z, LDZ, RHS, IPIV, JPIV,
         $                            SCALOC )
                         IF( SCALOC.NE.ONE ) THEN
                            DO 70 K = 1, N
                               CALL SSCAL( M, SCALOC, C( 1, K ), 1 )
                               CALL SSCAL( M, SCALOC, F( 1, K ), 1 )
       70                   CONTINUE
                            SCALE = SCALE*SCALOC
                         END IF
                      ELSE
                         CALL SLATDF( IJOB, ZDIM, Z, LDZ, RHS, RDSUM,
         $                            RDSCAL, IPIV, JPIV )
                      END IF
    *
    *                 Unpack solution vector(s)
    *
                      C( IS, JS ) = RHS( 1 )
                      C( ISP1, JS ) = RHS( 2 )
                      F( IS, JS ) = RHS( 3 )
                      F( ISP1, JS ) = RHS( 4 )
    *
    *                 Substitute R(I, J) and L(I, J) into remaining
    *                 equation.
    *
                      IF( I.GT.1 ) THEN
                         CALL SGEMV( 'N', IS-1, MB, -ONE, A( 1, IS ), LDA,
         $                           RHS( 1 ), 1, ONE, C( 1, JS ), 1 )
                         CALL SGEMV( 'N', IS-1, MB, -ONE, D( 1, IS ), LDD,
         $                           RHS( 1 ), 1, ONE, F( 1, JS ), 1 )
                      END IF
                      IF( J.LT.Q ) THEN
                         CALL SGER( MB, N-JE, ONE, RHS( 3 ), 1,
         $                          B( JS, JE+1 ), LDB, C( IS, JE+1 ), LDC )
                         CALL SGER( MB, N-JE, ONE, RHS( 3 ), 1,
         $                          E( JS, JE+1 ), LDE, F( IS, JE+1 ), LDF )
                      END IF
    *
                   ELSE IF( ( MB.EQ.2 ) .AND. ( NB.EQ.2 ) ) THEN
    *
    *                 Build an 8-by-8 system Z * x = RHS
    *
                      CALL SLASET( 'F', LDZ, LDZ, ZERO, ZERO, Z, LDZ )
    *
                      Z( 1, 1 ) = A( IS, IS )
                      Z( 2, 1 ) = A( ISP1, IS )
                      Z( 5, 1 ) = D( IS, IS )
    *
                      Z( 1, 2 ) = A( IS, ISP1 )
                      Z( 2, 2 ) = A( ISP1, ISP1 )
                      Z( 5, 2 ) = D( IS, ISP1 )
                      Z( 6, 2 ) = D( ISP1, ISP1 )
    *
                      Z( 3, 3 ) = A( IS, IS )
                      Z( 4, 3 ) = A( ISP1, IS )
                      Z( 7, 3 ) = D( IS, IS )
    *
                      Z( 3, 4 ) = A( IS, ISP1 )
                      Z( 4, 4 ) = A( ISP1, ISP1 )
                      Z( 7, 4 ) = D( IS, ISP1 )
                      Z( 8, 4 ) = D( ISP1, ISP1 )
    *
                      Z( 1, 5 ) = -B( JS, JS )
                      Z( 3, 5 ) = -B( JS, JSP1 )
                      Z( 5, 5 ) = -E( JS, JS )
                      Z( 7, 5 ) = -E( JS, JSP1 )
    *
                      Z( 2, 6 ) = -B( JS, JS )
                      Z( 4, 6 ) = -B( JS, JSP1 )
                      Z( 6, 6 ) = -E( JS, JS )
                      Z( 8, 6 ) = -E( JS, JSP1 )
    *
                      Z( 1, 7 ) = -B( JSP1, JS )
                      Z( 3, 7 ) = -B( JSP1, JSP1 )
                      Z( 7, 7 ) = -E( JSP1, JSP1 )
    *
                      Z( 2, 8 ) = -B( JSP1, JS )
                      Z( 4, 8 ) = -B( JSP1, JSP1 )
                      Z( 8, 8 ) = -E( JSP1, JSP1 )
    *
    *                 Set up right hand side(s)
    *
                      K = 1
                      II = MB*NB + 1
                      DO 80 JJ = 0, NB - 1
                         CALL SCOPY( MB, C( IS, JS+JJ ), 1, RHS( K ), 1 )
                         CALL SCOPY( MB, F( IS, JS+JJ ), 1, RHS( II ), 1 )
                         K = K + MB
                         II = II + MB
       80             CONTINUE
    *
    *                 Solve Z * x = RHS
    *
                      CALL SGETC2( ZDIM, Z, LDZ, IPIV, JPIV, IERR )
                      IF( IERR.GT.0 )
         $               INFO = IERR
                      IF( IJOB.EQ.0 ) THEN
                         CALL SGESC2( ZDIM, Z, LDZ, RHS, IPIV, JPIV,
         $                            SCALOC )
                         IF( SCALOC.NE.ONE ) THEN
                            DO 90 K = 1, N
                               CALL SSCAL( M, SCALOC, C( 1, K ), 1 )
                               CALL SSCAL( M, SCALOC, F( 1, K ), 1 )
       90                   CONTINUE
                            SCALE = SCALE*SCALOC
                         END IF
                      ELSE
                         CALL SLATDF( IJOB, ZDIM, Z, LDZ, RHS, RDSUM,
         $                            RDSCAL, IPIV, JPIV )
                      END IF
    *
    *                 Unpack solution vector(s)
    *
                      K = 1
                      II = MB*NB + 1
                      DO 100 JJ = 0, NB - 1
                         CALL SCOPY( MB, RHS( K ), 1, C( IS, JS+JJ ), 1 )
                         CALL SCOPY( MB, RHS( II ), 1, F( IS, JS+JJ ), 1 )
                         K = K + MB
                         II = II + MB
      100             CONTINUE
    *
    *                 Substitute R(I, J) and L(I, J) into remaining
    *                 equation.
    *
                      IF( I.GT.1 ) THEN
                         CALL SGEMM( 'N', 'N', IS-1, NB, MB, -ONE,
         $                           A( 1, IS ), LDA, RHS( 1 ), MB, ONE,
         $                           C( 1, JS ), LDC )
                         CALL SGEMM( 'N', 'N', IS-1, NB, MB, -ONE,
         $                           D( 1, IS ), LDD, RHS( 1 ), MB, ONE,
         $                           F( 1, JS ), LDF )
                      END IF
                      IF( J.LT.Q ) THEN
                         K = MB*NB + 1
                         CALL SGEMM( 'N', 'N', MB, N-JE, NB, ONE, RHS( K ),
         $                           MB, B( JS, JE+1 ), LDB, ONE,
         $                           C( IS, JE+1 ), LDC )
                         CALL SGEMM( 'N', 'N', MB, N-JE, NB, ONE, RHS( K ),
         $                           MB, E( JS, JE+1 ), LDE, ONE,
         $                           F( IS, JE+1 ), LDF )
                      END IF
    *
                   END IF
    *
      110       CONTINUE
      120    CONTINUE
          ELSE
    *
    *        Solve (I, J) - subsystem
    *             A(I, I)' * R(I, J) + D(I, I)' * L(J, J)  =  C(I, J)
    *             R(I, I)  * B(J, J) + L(I, J)  * E(J, J)  = -F(I, J)
    *        for I = 1, 2, ..., P, J = Q, Q - 1, ..., 1
    *
             SCALE = ONE
             SCALOC = ONE
             DO 200 I = 1, P
    *
                IS = IWORK( I )
                ISP1 = IS + 1
                IE = IWORK( I+1 ) - 1
                MB = IE - IS + 1
                DO 190 J = Q, P + 2, -1
    *
                   JS = IWORK( J )
                   JSP1 = JS + 1
                   JE = IWORK( J+1 ) - 1
                   NB = JE - JS + 1
                   ZDIM = MB*NB*2
                   IF( ( MB.EQ.1 ) .AND. ( NB.EQ.1 ) ) THEN
    *
    *                 Build a 2-by-2 system Z' * x = RHS
    *
                      Z( 1, 1 ) = A( IS, IS )
                      Z( 2, 1 ) = -B( JS, JS )
                      Z( 1, 2 ) = D( IS, IS )
                      Z( 2, 2 ) = -E( JS, JS )
    *
    *                 Set up right hand side(s)
    *
                      RHS( 1 ) = C( IS, JS )
                      RHS( 2 ) = F( IS, JS )
    *
    *                 Solve Z' * x = RHS
    *
                      CALL SGETC2( ZDIM, Z, LDZ, IPIV, JPIV, IERR )
                      IF( IERR.GT.0 )
         $               INFO = IERR
    *
                      CALL SGESC2( ZDIM, Z, LDZ, RHS, IPIV, JPIV, SCALOC )
                      IF( SCALOC.NE.ONE ) THEN
                         DO 130 K = 1, N
                            CALL SSCAL( M, SCALOC, C( 1, K ), 1 )
                            CALL SSCAL( M, SCALOC, F( 1, K ), 1 )
      130                CONTINUE
                         SCALE = SCALE*SCALOC
                      END IF
    *
    *                 Unpack solution vector(s)
    *
                      C( IS, JS ) = RHS( 1 )
                      F( IS, JS ) = RHS( 2 )
    *
    *                 Substitute R(I, J) and L(I, J) into remaining
    *                 equation.
    *
                      IF( J.GT.P+2 ) THEN
                         ALPHA = RHS( 1 )
                         CALL SAXPY( JS-1, ALPHA, B( 1, JS ), 1, F( IS, 1 ),
         $                           LDF )
                         ALPHA = RHS( 2 )
                         CALL SAXPY( JS-1, ALPHA, E( 1, JS ), 1, F( IS, 1 ),
         $                           LDF )
                      END IF
                      IF( I.LT.P ) THEN
                         ALPHA = -RHS( 1 )
                         CALL SAXPY( M-IE, ALPHA, A( IS, IE+1 ), LDA,
         $                           C( IE+1, JS ), 1 )
                         ALPHA = -RHS( 2 )
                         CALL SAXPY( M-IE, ALPHA, D( IS, IE+1 ), LDD,
         $                           C( IE+1, JS ), 1 )
                      END IF
    *
                   ELSE IF( ( MB.EQ.1 ) .AND. ( NB.EQ.2 ) ) THEN
    *
    *                 Build a 4-by-4 system Z' * x = RHS
    *
                      Z( 1, 1 ) = A( IS, IS )
                      Z( 2, 1 ) = ZERO
                      Z( 3, 1 ) = -B( JS, JS )
                      Z( 4, 1 ) = -B( JSP1, JS )
    *
                      Z( 1, 2 ) = ZERO
                      Z( 2, 2 ) = A( IS, IS )
                      Z( 3, 2 ) = -B( JS, JSP1 )
                      Z( 4, 2 ) = -B( JSP1, JSP1 )
    *
                      Z( 1, 3 ) = D( IS, IS )
                      Z( 2, 3 ) = ZERO
                      Z( 3, 3 ) = -E( JS, JS )
                      Z( 4, 3 ) = ZERO
    *
                      Z( 1, 4 ) = ZERO
                      Z( 2, 4 ) = D( IS, IS )
                      Z( 3, 4 ) = -E( JS, JSP1 )
                      Z( 4, 4 ) = -E( JSP1, JSP1 )
    *
    *                 Set up right hand side(s)
    *
                      RHS( 1 ) = C( IS, JS )
                      RHS( 2 ) = C( IS, JSP1 )
                      RHS( 3 ) = F( IS, JS )
                      RHS( 4 ) = F( IS, JSP1 )
    *
    *                 Solve Z' * x = RHS
    *
                      CALL SGETC2( ZDIM, Z, LDZ, IPIV, JPIV, IERR )
                      IF( IERR.GT.0 )
         $               INFO = IERR
                      CALL SGESC2( ZDIM, Z, LDZ, RHS, IPIV, JPIV, SCALOC )
                      IF( SCALOC.NE.ONE ) THEN
                         DO 140 K = 1, N
                            CALL SSCAL( M, SCALOC, C( 1, K ), 1 )
                            CALL SSCAL( M, SCALOC, F( 1, K ), 1 )
      140                CONTINUE
                         SCALE = SCALE*SCALOC
                      END IF
    *
    *                 Unpack solution vector(s)
    *
                      C( IS, JS ) = RHS( 1 )
                      C( IS, JSP1 ) = RHS( 2 )
                      F( IS, JS ) = RHS( 3 )
                      F( IS, JSP1 ) = RHS( 4 )
    *
    *                 Substitute R(I, J) and L(I, J) into remaining
    *                 equation.
    *
                      IF( J.GT.P+2 ) THEN
                         CALL SAXPY( JS-1, RHS( 1 ), B( 1, JS ), 1,
         $                           F( IS, 1 ), LDF )
                         CALL SAXPY( JS-1, RHS( 2 ), B( 1, JSP1 ), 1,
         $                           F( IS, 1 ), LDF )
                         CALL SAXPY( JS-1, RHS( 3 ), E( 1, JS ), 1,
         $                           F( IS, 1 ), LDF )
                         CALL SAXPY( JS-1, RHS( 4 ), E( 1, JSP1 ), 1,
         $                           F( IS, 1 ), LDF )
                      END IF
                      IF( I.LT.P ) THEN
                         CALL SGER( M-IE, NB, -ONE, A( IS, IE+1 ), LDA,
         $                          RHS( 1 ), 1, C( IE+1, JS ), LDC )
                         CALL SGER( M-IE, NB, -ONE, D( IS, IE+1 ), LDD,
         $                          RHS( 3 ), 1, C( IE+1, JS ), LDC )
                      END IF
    *
                   ELSE IF( ( MB.EQ.2 ) .AND. ( NB.EQ.1 ) ) THEN
    *
    *                 Build a 4-by-4 system Z' * x = RHS
    *
                      Z( 1, 1 ) = A( IS, IS )
                      Z( 2, 1 ) = A( IS, ISP1 )
                      Z( 3, 1 ) = -B( JS, JS )
                      Z( 4, 1 ) = ZERO
    *
                      Z( 1, 2 ) = A( ISP1, IS )
                      Z( 2, 2 ) = A( ISP1, ISP1 )
                      Z( 3, 2 ) = ZERO
                      Z( 4, 2 ) = -B( JS, JS )
    *
                      Z( 1, 3 ) = D( IS, IS )
                      Z( 2, 3 ) = D( IS, ISP1 )
                      Z( 3, 3 ) = -E( JS, JS )
                      Z( 4, 3 ) = ZERO
    *
                      Z( 1, 4 ) = ZERO
                      Z( 2, 4 ) = D( ISP1, ISP1 )
                      Z( 3, 4 ) = ZERO
                      Z( 4, 4 ) = -E( JS, JS )
    *
    *                 Set up right hand side(s)
    *
                      RHS( 1 ) = C( IS, JS )
                      RHS( 2 ) = C( ISP1, JS )
                      RHS( 3 ) = F( IS, JS )
                      RHS( 4 ) = F( ISP1, JS )
    *
    *                 Solve Z' * x = RHS
    *
                      CALL SGETC2( ZDIM, Z, LDZ, IPIV, JPIV, IERR )
                      IF( IERR.GT.0 )
         $               INFO = IERR
    *
                      CALL SGESC2( ZDIM, Z, LDZ, RHS, IPIV, JPIV, SCALOC )
                      IF( SCALOC.NE.ONE ) THEN
                         DO 150 K = 1, N
                            CALL SSCAL( M, SCALOC, C( 1, K ), 1 )
                            CALL SSCAL( M, SCALOC, F( 1, K ), 1 )
      150                CONTINUE
                         SCALE = SCALE*SCALOC
                      END IF
    *
    *                 Unpack solution vector(s)
    *
                      C( IS, JS ) = RHS( 1 )
                      C( ISP1, JS ) = RHS( 2 )
                      F( IS, JS ) = RHS( 3 )
                      F( ISP1, JS ) = RHS( 4 )
    *
    *                 Substitute R(I, J) and L(I, J) into remaining
    *                 equation.
    *
                      IF( J.GT.P+2 ) THEN
                         CALL SGER( MB, JS-1, ONE, RHS( 1 ), 1, B( 1, JS ),
         $                          1, F( IS, 1 ), LDF )
                         CALL SGER( MB, JS-1, ONE, RHS( 3 ), 1, E( 1, JS ),
         $                          1, F( IS, 1 ), LDF )
                      END IF
                      IF( I.LT.P ) THEN
                         CALL SGEMV( 'T', MB, M-IE, -ONE, A( IS, IE+1 ),
         $                           LDA, RHS( 1 ), 1, ONE, C( IE+1, JS ),
         $                           1 )
                         CALL SGEMV( 'T', MB, M-IE, -ONE, D( IS, IE+1 ),
         $                           LDD, RHS( 3 ), 1, ONE, C( IE+1, JS ),
         $                           1 )
                      END IF
    *
                   ELSE IF( ( MB.EQ.2 ) .AND. ( NB.EQ.2 ) ) THEN
    *
    *                 Build an 8-by-8 system Z' * x = RHS
    *
                      CALL SLASET( 'F', LDZ, LDZ, ZERO, ZERO, Z, LDZ )
    *
                      Z( 1, 1 ) = A( IS, IS )
                      Z( 2, 1 ) = A( IS, ISP1 )
                      Z( 5, 1 ) = -B( JS, JS )
                      Z( 7, 1 ) = -B( JSP1, JS )
    *
                      Z( 1, 2 ) = A( ISP1, IS )
                      Z( 2, 2 ) = A( ISP1, ISP1 )
                      Z( 6, 2 ) = -B( JS, JS )
                      Z( 8, 2 ) = -B( JSP1, JS )
    *
                      Z( 3, 3 ) = A( IS, IS )
                      Z( 4, 3 ) = A( IS, ISP1 )
                      Z( 5, 3 ) = -B( JS, JSP1 )
                      Z( 7, 3 ) = -B( JSP1, JSP1 )
    *
                      Z( 3, 4 ) = A( ISP1, IS )
                      Z( 4, 4 ) = A( ISP1, ISP1 )
                      Z( 6, 4 ) = -B( JS, JSP1 )
                      Z( 8, 4 ) = -B( JSP1, JSP1 )
    *
                      Z( 1, 5 ) = D( IS, IS )
                      Z( 2, 5 ) = D( IS, ISP1 )
                      Z( 5, 5 ) = -E( JS, JS )
    *
                      Z( 2, 6 ) = D( ISP1, ISP1 )
                      Z( 6, 6 ) = -E( JS, JS )
    *
                      Z( 3, 7 ) = D( IS, IS )
                      Z( 4, 7 ) = D( IS, ISP1 )
                      Z( 5, 7 ) = -E( JS, JSP1 )
                      Z( 7, 7 ) = -E( JSP1, JSP1 )
    *
                      Z( 4, 8 ) = D( ISP1, ISP1 )
                      Z( 6, 8 ) = -E( JS, JSP1 )
                      Z( 8, 8 ) = -E( JSP1, JSP1 )
    *
    *                 Set up right hand side(s)
    *
                      K = 1
                      II = MB*NB + 1
                      DO 160 JJ = 0, NB - 1
                         CALL SCOPY( MB, C( IS, JS+JJ ), 1, RHS( K ), 1 )
                         CALL SCOPY( MB, F( IS, JS+JJ ), 1, RHS( II ), 1 )
                         K = K + MB
                         II = II + MB
      160             CONTINUE
    *
    *
    *                 Solve Z' * x = RHS
    *
                      CALL SGETC2( ZDIM, Z, LDZ, IPIV, JPIV, IERR )
                      IF( IERR.GT.0 )
         $               INFO = IERR
    *
                      CALL SGESC2( ZDIM, Z, LDZ, RHS, IPIV, JPIV, SCALOC )
                      IF( SCALOC.NE.ONE ) THEN
                         DO 170 K = 1, N
                            CALL SSCAL( M, SCALOC, C( 1, K ), 1 )
                            CALL SSCAL( M, SCALOC, F( 1, K ), 1 )
      170                CONTINUE
                         SCALE = SCALE*SCALOC
                      END IF
    *
    *                 Unpack solution vector(s)
    *
                      K = 1
                      II = MB*NB + 1
                      DO 180 JJ = 0, NB - 1
                         CALL SCOPY( MB, RHS( K ), 1, C( IS, JS+JJ ), 1 )
                         CALL SCOPY( MB, RHS( II ), 1, F( IS, JS+JJ ), 1 )
                         K = K + MB
                         II = II + MB
      180             CONTINUE
    *
    *                 Substitute R(I, J) and L(I, J) into remaining
    *                 equation.
    *
                      IF( J.GT.P+2 ) THEN
                         CALL SGEMM( 'N', 'T', MB, JS-1, NB, ONE,
         $                           C( IS, JS ), LDC, B( 1, JS ), LDB, ONE,
         $                           F( IS, 1 ), LDF )
                         CALL SGEMM( 'N', 'T', MB, JS-1, NB, ONE,
         $                           F( IS, JS ), LDF, E( 1, JS ), LDE, ONE,
         $                           F( IS, 1 ), LDF )
                      END IF
                      IF( I.LT.P ) THEN
                         CALL SGEMM( 'T', 'N', M-IE, NB, MB, -ONE,
         $                           A( IS, IE+1 ), LDA, C( IS, JS ), LDC,
         $                           ONE, C( IE+1, JS ), LDC )
                         CALL SGEMM( 'T', 'N', M-IE, NB, MB, -ONE,
         $                           D( IS, IE+1 ), LDD, F( IS, JS ), LDF,
         $                           ONE, C( IE+1, JS ), LDC )
                      END IF
    *
                   END IF
    *
      190       CONTINUE
      200    CONTINUE
    *
          END IF
          RETURN
    *
    *     End of STGSY2
    *
          END