stgex2.f

          SUBROUTINE STGEX2( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z,
         $                   LDZ, J1, N1, N2, WORK, LWORK, INFO )
    *
    *  -- LAPACK auxiliary routine (version 3.1) --
    *     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
    *     November 2006
    *
    *     .. Scalar Arguments ..
          LOGICAL            WANTQ, WANTZ
          INTEGER            INFO, J1, LDA, LDB, LDQ, LDZ, LWORK, N, N1, N2
    *     ..
    *     .. Array Arguments ..
          REAL               A( LDA, * ), B( LDB, * ), Q( LDQ, * ),
         $                   WORK( * ), Z( LDZ, * )
    *     ..
    *
    *  Purpose
    *  =======
    *
    *  STGEX2 swaps adjacent diagonal blocks (A11, B11) and (A22, B22)
    *  of size 1-by-1 or 2-by-2 in an upper (quasi) triangular matrix pair
    *  (A, B) by an orthogonal equivalence transformation.
    *
    *  (A, B) must be in generalized real Schur canonical form (as returned
    *  by SGGES), i.e. A is block upper triangular with 1-by-1 and 2-by-2
    *  diagonal blocks. B is upper triangular.
    *
    *  Optionally, the matrices Q and Z of generalized Schur vectors are
    *  updated.
    *
    *         Q(in) * A(in) * Z(in)' = Q(out) * A(out) * Z(out)'
    *         Q(in) * B(in) * Z(in)' = Q(out) * B(out) * Z(out)'
    *
    *
    *  Arguments
    *  =========
    *
    *  WANTQ   (input) LOGICAL
    *          .TRUE. : update the left transformation matrix Q;
    *          .FALSE.: do not update Q.
    *
    *  WANTZ   (input) LOGICAL
    *          .TRUE. : update the right transformation matrix Z;
    *          .FALSE.: do not update Z.
    *
    *  N       (input) INTEGER
    *          The order of the matrices A and B. N >= 0.
    *
    *  A      (input/output) REAL arrays, dimensions (LDA,N)
    *          On entry, the matrix A in the pair (A, B).
    *          On exit, the updated matrix A.
    *
    *  LDA     (input)  INTEGER
    *          The leading dimension of the array A. LDA >= max(1,N).
    *
    *  B      (input/output) REAL arrays, dimensions (LDB,N)
    *          On entry, the matrix B in the pair (A, B).
    *          On exit, the updated matrix B.
    *
    *  LDB     (input)  INTEGER
    *          The leading dimension of the array B. LDB >= max(1,N).
    *
    *  Q       (input/output) REAL array, dimension (LDZ,N)
    *          On entry, if WANTQ = .TRUE., the orthogonal matrix Q.
    *          On exit, the updated matrix Q.
    *          Not referenced if WANTQ = .FALSE..
    *
    *  LDQ     (input) INTEGER
    *          The leading dimension of the array Q. LDQ >= 1.
    *          If WANTQ = .TRUE., LDQ >= N.
    *
    *  Z       (input/output) REAL array, dimension (LDZ,N)
    *          On entry, if WANTZ =.TRUE., the orthogonal matrix Z.
    *          On exit, the updated matrix Z.
    *          Not referenced if WANTZ = .FALSE..
    *
    *  LDZ     (input) INTEGER
    *          The leading dimension of the array Z. LDZ >= 1.
    *          If WANTZ = .TRUE., LDZ >= N.
    *
    *  J1      (input) INTEGER
    *          The index to the first block (A11, B11). 1 <= J1 <= N.
    *
    *  N1      (input) INTEGER
    *          The order of the first block (A11, B11). N1 = 0, 1 or 2.
    *
    *  N2      (input) INTEGER
    *          The order of the second block (A22, B22). N2 = 0, 1 or 2.
    *
    *  WORK    (workspace) REAL array, dimension (MAX(1,LWORK)).
    *
    *  LWORK   (input) INTEGER
    *          The dimension of the array WORK.
    *          LWORK >=  MAX( N*(N2+N1), (N2+N1)*(N2+N1)*2 )
    *
    *  INFO    (output) INTEGER
    *            =0: Successful exit
    *            >0: If INFO = 1, the transformed matrix (A, B) would be
    *                too far from generalized Schur form; the blocks are
    *                not swapped and (A, B) and (Q, Z) are unchanged.
    *                The problem of swapping is too ill-conditioned.
    *            <0: If INFO = -16: LWORK is too small. Appropriate value
    *                for LWORK is returned in WORK(1).
    *
    *  Further Details
    *  ===============
    *
    *  Based on contributions by
    *     Bo Kagstrom and Peter Poromaa, Department of Computing Science,
    *     Umea University, S-901 87 Umea, Sweden.
    *
    *  In the current code both weak and strong stability tests are
    *  performed. The user can omit the strong stability test by changing
    *  the internal logical parameter WANDS to .FALSE.. See ref. [2] for
    *  details.
    *
    *  [1] B. Kagstrom; A Direct Method for Reordering Eigenvalues in the
    *      Generalized Real Schur Form of a Regular Matrix Pair (A, B), in
    *      M.S. Moonen et al (eds), Linear Algebra for Large Scale and
    *      Real-Time Applications, Kluwer Academic Publ. 1993, pp 195-218.
    *
    *  [2] B. Kagstrom and P. Poromaa; Computing Eigenspaces with Specified
    *      Eigenvalues of a Regular Matrix Pair (A, B) and Condition
    *      Estimation: Theory, Algorithms and Software,
    *      Report UMINF - 94.04, Department of Computing Science, Umea
    *      University, S-901 87 Umea, Sweden, 1994. Also as LAPACK Working
    *      Note 87. To appear in Numerical Algorithms, 1996.
    *
    *  =====================================================================
    *  Replaced various illegal calls to SCOPY by calls to SLASET, or by DO
    *  loops. Sven Hammarling, 1/5/02.
    *
    *     .. Parameters ..
          REAL               ZERO, ONE
          PARAMETER          ( ZERO = 0.0E+0, ONE = 1.0E+0 )
          REAL               TEN
          PARAMETER          ( TEN = 1.0E+01 )
          INTEGER            LDST
          PARAMETER          ( LDST = 4 )
          LOGICAL            WANDS
          PARAMETER          ( WANDS = .TRUE. )
    *     ..
    *     .. Local Scalars ..
          LOGICAL            STRONG, WEAK
          INTEGER            I, IDUM, LINFO, M
          REAL               BQRA21, BRQA21, DDUM, DNORM, DSCALE, DSUM, EPS,
         $                   F, G, SA, SB, SCALE, SMLNUM, SS, THRESH, WS
    *     ..
    *     .. Local Arrays ..
          INTEGER            IWORK( LDST )
          REAL               AI( 2 ), AR( 2 ), BE( 2 ), IR( LDST, LDST ),
         $                   IRCOP( LDST, LDST ), LI( LDST, LDST ),
         $                   LICOP( LDST, LDST ), S( LDST, LDST ),
         $                   SCPY( LDST, LDST ), T( LDST, LDST ),
         $                   TAUL( LDST ), TAUR( LDST ), TCPY( LDST, LDST )
    *     ..
    *     .. External Functions ..
          REAL               SLAMCH
          EXTERNAL           SLAMCH
    *     ..
    *     .. External Subroutines ..
          EXTERNAL           SGEMM, SGEQR2, SGERQ2, SLACPY, SLAGV2, SLARTG,
         $                   SLASET, SLASSQ, SORG2R, SORGR2, SORM2R, SORMR2,
         $                   SROT, SSCAL, STGSY2
    *     ..
    *     .. Intrinsic Functions ..
          INTRINSIC          ABS, MAX, SQRT
    *     ..
    *     .. Executable Statements ..
    *
          INFO = 0
    *
    *     Quick return if possible
    *
          IF( N.LE.1 .OR. N1.LE.0 .OR. N2.LE.0 )
         $   RETURN
          IF( N1.GT.N .OR. ( J1+N1 ).GT.N )
         $   RETURN
          M = N1 + N2
          IF( LWORK.LT.MAX( N*M, M*M*2 ) ) THEN
             INFO = -16
             WORK( 1 ) = MAX( N*M, M*M*2 )
             RETURN
          END IF
    *
          WEAK = .FALSE.
          STRONG = .FALSE.
    *
    *     Make a local copy of selected block
    *
          CALL SLASET( 'Full', LDST, LDST, ZERO, ZERO, LI, LDST )
          CALL SLASET( 'Full', LDST, LDST, ZERO, ZERO, IR, LDST )
          CALL SLACPY( 'Full', M, M, A( J1, J1 ), LDA, S, LDST )
          CALL SLACPY( 'Full', M, M, B( J1, J1 ), LDB, T, LDST )
    *
    *     Compute threshold for testing acceptance of swapping.
    *
          EPS = SLAMCH( 'P' )
          SMLNUM = SLAMCH( 'S' ) / EPS
          DSCALE = ZERO
          DSUM = ONE
          CALL SLACPY( 'Full', M, M, S, LDST, WORK, M )
          CALL SLASSQ( M*M, WORK, 1, DSCALE, DSUM )
          CALL SLACPY( 'Full', M, M, T, LDST, WORK, M )
          CALL SLASSQ( M*M, WORK, 1, DSCALE, DSUM )
          DNORM = DSCALE*SQRT( DSUM )
          THRESH = MAX( TEN*EPS*DNORM, SMLNUM )
    *
          IF( M.EQ.2 ) THEN
    *
    *        CASE 1: Swap 1-by-1 and 1-by-1 blocks.
    *
    *        Compute orthogonal QL and RQ that swap 1-by-1 and 1-by-1 blocks
    *        using Givens rotations and perform the swap tentatively.
    *
             F = S( 2, 2 )*T( 1, 1 ) - T( 2, 2 )*S( 1, 1 )
             G = S( 2, 2 )*T( 1, 2 ) - T( 2, 2 )*S( 1, 2 )
             SB = ABS( T( 2, 2 ) )
             SA = ABS( S( 2, 2 ) )
             CALL SLARTG( F, G, IR( 1, 2 ), IR( 1, 1 ), DDUM )
             IR( 2, 1 ) = -IR( 1, 2 )
             IR( 2, 2 ) = IR( 1, 1 )
             CALL SROT( 2, S( 1, 1 ), 1, S( 1, 2 ), 1, IR( 1, 1 ),
         $              IR( 2, 1 ) )
             CALL SROT( 2, T( 1, 1 ), 1, T( 1, 2 ), 1, IR( 1, 1 ),
         $              IR( 2, 1 ) )
             IF( SA.GE.SB ) THEN
                CALL SLARTG( S( 1, 1 ), S( 2, 1 ), LI( 1, 1 ), LI( 2, 1 ),
         $                   DDUM )
             ELSE
                CALL SLARTG( T( 1, 1 ), T( 2, 1 ), LI( 1, 1 ), LI( 2, 1 ),
         $                   DDUM )
             END IF
             CALL SROT( 2, S( 1, 1 ), LDST, S( 2, 1 ), LDST, LI( 1, 1 ),
         $              LI( 2, 1 ) )
             CALL SROT( 2, T( 1, 1 ), LDST, T( 2, 1 ), LDST, LI( 1, 1 ),
         $              LI( 2, 1 ) )
             LI( 2, 2 ) = LI( 1, 1 )
             LI( 1, 2 ) = -LI( 2, 1 )
    *
    *        Weak stability test:
    *           |S21| + |T21| <= O(EPS * F-norm((S, T)))
    *
             WS = ABS( S( 2, 1 ) ) + ABS( T( 2, 1 ) )
             WEAK = WS.LE.THRESH
             IF( .NOT.WEAK )
         $      GO TO 70
    *
             IF( WANDS ) THEN
    *
    *           Strong stability test:
    *             F-norm((A-QL'*S*QR, B-QL'*T*QR)) <= O(EPS*F-norm((A,B)))
    *
                CALL SLACPY( 'Full', M, M, A( J1, J1 ), LDA, WORK( M*M+1 ),
         $                   M )
                CALL SGEMM( 'N', 'N', M, M, M, ONE, LI, LDST, S, LDST, ZERO,
         $                  WORK, M )
                CALL SGEMM( 'N', 'T', M, M, M, -ONE, WORK, M, IR, LDST, ONE,
         $                  WORK( M*M+1 ), M )
                DSCALE = ZERO
                DSUM = ONE
                CALL SLASSQ( M*M, WORK( M*M+1 ), 1, DSCALE, DSUM )
    *
                CALL SLACPY( 'Full', M, M, B( J1, J1 ), LDB, WORK( M*M+1 ),
         $                   M )
                CALL SGEMM( 'N', 'N', M, M, M, ONE, LI, LDST, T, LDST, ZERO,
         $                  WORK, M )
                CALL SGEMM( 'N', 'T', M, M, M, -ONE, WORK, M, IR, LDST, ONE,
         $                  WORK( M*M+1 ), M )
                CALL SLASSQ( M*M, WORK( M*M+1 ), 1, DSCALE, DSUM )
                SS = DSCALE*SQRT( DSUM )
                STRONG = SS.LE.THRESH
                IF( .NOT.STRONG )
         $         GO TO 70
             END IF
    *
    *        Update (A(J1:J1+M-1, M+J1:N), B(J1:J1+M-1, M+J1:N)) and
    *               (A(1:J1-1, J1:J1+M), B(1:J1-1, J1:J1+M)).
    *
             CALL SROT( J1+1, A( 1, J1 ), 1, A( 1, J1+1 ), 1, IR( 1, 1 ),
         $              IR( 2, 1 ) )
             CALL SROT( J1+1, B( 1, J1 ), 1, B( 1, J1+1 ), 1, IR( 1, 1 ),
         $              IR( 2, 1 ) )
             CALL SROT( N-J1+1, A( J1, J1 ), LDA, A( J1+1, J1 ), LDA,
         $              LI( 1, 1 ), LI( 2, 1 ) )
             CALL SROT( N-J1+1, B( J1, J1 ), LDB, B( J1+1, J1 ), LDB,
         $              LI( 1, 1 ), LI( 2, 1 ) )
    *
    *        Set  N1-by-N2 (2,1) - blocks to ZERO.
    *
             A( J1+1, J1 ) = ZERO
             B( J1+1, J1 ) = ZERO
    *
    *        Accumulate transformations into Q and Z if requested.
    *
             IF( WANTZ )
         $      CALL SROT( N, Z( 1, J1 ), 1, Z( 1, J1+1 ), 1, IR( 1, 1 ),
         $                 IR( 2, 1 ) )
             IF( WANTQ )
         $      CALL SROT( N, Q( 1, J1 ), 1, Q( 1, J1+1 ), 1, LI( 1, 1 ),
         $                 LI( 2, 1 ) )
    *
    *        Exit with INFO = 0 if swap was successfully performed.
    *
             RETURN
    *
          ELSE
    *
    *        CASE 2: Swap 1-by-1 and 2-by-2 blocks, or 2-by-2
    *                and 2-by-2 blocks.
    *
    *        Solve the generalized Sylvester equation
    *                 S11 * R - L * S22 = SCALE * S12
    *                 T11 * R - L * T22 = SCALE * T12
    *        for R and L. Solutions in LI and IR.
    *
             CALL SLACPY( 'Full', N1, N2, T( 1, N1+1 ), LDST, LI, LDST )
             CALL SLACPY( 'Full', N1, N2, S( 1, N1+1 ), LDST,
         $                IR( N2+1, N1+1 ), LDST )
             CALL STGSY2( 'N', 0, N1, N2, S, LDST, S( N1+1, N1+1 ), LDST,
         $                IR( N2+1, N1+1 ), LDST, T, LDST, T( N1+1, N1+1 ),
         $                LDST, LI, LDST, SCALE, DSUM, DSCALE, IWORK, IDUM,
         $                LINFO )
    *
    *        Compute orthogonal matrix QL:
    *
    *                    QL' * LI = [ TL ]
    *                               [ 0  ]
    *        where
    *                    LI =  [      -L              ]
    *                          [ SCALE * identity(N2) ]
    *
             DO 10 I = 1, N2
                CALL SSCAL( N1, -ONE, LI( 1, I ), 1 )
                LI( N1+I, I ) = SCALE
       10    CONTINUE
             CALL SGEQR2( M, N2, LI, LDST, TAUL, WORK, LINFO )
             IF( LINFO.NE.0 )
         $      GO TO 70
             CALL SORG2R( M, M, N2, LI, LDST, TAUL, WORK, LINFO )
             IF( LINFO.NE.0 )
         $      GO TO 70
    *
    *        Compute orthogonal matrix RQ:
    *
    *                    IR * RQ' =   [ 0  TR],
    *
    *         where IR = [ SCALE * identity(N1), R ]
    *
             DO 20 I = 1, N1
                IR( N2+I, I ) = SCALE
       20    CONTINUE
             CALL SGERQ2( N1, M, IR( N2+1, 1 ), LDST, TAUR, WORK, LINFO )
             IF( LINFO.NE.0 )
         $      GO TO 70
             CALL SORGR2( M, M, N1, IR, LDST, TAUR, WORK, LINFO )
             IF( LINFO.NE.0 )
         $      GO TO 70
    *
    *        Perform the swapping tentatively:
    *
             CALL SGEMM( 'T', 'N', M, M, M, ONE, LI, LDST, S, LDST, ZERO,
         $               WORK, M )
             CALL SGEMM( 'N', 'T', M, M, M, ONE, WORK, M, IR, LDST, ZERO, S,
         $               LDST )
             CALL SGEMM( 'T', 'N', M, M, M, ONE, LI, LDST, T, LDST, ZERO,
         $               WORK, M )
             CALL SGEMM( 'N', 'T', M, M, M, ONE, WORK, M, IR, LDST, ZERO, T,
         $               LDST )
             CALL SLACPY( 'F', M, M, S, LDST, SCPY, LDST )
             CALL SLACPY( 'F', M, M, T, LDST, TCPY, LDST )
             CALL SLACPY( 'F', M, M, IR, LDST, IRCOP, LDST )
             CALL SLACPY( 'F', M, M, LI, LDST, LICOP, LDST )
    *
    *        Triangularize the B-part by an RQ factorization.
    *        Apply transformation (from left) to A-part, giving S.
    *
             CALL SGERQ2( M, M, T, LDST, TAUR, WORK, LINFO )
             IF( LINFO.NE.0 )
         $      GO TO 70
             CALL SORMR2( 'R', 'T', M, M, M, T, LDST, TAUR, S, LDST, WORK,
         $                LINFO )
             IF( LINFO.NE.0 )
         $      GO TO 70
             CALL SORMR2( 'L', 'N', M, M, M, T, LDST, TAUR, IR, LDST, WORK,
         $                LINFO )
             IF( LINFO.NE.0 )
         $      GO TO 70
    *
    *        Compute F-norm(S21) in BRQA21. (T21 is 0.)
    *
             DSCALE = ZERO
             DSUM = ONE
             DO 30 I = 1, N2
                CALL SLASSQ( N1, S( N2+1, I ), 1, DSCALE, DSUM )
       30    CONTINUE
             BRQA21 = DSCALE*SQRT( DSUM )
    *
    *        Triangularize the B-part by a QR factorization.
    *        Apply transformation (from right) to A-part, giving S.
    *
             CALL SGEQR2( M, M, TCPY, LDST, TAUL, WORK, LINFO )
             IF( LINFO.NE.0 )
         $      GO TO 70
             CALL SORM2R( 'L', 'T', M, M, M, TCPY, LDST, TAUL, SCPY, LDST,
         $                WORK, INFO )
             CALL SORM2R( 'R', 'N', M, M, M, TCPY, LDST, TAUL, LICOP, LDST,
         $                WORK, INFO )
             IF( LINFO.NE.0 )
         $      GO TO 70
    *
    *        Compute F-norm(S21) in BQRA21. (T21 is 0.)
    *
             DSCALE = ZERO
             DSUM = ONE
             DO 40 I = 1, N2
                CALL SLASSQ( N1, SCPY( N2+1, I ), 1, DSCALE, DSUM )
       40    CONTINUE
             BQRA21 = DSCALE*SQRT( DSUM )
    *
    *        Decide which method to use.
    *          Weak stability test:
    *             F-norm(S21) <= O(EPS * F-norm((S, T)))
    *
             IF( BQRA21.LE.BRQA21 .AND. BQRA21.LE.THRESH ) THEN
                CALL SLACPY( 'F', M, M, SCPY, LDST, S, LDST )
                CALL SLACPY( 'F', M, M, TCPY, LDST, T, LDST )
                CALL SLACPY( 'F', M, M, IRCOP, LDST, IR, LDST )
                CALL SLACPY( 'F', M, M, LICOP, LDST, LI, LDST )
             ELSE IF( BRQA21.GE.THRESH ) THEN
                GO TO 70
             END IF
    *
    *        Set lower triangle of B-part to zero
    *
             CALL SLASET( 'Lower', M-1, M-1, ZERO, ZERO, T(2,1), LDST )
    *
             IF( WANDS ) THEN
    *
    *           Strong stability test:
    *              F-norm((A-QL*S*QR', B-QL*T*QR')) <= O(EPS*F-norm((A,B)))
    *
                CALL SLACPY( 'Full', M, M, A( J1, J1 ), LDA, WORK( M*M+1 ),
         $                   M )
                CALL SGEMM( 'N', 'N', M, M, M, ONE, LI, LDST, S, LDST, ZERO,
         $                  WORK, M )
                CALL SGEMM( 'N', 'N', M, M, M, -ONE, WORK, M, IR, LDST, ONE,
         $                  WORK( M*M+1 ), M )
                DSCALE = ZERO
                DSUM = ONE
                CALL SLASSQ( M*M, WORK( M*M+1 ), 1, DSCALE, DSUM )
    *
                CALL SLACPY( 'Full', M, M, B( J1, J1 ), LDB, WORK( M*M+1 ),
         $                   M )
                CALL SGEMM( 'N', 'N', M, M, M, ONE, LI, LDST, T, LDST, ZERO,
         $                  WORK, M )
                CALL SGEMM( 'N', 'N', M, M, M, -ONE, WORK, M, IR, LDST, ONE,
         $                  WORK( M*M+1 ), M )
                CALL SLASSQ( M*M, WORK( M*M+1 ), 1, DSCALE, DSUM )
                SS = DSCALE*SQRT( DSUM )
                STRONG = ( SS.LE.THRESH )
                IF( .NOT.STRONG )
         $         GO TO 70
    *
             END IF
    *
    *        If the swap is accepted ("weakly" and "strongly"), apply the
    *        transformations and set N1-by-N2 (2,1)-block to zero.
    *
             CALL SLASET( 'Full', N1, N2, ZERO, ZERO, S(N2+1,1), LDST )
    *
    *        copy back M-by-M diagonal block starting at index J1 of (A, B)
    *
             CALL SLACPY( 'F', M, M, S, LDST, A( J1, J1 ), LDA )
             CALL SLACPY( 'F', M, M, T, LDST, B( J1, J1 ), LDB )
             CALL SLASET( 'Full', LDST, LDST, ZERO, ZERO, T, LDST )
    *
    *        Standardize existing 2-by-2 blocks.
    *
             DO 50 I = 1, M*M
                WORK(I) = ZERO
       50    CONTINUE
             WORK( 1 ) = ONE
             T( 1, 1 ) = ONE
             IDUM = LWORK - M*M - 2
             IF( N2.GT.1 ) THEN
                CALL SLAGV2( A( J1, J1 ), LDA, B( J1, J1 ), LDB, AR, AI, BE,
         $                   WORK( 1 ), WORK( 2 ), T( 1, 1 ), T( 2, 1 ) )
                WORK( M+1 ) = -WORK( 2 )
                WORK( M+2 ) = WORK( 1 )
                T( N2, N2 ) = T( 1, 1 )
                T( 1, 2 ) = -T( 2, 1 )
             END IF
             WORK( M*M ) = ONE
             T( M, M ) = ONE
    *
             IF( N1.GT.1 ) THEN
                CALL SLAGV2( A( J1+N2, J1+N2 ), LDA, B( J1+N2, J1+N2 ), LDB,
         $                   TAUR, TAUL, WORK( M*M+1 ), WORK( N2*M+N2+1 ),
         $                   WORK( N2*M+N2+2 ), T( N2+1, N2+1 ),
         $                   T( M, M-1 ) )
                WORK( M*M ) = WORK( N2*M+N2+1 )
                WORK( M*M-1 ) = -WORK( N2*M+N2+2 )
                T( M, M ) = T( N2+1, N2+1 )
                T( M-1, M ) = -T( M, M-1 )
             END IF
             CALL SGEMM( 'T', 'N', N2, N1, N2, ONE, WORK, M, A( J1, J1+N2 ),
         $               LDA, ZERO, WORK( M*M+1 ), N2 )
             CALL SLACPY( 'Full', N2, N1, WORK( M*M+1 ), N2, A( J1, J1+N2 ),
         $                LDA )
             CALL SGEMM( 'T', 'N', N2, N1, N2, ONE, WORK, M, B( J1, J1+N2 ),
         $               LDB, ZERO, WORK( M*M+1 ), N2 )
             CALL SLACPY( 'Full', N2, N1, WORK( M*M+1 ), N2, B( J1, J1+N2 ),
         $                LDB )
             CALL SGEMM( 'N', 'N', M, M, M, ONE, LI, LDST, WORK, M, ZERO,
         $               WORK( M*M+1 ), M )
             CALL SLACPY( 'Full', M, M, WORK( M*M+1 ), M, LI, LDST )
             CALL SGEMM( 'N', 'N', N2, N1, N1, ONE, A( J1, J1+N2 ), LDA,
         $               T( N2+1, N2+1 ), LDST, ZERO, WORK, N2 )
             CALL SLACPY( 'Full', N2, N1, WORK, N2, A( J1, J1+N2 ), LDA )
             CALL SGEMM( 'N', 'N', N2, N1, N1, ONE, B( J1, J1+N2 ), LDB,
         $               T( N2+1, N2+1 ), LDST, ZERO, WORK, N2 )
             CALL SLACPY( 'Full', N2, N1, WORK, N2, B( J1, J1+N2 ), LDB )
             CALL SGEMM( 'T', 'N', M, M, M, ONE, IR, LDST, T, LDST, ZERO,
         $               WORK, M )
             CALL SLACPY( 'Full', M, M, WORK, M, IR, LDST )
    *
    *        Accumulate transformations into Q and Z if requested.
    *
             IF( WANTQ ) THEN
                CALL SGEMM( 'N', 'N', N, M, M, ONE, Q( 1, J1 ), LDQ, LI,
         $                  LDST, ZERO, WORK, N )
                CALL SLACPY( 'Full', N, M, WORK, N, Q( 1, J1 ), LDQ )
    *
             END IF
    *
             IF( WANTZ ) THEN
                CALL SGEMM( 'N', 'N', N, M, M, ONE, Z( 1, J1 ), LDZ, IR,
         $                  LDST, ZERO, WORK, N )
                CALL SLACPY( 'Full', N, M, WORK, N, Z( 1, J1 ), LDZ )
    *
             END IF
    *
    *        Update (A(J1:J1+M-1, M+J1:N), B(J1:J1+M-1, M+J1:N)) and
    *                (A(1:J1-1, J1:J1+M), B(1:J1-1, J1:J1+M)).
    *
             I = J1 + M
             IF( I.LE.N ) THEN
                CALL SGEMM( 'T', 'N', M, N-I+1, M, ONE, LI, LDST,
         $                  A( J1, I ), LDA, ZERO, WORK, M )
                CALL SLACPY( 'Full', M, N-I+1, WORK, M, A( J1, I ), LDA )
                CALL SGEMM( 'T', 'N', M, N-I+1, M, ONE, LI, LDST,
         $                  B( J1, I ), LDB, ZERO, WORK, M )
                CALL SLACPY( 'Full', M, N-I+1, WORK, M, B( J1, I ), LDB )
             END IF
             I = J1 - 1
             IF( I.GT.0 ) THEN
                CALL SGEMM( 'N', 'N', I, M, M, ONE, A( 1, J1 ), LDA, IR,
         $                  LDST, ZERO, WORK, I )
                CALL SLACPY( 'Full', I, M, WORK, I, A( 1, J1 ), LDA )
                CALL SGEMM( 'N', 'N', I, M, M, ONE, B( 1, J1 ), LDB, IR,
         $                  LDST, ZERO, WORK, I )
                CALL SLACPY( 'Full', I, M, WORK, I, B( 1, J1 ), LDB )
             END IF
    *
    *        Exit with INFO = 0 if swap was successfully performed.
    *
             RETURN
    *
          END IF
    *
    *     Exit with INFO = 1 if swap was rejected.
    *
       70 CONTINUE
    *
          INFO = 1
          RETURN
    *
    *     End of STGEX2
    *
          END