SUBROUTINE DTGEX2( 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 ..
DOUBLE PRECISION A( LDA, * ), B( LDB, * ), Q( LDQ, * ),
$ WORK( * ), Z( LDZ, * )
* ..
*
* Purpose
* =======
*
* DTGEX2 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 DGGES), 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) DOUBLE PRECISION 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) DOUBLE PRECISION 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) DOUBLE PRECISION 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) DOUBLE PRECISION 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) DOUBLE PRECISION array, dimension (MAX(1,LWORK)).
*
* LWORK (input) INTEGER
* The dimension of the array WORK.
* LWORK >= MAX( 1, 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 DCOPY by calls to DLASET, or by DO
* loops. Sven Hammarling, 1/5/02.
*
* .. Parameters ..
DOUBLE PRECISION ZERO, ONE
PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
DOUBLE PRECISION TEN
PARAMETER ( TEN = 1.0D+01 )
INTEGER LDST
PARAMETER ( LDST = 4 )
LOGICAL WANDS
PARAMETER ( WANDS = .TRUE. )
* ..
* .. Local Scalars ..
LOGICAL DTRONG, WEAK
INTEGER I, IDUM, LINFO, M
DOUBLE PRECISION BQRA21, BRQA21, DDUM, DNORM, DSCALE, DSUM, EPS,
$ F, G, SA, SB, SCALE, SMLNUM, SS, THRESH, WS
* ..
* .. Local Arrays ..
INTEGER IWORK( LDST )
DOUBLE PRECISION 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 ..
DOUBLE PRECISION DLAMCH
EXTERNAL DLAMCH
* ..
* .. External Subroutines ..
EXTERNAL DGEMM, DGEQR2, DGERQ2, DLACPY, DLAGV2, DLARTG,
$ DLASET, DLASSQ, DORG2R, DORGR2, DORM2R, DORMR2,
$ DROT, DSCAL, DTGSY2
* ..
* .. 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( 1, N*M, M*M*2 ) ) THEN
INFO = -16
WORK( 1 ) = MAX( 1, N*M, M*M*2 )
RETURN
END IF
*
WEAK = .FALSE.
DTRONG = .FALSE.
*
* Make a local copy of selected block
*
CALL DLASET( 'Full', LDST, LDST, ZERO, ZERO, LI, LDST )
CALL DLASET( 'Full', LDST, LDST, ZERO, ZERO, IR, LDST )
CALL DLACPY( 'Full', M, M, A( J1, J1 ), LDA, S, LDST )
CALL DLACPY( 'Full', M, M, B( J1, J1 ), LDB, T, LDST )
*
* Compute threshold for testing acceptance of swapping.
*
EPS = DLAMCH( 'P' )
SMLNUM = DLAMCH( 'S' ) / EPS
DSCALE = ZERO
DSUM = ONE
CALL DLACPY( 'Full', M, M, S, LDST, WORK, M )
CALL DLASSQ( M*M, WORK, 1, DSCALE, DSUM )
CALL DLACPY( 'Full', M, M, T, LDST, WORK, M )
CALL DLASSQ( 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 DLARTG( F, G, IR( 1, 2 ), IR( 1, 1 ), DDUM )
IR( 2, 1 ) = -IR( 1, 2 )
IR( 2, 2 ) = IR( 1, 1 )
CALL DROT( 2, S( 1, 1 ), 1, S( 1, 2 ), 1, IR( 1, 1 ),
$ IR( 2, 1 ) )
CALL DROT( 2, T( 1, 1 ), 1, T( 1, 2 ), 1, IR( 1, 1 ),
$ IR( 2, 1 ) )
IF( SA.GE.SB ) THEN
CALL DLARTG( S( 1, 1 ), S( 2, 1 ), LI( 1, 1 ), LI( 2, 1 ),
$ DDUM )
ELSE
CALL DLARTG( T( 1, 1 ), T( 2, 1 ), LI( 1, 1 ), LI( 2, 1 ),
$ DDUM )
END IF
CALL DROT( 2, S( 1, 1 ), LDST, S( 2, 1 ), LDST, LI( 1, 1 ),
$ LI( 2, 1 ) )
CALL DROT( 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 DLACPY( 'Full', M, M, A( J1, J1 ), LDA, WORK( M*M+1 ),
$ M )
CALL DGEMM( 'N', 'N', M, M, M, ONE, LI, LDST, S, LDST, ZERO,
$ WORK, M )
CALL DGEMM( 'N', 'T', M, M, M, -ONE, WORK, M, IR, LDST, ONE,
$ WORK( M*M+1 ), M )
DSCALE = ZERO
DSUM = ONE
CALL DLASSQ( M*M, WORK( M*M+1 ), 1, DSCALE, DSUM )
*
CALL DLACPY( 'Full', M, M, B( J1, J1 ), LDB, WORK( M*M+1 ),
$ M )
CALL DGEMM( 'N', 'N', M, M, M, ONE, LI, LDST, T, LDST, ZERO,
$ WORK, M )
CALL DGEMM( 'N', 'T', M, M, M, -ONE, WORK, M, IR, LDST, ONE,
$ WORK( M*M+1 ), M )
CALL DLASSQ( M*M, WORK( M*M+1 ), 1, DSCALE, DSUM )
SS = DSCALE*SQRT( DSUM )
DTRONG = SS.LE.THRESH
IF( .NOT.DTRONG )
$ 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 DROT( J1+1, A( 1, J1 ), 1, A( 1, J1+1 ), 1, IR( 1, 1 ),
$ IR( 2, 1 ) )
CALL DROT( J1+1, B( 1, J1 ), 1, B( 1, J1+1 ), 1, IR( 1, 1 ),
$ IR( 2, 1 ) )
CALL DROT( N-J1+1, A( J1, J1 ), LDA, A( J1+1, J1 ), LDA,
$ LI( 1, 1 ), LI( 2, 1 ) )
CALL DROT( 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 DROT( N, Z( 1, J1 ), 1, Z( 1, J1+1 ), 1, IR( 1, 1 ),
$ IR( 2, 1 ) )
IF( WANTQ )
$ CALL DROT( 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 DLACPY( 'Full', N1, N2, T( 1, N1+1 ), LDST, LI, LDST )
CALL DLACPY( 'Full', N1, N2, S( 1, N1+1 ), LDST,
$ IR( N2+1, N1+1 ), LDST )
CALL DTGSY2( '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 DSCAL( N1, -ONE, LI( 1, I ), 1 )
LI( N1+I, I ) = SCALE
10 CONTINUE
CALL DGEQR2( M, N2, LI, LDST, TAUL, WORK, LINFO )
IF( LINFO.NE.0 )
$ GO TO 70
CALL DORG2R( 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 DGERQ2( N1, M, IR( N2+1, 1 ), LDST, TAUR, WORK, LINFO )
IF( LINFO.NE.0 )
$ GO TO 70
CALL DORGR2( M, M, N1, IR, LDST, TAUR, WORK, LINFO )
IF( LINFO.NE.0 )
$ GO TO 70
*
* Perform the swapping tentatively:
*
CALL DGEMM( 'T', 'N', M, M, M, ONE, LI, LDST, S, LDST, ZERO,
$ WORK, M )
CALL DGEMM( 'N', 'T', M, M, M, ONE, WORK, M, IR, LDST, ZERO, S,
$ LDST )
CALL DGEMM( 'T', 'N', M, M, M, ONE, LI, LDST, T, LDST, ZERO,
$ WORK, M )
CALL DGEMM( 'N', 'T', M, M, M, ONE, WORK, M, IR, LDST, ZERO, T,
$ LDST )
CALL DLACPY( 'F', M, M, S, LDST, SCPY, LDST )
CALL DLACPY( 'F', M, M, T, LDST, TCPY, LDST )
CALL DLACPY( 'F', M, M, IR, LDST, IRCOP, LDST )
CALL DLACPY( '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 DGERQ2( M, M, T, LDST, TAUR, WORK, LINFO )
IF( LINFO.NE.0 )
$ GO TO 70
CALL DORMR2( 'R', 'T', M, M, M, T, LDST, TAUR, S, LDST, WORK,
$ LINFO )
IF( LINFO.NE.0 )
$ GO TO 70
CALL DORMR2( '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 DLASSQ( 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 DGEQR2( M, M, TCPY, LDST, TAUL, WORK, LINFO )
IF( LINFO.NE.0 )
$ GO TO 70
CALL DORM2R( 'L', 'T', M, M, M, TCPY, LDST, TAUL, SCPY, LDST,
$ WORK, INFO )
CALL DORM2R( '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 DLASSQ( 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 DLACPY( 'F', M, M, SCPY, LDST, S, LDST )
CALL DLACPY( 'F', M, M, TCPY, LDST, T, LDST )
CALL DLACPY( 'F', M, M, IRCOP, LDST, IR, LDST )
CALL DLACPY( '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 DLASET( '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 DLACPY( 'Full', M, M, A( J1, J1 ), LDA, WORK( M*M+1 ),
$ M )
CALL DGEMM( 'N', 'N', M, M, M, ONE, LI, LDST, S, LDST, ZERO,
$ WORK, M )
CALL DGEMM( 'N', 'N', M, M, M, -ONE, WORK, M, IR, LDST, ONE,
$ WORK( M*M+1 ), M )
DSCALE = ZERO
DSUM = ONE
CALL DLASSQ( M*M, WORK( M*M+1 ), 1, DSCALE, DSUM )
*
CALL DLACPY( 'Full', M, M, B( J1, J1 ), LDB, WORK( M*M+1 ),
$ M )
CALL DGEMM( 'N', 'N', M, M, M, ONE, LI, LDST, T, LDST, ZERO,
$ WORK, M )
CALL DGEMM( 'N', 'N', M, M, M, -ONE, WORK, M, IR, LDST, ONE,
$ WORK( M*M+1 ), M )
CALL DLASSQ( M*M, WORK( M*M+1 ), 1, DSCALE, DSUM )
SS = DSCALE*SQRT( DSUM )
DTRONG = ( SS.LE.THRESH )
IF( .NOT.DTRONG )
$ 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 DLASET( '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 DLACPY( 'F', M, M, S, LDST, A( J1, J1 ), LDA )
CALL DLACPY( 'F', M, M, T, LDST, B( J1, J1 ), LDB )
CALL DLASET( '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 DLAGV2( 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 DLAGV2( 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 DGEMM( 'T', 'N', N2, N1, N2, ONE, WORK, M, A( J1, J1+N2 ),
$ LDA, ZERO, WORK( M*M+1 ), N2 )
CALL DLACPY( 'Full', N2, N1, WORK( M*M+1 ), N2, A( J1, J1+N2 ),
$ LDA )
CALL DGEMM( 'T', 'N', N2, N1, N2, ONE, WORK, M, B( J1, J1+N2 ),
$ LDB, ZERO, WORK( M*M+1 ), N2 )
CALL DLACPY( 'Full', N2, N1, WORK( M*M+1 ), N2, B( J1, J1+N2 ),
$ LDB )
CALL DGEMM( 'N', 'N', M, M, M, ONE, LI, LDST, WORK, M, ZERO,
$ WORK( M*M+1 ), M )
CALL DLACPY( 'Full', M, M, WORK( M*M+1 ), M, LI, LDST )
CALL DGEMM( 'N', 'N', N2, N1, N1, ONE, A( J1, J1+N2 ), LDA,
$ T( N2+1, N2+1 ), LDST, ZERO, WORK, N2 )
CALL DLACPY( 'Full', N2, N1, WORK, N2, A( J1, J1+N2 ), LDA )
CALL DGEMM( 'N', 'N', N2, N1, N1, ONE, B( J1, J1+N2 ), LDB,
$ T( N2+1, N2+1 ), LDST, ZERO, WORK, N2 )
CALL DLACPY( 'Full', N2, N1, WORK, N2, B( J1, J1+N2 ), LDB )
CALL DGEMM( 'T', 'N', M, M, M, ONE, IR, LDST, T, LDST, ZERO,
$ WORK, M )
CALL DLACPY( 'Full', M, M, WORK, M, IR, LDST )
*
* Accumulate transformations into Q and Z if requested.
*
IF( WANTQ ) THEN
CALL DGEMM( 'N', 'N', N, M, M, ONE, Q( 1, J1 ), LDQ, LI,
$ LDST, ZERO, WORK, N )
CALL DLACPY( 'Full', N, M, WORK, N, Q( 1, J1 ), LDQ )
*
END IF
*
IF( WANTZ ) THEN
CALL DGEMM( 'N', 'N', N, M, M, ONE, Z( 1, J1 ), LDZ, IR,
$ LDST, ZERO, WORK, N )
CALL DLACPY( '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 DGEMM( 'T', 'N', M, N-I+1, M, ONE, LI, LDST,
$ A( J1, I ), LDA, ZERO, WORK, M )
CALL DLACPY( 'Full', M, N-I+1, WORK, M, A( J1, I ), LDA )
CALL DGEMM( 'T', 'N', M, N-I+1, M, ONE, LI, LDST,
$ B( J1, I ), LDA, ZERO, WORK, M )
CALL DLACPY( 'Full', M, N-I+1, WORK, M, B( J1, I ), LDB )
END IF
I = J1 - 1
IF( I.GT.0 ) THEN
CALL DGEMM( 'N', 'N', I, M, M, ONE, A( 1, J1 ), LDA, IR,
$ LDST, ZERO, WORK, I )
CALL DLACPY( 'Full', I, M, WORK, I, A( 1, J1 ), LDA )
CALL DGEMM( 'N', 'N', I, M, M, ONE, B( 1, J1 ), LDB, IR,
$ LDST, ZERO, WORK, I )
CALL DLACPY( '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 DTGEX2
*
END