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Cloned library LAPACK-3.11.0 with extra build files for internal package management.
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LAPACK-3.11.0/SRC/stgex2.f

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*> \brief \b STGEX2 swaps adjacent diagonal blocks in an upper (quasi) triangular matrix pair by an orthogonal equivalence transformation.
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download STGEX2 + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/stgex2.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/stgex2.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/stgex2.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE STGEX2( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z,
* LDZ, J1, N1, N2, WORK, LWORK, INFO )
*
* .. 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, * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> 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)**T = Q(out) * A(out) * Z(out)**T
*> Q(in) * B(in) * Z(in)**T = Q(out) * B(out) * Z(out)**T
*>
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] WANTQ
*> \verbatim
*> WANTQ is LOGICAL
*> .TRUE. : update the left transformation matrix Q;
*> .FALSE.: do not update Q.
*> \endverbatim
*>
*> \param[in] WANTZ
*> \verbatim
*> WANTZ is LOGICAL
*> .TRUE. : update the right transformation matrix Z;
*> .FALSE.: do not update Z.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The order of the matrices A and B. N >= 0.
*> \endverbatim
*>
*> \param[in,out] A
*> \verbatim
*> A is REAL array, dimension (LDA,N)
*> On entry, the matrix A in the pair (A, B).
*> On exit, the updated matrix A.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is INTEGER
*> The leading dimension of the array A. LDA >= max(1,N).
*> \endverbatim
*>
*> \param[in,out] B
*> \verbatim
*> B is REAL array, dimension (LDB,N)
*> On entry, the matrix B in the pair (A, B).
*> On exit, the updated matrix B.
*> \endverbatim
*>
*> \param[in] LDB
*> \verbatim
*> LDB is INTEGER
*> The leading dimension of the array B. LDB >= max(1,N).
*> \endverbatim
*>
*> \param[in,out] Q
*> \verbatim
*> Q is REAL array, dimension (LDQ,N)
*> On entry, if WANTQ = .TRUE., the orthogonal matrix Q.
*> On exit, the updated matrix Q.
*> Not referenced if WANTQ = .FALSE..
*> \endverbatim
*>
*> \param[in] LDQ
*> \verbatim
*> LDQ is INTEGER
*> The leading dimension of the array Q. LDQ >= 1.
*> If WANTQ = .TRUE., LDQ >= N.
*> \endverbatim
*>
*> \param[in,out] Z
*> \verbatim
*> Z is 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..
*> \endverbatim
*>
*> \param[in] LDZ
*> \verbatim
*> LDZ is INTEGER
*> The leading dimension of the array Z. LDZ >= 1.
*> If WANTZ = .TRUE., LDZ >= N.
*> \endverbatim
*>
*> \param[in] J1
*> \verbatim
*> J1 is INTEGER
*> The index to the first block (A11, B11). 1 <= J1 <= N.
*> \endverbatim
*>
*> \param[in] N1
*> \verbatim
*> N1 is INTEGER
*> The order of the first block (A11, B11). N1 = 0, 1 or 2.
*> \endverbatim
*>
*> \param[in] N2
*> \verbatim
*> N2 is INTEGER
*> The order of the second block (A22, B22). N2 = 0, 1 or 2.
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*> WORK is REAL array, dimension (MAX(1,LWORK)).
*> \endverbatim
*>
*> \param[in] LWORK
*> \verbatim
*> LWORK is INTEGER
*> The dimension of the array WORK.
*> LWORK >= MAX( N*(N2+N1), (N2+N1)*(N2+N1)*2 )
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*> INFO is 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).
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup realGEauxiliary
*
*> \par Further Details:
* =====================
*>
*> 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.
*
*> \par Contributors:
* ==================
*>
*> Bo Kagstrom and Peter Poromaa, Department of Computing Science,
*> Umea University, S-901 87 Umea, Sweden.
*
*> \par References:
* ================
*>
*> \verbatim
*>
*> [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.
*> \endverbatim
*>
* =====================================================================
SUBROUTINE STGEX2( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z,
$ LDZ, J1, N1, N2, WORK, LWORK, INFO )
*
* -- LAPACK auxiliary routine --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
* .. 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, * )
* ..
*
* =====================================================================
* 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 TWENTY
PARAMETER ( TWENTY = 2.0E+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, DNORMA, DNORMB,
$ DSCALE,
$ DSUM, EPS, F, G, SA, SB, SCALE, SMLNUM,
$ THRESHA, THRESHB
* ..
* .. 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 )
DNORMA = DSCALE*SQRT( DSUM )
DSCALE = ZERO
DSUM = ONE
CALL SLACPY( 'Full', M, M, T, LDST, WORK, M )
CALL SLASSQ( M*M, WORK, 1, DSCALE, DSUM )
DNORMB = DSCALE*SQRT( DSUM )
*
* THRES has been changed from
* THRESH = MAX( TEN*EPS*SA, SMLNUM )
* to
* THRESH = MAX( TWENTY*EPS*SA, SMLNUM )
* on 04/01/10.
* "Bug" reported by Ondra Kamenik, confirmed by Julie Langou, fixed by
* Jim Demmel and Guillaume Revy. See forum post 1783.
*
THRESHA = MAX( TWENTY*EPS*DNORMA, SMLNUM )
THRESHB = MAX( TWENTY*EPS*DNORMB, 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 )
SA = ABS( S( 2, 2 ) ) * ABS( T( 1, 1 ) )
SB = ABS( S( 1, 1 ) ) * ABS( T( 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| <= O(EPS F-norm((A)))
* and |T21| <= O(EPS F-norm((B)))
*
WEAK = ABS( S( 2, 1 ) ) .LE. THRESHA .AND.
$ ABS( T( 2, 1 ) ) .LE. THRESHB
IF( .NOT.WEAK )
$ GO TO 70
*
IF( WANDS ) THEN
*
* Strong stability test:
* F-norm((A-QL**H*S*QR)) <= O(EPS*F-norm((A)))
* and
* F-norm((B-QL**H*T*QR)) <= O(EPS*F-norm((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 )
SA = DSCALE*SQRT( 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 )
DSCALE = ZERO
DSUM = ONE
CALL SLASSQ( M*M, WORK( M*M+1 ), 1, DSCALE, DSUM )
SB = DSCALE*SQRT( DSUM )
STRONG = SA.LE.THRESHA .AND. SB.LE.THRESHB
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 )
IF( LINFO.NE.0 )
$ GO TO 70
*
* Compute orthogonal matrix QL:
*
* QL**T * 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**T = [ 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)))
*
IF( BQRA21.LE.BRQA21 .AND. BQRA21.LE.THRESHA ) 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.THRESHA ) 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**H*S*QR)) <= O(EPS*F-norm((A)))
* and
* F-norm((B-QL**H*T*QR)) <= O(EPS*F-norm((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 )
SA = DSCALE*SQRT( 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 )
DSCALE = ZERO
DSUM = ONE
CALL SLASSQ( M*M, WORK( M*M+1 ), 1, DSCALE, DSUM )
SB = DSCALE*SQRT( DSUM )
STRONG = SA.LE.THRESHA .AND. SB.LE.THRESHB
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.
*
CALL SLASET( 'Full', M, M, ZERO, ZERO, WORK, M )
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