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SUBROUTINE <a name="SLAEXC.1"></a><a href="slaexc.f.html#SLAEXC.1">SLAEXC</a>( WANTQ, N, T, LDT, Q, LDQ, J1, N1, N2, WORK,
$ INFO )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> -- LAPACK auxiliary routine (version 3.1) --
</span><span class="comment">*</span><span class="comment"> Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
</span><span class="comment">*</span><span class="comment"> November 2006
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> .. Scalar Arguments ..
</span> LOGICAL WANTQ
INTEGER INFO, J1, LDQ, LDT, N, N1, N2
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Array Arguments ..
</span> REAL Q( LDQ, * ), T( LDT, * ), WORK( * )
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Purpose
</span><span class="comment">*</span><span class="comment"> =======
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> <a name="SLAEXC.19"></a><a href="slaexc.f.html#SLAEXC.1">SLAEXC</a> swaps adjacent diagonal blocks T11 and T22 of order 1 or 2 in
</span><span class="comment">*</span><span class="comment"> an upper quasi-triangular matrix T by an orthogonal similarity
</span><span class="comment">*</span><span class="comment"> transformation.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> T must be in Schur canonical form, that is, block upper triangular
</span><span class="comment">*</span><span class="comment"> with 1-by-1 and 2-by-2 diagonal blocks; each 2-by-2 diagonal block
</span><span class="comment">*</span><span class="comment"> has its diagonal elemnts equal and its off-diagonal elements of
</span><span class="comment">*</span><span class="comment"> opposite sign.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Arguments
</span><span class="comment">*</span><span class="comment"> =========
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> WANTQ (input) LOGICAL
</span><span class="comment">*</span><span class="comment"> = .TRUE. : accumulate the transformation in the matrix Q;
</span><span class="comment">*</span><span class="comment"> = .FALSE.: do not accumulate the transformation.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> N (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The order of the matrix T. N >= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> T (input/output) REAL array, dimension (LDT,N)
</span><span class="comment">*</span><span class="comment"> On entry, the upper quasi-triangular matrix T, in Schur
</span><span class="comment">*</span><span class="comment"> canonical form.
</span><span class="comment">*</span><span class="comment"> On exit, the updated matrix T, again in Schur canonical form.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> LDT (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The leading dimension of the array T. LDT >= max(1,N).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Q (input/output) REAL array, dimension (LDQ,N)
</span><span class="comment">*</span><span class="comment"> On entry, if WANTQ is .TRUE., the orthogonal matrix Q.
</span><span class="comment">*</span><span class="comment"> On exit, if WANTQ is .TRUE., the updated matrix Q.
</span><span class="comment">*</span><span class="comment"> If WANTQ is .FALSE., Q is not referenced.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> LDQ (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The leading dimension of the array Q.
</span><span class="comment">*</span><span class="comment"> LDQ >= 1; and if WANTQ is .TRUE., LDQ >= N.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> J1 (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The index of the first row of the first block T11.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> N1 (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The order of the first block T11. N1 = 0, 1 or 2.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> N2 (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The order of the second block T22. N2 = 0, 1 or 2.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> WORK (workspace) REAL array, dimension (N)
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> INFO (output) INTEGER
</span><span class="comment">*</span><span class="comment"> = 0: successful exit
</span><span class="comment">*</span><span class="comment"> = 1: the transformed matrix T would be too far from Schur
</span><span class="comment">*</span><span class="comment"> form; the blocks are not swapped and T and Q are
</span><span class="comment">*</span><span class="comment"> unchanged.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> =====================================================================
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> .. Parameters ..
</span> REAL ZERO, ONE
PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 )
REAL TEN
PARAMETER ( TEN = 1.0E+1 )
INTEGER LDD, LDX
PARAMETER ( LDD = 4, LDX = 2 )
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Local Scalars ..
</span> INTEGER IERR, J2, J3, J4, K, ND
REAL CS, DNORM, EPS, SCALE, SMLNUM, SN, T11, T22,
$ T33, TAU, TAU1, TAU2, TEMP, THRESH, WI1, WI2,
$ WR1, WR2, XNORM
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Local Arrays ..
</span> REAL D( LDD, 4 ), U( 3 ), U1( 3 ), U2( 3 ),
$ X( LDX, 2 )
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. External Functions ..
</span> REAL <a name="SLAMCH.93"></a><a href="slamch.f.html#SLAMCH.1">SLAMCH</a>, <a name="SLANGE.93"></a><a href="slange.f.html#SLANGE.1">SLANGE</a>
EXTERNAL <a name="SLAMCH.94"></a><a href="slamch.f.html#SLAMCH.1">SLAMCH</a>, <a name="SLANGE.94"></a><a href="slange.f.html#SLANGE.1">SLANGE</a>
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. External Subroutines ..
</span> EXTERNAL <a name="SLACPY.97"></a><a href="slacpy.f.html#SLACPY.1">SLACPY</a>, <a name="SLANV2.97"></a><a href="slanv2.f.html#SLANV2.1">SLANV2</a>, <a name="SLARFG.97"></a><a href="slarfg.f.html#SLARFG.1">SLARFG</a>, <a name="SLARFX.97"></a><a href="slarfx.f.html#SLARFX.1">SLARFX</a>, <a name="SLARTG.97"></a><a href="slartg.f.html#SLARTG.1">SLARTG</a>, <a name="SLASY2.97"></a><a href="slasy2.f.html#SLASY2.1">SLASY2</a>,
$ SROT
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Intrinsic Functions ..
</span> INTRINSIC ABS, MAX
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Executable Statements ..
</span><span class="comment">*</span><span class="comment">
</span> INFO = 0
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Quick return if possible
</span><span class="comment">*</span><span class="comment">
</span> IF( N.EQ.0 .OR. N1.EQ.0 .OR. N2.EQ.0 )
$ RETURN
IF( J1+N1.GT.N )
$ RETURN
<span class="comment">*</span><span class="comment">
</span> J2 = J1 + 1
J3 = J1 + 2
J4 = J1 + 3
<span class="comment">*</span><span class="comment">
</span> IF( N1.EQ.1 .AND. N2.EQ.1 ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Swap two 1-by-1 blocks.
</span><span class="comment">*</span><span class="comment">
</span> T11 = T( J1, J1 )
T22 = T( J2, J2 )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Determine the transformation to perform the interchange.
</span><span class="comment">*</span><span class="comment">
</span> CALL <a name="SLARTG.127"></a><a href="slartg.f.html#SLARTG.1">SLARTG</a>( T( J1, J2 ), T22-T11, CS, SN, TEMP )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Apply transformation to the matrix T.
</span><span class="comment">*</span><span class="comment">
</span> IF( J3.LE.N )
$ CALL SROT( N-J1-1, T( J1, J3 ), LDT, T( J2, J3 ), LDT, CS,
$ SN )
CALL SROT( J1-1, T( 1, J1 ), 1, T( 1, J2 ), 1, CS, SN )
<span class="comment">*</span><span class="comment">
</span> T( J1, J1 ) = T22
T( J2, J2 ) = T11
<span class="comment">*</span><span class="comment">
</span> IF( WANTQ ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Accumulate transformation in the matrix Q.
</span><span class="comment">*</span><span class="comment">
</span> CALL SROT( N, Q( 1, J1 ), 1, Q( 1, J2 ), 1, CS, SN )
END IF
<span class="comment">*</span><span class="comment">
</span> ELSE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Swapping involves at least one 2-by-2 block.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Copy the diagonal block of order N1+N2 to the local array D
</span><span class="comment">*</span><span class="comment"> and compute its norm.
</span><span class="comment">*</span><span class="comment">
</span> ND = N1 + N2
CALL <a name="SLACPY.154"></a><a href="slacpy.f.html#SLACPY.1">SLACPY</a>( <span class="string">'Full'</span>, ND, ND, T( J1, J1 ), LDT, D, LDD )
DNORM = <a name="SLANGE.155"></a><a href="slange.f.html#SLANGE.1">SLANGE</a>( <span class="string">'Max'</span>, ND, ND, D, LDD, WORK )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Compute machine-dependent threshold for test for accepting
</span><span class="comment">*</span><span class="comment"> swap.
</span><span class="comment">*</span><span class="comment">
</span> EPS = <a name="SLAMCH.160"></a><a href="slamch.f.html#SLAMCH.1">SLAMCH</a>( <span class="string">'P'</span> )
SMLNUM = <a name="SLAMCH.161"></a><a href="slamch.f.html#SLAMCH.1">SLAMCH</a>( <span class="string">'S'</span> ) / EPS
THRESH = MAX( TEN*EPS*DNORM, SMLNUM )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Solve T11*X - X*T22 = scale*T12 for X.
</span><span class="comment">*</span><span class="comment">
</span> CALL <a name="SLASY2.166"></a><a href="slasy2.f.html#SLASY2.1">SLASY2</a>( .FALSE., .FALSE., -1, N1, N2, D, LDD,
$ D( N1+1, N1+1 ), LDD, D( 1, N1+1 ), LDD, SCALE, X,
$ LDX, XNORM, IERR )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Swap the adjacent diagonal blocks.
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