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|
*> \brief \b SGET34
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE SGET34( RMAX, LMAX, NINFO, KNT )
*
* .. Scalar Arguments ..
* INTEGER KNT, LMAX
* REAL RMAX
* ..
* .. Array Arguments ..
* INTEGER NINFO( 2 )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> SGET34 tests SLAEXC, a routine for swapping adjacent blocks (either
*> 1 by 1 or 2 by 2) on the diagonal of a matrix in real Schur form.
*> Thus, SLAEXC computes an orthogonal matrix Q such that
*>
*> Q' * [ A B ] * Q = [ C1 B1 ]
*> [ 0 C ] [ 0 A1 ]
*>
*> where C1 is similar to C and A1 is similar to A. Both A and C are
*> assumed to be in standard form (equal diagonal entries and
*> offdiagonal with differing signs) and A1 and C1 are returned with the
*> same properties.
*>
*> The test code verifies these last last assertions, as well as that
*> the residual in the above equation is small.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[out] RMAX
*> \verbatim
*> RMAX is REAL
*> Value of the largest test ratio.
*> \endverbatim
*>
*> \param[out] LMAX
*> \verbatim
*> LMAX is INTEGER
*> Example number where largest test ratio achieved.
*> \endverbatim
*>
*> \param[out] NINFO
*> \verbatim
*> NINFO is INTEGER array, dimension (2)
*> NINFO(J) is the number of examples where INFO=J occurred.
*> \endverbatim
*>
*> \param[out] KNT
*> \verbatim
*> KNT is INTEGER
*> Total number of examples tested.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date November 2011
*
*> \ingroup single_eig
*
* =====================================================================
SUBROUTINE SGET34( RMAX, LMAX, NINFO, KNT )
*
* -- LAPACK test routine (version 3.4.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* November 2011
*
* .. Scalar Arguments ..
INTEGER KNT, LMAX
REAL RMAX
* ..
* .. Array Arguments ..
INTEGER NINFO( 2 )
* ..
*
* =====================================================================
*
* .. Parameters ..
REAL ZERO, HALF, ONE
PARAMETER ( ZERO = 0.0E0, HALF = 0.5E0, ONE = 1.0E0 )
REAL TWO, THREE
PARAMETER ( TWO = 2.0E0, THREE = 3.0E0 )
INTEGER LWORK
PARAMETER ( LWORK = 32 )
* ..
* .. Local Scalars ..
INTEGER I, IA, IA11, IA12, IA21, IA22, IAM, IB, IC,
$ IC11, IC12, IC21, IC22, ICM, INFO, J
REAL BIGNUM, EPS, RES, SMLNUM, TNRM
* ..
* .. Local Arrays ..
REAL Q( 4, 4 ), RESULT( 2 ), T( 4, 4 ), T1( 4, 4 ),
$ VAL( 9 ), VM( 2 ), WORK( LWORK )
* ..
* .. External Functions ..
REAL SLAMCH
EXTERNAL SLAMCH
* ..
* .. External Subroutines ..
EXTERNAL SCOPY, SLAEXC
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, MAX, REAL, SIGN, SQRT
* ..
* .. Executable Statements ..
*
* Get machine parameters
*
EPS = SLAMCH( 'P' )
SMLNUM = SLAMCH( 'S' ) / EPS
BIGNUM = ONE / SMLNUM
CALL SLABAD( SMLNUM, BIGNUM )
*
* Set up test case parameters
*
VAL( 1 ) = ZERO
VAL( 2 ) = SQRT( SMLNUM )
VAL( 3 ) = ONE
VAL( 4 ) = TWO
VAL( 5 ) = SQRT( BIGNUM )
VAL( 6 ) = -SQRT( SMLNUM )
VAL( 7 ) = -ONE
VAL( 8 ) = -TWO
VAL( 9 ) = -SQRT( BIGNUM )
VM( 1 ) = ONE
VM( 2 ) = ONE + TWO*EPS
CALL SCOPY( 16, VAL( 4 ), 0, T( 1, 1 ), 1 )
*
NINFO( 1 ) = 0
NINFO( 2 ) = 0
KNT = 0
LMAX = 0
RMAX = ZERO
*
* Begin test loop
*
DO 40 IA = 1, 9
DO 30 IAM = 1, 2
DO 20 IB = 1, 9
DO 10 IC = 1, 9
T( 1, 1 ) = VAL( IA )*VM( IAM )
T( 2, 2 ) = VAL( IC )
T( 1, 2 ) = VAL( IB )
T( 2, 1 ) = ZERO
TNRM = MAX( ABS( T( 1, 1 ) ), ABS( T( 2, 2 ) ),
$ ABS( T( 1, 2 ) ) )
CALL SCOPY( 16, T, 1, T1, 1 )
CALL SCOPY( 16, VAL( 1 ), 0, Q, 1 )
CALL SCOPY( 4, VAL( 3 ), 0, Q, 5 )
CALL SLAEXC( .TRUE., 2, T, 4, Q, 4, 1, 1, 1, WORK,
$ INFO )
IF( INFO.NE.0 )
$ NINFO( INFO ) = NINFO( INFO ) + 1
CALL SHST01( 2, 1, 2, T1, 4, T, 4, Q, 4, WORK, LWORK,
$ RESULT )
RES = RESULT( 1 ) + RESULT( 2 )
IF( INFO.NE.0 )
$ RES = RES + ONE / EPS
IF( T( 1, 1 ).NE.T1( 2, 2 ) )
$ RES = RES + ONE / EPS
IF( T( 2, 2 ).NE.T1( 1, 1 ) )
$ RES = RES + ONE / EPS
IF( T( 2, 1 ).NE.ZERO )
$ RES = RES + ONE / EPS
KNT = KNT + 1
IF( RES.GT.RMAX ) THEN
LMAX = KNT
RMAX = RES
END IF
10 CONTINUE
20 CONTINUE
30 CONTINUE
40 CONTINUE
*
DO 110 IA = 1, 5
DO 100 IAM = 1, 2
DO 90 IB = 1, 5
DO 80 IC11 = 1, 5
DO 70 IC12 = 2, 5
DO 60 IC21 = 2, 4
DO 50 IC22 = -1, 1, 2
T( 1, 1 ) = VAL( IA )*VM( IAM )
T( 1, 2 ) = VAL( IB )
T( 1, 3 ) = -TWO*VAL( IB )
T( 2, 1 ) = ZERO
T( 2, 2 ) = VAL( IC11 )
T( 2, 3 ) = VAL( IC12 )
T( 3, 1 ) = ZERO
T( 3, 2 ) = -VAL( IC21 )
T( 3, 3 ) = VAL( IC11 )*REAL( IC22 )
TNRM = MAX( ABS( T( 1, 1 ) ),
$ ABS( T( 1, 2 ) ), ABS( T( 1, 3 ) ),
$ ABS( T( 2, 2 ) ), ABS( T( 2, 3 ) ),
$ ABS( T( 3, 2 ) ), ABS( T( 3, 3 ) ) )
CALL SCOPY( 16, T, 1, T1, 1 )
CALL SCOPY( 16, VAL( 1 ), 0, Q, 1 )
CALL SCOPY( 4, VAL( 3 ), 0, Q, 5 )
CALL SLAEXC( .TRUE., 3, T, 4, Q, 4, 1, 1, 2,
$ WORK, INFO )
IF( INFO.NE.0 )
$ NINFO( INFO ) = NINFO( INFO ) + 1
CALL SHST01( 3, 1, 3, T1, 4, T, 4, Q, 4,
$ WORK, LWORK, RESULT )
RES = RESULT( 1 ) + RESULT( 2 )
IF( INFO.EQ.0 ) THEN
IF( T1( 1, 1 ).NE.T( 3, 3 ) )
$ RES = RES + ONE / EPS
IF( T( 3, 1 ).NE.ZERO )
$ RES = RES + ONE / EPS
IF( T( 3, 2 ).NE.ZERO )
$ RES = RES + ONE / EPS
IF( T( 2, 1 ).NE.0 .AND.
$ ( T( 1, 1 ).NE.T( 2,
$ 2 ) .OR. SIGN( ONE, T( 1,
$ 2 ) ).EQ.SIGN( ONE, T( 2, 1 ) ) ) )
$ RES = RES + ONE / EPS
END IF
KNT = KNT + 1
IF( RES.GT.RMAX ) THEN
LMAX = KNT
RMAX = RES
END IF
50 CONTINUE
60 CONTINUE
70 CONTINUE
80 CONTINUE
90 CONTINUE
100 CONTINUE
110 CONTINUE
*
DO 180 IA11 = 1, 5
DO 170 IA12 = 2, 5
DO 160 IA21 = 2, 4
DO 150 IA22 = -1, 1, 2
DO 140 ICM = 1, 2
DO 130 IB = 1, 5
DO 120 IC = 1, 5
T( 1, 1 ) = VAL( IA11 )
T( 1, 2 ) = VAL( IA12 )
T( 1, 3 ) = -TWO*VAL( IB )
T( 2, 1 ) = -VAL( IA21 )
T( 2, 2 ) = VAL( IA11 )*REAL( IA22 )
T( 2, 3 ) = VAL( IB )
T( 3, 1 ) = ZERO
T( 3, 2 ) = ZERO
T( 3, 3 ) = VAL( IC )*VM( ICM )
TNRM = MAX( ABS( T( 1, 1 ) ),
$ ABS( T( 1, 2 ) ), ABS( T( 1, 3 ) ),
$ ABS( T( 2, 2 ) ), ABS( T( 2, 3 ) ),
$ ABS( T( 3, 2 ) ), ABS( T( 3, 3 ) ) )
CALL SCOPY( 16, T, 1, T1, 1 )
CALL SCOPY( 16, VAL( 1 ), 0, Q, 1 )
CALL SCOPY( 4, VAL( 3 ), 0, Q, 5 )
CALL SLAEXC( .TRUE., 3, T, 4, Q, 4, 1, 2, 1,
$ WORK, INFO )
IF( INFO.NE.0 )
$ NINFO( INFO ) = NINFO( INFO ) + 1
CALL SHST01( 3, 1, 3, T1, 4, T, 4, Q, 4,
$ WORK, LWORK, RESULT )
RES = RESULT( 1 ) + RESULT( 2 )
IF( INFO.EQ.0 ) THEN
IF( T1( 3, 3 ).NE.T( 1, 1 ) )
$ RES = RES + ONE / EPS
IF( T( 2, 1 ).NE.ZERO )
$ RES = RES + ONE / EPS
IF( T( 3, 1 ).NE.ZERO )
$ RES = RES + ONE / EPS
IF( T( 3, 2 ).NE.0 .AND.
$ ( T( 2, 2 ).NE.T( 3,
$ 3 ) .OR. SIGN( ONE, T( 2,
$ 3 ) ).EQ.SIGN( ONE, T( 3, 2 ) ) ) )
$ RES = RES + ONE / EPS
END IF
KNT = KNT + 1
IF( RES.GT.RMAX ) THEN
LMAX = KNT
RMAX = RES
END IF
120 CONTINUE
130 CONTINUE
140 CONTINUE
150 CONTINUE
160 CONTINUE
170 CONTINUE
180 CONTINUE
*
DO 300 IA11 = 1, 5
DO 290 IA12 = 2, 5
DO 280 IA21 = 2, 4
DO 270 IA22 = -1, 1, 2
DO 260 IB = 1, 5
DO 250 IC11 = 3, 4
DO 240 IC12 = 3, 4
DO 230 IC21 = 3, 4
DO 220 IC22 = -1, 1, 2
DO 210 ICM = 5, 7
IAM = 1
T( 1, 1 ) = VAL( IA11 )*VM( IAM )
T( 1, 2 ) = VAL( IA12 )*VM( IAM )
T( 1, 3 ) = -TWO*VAL( IB )
T( 1, 4 ) = HALF*VAL( IB )
T( 2, 1 ) = -T( 1, 2 )*VAL( IA21 )
T( 2, 2 ) = VAL( IA11 )*
$ REAL( IA22 )*VM( IAM )
T( 2, 3 ) = VAL( IB )
T( 2, 4 ) = THREE*VAL( IB )
T( 3, 1 ) = ZERO
T( 3, 2 ) = ZERO
T( 3, 3 ) = VAL( IC11 )*
$ ABS( VAL( ICM ) )
T( 3, 4 ) = VAL( IC12 )*
$ ABS( VAL( ICM ) )
T( 4, 1 ) = ZERO
T( 4, 2 ) = ZERO
T( 4, 3 ) = -T( 3, 4 )*VAL( IC21 )*
$ ABS( VAL( ICM ) )
T( 4, 4 ) = VAL( IC11 )*
$ REAL( IC22 )*
$ ABS( VAL( ICM ) )
TNRM = ZERO
DO 200 I = 1, 4
DO 190 J = 1, 4
TNRM = MAX( TNRM,
$ ABS( T( I, J ) ) )
190 CONTINUE
200 CONTINUE
CALL SCOPY( 16, T, 1, T1, 1 )
CALL SCOPY( 16, VAL( 1 ), 0, Q, 1 )
CALL SCOPY( 4, VAL( 3 ), 0, Q, 5 )
CALL SLAEXC( .TRUE., 4, T, 4, Q, 4,
$ 1, 2, 2, WORK, INFO )
IF( INFO.NE.0 )
$ NINFO( INFO ) = NINFO( INFO ) + 1
CALL SHST01( 4, 1, 4, T1, 4, T, 4,
$ Q, 4, WORK, LWORK,
$ RESULT )
RES = RESULT( 1 ) + RESULT( 2 )
IF( INFO.EQ.0 ) THEN
IF( T( 3, 1 ).NE.ZERO )
$ RES = RES + ONE / EPS
IF( T( 4, 1 ).NE.ZERO )
$ RES = RES + ONE / EPS
IF( T( 3, 2 ).NE.ZERO )
$ RES = RES + ONE / EPS
IF( T( 4, 2 ).NE.ZERO )
$ RES = RES + ONE / EPS
IF( T( 2, 1 ).NE.0 .AND.
$ ( T( 1, 1 ).NE.T( 2,
$ 2 ) .OR. SIGN( ONE, T( 1,
$ 2 ) ).EQ.SIGN( ONE, T( 2,
$ 1 ) ) ) )RES = RES +
$ ONE / EPS
IF( T( 4, 3 ).NE.0 .AND.
$ ( T( 3, 3 ).NE.T( 4,
$ 4 ) .OR. SIGN( ONE, T( 3,
$ 4 ) ).EQ.SIGN( ONE, T( 4,
$ 3 ) ) ) )RES = RES +
$ ONE / EPS
END IF
KNT = KNT + 1
IF( RES.GT.RMAX ) THEN
LMAX = KNT
RMAX = RES
END IF
210 CONTINUE
220 CONTINUE
230 CONTINUE
240 CONTINUE
250 CONTINUE
260 CONTINUE
270 CONTINUE
280 CONTINUE
290 CONTINUE
300 CONTINUE
*
RETURN
*
* End of SGET34
*
END
|
