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- *> \brief \b DGET34
- *
- * =========== DOCUMENTATION ===========
- *
- * Online html documentation available at
- * http://www.netlib.org/lapack/explore-html/
- *
- * Definition:
- * ===========
- *
- * SUBROUTINE DGET34( RMAX, LMAX, NINFO, KNT )
- *
- * .. Scalar Arguments ..
- * INTEGER KNT, LMAX
- * DOUBLE PRECISION RMAX
- * ..
- * .. Array Arguments ..
- * INTEGER NINFO( 2 )
- * ..
- *
- *
- *> \par Purpose:
- * =============
- *>
- *> \verbatim
- *>
- *> DGET34 tests DLAEXC, 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, DLAEXC 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 assertions, as well as that
- *> the residual in the above equation is small.
- *> \endverbatim
- *
- * Arguments:
- * ==========
- *
- *> \param[out] RMAX
- *> \verbatim
- *> RMAX is DOUBLE PRECISION
- *> 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.
- *
- *> \ingroup double_eig
- *
- * =====================================================================
- SUBROUTINE DGET34( RMAX, LMAX, NINFO, KNT )
- *
- * -- LAPACK test routine --
- * -- LAPACK is a software package provided by Univ. of Tennessee, --
- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
- *
- * .. Scalar Arguments ..
- INTEGER KNT, LMAX
- DOUBLE PRECISION RMAX
- * ..
- * .. Array Arguments ..
- INTEGER NINFO( 2 )
- * ..
- *
- * =====================================================================
- *
- * .. Parameters ..
- DOUBLE PRECISION ZERO, HALF, ONE
- PARAMETER ( ZERO = 0.0D0, HALF = 0.5D0, ONE = 1.0D0 )
- DOUBLE PRECISION TWO, THREE
- PARAMETER ( TWO = 2.0D0, THREE = 3.0D0 )
- INTEGER LWORK
- PARAMETER ( LWORK = 32 )
- * ..
- * .. Local Scalars ..
- INTEGER I, IA, IA11, IA12, IA21, IA22, IAM, IB, IC,
- $ IC11, IC12, IC21, IC22, ICM, INFO, J
- DOUBLE PRECISION BIGNUM, EPS, RES, SMLNUM, TNRM
- * ..
- * .. Local Arrays ..
- DOUBLE PRECISION Q( 4, 4 ), RESULT( 2 ), T( 4, 4 ), T1( 4, 4 ),
- $ VAL( 9 ), VM( 2 ), WORK( LWORK )
- * ..
- * .. External Functions ..
- DOUBLE PRECISION DLAMCH
- EXTERNAL DLAMCH
- * ..
- * .. External Subroutines ..
- EXTERNAL DCOPY, DHST01, DLABAD, DLAEXC
- * ..
- * .. Intrinsic Functions ..
- INTRINSIC ABS, DBLE, MAX, SIGN, SQRT
- * ..
- * .. Executable Statements ..
- *
- * Get machine parameters
- *
- EPS = DLAMCH( 'P' )
- SMLNUM = DLAMCH( 'S' ) / EPS
- BIGNUM = ONE / SMLNUM
- CALL DLABAD( 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 DCOPY( 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 DCOPY( 16, T, 1, T1, 1 )
- CALL DCOPY( 16, VAL( 1 ), 0, Q, 1 )
- CALL DCOPY( 4, VAL( 3 ), 0, Q, 5 )
- CALL DLAEXC( .TRUE., 2, T, 4, Q, 4, 1, 1, 1, WORK,
- $ INFO )
- IF( INFO.NE.0 )
- $ NINFO( INFO ) = NINFO( INFO ) + 1
- CALL DHST01( 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 )*DBLE( 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 DCOPY( 16, T, 1, T1, 1 )
- CALL DCOPY( 16, VAL( 1 ), 0, Q, 1 )
- CALL DCOPY( 4, VAL( 3 ), 0, Q, 5 )
- CALL DLAEXC( .TRUE., 3, T, 4, Q, 4, 1, 1, 2,
- $ WORK, INFO )
- IF( INFO.NE.0 )
- $ NINFO( INFO ) = NINFO( INFO ) + 1
- CALL DHST01( 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 )*DBLE( 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 DCOPY( 16, T, 1, T1, 1 )
- CALL DCOPY( 16, VAL( 1 ), 0, Q, 1 )
- CALL DCOPY( 4, VAL( 3 ), 0, Q, 5 )
- CALL DLAEXC( .TRUE., 3, T, 4, Q, 4, 1, 2, 1,
- $ WORK, INFO )
- IF( INFO.NE.0 )
- $ NINFO( INFO ) = NINFO( INFO ) + 1
- CALL DHST01( 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 )*
- $ DBLE( 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 )*
- $ DBLE( 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 DCOPY( 16, T, 1, T1, 1 )
- CALL DCOPY( 16, VAL( 1 ), 0, Q, 1 )
- CALL DCOPY( 4, VAL( 3 ), 0, Q, 5 )
- CALL DLAEXC( .TRUE., 4, T, 4, Q, 4,
- $ 1, 2, 2, WORK, INFO )
- IF( INFO.NE.0 )
- $ NINFO( INFO ) = NINFO( INFO ) + 1
- CALL DHST01( 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 DGET34
- *
- END
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