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*> \brief \b DGET36
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE DGET36( RMAX, LMAX, NINFO, KNT, NIN )
*
* .. Scalar Arguments ..
* INTEGER KNT, LMAX, NIN
* DOUBLE PRECISION RMAX
* ..
* .. Array Arguments ..
* INTEGER NINFO( 3 )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> DGET36 tests DTREXC, a routine for moving 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' * T1 * Q = T2
*>
*> and where one of the diagonal blocks of T1 (the one at row IFST) has
*> been moved to position ILST.
*>
*> The test code verifies that the residual Q'*T1*Q-T2 is small, that T2
*> is in Schur form, and that the final position of the IFST block is
*> ILST (within +-1).
*>
*> The test matrices are read from a file with logical unit number NIN.
*> \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 (3)
*> NINFO(J) is the number of examples where INFO=J.
*> \endverbatim
*>
*> \param[out] KNT
*> \verbatim
*> KNT is INTEGER
*> Total number of examples tested.
*> \endverbatim
*>
*> \param[in] NIN
*> \verbatim
*> NIN is INTEGER
*> Input logical unit number.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date December 2016
*
*> \ingroup double_eig
*
* =====================================================================
SUBROUTINE DGET36( RMAX, LMAX, NINFO, KNT, NIN )
*
* -- LAPACK test routine (version 3.7.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* December 2016
*
* .. Scalar Arguments ..
INTEGER KNT, LMAX, NIN
DOUBLE PRECISION RMAX
* ..
* .. Array Arguments ..
INTEGER NINFO( 3 )
* ..
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ZERO, ONE
PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 )
INTEGER LDT, LWORK
PARAMETER ( LDT = 10, LWORK = 2*LDT*LDT )
* ..
* .. Local Scalars ..
INTEGER I, IFST, IFST1, IFST2, IFSTSV, ILST, ILST1,
$ ILST2, ILSTSV, INFO1, INFO2, J, LOC, N
DOUBLE PRECISION EPS, RES
* ..
* .. Local Arrays ..
DOUBLE PRECISION Q( LDT, LDT ), RESULT( 2 ), T1( LDT, LDT ),
$ T2( LDT, LDT ), TMP( LDT, LDT ), WORK( LWORK )
* ..
* .. External Functions ..
DOUBLE PRECISION DLAMCH
EXTERNAL DLAMCH
* ..
* .. External Subroutines ..
EXTERNAL DHST01, DLACPY, DLASET, DTREXC
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, SIGN
* ..
* .. Executable Statements ..
*
EPS = DLAMCH( 'P' )
RMAX = ZERO
LMAX = 0
KNT = 0
NINFO( 1 ) = 0
NINFO( 2 ) = 0
NINFO( 3 ) = 0
*
* Read input data until N=0
*
10 CONTINUE
READ( NIN, FMT = * )N, IFST, ILST
IF( N.EQ.0 )
$ RETURN
KNT = KNT + 1
DO 20 I = 1, N
READ( NIN, FMT = * )( TMP( I, J ), J = 1, N )
20 CONTINUE
CALL DLACPY( 'F', N, N, TMP, LDT, T1, LDT )
CALL DLACPY( 'F', N, N, TMP, LDT, T2, LDT )
IFSTSV = IFST
ILSTSV = ILST
IFST1 = IFST
ILST1 = ILST
IFST2 = IFST
ILST2 = ILST
RES = ZERO
*
* Test without accumulating Q
*
CALL DLASET( 'Full', N, N, ZERO, ONE, Q, LDT )
CALL DTREXC( 'N', N, T1, LDT, Q, LDT, IFST1, ILST1, WORK, INFO1 )
DO 40 I = 1, N
DO 30 J = 1, N
IF( I.EQ.J .AND. Q( I, J ).NE.ONE )
$ RES = RES + ONE / EPS
IF( I.NE.J .AND. Q( I, J ).NE.ZERO )
$ RES = RES + ONE / EPS
30 CONTINUE
40 CONTINUE
*
* Test with accumulating Q
*
CALL DLASET( 'Full', N, N, ZERO, ONE, Q, LDT )
CALL DTREXC( 'V', N, T2, LDT, Q, LDT, IFST2, ILST2, WORK, INFO2 )
*
* Compare T1 with T2
*
DO 60 I = 1, N
DO 50 J = 1, N
IF( T1( I, J ).NE.T2( I, J ) )
$ RES = RES + ONE / EPS
50 CONTINUE
60 CONTINUE
IF( IFST1.NE.IFST2 )
$ RES = RES + ONE / EPS
IF( ILST1.NE.ILST2 )
$ RES = RES + ONE / EPS
IF( INFO1.NE.INFO2 )
$ RES = RES + ONE / EPS
*
* Test for successful reordering of T2
*
IF( INFO2.NE.0 ) THEN
NINFO( INFO2 ) = NINFO( INFO2 ) + 1
ELSE
IF( ABS( IFST2-IFSTSV ).GT.1 )
$ RES = RES + ONE / EPS
IF( ABS( ILST2-ILSTSV ).GT.1 )
$ RES = RES + ONE / EPS
END IF
*
* Test for small residual, and orthogonality of Q
*
CALL DHST01( N, 1, N, TMP, LDT, T2, LDT, Q, LDT, WORK, LWORK,
$ RESULT )
RES = RES + RESULT( 1 ) + RESULT( 2 )
*
* Test for T2 being in Schur form
*
LOC = 1
70 CONTINUE
IF( T2( LOC+1, LOC ).NE.ZERO ) THEN
*
* 2 by 2 block
*
IF( T2( LOC, LOC+1 ).EQ.ZERO .OR. T2( LOC, LOC ).NE.
$ T2( LOC+1, LOC+1 ) .OR. SIGN( ONE, T2( LOC, LOC+1 ) ).EQ.
$ SIGN( ONE, T2( LOC+1, LOC ) ) )RES = RES + ONE / EPS
DO 80 I = LOC + 2, N
IF( T2( I, LOC ).NE.ZERO )
$ RES = RES + ONE / RES
IF( T2( I, LOC+1 ).NE.ZERO )
$ RES = RES + ONE / RES
80 CONTINUE
LOC = LOC + 2
ELSE
*
* 1 by 1 block
*
DO 90 I = LOC + 1, N
IF( T2( I, LOC ).NE.ZERO )
$ RES = RES + ONE / RES
90 CONTINUE
LOC = LOC + 1
END IF
IF( LOC.LT.N )
$ GO TO 70
IF( RES.GT.RMAX ) THEN
RMAX = RES
LMAX = KNT
END IF
GO TO 10
*
* End of DGET36
*
END
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