250 lines
6.3 KiB
Fortran
250 lines
6.3 KiB
Fortran
*> \brief \b SGET36
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*
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* =========== DOCUMENTATION ===========
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*
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* Online html documentation available at
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* http://www.netlib.org/lapack/explore-html/
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*
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* Definition:
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* ===========
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*
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* SUBROUTINE SGET36( RMAX, LMAX, NINFO, KNT, NIN )
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*
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* .. Scalar Arguments ..
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* INTEGER KNT, LMAX, NIN
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* REAL RMAX
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* ..
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* .. Array Arguments ..
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* INTEGER NINFO( 3 )
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* ..
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*
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*
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*> \par Purpose:
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* =============
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*>
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*> \verbatim
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*>
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*> SGET36 tests STREXC, a routine for moving blocks (either 1 by 1 or
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*> 2 by 2) on the diagonal of a matrix in real Schur form. Thus, SLAEXC
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*> computes an orthogonal matrix Q such that
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*>
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*> Q' * T1 * Q = T2
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*>
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*> and where one of the diagonal blocks of T1 (the one at row IFST) has
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*> been moved to position ILST.
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*>
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*> The test code verifies that the residual Q'*T1*Q-T2 is small, that T2
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*> is in Schur form, and that the final position of the IFST block is
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*> ILST (within +-1).
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*>
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*> The test matrices are read from a file with logical unit number NIN.
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*> \endverbatim
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*
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* Arguments:
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* ==========
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*
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*> \param[out] RMAX
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*> \verbatim
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*> RMAX is REAL
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*> Value of the largest test ratio.
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*> \endverbatim
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*>
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*> \param[out] LMAX
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*> \verbatim
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*> LMAX is INTEGER
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*> Example number where largest test ratio achieved.
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*> \endverbatim
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*>
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*> \param[out] NINFO
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*> \verbatim
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*> NINFO is INTEGER array, dimension (3)
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*> NINFO(J) is the number of examples where INFO=J.
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*> \endverbatim
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*>
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*> \param[out] KNT
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*> \verbatim
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*> KNT is INTEGER
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*> Total number of examples tested.
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*> \endverbatim
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*>
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*> \param[in] NIN
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*> \verbatim
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*> NIN is INTEGER
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*> Input logical unit number.
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*> \endverbatim
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*
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* Authors:
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* ========
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*
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*> \author Univ. of Tennessee
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*> \author Univ. of California Berkeley
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*> \author Univ. of Colorado Denver
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*> \author NAG Ltd.
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*
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*> \date November 2011
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*
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*> \ingroup single_eig
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*
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* =====================================================================
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SUBROUTINE SGET36( RMAX, LMAX, NINFO, KNT, NIN )
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*
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* -- LAPACK test routine (version 3.4.0) --
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* -- LAPACK is a software package provided by Univ. of Tennessee, --
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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* November 2011
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*
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* .. Scalar Arguments ..
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INTEGER KNT, LMAX, NIN
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REAL RMAX
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* ..
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* .. Array Arguments ..
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INTEGER NINFO( 3 )
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* ..
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*
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* =====================================================================
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*
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* .. Parameters ..
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REAL ZERO, ONE
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PARAMETER ( ZERO = 0.0E0, ONE = 1.0E0 )
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INTEGER LDT, LWORK
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PARAMETER ( LDT = 10, LWORK = 2*LDT*LDT )
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* ..
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* .. Local Scalars ..
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INTEGER I, IFST, IFST1, IFST2, IFSTSV, ILST, ILST1,
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$ ILST2, ILSTSV, INFO1, INFO2, J, LOC, N
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REAL EPS, RES
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* ..
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* .. Local Arrays ..
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REAL Q( LDT, LDT ), RESULT( 2 ), T1( LDT, LDT ),
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$ T2( LDT, LDT ), TMP( LDT, LDT ), WORK( LWORK )
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* ..
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* .. External Functions ..
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REAL SLAMCH
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EXTERNAL SLAMCH
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* ..
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* .. External Subroutines ..
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EXTERNAL SHST01, SLACPY, SLASET, STREXC
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC ABS, SIGN
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* ..
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* .. Executable Statements ..
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*
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EPS = SLAMCH( 'P' )
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RMAX = ZERO
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LMAX = 0
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KNT = 0
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NINFO( 1 ) = 0
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NINFO( 2 ) = 0
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NINFO( 3 ) = 0
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*
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* Read input data until N=0
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*
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10 CONTINUE
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READ( NIN, FMT = * )N, IFST, ILST
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IF( N.EQ.0 )
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$ RETURN
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KNT = KNT + 1
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DO 20 I = 1, N
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READ( NIN, FMT = * )( TMP( I, J ), J = 1, N )
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20 CONTINUE
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CALL SLACPY( 'F', N, N, TMP, LDT, T1, LDT )
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CALL SLACPY( 'F', N, N, TMP, LDT, T2, LDT )
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IFSTSV = IFST
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ILSTSV = ILST
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IFST1 = IFST
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ILST1 = ILST
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IFST2 = IFST
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ILST2 = ILST
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RES = ZERO
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*
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* Test without accumulating Q
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*
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CALL SLASET( 'Full', N, N, ZERO, ONE, Q, LDT )
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CALL STREXC( 'N', N, T1, LDT, Q, LDT, IFST1, ILST1, WORK, INFO1 )
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DO 40 I = 1, N
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DO 30 J = 1, N
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IF( I.EQ.J .AND. Q( I, J ).NE.ONE )
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$ RES = RES + ONE / EPS
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IF( I.NE.J .AND. Q( I, J ).NE.ZERO )
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$ RES = RES + ONE / EPS
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30 CONTINUE
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40 CONTINUE
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*
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* Test with accumulating Q
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*
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CALL SLASET( 'Full', N, N, ZERO, ONE, Q, LDT )
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CALL STREXC( 'V', N, T2, LDT, Q, LDT, IFST2, ILST2, WORK, INFO2 )
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*
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* Compare T1 with T2
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*
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DO 60 I = 1, N
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DO 50 J = 1, N
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IF( T1( I, J ).NE.T2( I, J ) )
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$ RES = RES + ONE / EPS
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50 CONTINUE
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60 CONTINUE
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IF( IFST1.NE.IFST2 )
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$ RES = RES + ONE / EPS
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IF( ILST1.NE.ILST2 )
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$ RES = RES + ONE / EPS
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IF( INFO1.NE.INFO2 )
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$ RES = RES + ONE / EPS
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*
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* Test for successful reordering of T2
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*
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IF( INFO2.NE.0 ) THEN
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NINFO( INFO2 ) = NINFO( INFO2 ) + 1
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ELSE
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IF( ABS( IFST2-IFSTSV ).GT.1 )
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$ RES = RES + ONE / EPS
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IF( ABS( ILST2-ILSTSV ).GT.1 )
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$ RES = RES + ONE / EPS
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END IF
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*
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* Test for small residual, and orthogonality of Q
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*
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CALL SHST01( N, 1, N, TMP, LDT, T2, LDT, Q, LDT, WORK, LWORK,
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$ RESULT )
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RES = RES + RESULT( 1 ) + RESULT( 2 )
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*
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* Test for T2 being in Schur form
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*
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LOC = 1
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70 CONTINUE
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IF( T2( LOC+1, LOC ).NE.ZERO ) THEN
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*
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* 2 by 2 block
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*
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IF( T2( LOC, LOC+1 ).EQ.ZERO .OR. T2( LOC, LOC ).NE.
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$ T2( LOC+1, LOC+1 ) .OR. SIGN( ONE, T2( LOC, LOC+1 ) ).EQ.
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$ SIGN( ONE, T2( LOC+1, LOC ) ) )RES = RES + ONE / EPS
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DO 80 I = LOC + 2, N
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IF( T2( I, LOC ).NE.ZERO )
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$ RES = RES + ONE / RES
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IF( T2( I, LOC+1 ).NE.ZERO )
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$ RES = RES + ONE / RES
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80 CONTINUE
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LOC = LOC + 2
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ELSE
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*
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* 1 by 1 block
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*
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DO 90 I = LOC + 1, N
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IF( T2( I, LOC ).NE.ZERO )
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$ RES = RES + ONE / RES
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90 CONTINUE
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LOC = LOC + 1
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END IF
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IF( LOC.LT.N )
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$ GO TO 70
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IF( RES.GT.RMAX ) THEN
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RMAX = RES
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LMAX = KNT
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END IF
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GO TO 10
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*
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* End of SGET36
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*
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END
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