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220 lines
5.6 KiB
220 lines
5.6 KiB
2 years ago
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*> \brief \b ZGET36
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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 ZGET36( RMAX, LMAX, NINFO, KNT, NIN )
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*
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* .. Scalar Arguments ..
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* INTEGER KNT, LMAX, NIN, NINFO
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* DOUBLE PRECISION RMAX
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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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*> ZGET36 tests ZTREXC, a routine for reordering diagonal entries of a
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*> matrix in complex Schur form. Thus, ZLAEXC computes a unitary matrix
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*> 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.
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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 DOUBLE PRECISION
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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
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*> Number of examples where INFO is nonzero.
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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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*> \ingroup complex16_eig
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*
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* =====================================================================
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SUBROUTINE ZGET36( RMAX, LMAX, NINFO, KNT, NIN )
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*
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* -- LAPACK test routine --
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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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*
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* .. Scalar Arguments ..
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INTEGER KNT, LMAX, NIN, NINFO
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DOUBLE PRECISION RMAX
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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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DOUBLE PRECISION ZERO, ONE
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PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
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COMPLEX*16 CZERO, CONE
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PARAMETER ( CZERO = ( 0.0D+0, 0.0D+0 ),
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$ CONE = ( 1.0D+0, 0.0D+0 ) )
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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, ILST, INFO1, INFO2, J, N
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DOUBLE PRECISION EPS, RES
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COMPLEX*16 CTEMP
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* ..
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* .. Local Arrays ..
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DOUBLE PRECISION RESULT( 2 ), RWORK( LDT )
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COMPLEX*16 DIAG( LDT ), Q( LDT, LDT ), 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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DOUBLE PRECISION DLAMCH
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EXTERNAL DLAMCH
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* ..
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* .. External Subroutines ..
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EXTERNAL ZCOPY, ZHST01, ZLACPY, ZLASET, ZTREXC
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* ..
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* .. Executable Statements ..
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*
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EPS = DLAMCH( 'P' )
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RMAX = ZERO
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LMAX = 0
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KNT = 0
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NINFO = 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 ZLACPY( 'F', N, N, TMP, LDT, T1, LDT )
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CALL ZLACPY( 'F', N, N, TMP, LDT, T2, LDT )
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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 ZLASET( 'Full', N, N, CZERO, CONE, Q, LDT )
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CALL ZTREXC( 'N', N, T1, LDT, Q, LDT, IFST, ILST, 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.CONE )
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$ RES = RES + ONE / EPS
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IF( I.NE.J .AND. Q( I, J ).NE.CZERO )
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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 ZLASET( 'Full', N, N, CZERO, CONE, Q, LDT )
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CALL ZTREXC( 'V', N, T2, LDT, Q, LDT, IFST, ILST, 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( INFO1.NE.0 .OR. INFO2.NE.0 )
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$ NINFO = NINFO + 1
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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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CALL ZCOPY( N, TMP, LDT+1, DIAG, 1 )
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IF( IFST.LT.ILST ) THEN
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DO 70 I = IFST + 1, ILST
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CTEMP = DIAG( I )
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DIAG( I ) = DIAG( I-1 )
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DIAG( I-1 ) = CTEMP
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70 CONTINUE
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ELSE IF( IFST.GT.ILST ) THEN
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DO 80 I = IFST - 1, ILST, -1
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CTEMP = DIAG( I+1 )
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DIAG( I+1 ) = DIAG( I )
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DIAG( I ) = CTEMP
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80 CONTINUE
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END IF
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DO 90 I = 1, N
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IF( T2( I, I ).NE.DIAG( I ) )
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$ RES = RES + ONE / EPS
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90 CONTINUE
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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 ZHST01( N, 1, N, TMP, LDT, T2, LDT, Q, LDT, WORK, LWORK,
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$ RWORK, 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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DO 110 J = 1, N - 1
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DO 100 I = J + 1, N
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IF( T2( I, J ).NE.CZERO )
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$ RES = RES + ONE / EPS
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100 CONTINUE
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110 CONTINUE
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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 ZGET36
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*
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END
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