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SUBROUTINE ZGET36( RMAX, LMAX, NINFO, KNT, NIN )
*
* -- LAPACK test routine (version 3.0) --
* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
* Courant Institute, Argonne National Lab, and Rice University
* September 30, 1994
*
* .. Scalar Arguments ..
INTEGER KNT, LMAX, NIN, NINFO
DOUBLE PRECISION RMAX
* ..
*
* Purpose
* =======
*
* ZGET36 tests ZTREXC, a routine for reordering diagonal entries of a
* matrix in complex Schur form. Thus, ZLAEXC computes a unitary 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.
*
* The test matrices are read from a file with logical unit number NIN.
*
* Arguments
* ==========
*
* RMAX (output) DOUBLE PRECISION
* Value of the largest test ratio.
*
* LMAX (output) INTEGER
* Example number where largest test ratio achieved.
*
* NINFO (output) INTEGER
* Number of examples where INFO is nonzero.
*
* KNT (output) INTEGER
* Total number of examples tested.
*
* NIN (input) INTEGER
* Input logical unit number.
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ZERO, ONE
PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
COMPLEX*16 CZERO, CONE
PARAMETER ( CZERO = ( 0.0D+0, 0.0D+0 ),
$ CONE = ( 1.0D+0, 0.0D+0 ) )
INTEGER LDT, LWORK
PARAMETER ( LDT = 10, LWORK = 2*LDT*LDT )
* ..
* .. Local Scalars ..
INTEGER I, IFST, ILST, INFO1, INFO2, J, N
DOUBLE PRECISION EPS, RES
COMPLEX*16 CTEMP
* ..
* .. Local Arrays ..
DOUBLE PRECISION RESULT( 2 ), RWORK( LDT )
COMPLEX*16 DIAG( LDT ), Q( LDT, LDT ), T1( LDT, LDT ),
$ T2( LDT, LDT ), TMP( LDT, LDT ), WORK( LWORK )
* ..
* .. External Functions ..
DOUBLE PRECISION DLAMCH
EXTERNAL DLAMCH
* ..
* .. External Subroutines ..
EXTERNAL ZCOPY, ZHST01, ZLACPY, ZLASET, ZTREXC
* ..
* .. Executable Statements ..
*
EPS = DLAMCH( 'P' )
RMAX = ZERO
LMAX = 0
KNT = 0
NINFO = 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 ZLACPY( 'F', N, N, TMP, LDT, T1, LDT )
CALL ZLACPY( 'F', N, N, TMP, LDT, T2, LDT )
RES = ZERO
*
* Test without accumulating Q
*
CALL ZLASET( 'Full', N, N, CZERO, CONE, Q, LDT )
CALL ZTREXC( 'N', N, T1, LDT, Q, LDT, IFST, ILST, INFO1 )
DO 40 I = 1, N
DO 30 J = 1, N
IF( I.EQ.J .AND. Q( I, J ).NE.CONE )
$ RES = RES + ONE / EPS
IF( I.NE.J .AND. Q( I, J ).NE.CZERO )
$ RES = RES + ONE / EPS
30 CONTINUE
40 CONTINUE
*
* Test with accumulating Q
*
CALL ZLASET( 'Full', N, N, CZERO, CONE, Q, LDT )
CALL ZTREXC( 'V', N, T2, LDT, Q, LDT, IFST, ILST, 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( INFO1.NE.0 .OR. INFO2.NE.0 )
$ NINFO = NINFO + 1
IF( INFO1.NE.INFO2 )
$ RES = RES + ONE / EPS
*
* Test for successful reordering of T2
*
CALL ZCOPY( N, TMP, LDT+1, DIAG, 1 )
IF( IFST.LT.ILST ) THEN
DO 70 I = IFST + 1, ILST
CTEMP = DIAG( I )
DIAG( I ) = DIAG( I-1 )
DIAG( I-1 ) = CTEMP
70 CONTINUE
ELSE IF( IFST.GT.ILST ) THEN
DO 80 I = IFST - 1, ILST, -1
CTEMP = DIAG( I+1 )
DIAG( I+1 ) = DIAG( I )
DIAG( I ) = CTEMP
80 CONTINUE
END IF
DO 90 I = 1, N
IF( T2( I, I ).NE.DIAG( I ) )
$ RES = RES + ONE / EPS
90 CONTINUE
*
* Test for small residual, and orthogonality of Q
*
CALL ZHST01( N, 1, N, TMP, LDT, T2, LDT, Q, LDT, WORK, LWORK,
$ RWORK, RESULT )
RES = RES + RESULT( 1 ) + RESULT( 2 )
*
* Test for T2 being in Schur form
*
DO 110 J = 1, N - 1
DO 100 I = J + 1, N
IF( T2( I, J ).NE.CZERO )
$ RES = RES + ONE / EPS
100 CONTINUE
110 CONTINUE
IF( RES.GT.RMAX ) THEN
RMAX = RES
LMAX = KNT
END IF
GO TO 10
*
* End of ZGET36
*
END
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