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SUBROUTINE DGET32( RMAX, LMAX, NINFO, KNT )
* * -- LAPACK test routine (version 3.1) -- * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. * November 2006 * * .. Scalar Arguments .. INTEGER KNT, LMAX, NINFO DOUBLE PRECISION RMAX * .. * * Purpose * ======= * * DGET32 tests DLASY2, a routine for solving * * op(TL)*X + ISGN*X*op(TR) = SCALE*B * * where TL is N1 by N1, TR is N2 by N2, and N1,N2 =1 or 2 only. * X and B are N1 by N2, op() is an optional transpose, an * ISGN = 1 or -1. SCALE is chosen less than or equal to 1 to * avoid overflow in X. * * The test condition is that the scaled residual * * norm( op(TL)*X + ISGN*X*op(TR) = SCALE*B ) * / ( max( ulp*norm(TL), ulp*norm(TR)) * norm(X), SMLNUM ) * * should be on the order of 1. Here, ulp is the machine precision. * Also, it is verified that SCALE is less than or equal to 1, and * that XNORM = infinity-norm(X). * * 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 returned with INFO.NE.0. * * KNT (output) INTEGER * Total number of examples tested. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO, ONE PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 ) DOUBLE PRECISION TWO, FOUR, EIGHT PARAMETER ( TWO = 2.0D0, FOUR = 4.0D0, EIGHT = 8.0D0 ) * .. * .. Local Scalars .. LOGICAL LTRANL, LTRANR INTEGER IB, IB1, IB2, IB3, INFO, ISGN, ITL, ITLSCL, $ ITR, ITRANL, ITRANR, ITRSCL, N1, N2 DOUBLE PRECISION BIGNUM, DEN, EPS, RES, SCALE, SGN, SMLNUM, TMP, $ TNRM, XNORM, XNRM * .. * .. Local Arrays .. INTEGER ITVAL( 2, 2, 8 ) DOUBLE PRECISION B( 2, 2 ), TL( 2, 2 ), TR( 2, 2 ), VAL( 3 ), $ X( 2, 2 ) * .. * .. External Functions .. DOUBLE PRECISION DLAMCH EXTERNAL DLAMCH * .. * .. External Subroutines .. EXTERNAL DLABAD, DLASY2 * .. * .. Intrinsic Functions .. INTRINSIC ABS, MAX, MIN, SQRT * .. * .. Data statements .. DATA ITVAL / 8, 4, 2, 1, 4, 8, 1, 2, 2, 1, 8, 4, 1, $ 2, 4, 8, 9, 4, 2, 1, 4, 9, 1, 2, 2, 1, 9, 4, 1, $ 2, 4, 9 / * .. * .. 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 ) = SQRT( SMLNUM ) VAL( 2 ) = ONE VAL( 3 ) = SQRT( BIGNUM ) * KNT = 0 NINFO = 0 LMAX = 0 RMAX = ZERO * * Begin test loop * DO 230 ITRANL = 0, 1 DO 220 ITRANR = 0, 1 DO 210 ISGN = -1, 1, 2 SGN = ISGN LTRANL = ITRANL.EQ.1 LTRANR = ITRANR.EQ.1 * N1 = 1 N2 = 1 DO 30 ITL = 1, 3 DO 20 ITR = 1, 3 DO 10 IB = 1, 3 TL( 1, 1 ) = VAL( ITL ) TR( 1, 1 ) = VAL( ITR ) B( 1, 1 ) = VAL( IB ) KNT = KNT + 1 CALL DLASY2( LTRANL, LTRANR, ISGN, N1, N2, TL, $ 2, TR, 2, B, 2, SCALE, X, 2, XNORM, $ INFO ) IF( INFO.NE.0 ) $ NINFO = NINFO + 1 RES = ABS( ( TL( 1, 1 )+SGN*TR( 1, 1 ) )* $ X( 1, 1 )-SCALE*B( 1, 1 ) ) IF( INFO.EQ.0 ) THEN DEN = MAX( EPS*( ( ABS( TR( 1, $ 1 ) )+ABS( TL( 1, 1 ) ) )*ABS( X( 1, $ 1 ) ) ), SMLNUM ) ELSE DEN = SMLNUM*MAX( ABS( X( 1, 1 ) ), ONE ) END IF RES = RES / DEN IF( SCALE.GT.ONE ) $ RES = RES + ONE / EPS RES = RES + ABS( XNORM-ABS( X( 1, 1 ) ) ) / $ MAX( SMLNUM, XNORM ) / EPS IF( INFO.NE.0 .AND. INFO.NE.1 ) $ RES = RES + ONE / EPS IF( RES.GT.RMAX ) THEN LMAX = KNT RMAX = RES END IF 10 CONTINUE 20 CONTINUE 30 CONTINUE * N1 = 2 N2 = 1 DO 80 ITL = 1, 8 DO 70 ITLSCL = 1, 3 DO 60 ITR = 1, 3 DO 50 IB1 = 1, 3 DO 40 IB2 = 1, 3 B( 1, 1 ) = VAL( IB1 ) B( 2, 1 ) = -FOUR*VAL( IB2 ) TL( 1, 1 ) = ITVAL( 1, 1, ITL )* $ VAL( ITLSCL ) TL( 2, 1 ) = ITVAL( 2, 1, ITL )* $ VAL( ITLSCL ) TL( 1, 2 ) = ITVAL( 1, 2, ITL )* $ VAL( ITLSCL ) TL( 2, 2 ) = ITVAL( 2, 2, ITL )* $ VAL( ITLSCL ) TR( 1, 1 ) = VAL( ITR ) KNT = KNT + 1 CALL DLASY2( LTRANL, LTRANR, ISGN, N1, N2, $ TL, 2, TR, 2, B, 2, SCALE, X, $ 2, XNORM, INFO ) IF( INFO.NE.0 ) $ NINFO = NINFO + 1 IF( LTRANL ) THEN TMP = TL( 1, 2 ) TL( 1, 2 ) = TL( 2, 1 ) TL( 2, 1 ) = TMP END IF RES = ABS( ( TL( 1, 1 )+SGN*TR( 1, 1 ) )* $ X( 1, 1 )+TL( 1, 2 )*X( 2, 1 )- $ SCALE*B( 1, 1 ) ) RES = RES + ABS( ( TL( 2, 2 )+SGN*TR( 1, $ 1 ) )*X( 2, 1 )+TL( 2, 1 )* $ X( 1, 1 )-SCALE*B( 2, 1 ) ) TNRM = ABS( TR( 1, 1 ) ) + $ ABS( TL( 1, 1 ) ) + $ ABS( TL( 1, 2 ) ) + $ ABS( TL( 2, 1 ) ) + $ ABS( TL( 2, 2 ) ) XNRM = MAX( ABS( X( 1, 1 ) ), $ ABS( X( 2, 1 ) ) ) DEN = MAX( SMLNUM, SMLNUM*XNRM, $ ( TNRM*EPS )*XNRM ) RES = RES / DEN IF( SCALE.GT.ONE ) $ RES = RES + ONE / EPS RES = RES + ABS( XNORM-XNRM ) / $ MAX( SMLNUM, XNORM ) / EPS IF( RES.GT.RMAX ) THEN LMAX = KNT RMAX = RES END IF 40 CONTINUE 50 CONTINUE 60 CONTINUE 70 CONTINUE 80 CONTINUE * N1 = 1 N2 = 2 DO 130 ITR = 1, 8 DO 120 ITRSCL = 1, 3 DO 110 ITL = 1, 3 DO 100 IB1 = 1, 3 DO 90 IB2 = 1, 3 B( 1, 1 ) = VAL( IB1 ) B( 1, 2 ) = -TWO*VAL( IB2 ) TR( 1, 1 ) = ITVAL( 1, 1, ITR )* $ VAL( ITRSCL ) TR( 2, 1 ) = ITVAL( 2, 1, ITR )* $ VAL( ITRSCL ) TR( 1, 2 ) = ITVAL( 1, 2, ITR )* $ VAL( ITRSCL ) TR( 2, 2 ) = ITVAL( 2, 2, ITR )* $ VAL( ITRSCL ) TL( 1, 1 ) = VAL( ITL ) KNT = KNT + 1 CALL DLASY2( LTRANL, LTRANR, ISGN, N1, N2, $ TL, 2, TR, 2, B, 2, SCALE, X, $ 2, XNORM, INFO ) IF( INFO.NE.0 ) $ NINFO = NINFO + 1 IF( LTRANR ) THEN TMP = TR( 1, 2 ) TR( 1, 2 ) = TR( 2, 1 ) TR( 2, 1 ) = TMP END IF TNRM = ABS( TL( 1, 1 ) ) + $ ABS( TR( 1, 1 ) ) + $ ABS( TR( 1, 2 ) ) + $ ABS( TR( 2, 2 ) ) + $ ABS( TR( 2, 1 ) ) XNRM = ABS( X( 1, 1 ) ) + ABS( X( 1, 2 ) ) RES = ABS( ( ( TL( 1, 1 )+SGN*TR( 1, $ 1 ) ) )*( X( 1, 1 ) )+ $ ( SGN*TR( 2, 1 ) )*( X( 1, 2 ) )- $ ( SCALE*B( 1, 1 ) ) ) RES = RES + ABS( ( ( TL( 1, 1 )+SGN*TR( 2, $ 2 ) ) )*( X( 1, 2 ) )+ $ ( SGN*TR( 1, 2 ) )*( X( 1, 1 ) )- $ ( SCALE*B( 1, 2 ) ) ) DEN = MAX( SMLNUM, SMLNUM*XNRM, $ ( TNRM*EPS )*XNRM ) RES = RES / DEN IF( SCALE.GT.ONE ) $ RES = RES + ONE / EPS RES = RES + ABS( XNORM-XNRM ) / $ MAX( SMLNUM, XNORM ) / EPS IF( RES.GT.RMAX ) THEN LMAX = KNT RMAX = RES END IF 90 CONTINUE 100 CONTINUE 110 CONTINUE 120 CONTINUE 130 CONTINUE * N1 = 2 N2 = 2 DO 200 ITR = 1, 8 DO 190 ITRSCL = 1, 3 DO 180 ITL = 1, 8 DO 170 ITLSCL = 1, 3 DO 160 IB1 = 1, 3 DO 150 IB2 = 1, 3 DO 140 IB3 = 1, 3 B( 1, 1 ) = VAL( IB1 ) B( 2, 1 ) = -FOUR*VAL( IB2 ) B( 1, 2 ) = -TWO*VAL( IB3 ) B( 2, 2 ) = EIGHT* $ MIN( VAL( IB1 ), VAL $ ( IB2 ), VAL( IB3 ) ) TR( 1, 1 ) = ITVAL( 1, 1, ITR )* $ VAL( ITRSCL ) TR( 2, 1 ) = ITVAL( 2, 1, ITR )* $ VAL( ITRSCL ) TR( 1, 2 ) = ITVAL( 1, 2, ITR )* $ VAL( ITRSCL ) TR( 2, 2 ) = ITVAL( 2, 2, ITR )* $ VAL( ITRSCL ) TL( 1, 1 ) = ITVAL( 1, 1, ITL )* $ VAL( ITLSCL ) TL( 2, 1 ) = ITVAL( 2, 1, ITL )* $ VAL( ITLSCL ) TL( 1, 2 ) = ITVAL( 1, 2, ITL )* $ VAL( ITLSCL ) TL( 2, 2 ) = ITVAL( 2, 2, ITL )* $ VAL( ITLSCL ) KNT = KNT + 1 CALL DLASY2( LTRANL, LTRANR, ISGN, $ N1, N2, TL, 2, TR, 2, $ B, 2, SCALE, X, 2, $ XNORM, INFO ) IF( INFO.NE.0 ) $ NINFO = NINFO + 1 IF( LTRANR ) THEN TMP = TR( 1, 2 ) TR( 1, 2 ) = TR( 2, 1 ) TR( 2, 1 ) = TMP END IF IF( LTRANL ) THEN TMP = TL( 1, 2 ) TL( 1, 2 ) = TL( 2, 1 ) TL( 2, 1 ) = TMP END IF TNRM = ABS( TR( 1, 1 ) ) + $ ABS( TR( 2, 1 ) ) + $ ABS( TR( 1, 2 ) ) + $ ABS( TR( 2, 2 ) ) + $ ABS( TL( 1, 1 ) ) + $ ABS( TL( 2, 1 ) ) + $ ABS( TL( 1, 2 ) ) + $ ABS( TL( 2, 2 ) ) XNRM = MAX( ABS( X( 1, 1 ) )+ $ ABS( X( 1, 2 ) ), $ ABS( X( 2, 1 ) )+ $ ABS( X( 2, 2 ) ) ) RES = ABS( ( ( TL( 1, 1 )+SGN*TR( 1, $ 1 ) ) )*( X( 1, 1 ) )+ $ ( SGN*TR( 2, 1 ) )* $ ( X( 1, 2 ) )+( TL( 1, 2 ) )* $ ( X( 2, 1 ) )- $ ( SCALE*B( 1, 1 ) ) ) RES = RES + ABS( ( TL( 1, 1 ) )* $ ( X( 1, 2 ) )+ $ ( SGN*TR( 1, 2 ) )* $ ( X( 1, 1 ) )+ $ ( SGN*TR( 2, 2 ) )* $ ( X( 1, 2 ) )+( TL( 1, 2 ) )* $ ( X( 2, 2 ) )- $ ( SCALE*B( 1, 2 ) ) ) RES = RES + ABS( ( TL( 2, 1 ) )* $ ( X( 1, 1 ) )+ $ ( SGN*TR( 1, 1 ) )* $ ( X( 2, 1 ) )+ $ ( SGN*TR( 2, 1 ) )* $ ( X( 2, 2 ) )+( TL( 2, 2 ) )* $ ( X( 2, 1 ) )- $ ( SCALE*B( 2, 1 ) ) ) RES = RES + ABS( ( ( TL( 2, $ 2 )+SGN*TR( 2, 2 ) ) )* $ ( X( 2, 2 ) )+ $ ( SGN*TR( 1, 2 ) )* $ ( X( 2, 1 ) )+( TL( 2, 1 ) )* $ ( X( 1, 2 ) )- $ ( SCALE*B( 2, 2 ) ) ) DEN = MAX( SMLNUM, SMLNUM*XNRM, $ ( TNRM*EPS )*XNRM ) RES = RES / DEN IF( SCALE.GT.ONE ) $ RES = RES + ONE / EPS RES = RES + ABS( XNORM-XNRM ) / $ MAX( SMLNUM, XNORM ) / EPS IF( RES.GT.RMAX ) THEN LMAX = KNT RMAX = RES END IF 140 CONTINUE 150 CONTINUE 160 CONTINUE 170 CONTINUE 180 CONTINUE 190 CONTINUE 200 CONTINUE 210 CONTINUE 220 CONTINUE 230 CONTINUE * RETURN * * End of DGET32 * END |