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SUBROUTINE DGET39( 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 * ======= * * DGET39 tests DLAQTR, a routine for solving the real or * special complex quasi upper triangular system * * op(T)*p = scale*c, * or * op(T + iB)*(p+iq) = scale*(c+id), * * in real arithmetic. T is upper quasi-triangular. * If it is complex, then the first diagonal block of T must be * 1 by 1, B has the special structure * * B = [ b(1) b(2) ... b(n) ] * [ w ] * [ w ] * [ . ] * [ w ] * * op(A) = A or A', where A' denotes the conjugate transpose of * the matrix A. * * On input, X = [ c ]. On output, X = [ p ]. * [ d ] [ q ] * * Scale is an output less than or equal to 1, chosen to avoid * overflow in X. * This subroutine is specially designed for the condition number * estimation in the eigenproblem routine DTRSNA. * * The test code verifies that the following residual is order 1: * * ||(T+i*B)*(x1+i*x2) - scale*(d1+i*d2)|| * ----------------------------------------- * max(ulp*(||T||+||B||)*(||x1||+||x2||), * (||T||+||B||)*smlnum/ulp, * smlnum) * * (The (||T||+||B||)*smlnum/ulp term accounts for possible * (gradual or nongradual) underflow in x1 and x2.) * * 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. * * ===================================================================== * * .. Parameters .. INTEGER LDT, LDT2 PARAMETER ( LDT = 10, LDT2 = 2*LDT ) DOUBLE PRECISION ZERO, ONE PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 ) * .. * .. Local Scalars .. INTEGER I, INFO, IVM1, IVM2, IVM3, IVM4, IVM5, J, K, N, $ NDIM DOUBLE PRECISION BIGNUM, DOMIN, DUMM, EPS, NORM, NORMTB, RESID, $ SCALE, SMLNUM, W, XNORM * .. * .. External Functions .. INTEGER IDAMAX DOUBLE PRECISION DASUM, DDOT, DLAMCH, DLANGE EXTERNAL IDAMAX, DASUM, DDOT, DLAMCH, DLANGE * .. * .. External Subroutines .. EXTERNAL DCOPY, DGEMV, DLABAD, DLAQTR * .. * .. Intrinsic Functions .. INTRINSIC ABS, COS, DBLE, MAX, SIN, SQRT * .. * .. Local Arrays .. INTEGER IDIM( 6 ), IVAL( 5, 5, 6 ) DOUBLE PRECISION B( LDT ), D( LDT2 ), DUM( 1 ), T( LDT, LDT ), $ VM1( 5 ), VM2( 5 ), VM3( 5 ), VM4( 5 ), $ VM5( 3 ), WORK( LDT ), X( LDT2 ), Y( LDT2 ) * .. * .. Data statements .. DATA IDIM / 4, 5*5 / DATA IVAL / 3, 4*0, 1, 1, -1, 0, 0, 3, 2, 1, 0, 0, $ 4, 3, 2, 2, 0, 5*0, 1, 4*0, 2, 2, 3*0, 3, 3, 4, $ 0, 0, 4, 2, 2, 3, 0, 4*1, 5, 1, 4*0, 2, 4, -2, $ 0, 0, 3, 3, 4, 0, 0, 4, 2, 2, 3, 0, 5*1, 1, $ 4*0, 2, 1, -1, 0, 0, 9, 8, 1, 0, 0, 4, 9, 1, 2, $ -1, 5*2, 9, 4*0, 6, 4, 0, 0, 0, 3, 2, 1, 1, 0, $ 5, 1, -1, 1, 0, 5*2, 4, 4*0, 2, 2, 0, 0, 0, 1, $ 4, 4, 0, 0, 2, 4, 2, 2, -1, 5*2 / * .. * .. Executable Statements .. * * Get machine parameters * EPS = DLAMCH( 'P' ) SMLNUM = DLAMCH( 'S' ) BIGNUM = ONE / SMLNUM CALL DLABAD( SMLNUM, BIGNUM ) * * Set up test case parameters * VM1( 1 ) = ONE VM1( 2 ) = SQRT( SMLNUM ) VM1( 3 ) = SQRT( VM1( 2 ) ) VM1( 4 ) = SQRT( BIGNUM ) VM1( 5 ) = SQRT( VM1( 4 ) ) * VM2( 1 ) = ONE VM2( 2 ) = SQRT( SMLNUM ) VM2( 3 ) = SQRT( VM2( 2 ) ) VM2( 4 ) = SQRT( BIGNUM ) VM2( 5 ) = SQRT( VM2( 4 ) ) * VM3( 1 ) = ONE VM3( 2 ) = SQRT( SMLNUM ) VM3( 3 ) = SQRT( VM3( 2 ) ) VM3( 4 ) = SQRT( BIGNUM ) VM3( 5 ) = SQRT( VM3( 4 ) ) * VM4( 1 ) = ONE VM4( 2 ) = SQRT( SMLNUM ) VM4( 3 ) = SQRT( VM4( 2 ) ) VM4( 4 ) = SQRT( BIGNUM ) VM4( 5 ) = SQRT( VM4( 4 ) ) * VM5( 1 ) = ONE VM5( 2 ) = EPS VM5( 3 ) = SQRT( SMLNUM ) * * Initalization * KNT = 0 RMAX = ZERO NINFO = 0 SMLNUM = SMLNUM / EPS * * Begin test loop * DO 140 IVM5 = 1, 3 DO 130 IVM4 = 1, 5 DO 120 IVM3 = 1, 5 DO 110 IVM2 = 1, 5 DO 100 IVM1 = 1, 5 DO 90 NDIM = 1, 6 * N = IDIM( NDIM ) DO 20 I = 1, N DO 10 J = 1, N T( I, J ) = DBLE( IVAL( I, J, NDIM ) )* $ VM1( IVM1 ) IF( I.GE.J ) $ T( I, J ) = T( I, J )*VM5( IVM5 ) 10 CONTINUE 20 CONTINUE * W = ONE*VM2( IVM2 ) * DO 30 I = 1, N B( I ) = COS( DBLE( I ) )*VM3( IVM3 ) 30 CONTINUE * DO 40 I = 1, 2*N D( I ) = SIN( DBLE( I ) )*VM4( IVM4 ) 40 CONTINUE * NORM = DLANGE( '1', N, N, T, LDT, WORK ) K = IDAMAX( N, B, 1 ) NORMTB = NORM + ABS( B( K ) ) + ABS( W ) * CALL DCOPY( N, D, 1, X, 1 ) KNT = KNT + 1 CALL DLAQTR( .FALSE., .TRUE., N, T, LDT, DUM, $ DUMM, SCALE, X, WORK, INFO ) IF( INFO.NE.0 ) $ NINFO = NINFO + 1 * * || T*x - scale*d || / * max(ulp*||T||*||x||,smlnum/ulp*||T||,smlnum) * CALL DCOPY( N, D, 1, Y, 1 ) CALL DGEMV( 'No transpose', N, N, ONE, T, LDT, $ X, 1, -SCALE, Y, 1 ) XNORM = DASUM( N, X, 1 ) RESID = DASUM( N, Y, 1 ) DOMIN = MAX( SMLNUM, ( SMLNUM / EPS )*NORM, $ ( NORM*EPS )*XNORM ) RESID = RESID / DOMIN IF( RESID.GT.RMAX ) THEN RMAX = RESID LMAX = KNT END IF * CALL DCOPY( N, D, 1, X, 1 ) KNT = KNT + 1 CALL DLAQTR( .TRUE., .TRUE., N, T, LDT, DUM, $ DUMM, SCALE, X, WORK, INFO ) IF( INFO.NE.0 ) $ NINFO = NINFO + 1 * * || T*x - scale*d || / * max(ulp*||T||*||x||,smlnum/ulp*||T||,smlnum) * CALL DCOPY( N, D, 1, Y, 1 ) CALL DGEMV( 'Transpose', N, N, ONE, T, LDT, X, $ 1, -SCALE, Y, 1 ) XNORM = DASUM( N, X, 1 ) RESID = DASUM( N, Y, 1 ) DOMIN = MAX( SMLNUM, ( SMLNUM / EPS )*NORM, $ ( NORM*EPS )*XNORM ) RESID = RESID / DOMIN IF( RESID.GT.RMAX ) THEN RMAX = RESID LMAX = KNT END IF * CALL DCOPY( 2*N, D, 1, X, 1 ) KNT = KNT + 1 CALL DLAQTR( .FALSE., .FALSE., N, T, LDT, B, W, $ SCALE, X, WORK, INFO ) IF( INFO.NE.0 ) $ NINFO = NINFO + 1 * * ||(T+i*B)*(x1+i*x2) - scale*(d1+i*d2)|| / * max(ulp*(||T||+||B||)*(||x1||+||x2||), * smlnum/ulp * (||T||+||B||), smlnum ) * * CALL DCOPY( 2*N, D, 1, Y, 1 ) Y( 1 ) = DDOT( N, B, 1, X( 1+N ), 1 ) + $ SCALE*Y( 1 ) DO 50 I = 2, N Y( I ) = W*X( I+N ) + SCALE*Y( I ) 50 CONTINUE CALL DGEMV( 'No transpose', N, N, ONE, T, LDT, $ X, 1, -ONE, Y, 1 ) * Y( 1+N ) = DDOT( N, B, 1, X, 1 ) - $ SCALE*Y( 1+N ) DO 60 I = 2, N Y( I+N ) = W*X( I ) - SCALE*Y( I+N ) 60 CONTINUE CALL DGEMV( 'No transpose', N, N, ONE, T, LDT, $ X( 1+N ), 1, ONE, Y( 1+N ), 1 ) * RESID = DASUM( 2*N, Y, 1 ) DOMIN = MAX( SMLNUM, ( SMLNUM / EPS )*NORMTB, $ EPS*( NORMTB*DASUM( 2*N, X, 1 ) ) ) RESID = RESID / DOMIN IF( RESID.GT.RMAX ) THEN RMAX = RESID LMAX = KNT END IF * CALL DCOPY( 2*N, D, 1, X, 1 ) KNT = KNT + 1 CALL DLAQTR( .TRUE., .FALSE., N, T, LDT, B, W, $ SCALE, X, WORK, INFO ) IF( INFO.NE.0 ) $ NINFO = NINFO + 1 * * ||(T+i*B)*(x1+i*x2) - scale*(d1+i*d2)|| / * max(ulp*(||T||+||B||)*(||x1||+||x2||), * smlnum/ulp * (||T||+||B||), smlnum ) * CALL DCOPY( 2*N, D, 1, Y, 1 ) Y( 1 ) = B( 1 )*X( 1+N ) - SCALE*Y( 1 ) DO 70 I = 2, N Y( I ) = B( I )*X( 1+N ) + W*X( I+N ) - $ SCALE*Y( I ) 70 CONTINUE CALL DGEMV( 'Transpose', N, N, ONE, T, LDT, X, $ 1, ONE, Y, 1 ) * Y( 1+N ) = B( 1 )*X( 1 ) + SCALE*Y( 1+N ) DO 80 I = 2, N Y( I+N ) = B( I )*X( 1 ) + W*X( I ) + $ SCALE*Y( I+N ) 80 CONTINUE CALL DGEMV( 'Transpose', N, N, ONE, T, LDT, $ X( 1+N ), 1, -ONE, Y( 1+N ), 1 ) * RESID = DASUM( 2*N, Y, 1 ) DOMIN = MAX( SMLNUM, ( SMLNUM / EPS )*NORMTB, $ EPS*( NORMTB*DASUM( 2*N, X, 1 ) ) ) RESID = RESID / DOMIN IF( RESID.GT.RMAX ) THEN RMAX = RESID LMAX = KNT END IF * 90 CONTINUE 100 CONTINUE 110 CONTINUE 120 CONTINUE 130 CONTINUE 140 CONTINUE * RETURN * * End of DGET39 * END |