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|
*> \brief \b DGET39
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE DGET39( RMAX, LMAX, NINFO, KNT )
*
* .. Scalar Arguments ..
* INTEGER KNT, LMAX, NINFO
* DOUBLE PRECISION RMAX
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> 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.)
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[out] RMAX
*> \verbatim
*> RMAX is DOUBLE PRECISION
*> Value of the largest test ratio.
*> \endverbatim
*>
*> \param[out] LMAX
*> \verbatim
*> LMAX is INTEGER
*> Example number where largest test ratio achieved.
*> \endverbatim
*>
*> \param[out] NINFO
*> \verbatim
*> NINFO is INTEGER
*> Number of examples where INFO is nonzero.
*> \endverbatim
*>
*> \param[out] KNT
*> \verbatim
*> KNT is INTEGER
*> Total number of examples tested.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date December 2016
*
*> \ingroup double_eig
*
* =====================================================================
SUBROUTINE DGET39( RMAX, LMAX, NINFO, KNT )
*
* -- LAPACK test routine (version 3.7.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* December 2016
*
* .. Scalar Arguments ..
INTEGER KNT, LMAX, NINFO
DOUBLE PRECISION RMAX
* ..
*
* =====================================================================
*
* .. 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
|
