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366 lines
12 KiB
366 lines
12 KiB
2 years ago
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*> \brief \b SGET39
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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 SGET39( RMAX, LMAX, NINFO, KNT )
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*
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* .. Scalar Arguments ..
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* INTEGER KNT, LMAX, NINFO
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* REAL 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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*> SGET39 tests SLAQTR, a routine for solving the real or
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*> special complex quasi upper triangular system
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*>
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*> op(T)*p = scale*c,
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*> or
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*> op(T + iB)*(p+iq) = scale*(c+id),
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*>
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*> in real arithmetic. T is upper quasi-triangular.
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*> If it is complex, then the first diagonal block of T must be
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*> 1 by 1, B has the special structure
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*>
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*> B = [ b(1) b(2) ... b(n) ]
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*> [ w ]
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*> [ w ]
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*> [ . ]
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*> [ w ]
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*>
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*> op(A) = A or A', where A' denotes the conjugate transpose of
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*> the matrix A.
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*>
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*> On input, X = [ c ]. On output, X = [ p ].
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*> [ d ] [ q ]
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*>
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*> Scale is an output less than or equal to 1, chosen to avoid
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*> overflow in X.
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*> This subroutine is specially designed for the condition number
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*> estimation in the eigenproblem routine STRSNA.
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*>
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*> The test code verifies that the following residual is order 1:
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*>
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*> ||(T+i*B)*(x1+i*x2) - scale*(d1+i*d2)||
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*> -----------------------------------------
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*> max(ulp*(||T||+||B||)*(||x1||+||x2||),
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*> (||T||+||B||)*smlnum/ulp,
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*> smlnum)
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*>
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*> (The (||T||+||B||)*smlnum/ulp term accounts for possible
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*> (gradual or nongradual) underflow in x1 and x2.)
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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 REAL
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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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* 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 single_eig
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*
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* =====================================================================
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SUBROUTINE SGET39( RMAX, LMAX, NINFO, KNT )
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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, NINFO
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REAL 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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INTEGER LDT, LDT2
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PARAMETER ( LDT = 10, LDT2 = 2*LDT )
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REAL ZERO, ONE
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PARAMETER ( ZERO = 0.0, ONE = 1.0 )
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* ..
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* .. Local Scalars ..
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INTEGER I, INFO, IVM1, IVM2, IVM3, IVM4, IVM5, J, K, N,
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$ NDIM
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REAL BIGNUM, DOMIN, DUMM, EPS, NORM, NORMTB, RESID,
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$ SCALE, SMLNUM, W, XNORM
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* ..
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* .. External Functions ..
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INTEGER ISAMAX
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REAL SASUM, SDOT, SLAMCH, SLANGE
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EXTERNAL ISAMAX, SASUM, SDOT, SLAMCH, SLANGE
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* ..
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* .. External Subroutines ..
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EXTERNAL SCOPY, SGEMV, SLAQTR
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC ABS, COS, MAX, REAL, SIN, SQRT
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* ..
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* .. Local Arrays ..
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INTEGER IDIM( 6 ), IVAL( 5, 5, 6 )
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REAL B( LDT ), D( LDT2 ), DUM( 1 ), T( LDT, LDT ),
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$ VM1( 5 ), VM2( 5 ), VM3( 5 ), VM4( 5 ),
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$ VM5( 3 ), WORK( LDT ), X( LDT2 ), Y( LDT2 )
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* ..
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* .. Data statements ..
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DATA IDIM / 4, 5*5 /
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DATA IVAL / 3, 4*0, 1, 1, -1, 0, 0, 3, 2, 1, 0, 0,
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$ 4, 3, 2, 2, 0, 5*0, 1, 4*0, 2, 2, 3*0, 3, 3, 4,
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$ 0, 0, 4, 2, 2, 3, 0, 4*1, 5, 1, 4*0, 2, 4, -2,
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$ 0, 0, 3, 3, 4, 0, 0, 4, 2, 2, 3, 0, 5*1, 1,
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$ 4*0, 2, 1, -1, 0, 0, 9, 8, 1, 0, 0, 4, 9, 1, 2,
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$ -1, 5*2, 9, 4*0, 6, 4, 0, 0, 0, 3, 2, 1, 1, 0,
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$ 5, 1, -1, 1, 0, 5*2, 4, 4*0, 2, 2, 0, 0, 0, 1,
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$ 4, 4, 0, 0, 2, 4, 2, 2, -1, 5*2 /
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* ..
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* .. Executable Statements ..
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*
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* Get machine parameters
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*
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EPS = SLAMCH( 'P' )
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SMLNUM = SLAMCH( 'S' )
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BIGNUM = ONE / SMLNUM
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*
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* Set up test case parameters
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*
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VM1( 1 ) = ONE
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VM1( 2 ) = SQRT( SMLNUM )
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VM1( 3 ) = SQRT( VM1( 2 ) )
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VM1( 4 ) = SQRT( BIGNUM )
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VM1( 5 ) = SQRT( VM1( 4 ) )
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*
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VM2( 1 ) = ONE
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VM2( 2 ) = SQRT( SMLNUM )
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VM2( 3 ) = SQRT( VM2( 2 ) )
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VM2( 4 ) = SQRT( BIGNUM )
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VM2( 5 ) = SQRT( VM2( 4 ) )
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*
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VM3( 1 ) = ONE
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VM3( 2 ) = SQRT( SMLNUM )
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VM3( 3 ) = SQRT( VM3( 2 ) )
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VM3( 4 ) = SQRT( BIGNUM )
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VM3( 5 ) = SQRT( VM3( 4 ) )
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*
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VM4( 1 ) = ONE
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VM4( 2 ) = SQRT( SMLNUM )
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VM4( 3 ) = SQRT( VM4( 2 ) )
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VM4( 4 ) = SQRT( BIGNUM )
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VM4( 5 ) = SQRT( VM4( 4 ) )
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*
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VM5( 1 ) = ONE
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VM5( 2 ) = EPS
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VM5( 3 ) = SQRT( SMLNUM )
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*
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* Initialization
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*
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KNT = 0
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RMAX = ZERO
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NINFO = 0
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SMLNUM = SMLNUM / EPS
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*
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* Begin test loop
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*
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DO 140 IVM5 = 1, 3
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DO 130 IVM4 = 1, 5
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DO 120 IVM3 = 1, 5
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DO 110 IVM2 = 1, 5
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DO 100 IVM1 = 1, 5
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DO 90 NDIM = 1, 6
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*
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N = IDIM( NDIM )
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DO 20 I = 1, N
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DO 10 J = 1, N
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T( I, J ) = REAL( IVAL( I, J, NDIM ) )*
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$ VM1( IVM1 )
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IF( I.GE.J )
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$ T( I, J ) = T( I, J )*VM5( IVM5 )
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10 CONTINUE
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20 CONTINUE
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*
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W = ONE*VM2( IVM2 )
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*
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DO 30 I = 1, N
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B( I ) = COS( REAL( I ) )*VM3( IVM3 )
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30 CONTINUE
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*
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DO 40 I = 1, 2*N
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D( I ) = SIN( REAL( I ) )*VM4( IVM4 )
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40 CONTINUE
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*
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NORM = SLANGE( '1', N, N, T, LDT, WORK )
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K = ISAMAX( N, B, 1 )
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NORMTB = NORM + ABS( B( K ) ) + ABS( W )
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*
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CALL SCOPY( N, D, 1, X, 1 )
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KNT = KNT + 1
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CALL SLAQTR( .FALSE., .TRUE., N, T, LDT, DUM,
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$ DUMM, SCALE, X, WORK, INFO )
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IF( INFO.NE.0 )
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$ NINFO = NINFO + 1
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*
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* || T*x - scale*d || /
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* max(ulp*||T||*||x||,smlnum/ulp*||T||,smlnum)
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*
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CALL SCOPY( N, D, 1, Y, 1 )
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CALL SGEMV( 'No transpose', N, N, ONE, T, LDT,
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$ X, 1, -SCALE, Y, 1 )
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XNORM = SASUM( N, X, 1 )
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RESID = SASUM( N, Y, 1 )
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DOMIN = MAX( SMLNUM, ( SMLNUM / EPS )*NORM,
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$ ( NORM*EPS )*XNORM )
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RESID = RESID / DOMIN
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IF( RESID.GT.RMAX ) THEN
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RMAX = RESID
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LMAX = KNT
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END IF
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*
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CALL SCOPY( N, D, 1, X, 1 )
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KNT = KNT + 1
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CALL SLAQTR( .TRUE., .TRUE., N, T, LDT, DUM,
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$ DUMM, SCALE, X, WORK, INFO )
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IF( INFO.NE.0 )
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$ NINFO = NINFO + 1
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*
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* || T*x - scale*d || /
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* max(ulp*||T||*||x||,smlnum/ulp*||T||,smlnum)
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*
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CALL SCOPY( N, D, 1, Y, 1 )
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CALL SGEMV( 'Transpose', N, N, ONE, T, LDT, X,
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$ 1, -SCALE, Y, 1 )
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XNORM = SASUM( N, X, 1 )
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RESID = SASUM( N, Y, 1 )
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DOMIN = MAX( SMLNUM, ( SMLNUM / EPS )*NORM,
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$ ( NORM*EPS )*XNORM )
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RESID = RESID / DOMIN
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IF( RESID.GT.RMAX ) THEN
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RMAX = RESID
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LMAX = KNT
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END IF
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*
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CALL SCOPY( 2*N, D, 1, X, 1 )
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KNT = KNT + 1
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CALL SLAQTR( .FALSE., .FALSE., N, T, LDT, B, W,
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$ SCALE, X, WORK, INFO )
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IF( INFO.NE.0 )
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$ NINFO = NINFO + 1
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*
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* ||(T+i*B)*(x1+i*x2) - scale*(d1+i*d2)|| /
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* max(ulp*(||T||+||B||)*(||x1||+||x2||),
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* smlnum/ulp * (||T||+||B||), smlnum )
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*
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*
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CALL SCOPY( 2*N, D, 1, Y, 1 )
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Y( 1 ) = SDOT( N, B, 1, X( 1+N ), 1 ) +
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$ SCALE*Y( 1 )
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DO 50 I = 2, N
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Y( I ) = W*X( I+N ) + SCALE*Y( I )
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50 CONTINUE
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CALL SGEMV( 'No transpose', N, N, ONE, T, LDT,
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$ X, 1, -ONE, Y, 1 )
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*
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Y( 1+N ) = SDOT( N, B, 1, X, 1 ) -
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$ SCALE*Y( 1+N )
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DO 60 I = 2, N
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Y( I+N ) = W*X( I ) - SCALE*Y( I+N )
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60 CONTINUE
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CALL SGEMV( 'No transpose', N, N, ONE, T, LDT,
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$ X( 1+N ), 1, ONE, Y( 1+N ), 1 )
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*
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RESID = SASUM( 2*N, Y, 1 )
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DOMIN = MAX( SMLNUM, ( SMLNUM / EPS )*NORMTB,
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$ EPS*( NORMTB*SASUM( 2*N, X, 1 ) ) )
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RESID = RESID / DOMIN
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IF( RESID.GT.RMAX ) THEN
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RMAX = RESID
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LMAX = KNT
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END IF
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*
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CALL SCOPY( 2*N, D, 1, X, 1 )
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KNT = KNT + 1
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CALL SLAQTR( .TRUE., .FALSE., N, T, LDT, B, W,
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$ SCALE, X, WORK, INFO )
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IF( INFO.NE.0 )
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$ NINFO = NINFO + 1
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*
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* ||(T+i*B)*(x1+i*x2) - scale*(d1+i*d2)|| /
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* max(ulp*(||T||+||B||)*(||x1||+||x2||),
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* smlnum/ulp * (||T||+||B||), smlnum )
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*
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CALL SCOPY( 2*N, D, 1, Y, 1 )
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Y( 1 ) = B( 1 )*X( 1+N ) - SCALE*Y( 1 )
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DO 70 I = 2, N
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Y( I ) = B( I )*X( 1+N ) + W*X( I+N ) -
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$ SCALE*Y( I )
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70 CONTINUE
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CALL SGEMV( 'Transpose', N, N, ONE, T, LDT, X,
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$ 1, ONE, Y, 1 )
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*
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Y( 1+N ) = B( 1 )*X( 1 ) + SCALE*Y( 1+N )
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DO 80 I = 2, N
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Y( I+N ) = B( I )*X( 1 ) + W*X( I ) +
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$ SCALE*Y( I+N )
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80 CONTINUE
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CALL SGEMV( 'Transpose', N, N, ONE, T, LDT,
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$ X( 1+N ), 1, -ONE, Y( 1+N ), 1 )
|
||
|
|
*
|
||
|
|
RESID = SASUM( 2*N, Y, 1 )
|
||
|
|
DOMIN = MAX( SMLNUM, ( SMLNUM / EPS )*NORMTB,
|
||
|
|
$ EPS*( NORMTB*SASUM( 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 SGET39
|
||
|
|
*
|
||
|
|
END
|