*> \brief \b SGET39 * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE SGET39( RMAX, LMAX, NINFO, KNT ) * * .. Scalar Arguments .. * INTEGER KNT, LMAX, NINFO * REAL RMAX * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> SGET39 tests SLAQTR, 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 STRSNA. *> *> 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 REAL *> 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 single_eig * * ===================================================================== SUBROUTINE SGET39( 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 REAL RMAX * .. * * ===================================================================== * * .. Parameters .. INTEGER LDT, LDT2 PARAMETER ( LDT = 10, LDT2 = 2*LDT ) REAL ZERO, ONE PARAMETER ( ZERO = 0.0, ONE = 1.0 ) * .. * .. Local Scalars .. INTEGER I, INFO, IVM1, IVM2, IVM3, IVM4, IVM5, J, K, N, $ NDIM REAL BIGNUM, DOMIN, DUMM, EPS, NORM, NORMTB, RESID, $ SCALE, SMLNUM, W, XNORM * .. * .. External Functions .. INTEGER ISAMAX REAL SASUM, SDOT, SLAMCH, SLANGE EXTERNAL ISAMAX, SASUM, SDOT, SLAMCH, SLANGE * .. * .. External Subroutines .. EXTERNAL SCOPY, SGEMV, SLABAD, SLAQTR * .. * .. Intrinsic Functions .. INTRINSIC ABS, COS, MAX, REAL, SIN, SQRT * .. * .. Local Arrays .. INTEGER IDIM( 6 ), IVAL( 5, 5, 6 ) REAL 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 = SLAMCH( 'P' ) SMLNUM = SLAMCH( 'S' ) BIGNUM = ONE / SMLNUM CALL SLABAD( 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 ) = REAL( 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( REAL( I ) )*VM3( IVM3 ) 30 CONTINUE * DO 40 I = 1, 2*N D( I ) = SIN( REAL( I ) )*VM4( IVM4 ) 40 CONTINUE * NORM = SLANGE( '1', N, N, T, LDT, WORK ) K = ISAMAX( N, B, 1 ) NORMTB = NORM + ABS( B( K ) ) + ABS( W ) * CALL SCOPY( N, D, 1, X, 1 ) KNT = KNT + 1 CALL SLAQTR( .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 SCOPY( N, D, 1, Y, 1 ) CALL SGEMV( 'No transpose', N, N, ONE, T, LDT, $ X, 1, -SCALE, Y, 1 ) XNORM = SASUM( N, X, 1 ) RESID = SASUM( 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 SCOPY( N, D, 1, X, 1 ) KNT = KNT + 1 CALL SLAQTR( .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 SCOPY( N, D, 1, Y, 1 ) CALL SGEMV( 'Transpose', N, N, ONE, T, LDT, X, $ 1, -SCALE, Y, 1 ) XNORM = SASUM( N, X, 1 ) RESID = SASUM( 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 SCOPY( 2*N, D, 1, X, 1 ) KNT = KNT + 1 CALL SLAQTR( .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 SCOPY( 2*N, D, 1, Y, 1 ) Y( 1 ) = SDOT( 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 SGEMV( 'No transpose', N, N, ONE, T, LDT, $ X, 1, -ONE, Y, 1 ) * Y( 1+N ) = SDOT( 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 SGEMV( 'No transpose', N, N, ONE, T, LDT, $ 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 * CALL SCOPY( 2*N, D, 1, X, 1 ) KNT = KNT + 1 CALL SLAQTR( .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 SCOPY( 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 SGEMV( '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 SGEMV( 'Transpose', N, N, ONE, T, LDT, $ 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