1*> \brief \b ZGET07 2* 3* =========== DOCUMENTATION =========== 4* 5* Online html documentation available at 6* http://www.netlib.org/lapack/explore-html/ 7* 8* Definition: 9* =========== 10* 11* SUBROUTINE ZGET07( TRANS, N, NRHS, A, LDA, B, LDB, X, LDX, XACT, 12* LDXACT, FERR, CHKFERR, BERR, RESLTS ) 13* 14* .. Scalar Arguments .. 15* CHARACTER TRANS 16* LOGICAL CHKFERR 17* INTEGER LDA, LDB, LDX, LDXACT, N, NRHS 18* .. 19* .. Array Arguments .. 20* DOUBLE PRECISION BERR( * ), FERR( * ), RESLTS( * ) 21* COMPLEX*16 A( LDA, * ), B( LDB, * ), X( LDX, * ), 22* $ XACT( LDXACT, * ) 23* .. 24* 25* 26*> \par Purpose: 27* ============= 28*> 29*> \verbatim 30*> 31*> ZGET07 tests the error bounds from iterative refinement for the 32*> computed solution to a system of equations op(A)*X = B, where A is a 33*> general n by n matrix and op(A) = A or A**T, depending on TRANS. 34*> 35*> RESLTS(1) = test of the error bound 36*> = norm(X - XACT) / ( norm(X) * FERR ) 37*> 38*> A large value is returned if this ratio is not less than one. 39*> 40*> RESLTS(2) = residual from the iterative refinement routine 41*> = the maximum of BERR / ( (n+1)*EPS + (*) ), where 42*> (*) = (n+1)*UNFL / (min_i (abs(op(A))*abs(X) +abs(b))_i ) 43*> \endverbatim 44* 45* Arguments: 46* ========== 47* 48*> \param[in] TRANS 49*> \verbatim 50*> TRANS is CHARACTER*1 51*> Specifies the form of the system of equations. 52*> = 'N': A * X = B (No transpose) 53*> = 'T': A**T * X = B (Transpose) 54*> = 'C': A**H * X = B (Conjugate transpose = Transpose) 55*> \endverbatim 56*> 57*> \param[in] N 58*> \verbatim 59*> N is INTEGER 60*> The number of rows of the matrices X and XACT. N >= 0. 61*> \endverbatim 62*> 63*> \param[in] NRHS 64*> \verbatim 65*> NRHS is INTEGER 66*> The number of columns of the matrices X and XACT. NRHS >= 0. 67*> \endverbatim 68*> 69*> \param[in] A 70*> \verbatim 71*> A is COMPLEX*16 array, dimension (LDA,N) 72*> The original n by n matrix A. 73*> \endverbatim 74*> 75*> \param[in] LDA 76*> \verbatim 77*> LDA is INTEGER 78*> The leading dimension of the array A. LDA >= max(1,N). 79*> \endverbatim 80*> 81*> \param[in] B 82*> \verbatim 83*> B is COMPLEX*16 array, dimension (LDB,NRHS) 84*> The right hand side vectors for the system of linear 85*> equations. 86*> \endverbatim 87*> 88*> \param[in] LDB 89*> \verbatim 90*> LDB is INTEGER 91*> The leading dimension of the array B. LDB >= max(1,N). 92*> \endverbatim 93*> 94*> \param[in] X 95*> \verbatim 96*> X is COMPLEX*16 array, dimension (LDX,NRHS) 97*> The computed solution vectors. Each vector is stored as a 98*> column of the matrix X. 99*> \endverbatim 100*> 101*> \param[in] LDX 102*> \verbatim 103*> LDX is INTEGER 104*> The leading dimension of the array X. LDX >= max(1,N). 105*> \endverbatim 106*> 107*> \param[in] XACT 108*> \verbatim 109*> XACT is COMPLEX*16 array, dimension (LDX,NRHS) 110*> The exact solution vectors. Each vector is stored as a 111*> column of the matrix XACT. 112*> \endverbatim 113*> 114*> \param[in] LDXACT 115*> \verbatim 116*> LDXACT is INTEGER 117*> The leading dimension of the array XACT. LDXACT >= max(1,N). 118*> \endverbatim 119*> 120*> \param[in] FERR 121*> \verbatim 122*> FERR is DOUBLE PRECISION array, dimension (NRHS) 123*> The estimated forward error bounds for each solution vector 124*> X. If XTRUE is the true solution, FERR bounds the magnitude 125*> of the largest entry in (X - XTRUE) divided by the magnitude 126*> of the largest entry in X. 127*> \endverbatim 128*> 129*> \param[in] CHKFERR 130*> \verbatim 131*> CHKFERR is LOGICAL 132*> Set to .TRUE. to check FERR, .FALSE. not to check FERR. 133*> When the test system is ill-conditioned, the "true" 134*> solution in XACT may be incorrect. 135*> \endverbatim 136*> 137*> \param[in] BERR 138*> \verbatim 139*> BERR is DOUBLE PRECISION array, dimension (NRHS) 140*> The componentwise relative backward error of each solution 141*> vector (i.e., the smallest relative change in any entry of A 142*> or B that makes X an exact solution). 143*> \endverbatim 144*> 145*> \param[out] RESLTS 146*> \verbatim 147*> RESLTS is DOUBLE PRECISION array, dimension (2) 148*> The maximum over the NRHS solution vectors of the ratios: 149*> RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR ) 150*> RESLTS(2) = BERR / ( (n+1)*EPS + (*) ) 151*> \endverbatim 152* 153* Authors: 154* ======== 155* 156*> \author Univ. of Tennessee 157*> \author Univ. of California Berkeley 158*> \author Univ. of Colorado Denver 159*> \author NAG Ltd. 160* 161*> \date November 2011 162* 163*> \ingroup complex16_lin 164* 165* ===================================================================== 166 SUBROUTINE ZGET07( TRANS, N, NRHS, A, LDA, B, LDB, X, LDX, XACT, 167 $ LDXACT, FERR, CHKFERR, BERR, RESLTS ) 168* 169* -- LAPACK test routine (version 3.4.0) -- 170* -- LAPACK is a software package provided by Univ. of Tennessee, -- 171* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 172* November 2011 173* 174* .. Scalar Arguments .. 175 CHARACTER TRANS 176 LOGICAL CHKFERR 177 INTEGER LDA, LDB, LDX, LDXACT, N, NRHS 178* .. 179* .. Array Arguments .. 180 DOUBLE PRECISION BERR( * ), FERR( * ), RESLTS( * ) 181 COMPLEX*16 A( LDA, * ), B( LDB, * ), X( LDX, * ), 182 $ XACT( LDXACT, * ) 183* .. 184* 185* ===================================================================== 186* 187* .. Parameters .. 188 DOUBLE PRECISION ZERO, ONE 189 PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) 190* .. 191* .. Local Scalars .. 192 LOGICAL NOTRAN 193 INTEGER I, IMAX, J, K 194 DOUBLE PRECISION AXBI, DIFF, EPS, ERRBND, OVFL, TMP, UNFL, XNORM 195 COMPLEX*16 ZDUM 196* .. 197* .. External Functions .. 198 LOGICAL LSAME 199 INTEGER IZAMAX 200 DOUBLE PRECISION DLAMCH 201 EXTERNAL LSAME, IZAMAX, DLAMCH 202* .. 203* .. Intrinsic Functions .. 204 INTRINSIC ABS, DBLE, DIMAG, MAX, MIN 205* .. 206* .. Statement Functions .. 207 DOUBLE PRECISION CABS1 208* .. 209* .. Statement Function definitions .. 210 CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) ) 211* .. 212* .. Executable Statements .. 213* 214* Quick exit if N = 0 or NRHS = 0. 215* 216 IF( N.LE.0 .OR. NRHS.LE.0 ) THEN 217 RESLTS( 1 ) = ZERO 218 RESLTS( 2 ) = ZERO 219 RETURN 220 END IF 221* 222 EPS = DLAMCH( 'Epsilon' ) 223 UNFL = DLAMCH( 'Safe minimum' ) 224 OVFL = ONE / UNFL 225 NOTRAN = LSAME( TRANS, 'N' ) 226* 227* Test 1: Compute the maximum of 228* norm(X - XACT) / ( norm(X) * FERR ) 229* over all the vectors X and XACT using the infinity-norm. 230* 231 ERRBND = ZERO 232 IF( CHKFERR ) THEN 233 DO 30 J = 1, NRHS 234 IMAX = IZAMAX( N, X( 1, J ), 1 ) 235 XNORM = MAX( CABS1( X( IMAX, J ) ), UNFL ) 236 DIFF = ZERO 237 DO 10 I = 1, N 238 DIFF = MAX( DIFF, CABS1( X( I, J )-XACT( I, J ) ) ) 239 10 CONTINUE 240* 241 IF( XNORM.GT.ONE ) THEN 242 GO TO 20 243 ELSE IF( DIFF.LE.OVFL*XNORM ) THEN 244 GO TO 20 245 ELSE 246 ERRBND = ONE / EPS 247 GO TO 30 248 END IF 249* 250 20 CONTINUE 251 IF( DIFF / XNORM.LE.FERR( J ) ) THEN 252 ERRBND = MAX( ERRBND, ( DIFF / XNORM ) / FERR( J ) ) 253 ELSE 254 ERRBND = ONE / EPS 255 END IF 256 30 CONTINUE 257 END IF 258 RESLTS( 1 ) = ERRBND 259* 260* Test 2: Compute the maximum of BERR / ( (n+1)*EPS + (*) ), where 261* (*) = (n+1)*UNFL / (min_i (abs(op(A))*abs(X) +abs(b))_i ) 262* 263 DO 70 K = 1, NRHS 264 DO 60 I = 1, N 265 TMP = CABS1( B( I, K ) ) 266 IF( NOTRAN ) THEN 267 DO 40 J = 1, N 268 TMP = TMP + CABS1( A( I, J ) )*CABS1( X( J, K ) ) 269 40 CONTINUE 270 ELSE 271 DO 50 J = 1, N 272 TMP = TMP + CABS1( A( J, I ) )*CABS1( X( J, K ) ) 273 50 CONTINUE 274 END IF 275 IF( I.EQ.1 ) THEN 276 AXBI = TMP 277 ELSE 278 AXBI = MIN( AXBI, TMP ) 279 END IF 280 60 CONTINUE 281 TMP = BERR( K ) / ( ( N+1 )*EPS+( N+1 )*UNFL / 282 $ MAX( AXBI, ( N+1 )*UNFL ) ) 283 IF( K.EQ.1 ) THEN 284 RESLTS( 2 ) = TMP 285 ELSE 286 RESLTS( 2 ) = MAX( RESLTS( 2 ), TMP ) 287 END IF 288 70 CONTINUE 289* 290 RETURN 291* 292* End of ZGET07 293* 294 END 295