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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b CGET07 00002 * 00003 * =========== DOCUMENTATION =========== 00004 * 00005 * Online html documentation available at 00006 * http://www.netlib.org/lapack/explore-html/ 00007 * 00008 * Definition: 00009 * =========== 00010 * 00011 * SUBROUTINE CGET07( TRANS, N, NRHS, A, LDA, B, LDB, X, LDX, XACT, 00012 * LDXACT, FERR, CHKFERR, BERR, RESLTS ) 00013 * 00014 * .. Scalar Arguments .. 00015 * CHARACTER TRANS 00016 * LOGICAL CHKFERR 00017 * INTEGER LDA, LDB, LDX, LDXACT, N, NRHS 00018 * .. 00019 * .. Array Arguments .. 00020 * REAL BERR( * ), FERR( * ), RESLTS( * ) 00021 * COMPLEX A( LDA, * ), B( LDB, * ), X( LDX, * ), 00022 * $ XACT( LDXACT, * ) 00023 * .. 00024 * 00025 * 00026 *> \par Purpose: 00027 * ============= 00028 *> 00029 *> \verbatim 00030 *> 00031 *> CGET07 tests the error bounds from iterative refinement for the 00032 *> computed solution to a system of equations op(A)*X = B, where A is a 00033 *> general n by n matrix and op(A) = A or A**T, depending on TRANS. 00034 *> 00035 *> RESLTS(1) = test of the error bound 00036 *> = norm(X - XACT) / ( norm(X) * FERR ) 00037 *> 00038 *> A large value is returned if this ratio is not less than one. 00039 *> 00040 *> RESLTS(2) = residual from the iterative refinement routine 00041 *> = the maximum of BERR / ( (n+1)*EPS + (*) ), where 00042 *> (*) = (n+1)*UNFL / (min_i (abs(op(A))*abs(X) +abs(b))_i ) 00043 *> \endverbatim 00044 * 00045 * Arguments: 00046 * ========== 00047 * 00048 *> \param[in] TRANS 00049 *> \verbatim 00050 *> TRANS is CHARACTER*1 00051 *> Specifies the form of the system of equations. 00052 *> = 'N': A * X = B (No transpose) 00053 *> = 'T': A**T * X = B (Transpose) 00054 *> = 'C': A**H * X = B (Conjugate transpose = Transpose) 00055 *> \endverbatim 00056 *> 00057 *> \param[in] N 00058 *> \verbatim 00059 *> N is INTEGER 00060 *> The number of rows of the matrices X and XACT. N >= 0. 00061 *> \endverbatim 00062 *> 00063 *> \param[in] NRHS 00064 *> \verbatim 00065 *> NRHS is INTEGER 00066 *> The number of columns of the matrices X and XACT. NRHS >= 0. 00067 *> \endverbatim 00068 *> 00069 *> \param[in] A 00070 *> \verbatim 00071 *> A is COMPLEX array, dimension (LDA,N) 00072 *> The original n by n matrix A. 00073 *> \endverbatim 00074 *> 00075 *> \param[in] LDA 00076 *> \verbatim 00077 *> LDA is INTEGER 00078 *> The leading dimension of the array A. LDA >= max(1,N). 00079 *> \endverbatim 00080 *> 00081 *> \param[in] B 00082 *> \verbatim 00083 *> B is COMPLEX array, dimension (LDB,NRHS) 00084 *> The right hand side vectors for the system of linear 00085 *> equations. 00086 *> \endverbatim 00087 *> 00088 *> \param[in] LDB 00089 *> \verbatim 00090 *> LDB is INTEGER 00091 *> The leading dimension of the array B. LDB >= max(1,N). 00092 *> \endverbatim 00093 *> 00094 *> \param[in] X 00095 *> \verbatim 00096 *> X is COMPLEX array, dimension (LDX,NRHS) 00097 *> The computed solution vectors. Each vector is stored as a 00098 *> column of the matrix X. 00099 *> \endverbatim 00100 *> 00101 *> \param[in] LDX 00102 *> \verbatim 00103 *> LDX is INTEGER 00104 *> The leading dimension of the array X. LDX >= max(1,N). 00105 *> \endverbatim 00106 *> 00107 *> \param[in] XACT 00108 *> \verbatim 00109 *> XACT is COMPLEX array, dimension (LDX,NRHS) 00110 *> The exact solution vectors. Each vector is stored as a 00111 *> column of the matrix XACT. 00112 *> \endverbatim 00113 *> 00114 *> \param[in] LDXACT 00115 *> \verbatim 00116 *> LDXACT is INTEGER 00117 *> The leading dimension of the array XACT. LDXACT >= max(1,N). 00118 *> \endverbatim 00119 *> 00120 *> \param[in] FERR 00121 *> \verbatim 00122 *> FERR is REAL array, dimension (NRHS) 00123 *> The estimated forward error bounds for each solution vector 00124 *> X. If XTRUE is the true solution, FERR bounds the magnitude 00125 *> of the largest entry in (X - XTRUE) divided by the magnitude 00126 *> of the largest entry in X. 00127 *> \endverbatim 00128 *> 00129 *> \param[in] CHKFERR 00130 *> \verbatim 00131 *> CHKFERR is LOGICAL 00132 *> Set to .TRUE. to check FERR, .FALSE. not to check FERR. 00133 *> When the test system is ill-conditioned, the "true" 00134 *> solution in XACT may be incorrect. 00135 *> \endverbatim 00136 *> 00137 *> \param[in] BERR 00138 *> \verbatim 00139 *> BERR is REAL array, dimension (NRHS) 00140 *> The componentwise relative backward error of each solution 00141 *> vector (i.e., the smallest relative change in any entry of A 00142 *> or B that makes X an exact solution). 00143 *> \endverbatim 00144 *> 00145 *> \param[out] RESLTS 00146 *> \verbatim 00147 *> RESLTS is REAL array, dimension (2) 00148 *> The maximum over the NRHS solution vectors of the ratios: 00149 *> RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR ) 00150 *> RESLTS(2) = BERR / ( (n+1)*EPS + (*) ) 00151 *> \endverbatim 00152 * 00153 * Authors: 00154 * ======== 00155 * 00156 *> \author Univ. of Tennessee 00157 *> \author Univ. of California Berkeley 00158 *> \author Univ. of Colorado Denver 00159 *> \author NAG Ltd. 00160 * 00161 *> \date November 2011 00162 * 00163 *> \ingroup complex_lin 00164 * 00165 * ===================================================================== 00166 SUBROUTINE CGET07( TRANS, N, NRHS, A, LDA, B, LDB, X, LDX, XACT, 00167 $ LDXACT, FERR, CHKFERR, BERR, RESLTS ) 00168 * 00169 * -- LAPACK test routine (version 3.4.0) -- 00170 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00171 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00172 * November 2011 00173 * 00174 * .. Scalar Arguments .. 00175 CHARACTER TRANS 00176 LOGICAL CHKFERR 00177 INTEGER LDA, LDB, LDX, LDXACT, N, NRHS 00178 * .. 00179 * .. Array Arguments .. 00180 REAL BERR( * ), FERR( * ), RESLTS( * ) 00181 COMPLEX A( LDA, * ), B( LDB, * ), X( LDX, * ), 00182 $ XACT( LDXACT, * ) 00183 * .. 00184 * 00185 * ===================================================================== 00186 * 00187 * .. Parameters .. 00188 REAL ZERO, ONE 00189 PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 ) 00190 * .. 00191 * .. Local Scalars .. 00192 LOGICAL NOTRAN 00193 INTEGER I, IMAX, J, K 00194 REAL AXBI, DIFF, EPS, ERRBND, OVFL, TMP, UNFL, XNORM 00195 COMPLEX ZDUM 00196 * .. 00197 * .. External Functions .. 00198 LOGICAL LSAME 00199 INTEGER ICAMAX 00200 REAL SLAMCH 00201 EXTERNAL LSAME, ICAMAX, SLAMCH 00202 * .. 00203 * .. Intrinsic Functions .. 00204 INTRINSIC ABS, AIMAG, MAX, MIN, REAL 00205 * .. 00206 * .. Statement Functions .. 00207 REAL CABS1 00208 * .. 00209 * .. Statement Function definitions .. 00210 CABS1( ZDUM ) = ABS( REAL( ZDUM ) ) + ABS( AIMAG( ZDUM ) ) 00211 * .. 00212 * .. Executable Statements .. 00213 * 00214 * Quick exit if N = 0 or NRHS = 0. 00215 * 00216 IF( N.LE.0 .OR. NRHS.LE.0 ) THEN 00217 RESLTS( 1 ) = ZERO 00218 RESLTS( 2 ) = ZERO 00219 RETURN 00220 END IF 00221 * 00222 EPS = SLAMCH( 'Epsilon' ) 00223 UNFL = SLAMCH( 'Safe minimum' ) 00224 OVFL = ONE / UNFL 00225 NOTRAN = LSAME( TRANS, 'N' ) 00226 * 00227 * Test 1: Compute the maximum of 00228 * norm(X - XACT) / ( norm(X) * FERR ) 00229 * over all the vectors X and XACT using the infinity-norm. 00230 * 00231 ERRBND = ZERO 00232 IF( CHKFERR ) THEN 00233 DO 30 J = 1, NRHS 00234 IMAX = ICAMAX( N, X( 1, J ), 1 ) 00235 XNORM = MAX( CABS1( X( IMAX, J ) ), UNFL ) 00236 DIFF = ZERO 00237 DO 10 I = 1, N 00238 DIFF = MAX( DIFF, CABS1( X( I, J )-XACT( I, J ) ) ) 00239 10 CONTINUE 00240 * 00241 IF( XNORM.GT.ONE ) THEN 00242 GO TO 20 00243 ELSE IF( DIFF.LE.OVFL*XNORM ) THEN 00244 GO TO 20 00245 ELSE 00246 ERRBND = ONE / EPS 00247 GO TO 30 00248 END IF 00249 * 00250 20 CONTINUE 00251 IF( DIFF / XNORM.LE.FERR( J ) ) THEN 00252 ERRBND = MAX( ERRBND, ( DIFF / XNORM ) / FERR( J ) ) 00253 ELSE 00254 ERRBND = ONE / EPS 00255 END IF 00256 30 CONTINUE 00257 END IF 00258 RESLTS( 1 ) = ERRBND 00259 * 00260 * Test 2: Compute the maximum of BERR / ( (n+1)*EPS + (*) ), where 00261 * (*) = (n+1)*UNFL / (min_i (abs(op(A))*abs(X) +abs(b))_i ) 00262 * 00263 DO 70 K = 1, NRHS 00264 DO 60 I = 1, N 00265 TMP = CABS1( B( I, K ) ) 00266 IF( NOTRAN ) THEN 00267 DO 40 J = 1, N 00268 TMP = TMP + CABS1( A( I, J ) )*CABS1( X( J, K ) ) 00269 40 CONTINUE 00270 ELSE 00271 DO 50 J = 1, N 00272 TMP = TMP + CABS1( A( J, I ) )*CABS1( X( J, K ) ) 00273 50 CONTINUE 00274 END IF 00275 IF( I.EQ.1 ) THEN 00276 AXBI = TMP 00277 ELSE 00278 AXBI = MIN( AXBI, TMP ) 00279 END IF 00280 60 CONTINUE 00281 TMP = BERR( K ) / ( ( N+1 )*EPS+( N+1 )*UNFL / 00282 $ MAX( AXBI, ( N+1 )*UNFL ) ) 00283 IF( K.EQ.1 ) THEN 00284 RESLTS( 2 ) = TMP 00285 ELSE 00286 RESLTS( 2 ) = MAX( RESLTS( 2 ), TMP ) 00287 END IF 00288 70 CONTINUE 00289 * 00290 RETURN 00291 * 00292 * End of CGET07 00293 * 00294 END