numeric-linalg
Educational material on the SciPy implementation of numerical linear algebra algorithms
| Name | Size | Mode | |
| .. | |||
| lapack/TESTING/LIN/dget07.f | 8385B | -rw-r--r-- |
001 002 003 004 005 006 007 008 009 010 011 012 013 014 015 016 017 018 019 020 021 022 023 024 025 026 027 028 029 030 031 032 033 034 035 036 037 038 039 040 041 042 043 044 045 046 047 048 049 050 051 052 053 054 055 056 057 058 059 060 061 062 063 064 065 066 067 068 069 070 071 072 073 074 075 076 077 078 079 080 081 082 083 084 085 086 087 088 089 090 091 092 093 094 095 096 097 098 099 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282
*> \brief \b DGET07 * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE DGET07( TRANS, N, NRHS, A, LDA, B, LDB, X, LDX, XACT, * LDXACT, FERR, CHKFERR, BERR, RESLTS ) * * .. Scalar Arguments .. * CHARACTER TRANS * LOGICAL CHKFERR * INTEGER LDA, LDB, LDX, LDXACT, N, NRHS * .. * .. Array Arguments .. * DOUBLE PRECISION A( LDA, * ), B( LDB, * ), BERR( * ), FERR( * ), * $ RESLTS( * ), X( LDX, * ), XACT( LDXACT, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DGET07 tests the error bounds from iterative refinement for the *> computed solution to a system of equations op(A)*X = B, where A is a *> general n by n matrix and op(A) = A or A**T, depending on TRANS. *> *> RESLTS(1) = test of the error bound *> = norm(X - XACT) / ( norm(X) * FERR ) *> *> A large value is returned if this ratio is not less than one. *> *> RESLTS(2) = residual from the iterative refinement routine *> = the maximum of BERR / ( (n+1)*EPS + (*) ), where *> (*) = (n+1)*UNFL / (min_i (abs(op(A))*abs(X) +abs(b))_i ) *> \endverbatim * * Arguments: * ========== * *> \param[in] TRANS *> \verbatim *> TRANS is CHARACTER*1 *> Specifies the form of the system of equations. *> = 'N': A * X = B (No transpose) *> = 'T': A**T * X = B (Transpose) *> = 'C': A**H * X = B (Conjugate transpose = Transpose) *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The number of rows of the matrices X and XACT. N >= 0. *> \endverbatim *> *> \param[in] NRHS *> \verbatim *> NRHS is INTEGER *> The number of columns of the matrices X and XACT. NRHS >= 0. *> \endverbatim *> *> \param[in] A *> \verbatim *> A is DOUBLE PRECISION array, dimension (LDA,N) *> The original n by n matrix A. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. LDA >= max(1,N). *> \endverbatim *> *> \param[in] B *> \verbatim *> B is DOUBLE PRECISION array, dimension (LDB,NRHS) *> The right hand side vectors for the system of linear *> equations. *> \endverbatim *> *> \param[in] LDB *> \verbatim *> LDB is INTEGER *> The leading dimension of the array B. LDB >= max(1,N). *> \endverbatim *> *> \param[in] X *> \verbatim *> X is DOUBLE PRECISION array, dimension (LDX,NRHS) *> The computed solution vectors. Each vector is stored as a *> column of the matrix X. *> \endverbatim *> *> \param[in] LDX *> \verbatim *> LDX is INTEGER *> The leading dimension of the array X. LDX >= max(1,N). *> \endverbatim *> *> \param[in] XACT *> \verbatim *> XACT is DOUBLE PRECISION array, dimension (LDX,NRHS) *> The exact solution vectors. Each vector is stored as a *> column of the matrix XACT. *> \endverbatim *> *> \param[in] LDXACT *> \verbatim *> LDXACT is INTEGER *> The leading dimension of the array XACT. LDXACT >= max(1,N). *> \endverbatim *> *> \param[in] FERR *> \verbatim *> FERR is DOUBLE PRECISION array, dimension (NRHS) *> The estimated forward error bounds for each solution vector *> X. If XTRUE is the true solution, FERR bounds the magnitude *> of the largest entry in (X - XTRUE) divided by the magnitude *> of the largest entry in X. *> \endverbatim *> *> \param[in] CHKFERR *> \verbatim *> CHKFERR is LOGICAL *> Set to .TRUE. to check FERR, .FALSE. not to check FERR. *> When the test system is ill-conditioned, the "true" *> solution in XACT may be incorrect. *> \endverbatim *> *> \param[in] BERR *> \verbatim *> BERR is DOUBLE PRECISION array, dimension (NRHS) *> The componentwise relative backward error of each solution *> vector (i.e., the smallest relative change in any entry of A *> or B that makes X an exact solution). *> \endverbatim *> *> \param[out] RESLTS *> \verbatim *> RESLTS is DOUBLE PRECISION array, dimension (2) *> The maximum over the NRHS solution vectors of the ratios: *> RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR ) *> RESLTS(2) = BERR / ( (n+1)*EPS + (*) ) *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \ingroup double_lin * * ===================================================================== SUBROUTINE DGET07( TRANS, N, NRHS, A, LDA, B, LDB, X, LDX, XACT, $ LDXACT, FERR, CHKFERR, BERR, RESLTS ) * * -- LAPACK test routine -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * * .. Scalar Arguments .. CHARACTER TRANS LOGICAL CHKFERR INTEGER LDA, LDB, LDX, LDXACT, N, NRHS * .. * .. Array Arguments .. DOUBLE PRECISION A( LDA, * ), B( LDB, * ), BERR( * ), FERR( * ), $ RESLTS( * ), X( LDX, * ), XACT( LDXACT, * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO, ONE PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) * .. * .. Local Scalars .. LOGICAL NOTRAN INTEGER I, IMAX, J, K DOUBLE PRECISION AXBI, DIFF, EPS, ERRBND, OVFL, TMP, UNFL, XNORM * .. * .. External Functions .. LOGICAL LSAME INTEGER IDAMAX DOUBLE PRECISION DLAMCH EXTERNAL LSAME, IDAMAX, DLAMCH * .. * .. Intrinsic Functions .. INTRINSIC ABS, MAX, MIN * .. * .. Executable Statements .. * * Quick exit if N = 0 or NRHS = 0. * IF( N.LE.0 .OR. NRHS.LE.0 ) THEN RESLTS( 1 ) = ZERO RESLTS( 2 ) = ZERO RETURN END IF * EPS = DLAMCH( 'Epsilon' ) UNFL = DLAMCH( 'Safe minimum' ) OVFL = ONE / UNFL NOTRAN = LSAME( TRANS, 'N' ) * * Test 1: Compute the maximum of * norm(X - XACT) / ( norm(X) * FERR ) * over all the vectors X and XACT using the infinity-norm. * ERRBND = ZERO IF( CHKFERR ) THEN DO 30 J = 1, NRHS IMAX = IDAMAX( N, X( 1, J ), 1 ) XNORM = MAX( ABS( X( IMAX, J ) ), UNFL ) DIFF = ZERO DO 10 I = 1, N DIFF = MAX( DIFF, ABS( X( I, J )-XACT( I, J ) ) ) 10 CONTINUE * IF( XNORM.GT.ONE ) THEN GO TO 20 ELSE IF( DIFF.LE.OVFL*XNORM ) THEN GO TO 20 ELSE ERRBND = ONE / EPS GO TO 30 END IF * 20 CONTINUE IF( DIFF / XNORM.LE.FERR( J ) ) THEN ERRBND = MAX( ERRBND, ( DIFF / XNORM ) / FERR( J ) ) ELSE ERRBND = ONE / EPS END IF 30 CONTINUE END IF RESLTS( 1 ) = ERRBND * * Test 2: Compute the maximum of BERR / ( (n+1)*EPS + (*) ), where * (*) = (n+1)*UNFL / (min_i (abs(op(A))*abs(X) +abs(b))_i ) * DO 70 K = 1, NRHS DO 60 I = 1, N TMP = ABS( B( I, K ) ) IF( NOTRAN ) THEN DO 40 J = 1, N TMP = TMP + ABS( A( I, J ) )*ABS( X( J, K ) ) 40 CONTINUE ELSE DO 50 J = 1, N TMP = TMP + ABS( A( J, I ) )*ABS( X( J, K ) ) 50 CONTINUE END IF IF( I.EQ.1 ) THEN AXBI = TMP ELSE AXBI = MIN( AXBI, TMP ) END IF 60 CONTINUE TMP = BERR( K ) / ( ( N+1 )*EPS+( N+1 )*UNFL / $ MAX( AXBI, ( N+1 )*UNFL ) ) IF( K.EQ.1 ) THEN RESLTS( 2 ) = TMP ELSE RESLTS( 2 ) = MAX( RESLTS( 2 ), TMP ) END IF 70 CONTINUE * RETURN * * End of DGET07 * END