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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b SEBCHVXX 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 SEBCHVXX( THRESH, PATH ) 00012 * 00013 * .. Scalar Arguments .. 00014 * REAL THRESH 00015 * CHARACTER*3 PATH 00016 * .. 00017 * 00018 * 00019 *> \par Purpose: 00020 * ============= 00021 *> 00022 *> \verbatim 00023 *> 00024 *> SEBCHVXX will run S**SVXX on a series of Hilbert matrices and then 00025 *> compare the error bounds returned by SGESVXX to see if the returned 00026 *> answer indeed falls within those bounds. 00027 *> 00028 *> Eight test ratios will be computed. The tests will pass if they are .LT. 00029 *> THRESH. There are two cases that are determined by 1 / (SQRT( N ) * EPS). 00030 *> If that value is .LE. to the component wise reciprocal condition number, 00031 *> it uses the guaranteed case, other wise it uses the unguaranteed case. 00032 *> 00033 *> Test ratios: 00034 *> Let Xc be X_computed and Xt be X_truth. 00035 *> The norm used is the infinity norm. 00036 *> 00037 *> Let A be the guaranteed case and B be the unguaranteed case. 00038 *> 00039 *> 1. Normwise guaranteed forward error bound. 00040 *> A: norm ( abs( Xc - Xt ) / norm ( Xt ) .LE. ERRBND( *, nwise_i, bnd_i ) and 00041 *> ERRBND( *, nwise_i, bnd_i ) .LE. MAX(SQRT(N),10) * EPS. 00042 *> If these conditions are met, the test ratio is set to be 00043 *> ERRBND( *, nwise_i, bnd_i ) / MAX(SQRT(N), 10). Otherwise it is 1/EPS. 00044 *> B: For this case, SGESVXX should just return 1. If it is less than 00045 *> one, treat it the same as in 1A. Otherwise it fails. (Set test 00046 *> ratio to ERRBND( *, nwise_i, bnd_i ) * THRESH?) 00047 *> 00048 *> 2. Componentwise guaranteed forward error bound. 00049 *> A: norm ( abs( Xc(j) - Xt(j) ) ) / norm (Xt(j)) .LE. ERRBND( *, cwise_i, bnd_i ) 00050 *> for all j .AND. ERRBND( *, cwise_i, bnd_i ) .LE. MAX(SQRT(N), 10) * EPS. 00051 *> If these conditions are met, the test ratio is set to be 00052 *> ERRBND( *, cwise_i, bnd_i ) / MAX(SQRT(N), 10). Otherwise it is 1/EPS. 00053 *> B: Same as normwise test ratio. 00054 *> 00055 *> 3. Backwards error. 00056 *> A: The test ratio is set to BERR/EPS. 00057 *> B: Same test ratio. 00058 *> 00059 *> 4. Reciprocal condition number. 00060 *> A: A condition number is computed with Xt and compared with the one 00061 *> returned from SGESVXX. Let RCONDc be the RCOND returned by SGESVXX 00062 *> and RCONDt be the RCOND from the truth value. Test ratio is set to 00063 *> MAX(RCONDc/RCONDt, RCONDt/RCONDc). 00064 *> B: Test ratio is set to 1 / (EPS * RCONDc). 00065 *> 00066 *> 5. Reciprocal normwise condition number. 00067 *> A: The test ratio is set to 00068 *> MAX(ERRBND( *, nwise_i, cond_i ) / NCOND, NCOND / ERRBND( *, nwise_i, cond_i )). 00069 *> B: Test ratio is set to 1 / (EPS * ERRBND( *, nwise_i, cond_i )). 00070 *> 00071 *> 7. Reciprocal componentwise condition number. 00072 *> A: Test ratio is set to 00073 *> MAX(ERRBND( *, cwise_i, cond_i ) / CCOND, CCOND / ERRBND( *, cwise_i, cond_i )). 00074 *> B: Test ratio is set to 1 / (EPS * ERRBND( *, cwise_i, cond_i )). 00075 *> 00076 *> .. Parameters .. 00077 *> NMAX is determined by the largest number in the inverse of the Hilbert 00078 *> matrix. Precision is exhausted when the largest entry in it is greater 00079 *> than 2 to the power of the number of bits in the fraction of the data 00080 *> type used plus one, which is 24 for single precision. 00081 *> NMAX should be 6 for single and 11 for double. 00082 *> \endverbatim 00083 * 00084 * Authors: 00085 * ======== 00086 * 00087 *> \author Univ. of Tennessee 00088 *> \author Univ. of California Berkeley 00089 *> \author Univ. of Colorado Denver 00090 *> \author NAG Ltd. 00091 * 00092 *> \date November 2011 00093 * 00094 *> \ingroup single_lin 00095 * 00096 * ===================================================================== 00097 SUBROUTINE SEBCHVXX( THRESH, PATH ) 00098 IMPLICIT NONE 00099 * .. Scalar Arguments .. 00100 REAL THRESH 00101 CHARACTER*3 PATH 00102 00103 INTEGER NMAX, NPARAMS, NERRBND, NTESTS, KL, KU 00104 PARAMETER (NMAX = 6, NPARAMS = 2, NERRBND = 3, 00105 $ NTESTS = 6) 00106 00107 * .. Local Scalars .. 00108 INTEGER N, NRHS, INFO, I ,J, k, NFAIL, LDA, LDAB, 00109 $ LDAFB, N_AUX_TESTS 00110 CHARACTER FACT, TRANS, UPLO, EQUED 00111 CHARACTER*2 C2 00112 CHARACTER(3) NGUAR, CGUAR 00113 LOGICAL printed_guide 00114 REAL NCOND, CCOND, M, NORMDIF, NORMT, RCOND, 00115 $ RNORM, RINORM, SUMR, SUMRI, EPS, 00116 $ BERR(NMAX), RPVGRW, ORCOND, 00117 $ CWISE_ERR, NWISE_ERR, CWISE_BND, NWISE_BND, 00118 $ CWISE_RCOND, NWISE_RCOND, 00119 $ CONDTHRESH, ERRTHRESH 00120 00121 * .. Local Arrays .. 00122 REAL TSTRAT(NTESTS), RINV(NMAX), PARAMS(NPARAMS), 00123 $ A(NMAX, NMAX), ACOPY(NMAX, NMAX), 00124 $ INVHILB(NMAX, NMAX), R(NMAX), C(NMAX), S(NMAX), 00125 $ WORK(NMAX * 5), B(NMAX, NMAX), X(NMAX, NMAX), 00126 $ DIFF(NMAX, NMAX), AF(NMAX, NMAX), 00127 $ AB( (NMAX-1)+(NMAX-1)+1, NMAX ), 00128 $ ABCOPY( (NMAX-1)+(NMAX-1)+1, NMAX ), 00129 $ AFB( 2*(NMAX-1)+(NMAX-1)+1, NMAX ), 00130 $ ERRBND_N(NMAX*3), ERRBND_C(NMAX*3) 00131 INTEGER IWORK(NMAX), IPIV(NMAX) 00132 00133 * .. External Functions .. 00134 REAL SLAMCH 00135 00136 * .. External Subroutines .. 00137 EXTERNAL SLAHILB, SGESVXX, SSYSVXX, SPOSVXX, SGBSVXX, 00138 $ SLACPY, LSAMEN 00139 LOGICAL LSAMEN 00140 00141 * .. Intrinsic Functions .. 00142 INTRINSIC SQRT, MAX, ABS 00143 00144 * .. Parameters .. 00145 INTEGER NWISE_I, CWISE_I 00146 PARAMETER (NWISE_I = 1, CWISE_I = 1) 00147 INTEGER BND_I, COND_I 00148 PARAMETER (BND_I = 2, COND_I = 3) 00149 00150 * Create the loop to test out the Hilbert matrices 00151 00152 FACT = 'E' 00153 UPLO = 'U' 00154 TRANS = 'N' 00155 EQUED = 'N' 00156 EPS = SLAMCH('Epsilon') 00157 NFAIL = 0 00158 N_AUX_TESTS = 0 00159 LDA = NMAX 00160 LDAB = (NMAX-1)+(NMAX-1)+1 00161 LDAFB = 2*(NMAX-1)+(NMAX-1)+1 00162 C2 = PATH( 2: 3 ) 00163 00164 * Main loop to test the different Hilbert Matrices. 00165 00166 printed_guide = .false. 00167 00168 DO N = 1 , NMAX 00169 PARAMS(1) = -1 00170 PARAMS(2) = -1 00171 00172 KL = N-1 00173 KU = N-1 00174 NRHS = n 00175 M = MAX(SQRT(REAL(N)), 10.0) 00176 00177 * Generate the Hilbert matrix, its inverse, and the 00178 * right hand side, all scaled by the LCM(1,..,2N-1). 00179 CALL SLAHILB(N, N, A, LDA, INVHILB, LDA, B, LDA, WORK, INFO) 00180 00181 * Copy A into ACOPY. 00182 CALL SLACPY('ALL', N, N, A, NMAX, ACOPY, NMAX) 00183 00184 * Store A in band format for GB tests 00185 DO J = 1, N 00186 DO I = 1, KL+KU+1 00187 AB( I, J ) = 0.0E+0 00188 END DO 00189 END DO 00190 DO J = 1, N 00191 DO I = MAX( 1, J-KU ), MIN( N, J+KL ) 00192 AB( KU+1+I-J, J ) = A( I, J ) 00193 END DO 00194 END DO 00195 00196 * Copy AB into ABCOPY. 00197 DO J = 1, N 00198 DO I = 1, KL+KU+1 00199 ABCOPY( I, J ) = 0.0E+0 00200 END DO 00201 END DO 00202 CALL SLACPY('ALL', KL+KU+1, N, AB, LDAB, ABCOPY, LDAB) 00203 00204 * Call S**SVXX with default PARAMS and N_ERR_BND = 3. 00205 IF ( LSAMEN( 2, C2, 'SY' ) ) THEN 00206 CALL SSYSVXX(FACT, UPLO, N, NRHS, ACOPY, LDA, AF, LDA, 00207 $ IPIV, EQUED, S, B, LDA, X, LDA, ORCOND, 00208 $ RPVGRW, BERR, NERRBND, ERRBND_N, ERRBND_C, NPARAMS, 00209 $ PARAMS, WORK, IWORK, INFO) 00210 ELSE IF ( LSAMEN( 2, C2, 'PO' ) ) THEN 00211 CALL SPOSVXX(FACT, UPLO, N, NRHS, ACOPY, LDA, AF, LDA, 00212 $ EQUED, S, B, LDA, X, LDA, ORCOND, 00213 $ RPVGRW, BERR, NERRBND, ERRBND_N, ERRBND_C, NPARAMS, 00214 $ PARAMS, WORK, IWORK, INFO) 00215 ELSE IF ( LSAMEN( 2, C2, 'GB' ) ) THEN 00216 CALL SGBSVXX(FACT, TRANS, N, KL, KU, NRHS, ABCOPY, 00217 $ LDAB, AFB, LDAFB, IPIV, EQUED, R, C, B, 00218 $ LDA, X, LDA, ORCOND, RPVGRW, BERR, NERRBND, 00219 $ ERRBND_N, ERRBND_C, NPARAMS, PARAMS, WORK, IWORK, 00220 $ INFO) 00221 ELSE 00222 CALL SGESVXX(FACT, TRANS, N, NRHS, ACOPY, LDA, AF, LDA, 00223 $ IPIV, EQUED, R, C, B, LDA, X, LDA, ORCOND, 00224 $ RPVGRW, BERR, NERRBND, ERRBND_N, ERRBND_C, NPARAMS, 00225 $ PARAMS, WORK, IWORK, INFO) 00226 END IF 00227 00228 N_AUX_TESTS = N_AUX_TESTS + 1 00229 IF (ORCOND .LT. EPS) THEN 00230 ! Either factorization failed or the matrix is flagged, and 1 <= 00231 ! INFO <= N+1. We don't decide based on rcond anymore. 00232 ! IF (INFO .EQ. 0 .OR. INFO .GT. N+1) THEN 00233 ! NFAIL = NFAIL + 1 00234 ! WRITE (*, FMT=8000) N, INFO, ORCOND, RCOND 00235 ! END IF 00236 ELSE 00237 ! Either everything succeeded (INFO == 0) or some solution failed 00238 ! to converge (INFO > N+1). 00239 IF (INFO .GT. 0 .AND. INFO .LE. N+1) THEN 00240 NFAIL = NFAIL + 1 00241 WRITE (*, FMT=8000) C2, N, INFO, ORCOND, RCOND 00242 END IF 00243 END IF 00244 00245 * Calculating the difference between S**SVXX's X and the true X. 00246 DO I = 1, N 00247 DO J = 1, NRHS 00248 DIFF( I, J ) = X( I, J ) - INVHILB( I, J ) 00249 END DO 00250 END DO 00251 00252 * Calculating the RCOND 00253 RNORM = 0 00254 RINORM = 0 00255 IF ( LSAMEN( 2, C2, 'PO' ) .OR. LSAMEN( 2, C2, 'SY' ) ) THEN 00256 DO I = 1, N 00257 SUMR = 0 00258 SUMRI = 0 00259 DO J = 1, N 00260 SUMR = SUMR + ABS(S(I) * A(I,J) * S(J)) 00261 SUMRI = SUMRI + ABS(INVHILB(I, J) / S(J) / S(I)) 00262 END DO 00263 RNORM = MAX(RNORM,SUMR) 00264 RINORM = MAX(RINORM,SUMRI) 00265 END DO 00266 ELSE IF ( LSAMEN( 2, C2, 'GE' ) .OR. LSAMEN( 2, C2, 'GB' ) ) 00267 $ THEN 00268 DO I = 1, N 00269 SUMR = 0 00270 SUMRI = 0 00271 DO J = 1, N 00272 SUMR = SUMR + ABS(R(I) * A(I,J) * C(J)) 00273 SUMRI = SUMRI + ABS(INVHILB(I, J) / R(J) / C(I)) 00274 END DO 00275 RNORM = MAX(RNORM,SUMR) 00276 RINORM = MAX(RINORM,SUMRI) 00277 END DO 00278 END IF 00279 00280 RNORM = RNORM / A(1, 1) 00281 RCOND = 1.0/(RNORM * RINORM) 00282 00283 * Calculating the R for normwise rcond. 00284 DO I = 1, N 00285 RINV(I) = 0.0 00286 END DO 00287 DO J = 1, N 00288 DO I = 1, N 00289 RINV(I) = RINV(I) + ABS(A(I,J)) 00290 END DO 00291 END DO 00292 00293 * Calculating the Normwise rcond. 00294 RINORM = 0.0 00295 DO I = 1, N 00296 SUMRI = 0.0 00297 DO J = 1, N 00298 SUMRI = SUMRI + ABS(INVHILB(I,J) * RINV(J)) 00299 END DO 00300 RINORM = MAX(RINORM, SUMRI) 00301 END DO 00302 00303 ! invhilb is the inverse *unscaled* Hilbert matrix, so scale its norm 00304 ! by 1/A(1,1) to make the scaling match A (the scaled Hilbert matrix) 00305 NCOND = A(1,1) / RINORM 00306 00307 CONDTHRESH = M * EPS 00308 ERRTHRESH = M * EPS 00309 00310 DO K = 1, NRHS 00311 NORMT = 0.0 00312 NORMDIF = 0.0 00313 CWISE_ERR = 0.0 00314 DO I = 1, N 00315 NORMT = MAX(ABS(INVHILB(I, K)), NORMT) 00316 NORMDIF = MAX(ABS(X(I,K) - INVHILB(I,K)), NORMDIF) 00317 IF (INVHILB(I,K) .NE. 0.0) THEN 00318 CWISE_ERR = MAX(ABS(X(I,K) - INVHILB(I,K)) 00319 $ /ABS(INVHILB(I,K)), CWISE_ERR) 00320 ELSE IF (X(I, K) .NE. 0.0) THEN 00321 CWISE_ERR = SLAMCH('OVERFLOW') 00322 END IF 00323 END DO 00324 IF (NORMT .NE. 0.0) THEN 00325 NWISE_ERR = NORMDIF / NORMT 00326 ELSE IF (NORMDIF .NE. 0.0) THEN 00327 NWISE_ERR = SLAMCH('OVERFLOW') 00328 ELSE 00329 NWISE_ERR = 0.0 00330 ENDIF 00331 00332 DO I = 1, N 00333 RINV(I) = 0.0 00334 END DO 00335 DO J = 1, N 00336 DO I = 1, N 00337 RINV(I) = RINV(I) + ABS(A(I, J) * INVHILB(J, K)) 00338 END DO 00339 END DO 00340 RINORM = 0.0 00341 DO I = 1, N 00342 SUMRI = 0.0 00343 DO J = 1, N 00344 SUMRI = SUMRI 00345 $ + ABS(INVHILB(I, J) * RINV(J) / INVHILB(I, K)) 00346 END DO 00347 RINORM = MAX(RINORM, SUMRI) 00348 END DO 00349 ! invhilb is the inverse *unscaled* Hilbert matrix, so scale its norm 00350 ! by 1/A(1,1) to make the scaling match A (the scaled Hilbert matrix) 00351 CCOND = A(1,1)/RINORM 00352 00353 ! Forward error bound tests 00354 NWISE_BND = ERRBND_N(K + (BND_I-1)*NRHS) 00355 CWISE_BND = ERRBND_C(K + (BND_I-1)*NRHS) 00356 NWISE_RCOND = ERRBND_N(K + (COND_I-1)*NRHS) 00357 CWISE_RCOND = ERRBND_C(K + (COND_I-1)*NRHS) 00358 ! write (*,*) 'nwise : ', n, k, ncond, nwise_rcond, 00359 ! $ condthresh, ncond.ge.condthresh 00360 ! write (*,*) 'nwise2: ', k, nwise_bnd, nwise_err, errthresh 00361 00362 IF (NCOND .GE. CONDTHRESH) THEN 00363 NGUAR = 'YES' 00364 IF (NWISE_BND .GT. ERRTHRESH) THEN 00365 TSTRAT(1) = 1/(2.0*EPS) 00366 ELSE 00367 00368 IF (NWISE_BND .NE. 0.0) THEN 00369 TSTRAT(1) = NWISE_ERR / NWISE_BND 00370 ELSE IF (NWISE_ERR .NE. 0.0) THEN 00371 TSTRAT(1) = 1/(16.0*EPS) 00372 ELSE 00373 TSTRAT(1) = 0.0 00374 END IF 00375 IF (TSTRAT(1) .GT. 1.0) THEN 00376 TSTRAT(1) = 1/(4.0*EPS) 00377 END IF 00378 END IF 00379 ELSE 00380 NGUAR = 'NO' 00381 IF (NWISE_BND .LT. 1.0) THEN 00382 TSTRAT(1) = 1/(8.0*EPS) 00383 ELSE 00384 TSTRAT(1) = 1.0 00385 END IF 00386 END IF 00387 ! write (*,*) 'cwise : ', n, k, ccond, cwise_rcond, 00388 ! $ condthresh, ccond.ge.condthresh 00389 ! write (*,*) 'cwise2: ', k, cwise_bnd, cwise_err, errthresh 00390 IF (CCOND .GE. CONDTHRESH) THEN 00391 CGUAR = 'YES' 00392 00393 IF (CWISE_BND .GT. ERRTHRESH) THEN 00394 TSTRAT(2) = 1/(2.0*EPS) 00395 ELSE 00396 IF (CWISE_BND .NE. 0.0) THEN 00397 TSTRAT(2) = CWISE_ERR / CWISE_BND 00398 ELSE IF (CWISE_ERR .NE. 0.0) THEN 00399 TSTRAT(2) = 1/(16.0*EPS) 00400 ELSE 00401 TSTRAT(2) = 0.0 00402 END IF 00403 IF (TSTRAT(2) .GT. 1.0) TSTRAT(2) = 1/(4.0*EPS) 00404 END IF 00405 ELSE 00406 CGUAR = 'NO' 00407 IF (CWISE_BND .LT. 1.0) THEN 00408 TSTRAT(2) = 1/(8.0*EPS) 00409 ELSE 00410 TSTRAT(2) = 1.0 00411 END IF 00412 END IF 00413 00414 ! Backwards error test 00415 TSTRAT(3) = BERR(K)/EPS 00416 00417 ! Condition number tests 00418 TSTRAT(4) = RCOND / ORCOND 00419 IF (RCOND .GE. CONDTHRESH .AND. TSTRAT(4) .LT. 1.0) 00420 $ TSTRAT(4) = 1.0 / TSTRAT(4) 00421 00422 TSTRAT(5) = NCOND / NWISE_RCOND 00423 IF (NCOND .GE. CONDTHRESH .AND. TSTRAT(5) .LT. 1.0) 00424 $ TSTRAT(5) = 1.0 / TSTRAT(5) 00425 00426 TSTRAT(6) = CCOND / NWISE_RCOND 00427 IF (CCOND .GE. CONDTHRESH .AND. TSTRAT(6) .LT. 1.0) 00428 $ TSTRAT(6) = 1.0 / TSTRAT(6) 00429 00430 DO I = 1, NTESTS 00431 IF (TSTRAT(I) .GT. THRESH) THEN 00432 IF (.NOT.PRINTED_GUIDE) THEN 00433 WRITE(*,*) 00434 WRITE( *, 9996) 1 00435 WRITE( *, 9995) 2 00436 WRITE( *, 9994) 3 00437 WRITE( *, 9993) 4 00438 WRITE( *, 9992) 5 00439 WRITE( *, 9991) 6 00440 WRITE( *, 9990) 7 00441 WRITE( *, 9989) 8 00442 WRITE(*,*) 00443 PRINTED_GUIDE = .TRUE. 00444 END IF 00445 WRITE( *, 9999) C2, N, K, NGUAR, CGUAR, I, TSTRAT(I) 00446 NFAIL = NFAIL + 1 00447 END IF 00448 END DO 00449 END DO 00450 00451 c$$$ WRITE(*,*) 00452 c$$$ WRITE(*,*) 'Normwise Error Bounds' 00453 c$$$ WRITE(*,*) 'Guaranteed error bound: ',ERRBND(NRHS,nwise_i,bnd_i) 00454 c$$$ WRITE(*,*) 'Reciprocal condition number: ',ERRBND(NRHS,nwise_i,cond_i) 00455 c$$$ WRITE(*,*) 'Raw error estimate: ',ERRBND(NRHS,nwise_i,rawbnd_i) 00456 c$$$ WRITE(*,*) 00457 c$$$ WRITE(*,*) 'Componentwise Error Bounds' 00458 c$$$ WRITE(*,*) 'Guaranteed error bound: ',ERRBND(NRHS,cwise_i,bnd_i) 00459 c$$$ WRITE(*,*) 'Reciprocal condition number: ',ERRBND(NRHS,cwise_i,cond_i) 00460 c$$$ WRITE(*,*) 'Raw error estimate: ',ERRBND(NRHS,cwise_i,rawbnd_i) 00461 c$$$ print *, 'Info: ', info 00462 c$$$ WRITE(*,*) 00463 * WRITE(*,*) 'TSTRAT: ',TSTRAT 00464 00465 END DO 00466 00467 WRITE(*,*) 00468 IF( NFAIL .GT. 0 ) THEN 00469 WRITE(*,9998) C2, NFAIL, NTESTS*N+N_AUX_TESTS 00470 ELSE 00471 WRITE(*,9997) C2 00472 END IF 00473 9999 FORMAT( ' S', A2, 'SVXX: N =', I2, ', RHS = ', I2, 00474 $ ', NWISE GUAR. = ', A, ', CWISE GUAR. = ', A, 00475 $ ' test(',I1,') =', G12.5 ) 00476 9998 FORMAT( ' S', A2, 'SVXX: ', I6, ' out of ', I6, 00477 $ ' tests failed to pass the threshold' ) 00478 9997 FORMAT( ' S', A2, 'SVXX passed the tests of error bounds' ) 00479 * Test ratios. 00480 9996 FORMAT( 3X, I2, ': Normwise guaranteed forward error', / 5X, 00481 $ 'Guaranteed case: if norm ( abs( Xc - Xt )', 00482 $ ' / norm ( Xt ) .LE. ERRBND( *, nwise_i, bnd_i ), then', 00483 $ / 5X, 00484 $ 'ERRBND( *, nwise_i, bnd_i ) .LE. MAX(SQRT(N), 10) * EPS') 00485 9995 FORMAT( 3X, I2, ': Componentwise guaranteed forward error' ) 00486 9994 FORMAT( 3X, I2, ': Backwards error' ) 00487 9993 FORMAT( 3X, I2, ': Reciprocal condition number' ) 00488 9992 FORMAT( 3X, I2, ': Reciprocal normwise condition number' ) 00489 9991 FORMAT( 3X, I2, ': Raw normwise error estimate' ) 00490 9990 FORMAT( 3X, I2, ': Reciprocal componentwise condition number' ) 00491 9989 FORMAT( 3X, I2, ': Raw componentwise error estimate' ) 00492 00493 8000 FORMAT( ' S', A2, 'SVXX: N =', I2, ', INFO = ', I3, 00494 $ ', ORCOND = ', G12.5, ', real RCOND = ', G12.5 ) 00495 00496 END