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LAPACK 3.3.0
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LAPACK 3.3.0
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00001 SUBROUTINE ZEBCHVXX( THRESH, PATH ) 00002 IMPLICIT NONE 00003 * .. Scalar Arguments .. 00004 DOUBLE PRECISION THRESH 00005 CHARACTER*3 PATH 00006 * 00007 * Purpose 00008 * ====== 00009 * 00010 * ZEBCHVXX will run Z**SVXX on a series of Hilbert matrices and then 00011 * compare the error bounds returned by Z**SVXX to see if the returned 00012 * answer indeed falls within those bounds. 00013 * 00014 * Eight test ratios will be computed. The tests will pass if they are .LT. 00015 * THRESH. There are two cases that are determined by 1 / (SQRT( N ) * EPS). 00016 * If that value is .LE. to the component wise reciprocal condition number, 00017 * it uses the guaranteed case, other wise it uses the unguaranteed case. 00018 * 00019 * Test ratios: 00020 * Let Xc be X_computed and Xt be X_truth. 00021 * The norm used is the infinity norm. 00022 00023 * Let A be the guaranteed case and B be the unguaranteed case. 00024 * 00025 * 1. Normwise guaranteed forward error bound. 00026 * A: norm ( abs( Xc - Xt ) / norm ( Xt ) .LE. ERRBND( *, nwise_i, bnd_i ) and 00027 * ERRBND( *, nwise_i, bnd_i ) .LE. MAX(SQRT(N),10) * EPS. 00028 * If these conditions are met, the test ratio is set to be 00029 * ERRBND( *, nwise_i, bnd_i ) / MAX(SQRT(N), 10). Otherwise it is 1/EPS. 00030 * B: For this case, CGESVXX should just return 1. If it is less than 00031 * one, treat it the same as in 1A. Otherwise it fails. (Set test 00032 * ratio to ERRBND( *, nwise_i, bnd_i ) * THRESH?) 00033 * 00034 * 2. Componentwise guaranteed forward error bound. 00035 * A: norm ( abs( Xc(j) - Xt(j) ) ) / norm (Xt(j)) .LE. ERRBND( *, cwise_i, bnd_i ) 00036 * for all j .AND. ERRBND( *, cwise_i, bnd_i ) .LE. MAX(SQRT(N), 10) * EPS. 00037 * If these conditions are met, the test ratio is set to be 00038 * ERRBND( *, cwise_i, bnd_i ) / MAX(SQRT(N), 10). Otherwise it is 1/EPS. 00039 * B: Same as normwise test ratio. 00040 * 00041 * 3. Backwards error. 00042 * A: The test ratio is set to BERR/EPS. 00043 * B: Same test ratio. 00044 * 00045 * 4. Reciprocal condition number. 00046 * A: A condition number is computed with Xt and compared with the one 00047 * returned from CGESVXX. Let RCONDc be the RCOND returned by CGESVXX 00048 * and RCONDt be the RCOND from the truth value. Test ratio is set to 00049 * MAX(RCONDc/RCONDt, RCONDt/RCONDc). 00050 * B: Test ratio is set to 1 / (EPS * RCONDc). 00051 * 00052 * 5. Reciprocal normwise condition number. 00053 * A: The test ratio is set to 00054 * MAX(ERRBND( *, nwise_i, cond_i ) / NCOND, NCOND / ERRBND( *, nwise_i, cond_i )). 00055 * B: Test ratio is set to 1 / (EPS * ERRBND( *, nwise_i, cond_i )). 00056 * 00057 * 6. Reciprocal componentwise condition number. 00058 * A: Test ratio is set to 00059 * MAX(ERRBND( *, cwise_i, cond_i ) / CCOND, CCOND / ERRBND( *, cwise_i, cond_i )). 00060 * B: Test ratio is set to 1 / (EPS * ERRBND( *, cwise_i, cond_i )). 00061 * 00062 * .. Parameters .. 00063 * NMAX is determined by the largest number in the inverse of the hilbert 00064 * matrix. Precision is exhausted when the largest entry in it is greater 00065 * than 2 to the power of the number of bits in the fraction of the data 00066 * type used plus one, which is 24 for single precision. 00067 * NMAX should be 6 for single and 11 for double. 00068 00069 INTEGER NMAX, NPARAMS, NERRBND, NTESTS, KL, KU 00070 PARAMETER (NMAX = 10, NPARAMS = 2, NERRBND = 3, 00071 $ NTESTS = 6) 00072 00073 * .. Local Scalars .. 00074 INTEGER N, NRHS, INFO, I ,J, k, NFAIL, LDA, 00075 $ N_AUX_TESTS, LDAB, LDAFB 00076 CHARACTER FACT, TRANS, UPLO, EQUED 00077 CHARACTER*2 C2 00078 CHARACTER(3) NGUAR, CGUAR 00079 LOGICAL printed_guide 00080 DOUBLE PRECISION NCOND, CCOND, M, NORMDIF, NORMT, RCOND, 00081 $ RNORM, RINORM, SUMR, SUMRI, EPS, 00082 $ BERR(NMAX), RPVGRW, ORCOND, 00083 $ CWISE_ERR, NWISE_ERR, CWISE_BND, NWISE_BND, 00084 $ CWISE_RCOND, NWISE_RCOND, 00085 $ CONDTHRESH, ERRTHRESH 00086 COMPLEX*16 ZDUM 00087 00088 * .. Local Arrays .. 00089 DOUBLE PRECISION TSTRAT(NTESTS), RINV(NMAX), PARAMS(NPARAMS), 00090 $ S(NMAX),R(NMAX),C(NMAX),RWORK(3*NMAX), 00091 $ DIFF(NMAX, NMAX), 00092 $ ERRBND_N(NMAX*3), ERRBND_C(NMAX*3) 00093 INTEGER IPIV(NMAX) 00094 COMPLEX*16 A(NMAX,NMAX),INVHILB(NMAX,NMAX),X(NMAX,NMAX), 00095 $ WORK(NMAX*3*5), AF(NMAX, NMAX),B(NMAX, NMAX), 00096 $ ACOPY(NMAX, NMAX), 00097 $ AB( (NMAX-1)+(NMAX-1)+1, NMAX ), 00098 $ ABCOPY( (NMAX-1)+(NMAX-1)+1, NMAX ), 00099 $ AFB( 2*(NMAX-1)+(NMAX-1)+1, NMAX ) 00100 00101 * .. External Functions .. 00102 DOUBLE PRECISION DLAMCH 00103 00104 * .. External Subroutines .. 00105 EXTERNAL ZLAHILB, ZGESVXX, ZPOSVXX, ZSYSVXX, 00106 $ ZGBSVXX, ZLACPY, LSAMEN 00107 LOGICAL LSAMEN 00108 00109 * .. Intrinsic Functions .. 00110 INTRINSIC SQRT, MAX, ABS, DBLE, DIMAG 00111 00112 * .. Statement Functions .. 00113 DOUBLE PRECISION CABS1 00114 00115 * .. Statement Function Definitions .. 00116 CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) ) 00117 00118 * .. Parameters .. 00119 INTEGER NWISE_I, CWISE_I 00120 PARAMETER (NWISE_I = 1, CWISE_I = 1) 00121 INTEGER BND_I, COND_I 00122 PARAMETER (BND_I = 2, COND_I = 3) 00123 00124 * Create the loop to test out the Hilbert matrices 00125 00126 FACT = 'E' 00127 UPLO = 'U' 00128 TRANS = 'N' 00129 EQUED = 'N' 00130 EPS = DLAMCH('Epsilon') 00131 NFAIL = 0 00132 N_AUX_TESTS = 0 00133 LDA = NMAX 00134 LDAB = (NMAX-1)+(NMAX-1)+1 00135 LDAFB = 2*(NMAX-1)+(NMAX-1)+1 00136 C2 = PATH( 2: 3 ) 00137 00138 * Main loop to test the different Hilbert Matrices. 00139 00140 printed_guide = .false. 00141 00142 DO N = 1 , NMAX 00143 PARAMS(1) = -1 00144 PARAMS(2) = -1 00145 00146 KL = N-1 00147 KU = N-1 00148 NRHS = n 00149 M = MAX(SQRT(DBLE(N)), 10.0D+0) 00150 00151 * Generate the Hilbert matrix, its inverse, and the 00152 * right hand side, all scaled by the LCM(1,..,2N-1). 00153 CALL ZLAHILB(N, N, A, LDA, INVHILB, LDA, B, 00154 $ LDA, WORK, INFO, PATH) 00155 00156 * Copy A into ACOPY. 00157 CALL ZLACPY('ALL', N, N, A, NMAX, ACOPY, NMAX) 00158 00159 * Store A in band format for GB tests 00160 DO J = 1, N 00161 DO I = 1, KL+KU+1 00162 AB( I, J ) = (0.0D+0,0.0D+0) 00163 END DO 00164 END DO 00165 DO J = 1, N 00166 DO I = MAX( 1, J-KU ), MIN( N, J+KL ) 00167 AB( KU+1+I-J, J ) = A( I, J ) 00168 END DO 00169 END DO 00170 00171 * Copy AB into ABCOPY. 00172 DO J = 1, N 00173 DO I = 1, KL+KU+1 00174 ABCOPY( I, J ) = (0.0D+0,0.0D+0) 00175 END DO 00176 END DO 00177 CALL ZLACPY('ALL', KL+KU+1, N, AB, LDAB, ABCOPY, LDAB) 00178 00179 * Call Z**SVXX with default PARAMS and N_ERR_BND = 3. 00180 IF ( LSAMEN( 2, C2, 'SY' ) ) THEN 00181 CALL ZSYSVXX(FACT, UPLO, N, NRHS, ACOPY, LDA, AF, LDA, 00182 $ IPIV, EQUED, S, B, LDA, X, LDA, ORCOND, 00183 $ RPVGRW, BERR, NERRBND, ERRBND_N, ERRBND_C, NPARAMS, 00184 $ PARAMS, WORK, RWORK, INFO) 00185 ELSE IF ( LSAMEN( 2, C2, 'PO' ) ) THEN 00186 CALL ZPOSVXX(FACT, UPLO, N, NRHS, ACOPY, LDA, AF, LDA, 00187 $ EQUED, S, B, LDA, X, LDA, ORCOND, 00188 $ RPVGRW, BERR, NERRBND, ERRBND_N, ERRBND_C, NPARAMS, 00189 $ PARAMS, WORK, RWORK, INFO) 00190 ELSE IF ( LSAMEN( 2, C2, 'HE' ) ) THEN 00191 CALL ZHESVXX(FACT, UPLO, N, NRHS, ACOPY, LDA, AF, LDA, 00192 $ IPIV, EQUED, S, B, LDA, X, LDA, ORCOND, 00193 $ RPVGRW, BERR, NERRBND, ERRBND_N, ERRBND_C, NPARAMS, 00194 $ PARAMS, WORK, RWORK, INFO) 00195 ELSE IF ( LSAMEN( 2, C2, 'GB' ) ) THEN 00196 CALL ZGBSVXX(FACT, TRANS, N, KL, KU, NRHS, ABCOPY, 00197 $ LDAB, AFB, LDAFB, IPIV, EQUED, R, C, B, 00198 $ LDA, X, LDA, ORCOND, RPVGRW, BERR, NERRBND, 00199 $ ERRBND_N, ERRBND_C, NPARAMS, PARAMS, WORK, RWORK, 00200 $ INFO) 00201 ELSE 00202 CALL ZGESVXX(FACT, TRANS, N, NRHS, ACOPY, LDA, AF, LDA, 00203 $ IPIV, EQUED, R, C, B, LDA, X, LDA, ORCOND, 00204 $ RPVGRW, BERR, NERRBND, ERRBND_N, ERRBND_C, NPARAMS, 00205 $ PARAMS, WORK, RWORK, INFO) 00206 END IF 00207 00208 N_AUX_TESTS = N_AUX_TESTS + 1 00209 IF (ORCOND .LT. EPS) THEN 00210 ! Either factorization failed or the matrix is flagged, and 1 <= 00211 ! INFO <= N+1. We don't decide based on rcond anymore. 00212 ! IF (INFO .EQ. 0 .OR. INFO .GT. N+1) THEN 00213 ! NFAIL = NFAIL + 1 00214 ! WRITE (*, FMT=8000) N, INFO, ORCOND, RCOND 00215 ! END IF 00216 ELSE 00217 ! Either everything succeeded (INFO == 0) or some solution failed 00218 ! to converge (INFO > N+1). 00219 IF (INFO .GT. 0 .AND. INFO .LE. N+1) THEN 00220 NFAIL = NFAIL + 1 00221 WRITE (*, FMT=8000) C2, N, INFO, ORCOND, RCOND 00222 END IF 00223 END IF 00224 00225 * Calculating the difference between Z**SVXX's X and the true X. 00226 DO I = 1,N 00227 DO J =1,NRHS 00228 DIFF(I,J) = X(I,J) - INVHILB(I,J) 00229 END DO 00230 END DO 00231 00232 * Calculating the RCOND 00233 RNORM = 0 00234 RINORM = 0 00235 IF ( LSAMEN( 2, C2, 'PO' ) .OR. LSAMEN( 2, C2, 'SY' ) .OR. 00236 $ LSAMEN( 2, C2, 'HE' ) ) THEN 00237 DO I = 1, N 00238 SUMR = 0 00239 SUMRI = 0 00240 DO J = 1, N 00241 SUMR = SUMR + S(I) * CABS1(A(I,J)) * S(J) 00242 SUMRI = SUMRI + CABS1(INVHILB(I, J)) / (S(J) * S(I)) 00243 END DO 00244 RNORM = MAX(RNORM,SUMR) 00245 RINORM = MAX(RINORM,SUMRI) 00246 END DO 00247 ELSE IF ( LSAMEN( 2, C2, 'GE' ) .OR. LSAMEN( 2, C2, 'GB' ) ) 00248 $ THEN 00249 DO I = 1, N 00250 SUMR = 0 00251 SUMRI = 0 00252 DO J = 1, N 00253 SUMR = SUMR + R(I) * CABS1(A(I,J)) * C(J) 00254 SUMRI = SUMRI + CABS1(INVHILB(I, J)) / (R(J) * C(I)) 00255 END DO 00256 RNORM = MAX(RNORM,SUMR) 00257 RINORM = MAX(RINORM,SUMRI) 00258 END DO 00259 END IF 00260 00261 RNORM = RNORM / CABS1(A(1, 1)) 00262 RCOND = 1.0D+0/(RNORM * RINORM) 00263 00264 * Calculating the R for normwise rcond. 00265 DO I = 1, N 00266 RINV(I) = 0.0D+0 00267 END DO 00268 DO J = 1, N 00269 DO I = 1, N 00270 RINV(I) = RINV(I) + CABS1(A(I,J)) 00271 END DO 00272 END DO 00273 00274 * Calculating the Normwise rcond. 00275 RINORM = 0.0D+0 00276 DO I = 1, N 00277 SUMRI = 0.0D+0 00278 DO J = 1, N 00279 SUMRI = SUMRI + CABS1(INVHILB(I,J) * RINV(J)) 00280 END DO 00281 RINORM = MAX(RINORM, SUMRI) 00282 END DO 00283 00284 ! invhilb is the inverse *unscaled* Hilbert matrix, so scale its norm 00285 ! by 1/A(1,1) to make the scaling match A (the scaled Hilbert matrix) 00286 NCOND = CABS1(A(1,1)) / RINORM 00287 00288 CONDTHRESH = M * EPS 00289 ERRTHRESH = M * EPS 00290 00291 DO K = 1, NRHS 00292 NORMT = 0.0D+0 00293 NORMDIF = 0.0D+0 00294 CWISE_ERR = 0.0D+0 00295 DO I = 1, N 00296 NORMT = MAX(CABS1(INVHILB(I, K)), NORMT) 00297 NORMDIF = MAX(CABS1(X(I,K) - INVHILB(I,K)), NORMDIF) 00298 IF (INVHILB(I,K) .NE. 0.0D+0) THEN 00299 CWISE_ERR = MAX(CABS1(X(I,K) - INVHILB(I,K)) 00300 $ /CABS1(INVHILB(I,K)), CWISE_ERR) 00301 ELSE IF (X(I, K) .NE. 0.0D+0) THEN 00302 CWISE_ERR = DLAMCH('OVERFLOW') 00303 END IF 00304 END DO 00305 IF (NORMT .NE. 0.0D+0) THEN 00306 NWISE_ERR = NORMDIF / NORMT 00307 ELSE IF (NORMDIF .NE. 0.0D+0) THEN 00308 NWISE_ERR = DLAMCH('OVERFLOW') 00309 ELSE 00310 NWISE_ERR = 0.0D+0 00311 ENDIF 00312 00313 DO I = 1, N 00314 RINV(I) = 0.0D+0 00315 END DO 00316 DO J = 1, N 00317 DO I = 1, N 00318 RINV(I) = RINV(I) + CABS1(A(I, J) * INVHILB(J, K)) 00319 END DO 00320 END DO 00321 RINORM = 0.0D+0 00322 DO I = 1, N 00323 SUMRI = 0.0D+0 00324 DO J = 1, N 00325 SUMRI = SUMRI 00326 $ + CABS1(INVHILB(I, J) * RINV(J) / INVHILB(I, K)) 00327 END DO 00328 RINORM = MAX(RINORM, SUMRI) 00329 END DO 00330 ! invhilb is the inverse *unscaled* Hilbert matrix, so scale its norm 00331 ! by 1/A(1,1) to make the scaling match A (the scaled Hilbert matrix) 00332 CCOND = CABS1(A(1,1))/RINORM 00333 00334 ! Forward error bound tests 00335 NWISE_BND = ERRBND_N(K + (BND_I-1)*NRHS) 00336 CWISE_BND = ERRBND_C(K + (BND_I-1)*NRHS) 00337 NWISE_RCOND = ERRBND_N(K + (COND_I-1)*NRHS) 00338 CWISE_RCOND = ERRBND_C(K + (COND_I-1)*NRHS) 00339 ! write (*,*) 'nwise : ', n, k, ncond, nwise_rcond, 00340 ! $ condthresh, ncond.ge.condthresh 00341 ! write (*,*) 'nwise2: ', k, nwise_bnd, nwise_err, errthresh 00342 IF (NCOND .GE. CONDTHRESH) THEN 00343 NGUAR = 'YES' 00344 IF (NWISE_BND .GT. ERRTHRESH) THEN 00345 TSTRAT(1) = 1/(2.0D+0*EPS) 00346 ELSE 00347 IF (NWISE_BND .NE. 0.0D+0) THEN 00348 TSTRAT(1) = NWISE_ERR / NWISE_BND 00349 ELSE IF (NWISE_ERR .NE. 0.0D+0) THEN 00350 TSTRAT(1) = 1/(16.0*EPS) 00351 ELSE 00352 TSTRAT(1) = 0.0D+0 00353 END IF 00354 IF (TSTRAT(1) .GT. 1.0D+0) THEN 00355 TSTRAT(1) = 1/(4.0D+0*EPS) 00356 END IF 00357 END IF 00358 ELSE 00359 NGUAR = 'NO' 00360 IF (NWISE_BND .LT. 1.0D+0) THEN 00361 TSTRAT(1) = 1/(8.0D+0*EPS) 00362 ELSE 00363 TSTRAT(1) = 1.0D+0 00364 END IF 00365 END IF 00366 ! write (*,*) 'cwise : ', n, k, ccond, cwise_rcond, 00367 ! $ condthresh, ccond.ge.condthresh 00368 ! write (*,*) 'cwise2: ', k, cwise_bnd, cwise_err, errthresh 00369 IF (CCOND .GE. CONDTHRESH) THEN 00370 CGUAR = 'YES' 00371 IF (CWISE_BND .GT. ERRTHRESH) THEN 00372 TSTRAT(2) = 1/(2.0D+0*EPS) 00373 ELSE 00374 IF (CWISE_BND .NE. 0.0D+0) THEN 00375 TSTRAT(2) = CWISE_ERR / CWISE_BND 00376 ELSE IF (CWISE_ERR .NE. 0.0D+0) THEN 00377 TSTRAT(2) = 1/(16.0D+0*EPS) 00378 ELSE 00379 TSTRAT(2) = 0.0D+0 00380 END IF 00381 IF (TSTRAT(2) .GT. 1.0D+0) TSTRAT(2) = 1/(4.0D+0*EPS) 00382 END IF 00383 ELSE 00384 CGUAR = 'NO' 00385 IF (CWISE_BND .LT. 1.0D+0) THEN 00386 TSTRAT(2) = 1/(8.0D+0*EPS) 00387 ELSE 00388 TSTRAT(2) = 1.0D+0 00389 END IF 00390 END IF 00391 00392 ! Backwards error test 00393 TSTRAT(3) = BERR(K)/EPS 00394 00395 ! Condition number tests 00396 TSTRAT(4) = RCOND / ORCOND 00397 IF (RCOND .GE. CONDTHRESH .AND. TSTRAT(4) .LT. 1.0D+0) 00398 $ TSTRAT(4) = 1.0D+0 / TSTRAT(4) 00399 00400 TSTRAT(5) = NCOND / NWISE_RCOND 00401 IF (NCOND .GE. CONDTHRESH .AND. TSTRAT(5) .LT. 1.0D+0) 00402 $ TSTRAT(5) = 1.0D+0 / TSTRAT(5) 00403 00404 TSTRAT(6) = CCOND / NWISE_RCOND 00405 IF (CCOND .GE. CONDTHRESH .AND. TSTRAT(6) .LT. 1.0D+0) 00406 $ TSTRAT(6) = 1.0D+0 / TSTRAT(6) 00407 00408 DO I = 1, NTESTS 00409 IF (TSTRAT(I) .GT. THRESH) THEN 00410 IF (.NOT.PRINTED_GUIDE) THEN 00411 WRITE(*,*) 00412 WRITE( *, 9996) 1 00413 WRITE( *, 9995) 2 00414 WRITE( *, 9994) 3 00415 WRITE( *, 9993) 4 00416 WRITE( *, 9992) 5 00417 WRITE( *, 9991) 6 00418 WRITE( *, 9990) 7 00419 WRITE( *, 9989) 8 00420 WRITE(*,*) 00421 PRINTED_GUIDE = .TRUE. 00422 END IF 00423 WRITE( *, 9999) C2, N, K, NGUAR, CGUAR, I, TSTRAT(I) 00424 NFAIL = NFAIL + 1 00425 END IF 00426 END DO 00427 END DO 00428 00429 c$$$ WRITE(*,*) 00430 c$$$ WRITE(*,*) 'Normwise Error Bounds' 00431 c$$$ WRITE(*,*) 'Guaranteed error bound: ',ERRBND(NRHS,nwise_i,bnd_i) 00432 c$$$ WRITE(*,*) 'Reciprocal condition number: ',ERRBND(NRHS,nwise_i,cond_i) 00433 c$$$ WRITE(*,*) 'Raw error estimate: ',ERRBND(NRHS,nwise_i,rawbnd_i) 00434 c$$$ WRITE(*,*) 00435 c$$$ WRITE(*,*) 'Componentwise Error Bounds' 00436 c$$$ WRITE(*,*) 'Guaranteed error bound: ',ERRBND(NRHS,cwise_i,bnd_i) 00437 c$$$ WRITE(*,*) 'Reciprocal condition number: ',ERRBND(NRHS,cwise_i,cond_i) 00438 c$$$ WRITE(*,*) 'Raw error estimate: ',ERRBND(NRHS,cwise_i,rawbnd_i) 00439 c$$$ print *, 'Info: ', info 00440 c$$$ WRITE(*,*) 00441 * WRITE(*,*) 'TSTRAT: ',TSTRAT 00442 00443 END DO 00444 00445 WRITE(*,*) 00446 IF( NFAIL .GT. 0 ) THEN 00447 WRITE(*,9998) C2, NFAIL, NTESTS*N+N_AUX_TESTS 00448 ELSE 00449 WRITE(*,9997) C2 00450 END IF 00451 9999 FORMAT( ' Z', A2, 'SVXX: N =', I2, ', RHS = ', I2, 00452 $ ', NWISE GUAR. = ', A, ', CWISE GUAR. = ', A, 00453 $ ' test(',I1,') =', G12.5 ) 00454 9998 FORMAT( ' Z', A2, 'SVXX: ', I6, ' out of ', I6, 00455 $ ' tests failed to pass the threshold' ) 00456 9997 FORMAT( ' Z', A2, 'SVXX passed the tests of error bounds' ) 00457 * Test ratios. 00458 9996 FORMAT( 3X, I2, ': Normwise guaranteed forward error', / 5X, 00459 $ 'Guaranteed case: if norm ( abs( Xc - Xt )', 00460 $ ' / norm ( Xt ) .LE. ERRBND( *, nwise_i, bnd_i ), then', 00461 $ / 5X, 00462 $ 'ERRBND( *, nwise_i, bnd_i ) .LE. MAX(SQRT(N), 10) * EPS') 00463 9995 FORMAT( 3X, I2, ': Componentwise guaranteed forward error' ) 00464 9994 FORMAT( 3X, I2, ': Backwards error' ) 00465 9993 FORMAT( 3X, I2, ': Reciprocal condition number' ) 00466 9992 FORMAT( 3X, I2, ': Reciprocal normwise condition number' ) 00467 9991 FORMAT( 3X, I2, ': Raw normwise error estimate' ) 00468 9990 FORMAT( 3X, I2, ': Reciprocal componentwise condition number' ) 00469 9989 FORMAT( 3X, I2, ': Raw componentwise error estimate' ) 00470 00471 8000 FORMAT( ' Z', A2, 'SVXX: N =', I2, ', INFO = ', I3, 00472 $ ', ORCOND = ', G12.5, ', real RCOND = ', G12.5 ) 00473 00474 END
1.7.3 
