📄 lsqr.txt
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-------------------------------------------------------------------- Least-Squares Test Problem P( 2000 1000 40 5 1.00E-05 ) Condition no. = 9.9995E+04 Residual function = 3.162277952E+01 -------------------------------------------------------------------- Enter Acheck. Test of Aprod for LSQR and CRAIG Aprod seems OK. Relative error = 4.1E-16 Enter LSQR. Least-squares solution of Ax = b The matrix A has 2000 rows and 1000 columns damp = 1.00000000000000E-05 wantse = F atol = 3.18E-16 conlim = 1.00E+08 btol = 3.18E-16 itnlim = 12200 Itn x(1) Function Compatible LS Norm Abar Cond Abar alfa_opt 0 0.000000000E+00 9.715494280E+02 1.00E+00 8.45E-04 1 -2.412106255E+01 4.116661449E+02 4.24E-01 6.34E-01 9.06E-01 1.00E+00 6.2E-01 2 -1.824596475E+01 2.396665268E+02 2.47E-01 3.74E-01 1.18E+00 2.18E+00 3.3E-01 3 -7.118200999E+00 1.585407923E+02 1.63E-01 2.56E-01 1.36E+00 3.57E+00 2.1E-01 4 2.622411380E+00 1.122939283E+02 1.16E-01 1.84E-01 1.47E+00 5.19E+00 1.5E-01 5 9.349109039E+00 8.319678233E+01 8.56E-02 1.34E-01 1.55E+00 7.12E+00 1.1E-01 6 1.286861547E+01 6.400705208E+01 6.59E-02 9.65E-02 1.60E+00 9.44E+00 8.4E-02 7 1.344322969E+01 5.123460276E+01 5.27E-02 6.67E-02 1.63E+00 1.23E+01 6.5E-02 8 1.153766988E+01 4.292241224E+01 4.42E-02 4.35E-02 1.65E+00 1.60E+01 5.2E-02 9 7.760937243E+00 3.776482006E+01 3.89E-02 2.63E-02 1.66E+00 2.08E+01 4.3E-02 10 2.839815541E+00 3.476092705E+01 3.58E-02 1.47E-02 1.67E+00 2.74E+01 3.5E-02 20 -1.336581893E+01 3.166056236E+01 3.26E-02 7.45E-04 2.28E+00 2.01E+02 1.4E-02 30 -6.132881595E+00 3.162353433E+01 3.25E-02 1.01E-04 2.88E+00 1.07E+03 6.8E-03 40 -2.843186170E+00 3.162290761E+01 3.25E-02 6.41E-07 3.37E+00 2.35E+03 5.0E-03 50 -2.829155842E-01 3.162279982E+01 3.25E-02 7.47E-07 3.69E+00 5.34E+03 3.5E-03 60 1.199589697E+00 3.162278591E+01 3.25E-02 2.80E-07 4.02E+00 1.39E+04 2.2E-03 70 1.546444780E+00 3.162278484E+01 3.25E-02 6.34E-08 4.34E+00 4.39E+04 1.3E-03 80 1.546393831E+00 3.162278484E+01 3.25E-02 8.66E-09 4.61E+00 4.67E+04 1.3E-03 90 9.678250921E-01 3.162278480E+01 3.25E-02 7.64E-10 4.89E+00 1.90E+05 6.7E-04 100 9.677892749E-01 3.162278480E+01 3.25E-02 5.79E-10 5.15E+00 2.00E+05 6.7E-04 110 9.540917752E-01 3.162278480E+01 3.25E-02 2.34E-08 5.49E+00 2.23E+05 6.5E-04 120 1.229254088E-01 3.162278480E+01 3.25E-02 9.36E-09 5.71E+00 5.88E+05 4.1E-04 130 1.228633290E-01 3.162278480E+01 3.25E-02 2.18E-11 5.93E+00 6.11E+05 4.1E-04 140 1.228584680E-01 3.162278480E+01 3.25E-02 8.59E-11 6.15E+00 6.33E+05 4.1E-04 150 1.000087339E-01 3.162278480E+01 3.25E-02 1.06E-10 6.37E+00 9.12E+05 3.5E-04 160 1.000010912E-01 3.162278480E+01 3.25E-02 9.94E-12 6.57E+00 9.41E+05 3.5E-04 170 9.999993804E-02 3.162278480E+01 3.25E-02 4.39E-13 6.76E+00 9.69E+05 3.5E-04 173 9.999993804E-02 3.162278480E+01 3.25E-02 2.38E-16 6.85E+00 9.82E+05 3.5E-04 Exit LSQR. istop = 3 itn = 173 Exit LSQR. Anorm = 6.84982E+00 Acond = 9.81551E+05 Exit LSQR. bnorm = 9.71549E+02 xnorm = 1.82711E+03 Exit LSQR. rnorm = 3.16228E+01 Arnorm = 5.15827E-14 Exit LSQR. max dx = 9.7E+02 occurred at itn 1 Exit LSQR. = 5.3E-01*xnorm Exit LSQR. A damped least-squares solution was found, given atol Enter xcheck. Does x solve Ax = b, etc? damp = 1.000E-05 norm(x) = 1.827E+03 norm(r) = 3.16227795E+01 = rho1 norm(A'r) = 1.827E-07 = sigma1 norm(s) = 3.162E+06 norm(x,s) = 3.162E+06 norm(rbar) = 3.16227848E+01 = rho2 norm(Abar'rbar) = 7.212E-13 = sigma2 inform = 2 tol = 1.490E-08 test1 = 2.345E-03 (Ax = b) test2 = 8.435E-10 (least-squares) test3 = 3.329E-15 (damped least-squares) Solution x: 1 0.999999E-01 2 0.200000 3 0.300000 4 0.400000 5 0.500000 6 0.600000 7 0.700000 8 0.800000 LSQR appears to be successful. Relative error in x = 1.26E-09 -------------------------------------------------------------------- Least-Squares Test Problem P( 2000 1000 40 6 1.00E-06 ) Condition no. = 9.9999E+05 Residual function = 3.162277678E+01 -------------------------------------------------------------------- Enter Acheck. Test of Aprod for LSQR and CRAIG Aprod seems OK. Relative error = 7.5E-16 Enter LSQR. Least-squares solution of Ax = b The matrix A has 2000 rows and 1000 columns damp = 1.00000000000000E-06 wantse = F atol = 3.18E-16 conlim = 1.00E+09 btol = 3.18E-16 itnlim = 12200 Itn x(1) Function Compatible LS Norm Abar Cond Abar alfa_opt 0 0.000000000E+00 9.210791621E+02 1.00E+00 8.97E-04 1 -2.443055276E+01 3.951289622E+02 4.29E-01 6.18E-01 9.14E-01 1.00E+00 6.3E-01 2 -2.224414133E+01 2.299330661E+02 2.50E-01 3.58E-01 1.18E+00 2.19E+00 3.3E-01 3 -1.321097804E+01 1.506103813E+02 1.64E-01 2.38E-01 1.34E+00 3.62E+00 2.1E-01 4 -3.367416061E+00 1.049231608E+02 1.14E-01 1.66E-01 1.44E+00 5.35E+00 1.4E-01 5 5.036316961E+00 7.625044979E+01 8.28E-02 1.15E-01 1.50E+00 7.50E+00 1.0E-01 6 1.099397591E+01 5.775402451E+01 6.27E-02 7.77E-02 1.53E+00 1.02E+01 7.6E-02 7 1.404999112E+01 4.603739656E+01 5.00E-02 4.91E-02 1.55E+00 1.39E+01 5.8E-02 8 1.413848446E+01 3.901907204E+01 4.24E-02 2.85E-02 1.56E+00 1.88E+01 4.5E-02 9 1.156137776E+01 3.514014564E+01 3.82E-02 1.50E-02 1.57E+00 2.59E+01 3.6E-02 10 6.963810705E+00 3.317616264E+01 3.60E-02 7.17E-03 1.57E+00 3.61E+01 2.9E-02 20 -1.262942115E+01 3.164961571E+01 3.44E-02 1.91E-03 2.20E+00 2.50E+02 1.3E-02 30 -1.024518441E+01 3.162317765E+01 3.43E-02 4.92E-06 2.85E+00 1.60E+03 5.6E-03 40 -6.777780822E+00 3.162284358E+01 3.43E-02 2.11E-06 3.21E+00 3.53E+03 4.0E-03 50 -3.250362707E+00 3.162278508E+01 3.43E-02 3.66E-07 3.57E+00 8.53E+03 2.7E-03 60 -4.552765447E-01 3.162277752E+01 3.43E-02 1.52E-07 3.98E+00 2.29E+04 1.7E-03 70 1.137756881E+00 3.162277688E+01 3.43E-02 3.71E-06 4.29E+00 7.08E+04 1.0E-03 80 1.171195877E+00 3.162277687E+01 3.43E-02 2.00E-09 4.60E+00 7.67E+04 1.0E-03 90 1.567813277E+00 3.162277684E+01 3.43E-02 1.16E-09 4.88E+00 3.01E+05 5.3E-04 100 1.568889007E+00 3.162277684E+01 3.43E-02 1.17E-10 5.18E+00 3.20E+05 5.3E-04 110 1.568273996E+00 3.162277684E+01 3.43E-02 1.76E-09 5.41E+00 3.38E+05 5.3E-04 120 1.096480257E+00 3.162277684E+01 3.43E-02 8.60E-09 5.63E+00 1.70E+06 2.4E-04 130 1.021497918E+00 3.162277684E+01 3.43E-02 3.87E-10 5.81E+00 1.88E+06 2.3E-04 140 1.021342806E+00 3.162277684E+01 3.43E-02 1.63E-12 6.09E+00 1.97E+06 2.3E-04 150 4.670017401E-01 3.162277684E+01 3.43E-02 2.41E-10 6.31E+00 5.21E+06 1.4E-04 160 3.521633464E-01 3.162277684E+01 3.43E-02 1.25E-09 6.45E+00 5.78E+06 1.4E-04 170 1.155926470E-01 3.162277684E+01 3.43E-02 1.71E-10 6.70E+00 6.85E+06 1.3E-04 180 1.155906913E-01 3.162277684E+01 3.43E-02 1.75E-12 6.88E+00 7.04E+06 1.3E-04 190 1.155905699E-01 3.162277684E+01 3.43E-02 2.59E-14 7.08E+00 7.24E+06 1.3E-04 200 1.155782202E-01 3.162277684E+01 3.43E-02 1.89E-14 7.26E+00 7.43E+06 1.3E-04 210 1.155782144E-01 3.162277684E+01 3.43E-02 5.03E-14 7.41E+00 7.58E+06 1.3E-04 220 1.030994471E-01 3.162277684E+01 3.43E-02 2.91E-12 7.63E+00 1.04E+07 1.1E-04 230 1.000000240E-01 3.162277684E+01 3.43E-02 3.71E-12 7.79E+00 1.11E+07 1.1E-04 239 9.999794679E-02 3.162277684E+01 3.43E-02 2.51E-15 7.94E+00 1.13E+07 1.1E-04 240 9.999794679E-02 3.162277684E+01 3.43E-02 5.11E-16 7.94E+00 1.13E+07 1.1E-04 241 9.999794679E-02 3.162277684E+01 3.43E-02 1.51E-17 7.94E+00 1.13E+07 1.1E-04 Exit LSQR. istop = 3 itn = 241 Exit LSQR. Anorm = 7.94322E+00 Acond = 1.13469E+07 Exit LSQR. bnorm = 9.21079E+02 xnorm = 1.82711E+03 Exit LSQR. rnorm = 3.16228E+01 Arnorm = 3.80535E-15 Exit LSQR. max dx = 9.1E+02 occurred at itn 1 Exit LSQR. = 5.0E-01*xnorm Exit LSQR. A damped least-squares solution was found, given atol Enter xcheck. Does x solve Ax = b, etc? damp = 1.000E-06 norm(x) = 1.827E+03 norm(r) = 3.16227768E+01 = rho1 norm(A'r) = 1.827E-09 = sigma1 norm(s) = 3.162E+07 norm(x,s) = 3.162E+07 norm(rbar) = 3.16227768E+01 = rho2 norm(Abar'rbar) = 7.747E-13 = sigma2 inform = 2 tol = 1.490E-08 test1 = 2.049E-03 (Ax = b) test2 = 7.273E-12 (least-squares) test3 = 3.084E-15 (damped least-squares) Solution x: 1 0.999979E-01 2 0.199995 3 0.299994 4 0.399991 5 0.499991 6 0.600000 7 0.700001 8 0.799985 LSQR appears to be successful. Relative error in x = 7.32E-08 -------------------------------------------------------------------- Least-Squares Test Problem P( 2000 1000 40 7 1.00E-07 ) Condition no. = 1.0000E+07 Residual function = 3.162277661E+01 -------------------------------------------------------------------- Enter Acheck. Test of Aprod for LSQR and CRAIG Aprod seems OK. Relative error = 8.3E-16 Enter LSQR. Least-squares solution of Ax = b The matrix A has 2000 rows and 1000 columns damp = 1.00000000000000E-07 wantse = F atol = 3.18E-16 conlim = 1.00E+10 btol = 3.18E-16 itnlim = 12200 Itn x(1) Function Compatible LS Norm Abar Cond Abar alfa_opt 0 0.000000000E+00 8.808458173E+02 1.00E+00 9.45E-04 1 -2.422195397E+01 3.796781520E+02 4.31E-01 6.03E-01 9.23E-01 1.00E+00 6.4E-01 2 -2.477913716E+01 2.193708762E+02 2.49E-01 3.41E-01 1.18E+00 2.20E+00 3.3E-01 3 -1.776850890E+01 1.414330764E+02 1.61E-01 2.21E-01 1.32E+00 3.69E+00 2.0E-01 4 -8.448828545E+00 9.648095039E+01 1.10E-01 1.48E-01 1.40E+00 5.56E+00 1.4E-01 5 7.462713431E-01 6.872328235E+01 7.80E-02 9.74E-02 1.44E+00 7.99E+00 9.4E-02 6 8.324225295E+00 5.155052190E+01 5.85E-02 6.06E-02 1.47E+00 1.13E+01 6.7E-02 7 1.328456786E+01 4.146406785E+01 4.71E-02 3.44E-02 1.48E+00 1.60E+01 5.0E-02 8 1.508697446E+01 3.605910766E+01 4.09E-02 1.73E-02 1.48E+00 2.29E+01 3.9E-02 9 1.370776303E+01 3.345655263E+01 3.80E-02 7.84E-03 1.49E+00 3.32E+01 3.0E-02 10 9.669404920E+00 3.232530691E+01 3.67E-02 9.36E-03 1.49E+00 4.93E+01 2.4E-02 20 -1.212587523E+01 3.162906029E+01 3.59E-02 3.93E-05 2.31E+00 5.05E+02 9.1E-03 30 -1.326379497E+01 3.162306620E+01 3.59E-02 1.10E-05 2.74E+00 2.01E+03 4.9E-03 40 -9.569977066E+00 3.162280973E+01 3.59E-02 2.34E-05 3.19E+00 7.22E+03 2.8E-03 50 -6.205881384E+00 3.162278105E+01 3.59E-02 1.34E-05 3.57E+00 1.81E+04 1.9E-03 60 -3.516189567E+00 3.162277714E+01 3.59E-02 3.14E-08 3.92E+00 3.20E+04 1.5E-03 70 -5.571805067E-01 3.162277664E+01 3.59E-02 7.95E-10 4.19E+00 9.78E+04 8.6E-04 80 -5.562457015E-01 3.162277664E+01 3.59E-02 1.90E-08 4.54E+00 1.06E+05 8.6E-04 90 1.154552315E+00 3.162277661E+01 3.59E-02 6.98E-10 4.78E+00 3.90E+05 4.6E-04 100 1.155178149E+00 3.162277661E+01 3.59E-02 1.01E-08 5.00E+00 4.09E+05 4.6E-04 110 1.155909078E+00 3.162277661E+01 3.59E-02 4.67E-09 5.27E+00 4.37E+05 4.6E-04 120 1.579373051E+00 3.162277661E+01 3.59E-02 4.12E-11 5.55E+00 2.11E+06 2.1E-04 130 1.579280548E+00 3.162277661E+01 3.59E-02 1.57E-10 5.74E+00 2.19E+06 2.1E-04 140 1.579264864E+00 3.162277661E+01 3.59E-02 4.91E-10 5.93E+00 2.26E+06 2.1E-04 150 1.576149841E+00 3.162277661E+01 3.59E-02 6.85E-12 6.18E+00 2.66E+06 2.0E-04 160 1.575634079E+00 3.162277661E+01 3.59E-02 1.70E-10 6.36E+00 2.78E+06 2.0E-04 170 1.056933998E+00 3.162277661E+01 3.59E-02 3.68E-13 6.57E+00 1.79E+07 8.0E-05 180 1.056933787E+00 3.162277661E+01 3.59E-02 7.46E-13 6.80E+00 1.85E+07 8.0E-05 190 1.056933152E+00 3.162277661E+01 3.59E-02 1.47E-11 6.95E+00 1.89E+07 8.0E-05 197 1.056891898E+00 3.162277661E+01 3.59E-02 2.01E-15 7.10E+00 1.93E+07 8.0E-05 200 1.056891894E+00 3.162277661E+01 3.59E-02 1.43E-14 7.11E+00 1.93E+07 8.0E-05 210 1.055783542E+00 3.162277661E+01 3.59E-02 6.14E-13 7.32E+00 2.01E+07 8.0E-05 220 1.038458046E+00 3.162277661E+01 3.59E-02 7.65E-11 7.47E+00 2.27E+07 7.5E-05 230 1.096247569E-01 3.162277661E+01 3.59E-02 1.81E-14 7.65E+00 7.78E+07 4.1E-05 240 1.096247523E-01 3.162277661E+01 3.59E-02 4.11E-14 7.79E+00 7.93E+07 4.1E-05⌨️ 快捷键说明
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