test_simeq_newton5.adb running a random number= 7.96133E-01 test_case_1 A( 1, 1)= 1.000000E+00 A( 1, 2)= 1.000000E+00 A( 1, 3)= 1.000000E+00 A( 1, 4)= 0.000000E+00 A( 2, 1)= 1.000000E+00 A( 2, 2)= 1.000000E+00 A( 2, 3)= 0.000000E+00 A( 2, 4)= 1.000000E+00 X_soln( 1)= 1.000000E+00 X_soln( 2)= 2.000000E+00 Y( 1)= 4.000000E+00 Y( 2)= 7.000000E+00 system of equations to be solved, i=1.. 2 A(i, 1)*X1+ A(i, 2)*X2+ A(i, 3)*X1*X1+ A(i, 4)*X2*X2 = Y(i) initial guess X( 1)= 5.000000E-01 X( 2)= 5.000000E-01 simeq_newton5.adb running itr 0, initial residual= 8.50000000000000E+00 itr 1, prev= 8.50000000000000E+00, residual= 8.51388888888889E+00 b reduced to 5.00000000000000E-01 itr 2, prev= 8.50000000000000E+00, residual= 2.12152777777778E+00 b increased to 7.07150000000000E-01 itr 3, prev= 2.12152777777778E+00, residual= 3.67252328050016E-01 b increased to 1.00000000000000E+00 itr 4, prev= 3.67252328050016E-01, residual= 2.80087177080279E-03 itr 5, prev= 2.80087177080279E-03, residual= 2.12293673307329E-07 simeq_newton5 found solution test case1 solution X( 1)= 1.00000006105699E+00, soln= 1.00000000000000E+00, err=-6.10569896863922E-08 X( 2)= 1.99999999467762E+00, soln= 2.00000000000000E+00, err= 5.32238142447738E-09 residual= 2.12293673307329E-07 test_case_2 A( 1, 1)= 1.004481E-01 A( 1, 2)= 3.038947E-02 A( 1, 3)= 8.489690E-01 A( 1, 4)= 6.113836E-01 A( 1, 5)= 2.318349E-01 A( 1, 6)= 1.780247E-01 A( 1, 7)= 5.044825E-02 A( 2, 1)= 9.223490E-01 A( 2, 2)= 3.931202E-02 A( 2, 3)= 2.046376E-01 A( 2, 4)= 2.252655E-01 A( 2, 5)= 8.072153E-01 A( 2, 6)= 7.362546E-01 A( 2, 7)= 8.029963E-01 A( 3, 1)= 6.424139E-02 A( 3, 2)= 2.017120E-01 A( 3, 3)= 2.285489E-01 A( 3, 4)= 8.090473E-01 A( 3, 5)= 6.413768E-01 A( 3, 6)= 7.682273E-01 A( 3, 7)= 4.818126E-01 X_soln( 1)= 1.100000E+00 X_soln( 2)= 1.200000E+00 X_soln( 3)= 1.400000E+00 Y( 1)= 2.796773E+00 Y( 2)= 4.449323E+00 Y( 3)= 3.979317E+00 system of equations to be solved, i=1.. 3 A(i, 1)*X1+ A(i, 2)*X2+ A(i, 3)*X3+ A(i, 4)*X1*X2+ A(i, 5)*X3*X2*X2+ A(i, 6)*X2/(X3)+ A(i, 7)*X1*X1*X1/(X3*X3) = Y(i) initial guess X( 1)= 1.000000E+00 X( 2)= 1.000000E+00 X( 3)= 1.000000E+00 simeq_newton5.adb running itr 0, initial residual= 2.24091877137649E+00 itr 1, prev= 2.24091877137649E+00, residual= 6.68547391249564E-01 itr 2, prev= 6.68547391249564E-01, residual= 2.09751485926630E-02 itr 3, prev= 2.09751485926630E-02, residual= 6.06158481120112E-05 itr 4, prev= 6.06158481120112E-05, residual= 1.15975717918104E-09 simeq_newton5 found solution test case2 solution X( 1)= 1.10000000033516E+00, soln= 1.10000000000000E+00, err=-3.35164784814879E-10 X( 2)= 1.19999999995085E+00, soln= 1.20000000000000E+00, err= 4.91455764972670E-11 X( 3)= 1.39999999981368E+00, soln= 1.40000000000000E+00, err= 1.86314963457335E-10 residual= 1.15975717918104E-09 test_case_3 A( 1, 1)= 7.910778E-01 A( 1, 2)= 6.442950E-01 A( 1, 3)= 6.658510E-01 A( 1, 4)= 9.577035E-01 A( 1, 5)= 1.223651E-01 A( 1, 6)= 5.898427E-01 A( 1, 7)= 4.864346E-01 A( 2, 1)= 5.060496E-01 A( 2, 2)= 1.750984E-01 A( 2, 3)= 8.782248E-01 A( 2, 4)= 3.246958E-01 A( 2, 5)= 1.620386E-01 A( 2, 6)= 3.833710E-01 A( 2, 7)= 3.158238E-01 A( 3, 1)= 5.133576E-02 A( 3, 2)= 8.000549E-01 A( 3, 3)= 5.223173E-01 A( 3, 4)= 5.863344E-01 A( 3, 5)= 5.226468E-01 A( 3, 6)= 1.255568E-01 A( 3, 7)= 2.337342E-01 A( 4, 1)= 3.708149E-01 A( 4, 2)= 2.857049E-01 A( 4, 3)= 8.418347E-01 A( 4, 4)= 7.152572E-01 A( 4, 5)= 3.275851E-01 A( 4, 6)= 7.227268E-01 A( 4, 7)= 8.689656E-01 X_soln( 1)= 1.100000E+00 X_soln( 2)= 1.200000E+00 X_soln( 3)= 1.400000E+00 X_soln( 4)= 1.500000E+00 Y( 1)= 6.814518E+00 Y( 2)= 4.412558E+00 Y( 3)= 4.318721E+00 Y( 4)= 7.591667E+00 system of equations to be solved, i=1.. 4 A(i, 1)*X1+ A(i, 2)*X2+ A(i, 3)*X3+ A(i, 4)*X4+ A(i, 5)*X1*X2+ A(i, 6)*X1*X1*X3+ A(i, 7)*X4*X4*X4 = Y(i) initial guess X( 1)= 1.000000E+00 X( 2)= 1.000000E+00 X( 3)= 1.000000E+00 X( 4)= 1.000000E+00 simeq_newton5.adb running itr 0, initial residual= 9.15972339520032E+00 itr 1, prev= 9.15972339520032E+00, residual= 4.53751158658076E+00 itr 2, prev= 4.53751158658076E+00, residual= 6.62186950662226E-01 itr 3, prev= 6.62186950662226E-01, residual= 2.09079174881861E-02 itr 4, prev= 2.09079174881861E-02, residual= 2.65158073409211E-05 itr 5, prev= 2.65158073409211E-05, residual= 4.32809343919871E-11 simeq_newton5 found solution test case3 solution X( 1)= 1.09999999999646E+00, soln= 1.10000000000000E+00, err= 3.54205553776410E-12 X( 2)= 1.19999999999939E+00, soln= 1.20000000000000E+00, err= 6.07958128284736E-13 X( 3)= 1.40000000000323E+00, soln= 1.40000000000000E+00, err=-3.23407967073308E-12 X( 4)= 1.50000000000385E+00, soln= 1.50000000000000E+00, err=-3.84958731558527E-12 residual= 4.32809343919871E-11 test_case_4 A( 1, 1)= 7.055294E-01 A( 1, 2)= 8.333382E-01 A( 1, 3)= 9.146897E-01 A( 1, 4)= 1.905640E-01 A( 1, 5)= 8.099251E-01 A( 1, 6)= 4.112297E-01 A( 1, 7)= 5.375608E-01 A( 1, 8)= 7.839017E-01 A( 1, 9)= 3.662632E-02 A( 1,10)= 5.785426E-01 A( 2, 1)= 5.660214E-01 A( 2, 2)= 1.217688E-01 A( 2, 3)= 5.680125E-01 A( 2, 4)= 5.864237E-01 A( 2, 5)= 2.326706E-02 A( 2, 6)= 4.951762E-02 A( 2, 7)= 2.426066E-01 A( 2, 8)= 4.884598E-01 A( 2, 9)= 5.430390E-01 A( 2,10)= 8.572620E-01 A( 3, 1)= 2.925539E-03 A( 3, 2)= 1.695327E-01 A( 3, 3)= 3.362855E-01 A( 3, 4)= 9.501404E-01 A( 3, 5)= 1.036527E-02 A( 3, 6)= 2.091021E-01 A( 3, 7)= 3.791880E-01 A( 3, 8)= 1.246447E-02 A( 3, 9)= 4.903669E-01 A( 3,10)= 5.965996E-01 A( 4, 1)= 4.931436E-02 A( 4, 2)= 8.264277E-01 A( 4, 3)= 7.700864E-01 A( 4, 4)= 8.423222E-01 A( 4, 5)= 9.092780E-01 A( 4, 6)= 2.348641E-01 A( 4, 7)= 3.605372E-01 A( 4, 8)= 5.494863E-01 A( 4, 9)= 2.166863E-01 A( 4,10)= 8.464032E-01 X_soln( 1)= 1.100000E+00 X_soln( 2)= 1.200000E+00 X_soln( 3)= 1.400000E+00 X_soln( 4)= 1.500000E+00 Y( 1)= 1.077746E+01 Y( 2)= 8.038235E+00 Y( 3)= 5.969981E+00 Y( 4)= 1.038086E+01 system of equations to be solved, i=1.. 4 A(i, 1)*X1+ A(i, 2)*X2+ A(i, 3)*X3+ A(i, 4)*X4+ A(i, 5)*X1*X1*X1+ A(i, 6)*X2*X2*X2+ A(i, 7)*X3*X3*X3+ A(i, 8)*X4*X4*X4+ A(i, 9)*X1*X2*X3+ A(i, 10)*X2*X3*X4 = Y(i) initial guess X_init( 1)= 7.000000E-01 X_init( 2)= 7.500000E-01 X_init( 3)= 8.000000E-01 X_init( 4)= 8.500000E-01 simeq_newton5.adb running itr 0, initial residual= 2.36250984366996E+01 itr 1, prev= 2.36250984366996E+01, residual= 2.52350348986442E+01 b reduced to 5.00000000000000E-01 itr 2, prev= 2.36250984366996E+01, residual= 6.36443196865661E+00 b increased to 7.07150000000000E-01 itr 3, prev= 6.36443196865661E+00, residual= 1.53794475654719E+00 b increased to 1.00000000000000E+00 itr 4, prev= 1.53794475654719E+00, residual= 4.42093996293655E-02 itr 5, prev= 4.42093996293655E-02, residual= 1.60825555173449E-03 itr 6, prev= 1.60825555173449E-03, residual= 1.10949181033604E-05 itr 7, prev= 1.10949181033604E-05, residual= 4.85578688369515E-10 simeq_newton5 found solution test case4 solution X( 1)= 1.10000000023164E+00, soln= 1.10000000000000E+00, err=-2.31642482972916E-10 X( 2)= 1.19999999961425E+00, soln= 1.20000000000000E+00, err= 3.85752096931924E-10 X( 3)= 1.40000000028025E+00, soln= 1.40000000000000E+00, err=-2.80245382455746E-10 X( 4)= 1.49999999991447E+00, soln= 1.50000000000000E+00, err= 8.55315818171221E-11 sum of errors= 4.85581352904774E-10 test_case_5 A( 1, 1)= 1.000000E+00 A( 1, 2)= 0.000000E+00 A( 1, 3)= 0.000000E+00 A( 1, 4)= 0.000000E+00 A( 1, 5)= 0.000000E+00 A( 1, 6)= 0.000000E+00 A( 1, 7)= 0.000000E+00 A( 1, 8)= 0.000000E+00 A( 1, 9)= 0.000000E+00 A( 1,10)= 0.000000E+00 A( 1,11)= 0.000000E+00 A( 1,12)= 0.000000E+00 A( 1,13)= 0.000000E+00 A( 1,14)= 0.000000E+00 A( 1,15)= 0.000000E+00 A( 1,16)= 0.000000E+00 A( 1,17)= 0.000000E+00 A( 1,18)= 0.000000E+00 A( 1,19)= 0.000000E+00 A( 1,20)= 0.000000E+00 A( 2, 1)= 0.000000E+00 A( 2, 2)= 1.000000E+00 A( 2, 3)= 0.000000E+00 A( 2, 4)= 0.000000E+00 A( 2, 5)= 0.000000E+00 A( 2, 6)= 4.987955E-01 A( 2, 7)= 2.563720E-01 A( 2, 8)= 8.437223E-01 A( 2, 9)= 4.406502E-01 A( 2,10)= 8.642795E-03 A( 2,11)= 2.594640E-01 A( 2,12)= 8.108377E-01 A( 2,13)= 7.485342E-01 A( 2,14)= 6.148338E-01 A( 2,15)= 5.113861E-01 A( 2,16)= 8.655562E-01 A( 2,17)= 4.026303E-01 A( 2,18)= 7.631819E-03 A( 2,19)= 2.679859E-01 A( 2,20)= 3.820050E-02 A( 3, 1)= 0.000000E+00 A( 3, 2)= 0.000000E+00 A( 3, 3)= 1.000000E+00 A( 3, 4)= 0.000000E+00 A( 3, 5)= 0.000000E+00 A( 3, 6)= 3.575609E-02 A( 3, 7)= 9.526707E-01 A( 3, 8)= 5.367662E-01 A( 3, 9)= 4.292826E-01 A( 3,10)= 9.533748E-01 A( 3,11)= 3.697513E-01 A( 3,12)= 4.096122E-01 A( 3,13)= 3.530037E-01 A( 3,14)= 9.329113E-01 A( 3,15)= 4.410107E-01 A( 3,16)= 6.726220E-02 A( 3,17)= 4.758614E-01 A( 3,18)= 8.033032E-01 A( 3,19)= 1.165100E-01 A( 3,20)= 1.835644E-01 A( 4, 1)= 0.000000E+00 A( 4, 2)= 0.000000E+00 A( 4, 3)= 0.000000E+00 A( 4, 4)= 1.000000E+00 A( 4, 5)= 0.000000E+00 A( 4, 6)= 1.673390E-01 A( 4, 7)= 4.672617E-01 A( 4, 8)= 2.670349E-01 A( 4, 9)= 5.498571E-02 A( 4,10)= 1.448276E-01 A( 4,11)= 1.179456E-01 A( 4,12)= 3.124487E-01 A( 4,13)= 3.250913E-01 A( 4,14)= 8.101167E-01 A( 4,15)= 6.313580E-01 A( 4,16)= 2.343411E-01 A( 4,17)= 5.712976E-01 A( 4,18)= 7.988057E-01 A( 4,19)= 5.273069E-01 A( 4,20)= 4.473994E-01 A( 5, 1)= 0.000000E+00 A( 5, 2)= 0.000000E+00 A( 5, 3)= 0.000000E+00 A( 5, 4)= 0.000000E+00 A( 5, 5)= 1.000000E+00 A( 5, 6)= 0.000000E+00 A( 5, 7)= 0.000000E+00 A( 5, 8)= 0.000000E+00 A( 5, 9)= 0.000000E+00 A( 5,10)= 0.000000E+00 A( 5,11)= 0.000000E+00 A( 5,12)= 0.000000E+00 A( 5,13)= 0.000000E+00 A( 5,14)= 0.000000E+00 A( 5,15)= 0.000000E+00 A( 5,16)= 0.000000E+00 A( 5,17)= 0.000000E+00 A( 5,18)= 0.000000E+00 A( 5,19)= 0.000000E+00 A( 5,20)= 0.000000E+00 X_soln( 1)= 1.100000E+00 X_soln( 2)= 1.200000E+00 X_soln( 3)= 1.400000E+00 X_soln( 4)= 1.500000E+00 X_soln( 5)= 1.700000E+00 Y( 1)= 1.100000E+00 Y( 2)= 1.532679E+01 Y( 3)= 1.690444E+01 Y( 4)= 1.576443E+01 Y( 5)= 1.700000E+00 system of equations to be solved, i=1.. 5 A(i, 1)*X1+ A(i, 2)*X2+ A(i, 3)*X3+ A(i, 4)*X4+ A(i, 5)*X5+ A(i, 6)*X2*X2+ A(i, 7)*X2*X3+ A(i, 8)*X2*X4+ A(i, 9)*X3*X3+ A(i, 10)*X3*X4+ A(i, 11)*X4*X4+ A(i, 12)*X2*X2*X2+ A(i, 13)*X2*X2*X3+ A(i, 14)*X2*X2*X4+ A(i, 15)*X3*X3*X2+ A(i, 16)*X3*X3*X3+ A(i, 17)*X3*X3*X4+ A(i, 18)*X4*X4*X2+ A(i, 19)*X4*X4*X3+ A(i, 20)*X4*X4*X4 = Y(i) initial guess X_init( 1)= 1.000000E+00 X_init( 2)= 1.000000E+00 X_init( 3)= 1.000000E+00 X_init( 4)= 1.000000E+00 X_init( 5)= 1.000000E+00 simeq_newton5.adb running itr 0, initial residual= 2.62822197528776E+01 itr 1, prev= 2.62822197528776E+01, residual= 1.19590130720924E+01 itr 2, prev= 1.19590130720924E+01, residual= 8.85007691536389E-01 itr 3, prev= 8.85007691536389E-01, residual= 6.40479815994688E-03 itr 4, prev= 6.40479815994688E-03, residual= 3.77604593531089E-05 simeq_newton5 found solution test case5 solution, computed, expected not unique X( 1)= 1.10000000000000E+00, soln= 1.10000000000000E+00, err= 0.00000000000000E+00 X( 2)= 1.38410284969817E+00, soln= 1.20000000000000E+00, err=-1.84102849698167E-01 X( 3)= 1.16634027567524E+00, soln= 1.40000000000000E+00, err= 2.33659724324764E-01 X( 4)= 1.50410681381923E+00, soln= 1.50000000000000E+00, err=-4.10681381923350E-03 X( 5)= 1.70000000000000E+00, soln= 1.70000000000000E+00, err= 0.00000000000000E+00 sum of errors= 3.77604593531089E-05 check when given solution as initial condition simeq_newton5.adb running itr 0, initial residual= 1.77635683940025E-15 simeq_newton5 found solution test_case_6 A( 1, 1)= 4.409318E-01 A( 1, 2)= 7.403091E-01 A( 1, 3)= 3.754196E-01 A( 1, 4)= 6.765303E-01 A( 1, 5)= 4.452925E-01 A( 1, 6)= 3.122843E-02 A( 2, 1)= 8.562563E-01 A( 2, 2)= 9.962713E-02 A( 2, 3)= 4.331546E-01 A( 2, 4)= 2.867252E-02 A( 2, 5)= 8.990138E-01 A( 2, 6)= 7.242093E-01 A( 3, 1)= 7.859809E-01 A( 3, 2)= 9.816233E-01 A( 3, 3)= 1.433489E-01 A( 3, 4)= 2.645979E-01 A( 3, 5)= 9.626134E-02 A( 3, 6)= 8.643767E-01 A( 4, 1)= 5.790318E-01 A( 4, 2)= 7.871371E-01 A( 4, 3)= 4.128703E-01 A( 4, 4)= 1.114484E-01 A( 4, 5)= 1.137011E-01 A( 4, 6)= 9.745998E-01 A( 5, 1)= 9.928572E-02 A( 5, 2)= 6.951737E-01 A( 5, 3)= 7.839175E-01 A( 5, 4)= 3.009932E-01 A( 5, 5)= 7.934883E-01 A( 5, 6)= 1.581998E-01 X_soln( 1)= 1.100000E+00 X_soln( 2)= 1.200000E+00 X_soln( 3)= 1.400000E+00 X_soln( 4)= 1.500000E+00 X_soln( 5)= 1.900000E+00 Y( 1)= 3.780084E+00 Y( 2)= 3.888578E+00 Y( 3)= 3.383489E+00 Y( 4)= 3.174674E+00 Y( 5)= 4.102605E+00 system of equations to be solved, i=1.. 5 A(i, 1)*X1+ A(i, 2)*X2+ A(i, 3)*X3+ A(i, 4)*X4+ A(i, 5)*X5+ A(i, 6)*X1*X2*X3/(X4*X5) = Y(i) initial guess X_init( 1)= 7.000000E-01 X_init( 2)= 7.500000E-01 X_init( 3)= 5.000000E-01 X_init( 4)= 9.000000E-01 X_init( 5)= 6.000000E-01 simeq_newton5.adb running itr 0, initial residual= 8.85338218668715E+00 itr 1, prev= 8.85338218668715E+00, residual= 1.97594517409938E-01 itr 2, prev= 1.97594517409938E-01, residual= 3.84477061929411E-03 itr 3, prev= 3.84477061929411E-03, residual= 1.51006250037611E-06 simeq_newton5 found solution test case6 solution X( 1)= 1.10000021037613E+00, soln= 1.10000000000000E+00, err=-2.10376129849976E-07 X( 2)= 1.20000004287026E+00, soln= 1.20000000000000E+00, err=-4.28702591204200E-08 X( 3)= 1.40000017332606E+00, soln= 1.40000000000000E+00, err=-1.73326060171064E-07 X( 4)= 1.49999981047810E+00, soln= 1.50000000000000E+00, err= 1.89521899063294E-07 X( 5)= 1.89999987603110E+00, soln= 1.90000000000000E+00, err= 1.23968903364968E-07 sum of errors= 1.51006249993202E-06 end test_simeq_newton5