test_simeq_newton5.java running test case 1, n=2, nlin=2 A[0][0]=1.0 A[0][1]=1.0 A[0][2]=1.0 A[0][3]=0.0 A[1][0]=1.0 A[1][1]=1.0 A[1][2]=0.0 A[1][3]=1.0 Y[0]=4.0 Y[1]=7.0 solve system of equations A X = Y for X the equations are for i=0,1 A[i][0]*X0+ A[i][1]*X1+ A[i][2]*X0*X0+ A[i][3]*X1*X1 = Y[i] desired solution, may not be unique X_soln[0]=1.0 X_soln[1]=2.0 initial guess X[0]=0.5 X[1]=0.5 simeq_newton5 itr 1, prev=8.5, residual=8.513888888888888 b reduced to 0.5 simeq_newton5 itr 2, prev=8.5, residual=2.121527777777778 b increased to 0.70715 simeq_newton5 itr 3, prev=2.121527777777778, residual=0.36725232805001573 b increased to 1.0 simeq_newton5 itr 4, prev=0.36725232805001573, residual=0.002800871770802793 simeq_newton5 itr 5, prev=0.002800871770802793, residual=2.1229367330732885E-7 Returned solution vs expected solution X[0]=1.0000000610569897 err=6.105698968639217E-8 X[1]=1.9999999946776186 err=-5.322381424477385E-9 Returned solution in given equation, sum of errors=2.1229367330732885E-7 test 1 finished test case 2, n=3, nlin=4 first A generated A[0][0]=0.24346082016192794 A[0][1]=0.14923961761562476 A[0][2]=0.6272866061713837 A[0][3]=0.8234772618472931 A[0][4]=0.5943820433729802 A[0][5]=0.8323086020333372 A[0][6]=0.5992483105393138 A[1][0]=0.4116792106592976 A[1][1]=0.5537897514487559 A[1][2]=0.4203105164142309 A[1][3]=0.8153744337636625 A[1][4]=0.09746520278452908 A[1][5]=0.12999531662243746 A[1][6]=0.8822731019000624 A[2][0]=0.10219028796530316 A[2][1]=0.26418078517831634 A[2][2]=0.5790416884593746 A[2][3]=0.37434246655280523 A[2][4]=0.11101659368656913 A[2][5]=0.5759448611885859 A[2][6]=0.540946890648486 Y[0]=4.730705771292221 Y[1]=3.689173673414425 Y[2]=2.8190402530968655 solve system of equations A X = Y for X the equations are for i=0,2 A[i][0]*X0+ A[i][1]*X1+ A[i][2]*X2+ A[i][3]*X0*X1+ A[i][4]*X2*X1*X1+ A[i][5]*X1/(X2)+ A[i][6]*X0*X0*X0/(X2*X2) = Y[i] desired solution, may not be unique X_soln[0]=1.1 X_soln[1]=1.2 X_soln[2]=1.4 initial guess X[0]=1.0 X[1]=1.0 X[2]=1.0 simeq_newton5 itr 1, prev=1.5109653287892333, residual=0.6674237366862741 simeq_newton5 itr 2, prev=0.6674237366862741, residual=0.009346536783815473 simeq_newton5 itr 3, prev=0.009346536783815473, residual=2.269492203499368E-6 simeq_newton5 itr 4, prev=2.269492203499368E-6, residual=1.3112133601111964E-10 Returned solution vs expected solution X[0]=1.0999999998502332 err=-1.4976686557588437E-10 X[1]=1.200000000158677 err=1.5867707148231602E-10 X[2]=1.3999999995037389 err=-4.962610322678529E-10 Returned solution in given equation, sum of errors=1.3112133601111964E-10 test 2 finished test case 3, n=4, nlin=3 first A generated A[0][0]=0.26619026531676704 A[0][1]=0.13053055194844665 A[0][2]=0.3907055238539393 A[0][3]=0.2709306292368594 A[0][4]=0.2973847427129327 A[0][5]=0.2530535077136986 A[0][6]=0.8541171250472884 A[1][0]=0.25972189095806963 A[1][1]=0.6346301329082957 A[1][2]=0.3551666603247676 A[1][3]=0.17805383689938126 A[1][4]=0.9091157534365126 A[1][5]=0.16816186355022078 A[1][6]=0.42845213580262564 A[2][0]=0.0030814126246764273 A[2][1]=0.957267890691114 A[2][2]=0.8592177645284279 A[2][3]=0.027601865518819046 A[2][4]=0.5459682889833226 A[2][5]=0.03278578023880374 A[2][6]=0.33038810022966536 A[3][0]=0.990831816042379 A[3][1]=0.44132340816561 A[3][2]=0.057495463438021366 A[3][3]=0.1767803199289779 A[3][4]=0.13148491607292212 A[3][5]=0.8007073568610487 A[3][6]=0.21483366665454262 Y[0]=5.106695430920059 Y[1]=4.742489269071711 Y[2]=4.287695782792149 Y[3]=4.22018919285 solve system of equations A X = Y for X the equations are for i=0,3 A[i][0]*X0+ A[i][1]*X1+ A[i][2]*X2+ A[i][3]*X3+ A[i][4]*X0*X1+ A[i][5]*X0*X0*X2+ A[i][6]*X3*X3*X3 = Y[i] desired solution, may not be unique X_soln[0]=1.1 X_soln[1]=1.2 X_soln[2]=1.4 X_soln[3]=1.5 initial guess X[0]=1.0 X[1]=1.0 X[2]=1.0 X[3]=1.0 simeq_newton5 itr 1, prev=7.391087005945782, residual=4.180723208858469 simeq_newton5 itr 2, prev=4.180723208858469, residual=0.4774173213195203 simeq_newton5 itr 3, prev=0.4774173213195203, residual=0.010364506779065863 simeq_newton5 itr 4, prev=0.010364506779065863, residual=5.302475849511268E-6 simeq_newton5 itr 5, prev=5.302475849511268E-6, residual=1.3917755836700962E-12 Returned solution vs expected solution X[0]=1.0999999999999919 err=-8.215650382226158E-15 X[1]=1.200000000000001 err=1.1102230246251565E-15 X[2]=1.400000000000015 err=1.509903313490213E-14 X[3]=1.500000000000108 err=1.0791367799356522E-13 Returned solution in given equation, sum of errors=1.3917755836700962E-12 test 3 finished test case 4, n=4, nlin=6 first A generated A[0][0]=0.6683171361528171 A[0][1]=0.29990079976646566 A[0][2]=0.03307020065053812 A[0][3]=0.8541347731903424 A[0][4]=0.6121193421879261 A[0][5]=0.07107615369100995 A[0][6]=0.3971275622353464 A[0][7]=0.010652899074464095 A[0][8]=0.14880756308781784 A[0][9]=0.32633470581261725 A[1][0]=0.08929466658281404 A[1][1]=0.1869793965348001 A[1][2]=0.16768997405157526 A[1][3]=0.16617107203625037 A[1][4]=0.9100550925352872 A[1][5]=0.663586545233721 A[1][6]=0.8431859308187835 A[1][7]=0.9166281067345668 A[1][8]=0.19714971962100847 A[1][9]=0.8845484716180051 A[2][0]=0.5184680662106359 A[2][1]=0.47301268606085034 A[2][2]=0.7657282644448924 A[2][3]=0.3990604908068145 A[2][4]=0.7921883409994044 A[2][5]=0.8624503740894817 A[2][6]=0.0536142605880241 A[2][7]=0.43019876387280775 A[2][8]=0.20028652768562483 A[2][9]=0.7007239600636026 A[3][0]=0.5340920248261962 A[3][1]=0.3894319607482364 A[3][2]=0.32726187764414993 A[3][3]=0.16903747989409557 A[3][4]=0.7291315773293328 A[3][5]=0.5587174524609827 A[3][6]=0.5299222573210903 A[3][7]=0.24279136758209485 A[3][8]=0.8327258066158009 A[3][9]=0.7215845186263519 Y[0]=5.583112088598509 Y[1]=11.165299743870674 Y[2]=9.0882495724822 Y[3]=9.333278133270621 solve system of equations A X = Y for X the equations are for i=0,3 A[i][0]*X0+ A[i][1]*X1+ A[i][2]*X2+ A[i][3]*X3+ A[i][4]*X0*X0*X0+ A[i][5]*X1*X1*X1+ A[i][6]*X2*X2*X2+ A[i][7]*X3*X3*X3+ A[i][8]*X0*X1*X2+ A[i][9]*X1*X2*X3 = Y[i] desired solution, may not be unique X_soln[0]=1.1 X_soln[1]=1.2 X_soln[2]=1.4 X_soln[3]=1.5 initial guess X[0]=1.0 X[1]=1.0 X[2]=1.0 X[3]=1.0 simeq_newton5 itr 1, prev=16.49268136873538, residual=10.11483937851255 simeq_newton5 itr 2, prev=10.11483937851255, residual=1.529228965352126 simeq_newton5 itr 3, prev=1.529228965352126, residual=0.037110858318437856 simeq_newton5 itr 4, prev=0.037110858318437856, residual=5.5329883012156245E-5 simeq_newton5 itr 5, prev=5.5329883012156245E-5, residual=9.196199357575097E-11 Returned solution vs expected solution X[0]=1.099999999996498 err=-3.5020875088775938E-12 X[1]=1.2000000000011217 err=1.1217693440812582E-12 X[2]=1.400000000001164 err=1.1641798636219391E-12 X[3]=1.5000000000061218 err=6.121769757783113E-12 Returned solution in given equation, sum of errors=9.196199357575097E-11 test 4 finished test case 5, n=5, nlin=15 first A generated A[0][0]=0.7115072300203941 A[0][1]=0.16715033748078656 A[0][2]=0.03702178208297746 A[0][3]=0.7404273391819015 A[0][4]=0.7452146861890832 A[0][5]=0.5931311218877856 A[0][6]=0.14318576297608365 A[0][7]=0.9493011730570199 A[0][8]=0.2135435396045282 A[0][9]=0.36313155020999544 A[0][10]=0.9344494754179178 A[0][11]=0.7598353061536314 A[0][12]=0.10349735185777276 A[0][13]=0.6662691129379633 A[0][14]=0.0905430325562786 A[0][15]=0.062446240592098134 A[0][16]=0.9775771025368623 A[0][17]=0.17159133753474476 A[0][18]=0.1307276656098162 A[0][19]=0.8458557314666935 A[1][0]=0.9266237801947877 A[1][1]=0.7911658734859572 A[1][2]=0.9868989175835605 A[1][3]=0.9549877655326804 A[1][4]=0.30295457925876834 A[1][5]=0.9252543653126252 A[1][6]=0.32873957209509685 A[1][7]=0.060639577358211905 A[1][8]=0.8308687305827313 A[1][9]=0.3982177964681295 A[1][10]=0.6896583519678713 A[1][11]=0.7238914514960196 A[1][12]=0.1964826929441551 A[1][13]=0.8064982573115871 A[1][14]=0.7752591854101837 A[1][15]=0.9040409569642355 A[1][16]=0.6299863260856092 A[1][17]=0.6689657997091476 A[1][18]=0.07534299562603497 A[1][19]=0.3809173464124399 A[2][0]=0.31079509076047074 A[2][1]=0.5951152838369069 A[2][2]=0.04595208559687869 A[2][3]=0.34075188674737966 A[2][4]=0.6497060275860754 A[2][5]=0.6680430102413561 A[2][6]=0.6797250714385779 A[2][7]=0.8093507945747348 A[2][8]=0.6320477311731325 A[2][9]=0.37682856321921077 A[2][10]=0.24083768205343092 A[2][11]=0.7071370530093157 A[2][12]=0.4419479361793268 A[2][13]=0.7268921799920054 A[2][14]=0.30506330339654397 A[2][15]=0.04769853233790522 A[2][16]=0.5302244026511548 A[2][17]=0.6070937729020238 A[2][18]=0.015994086239612848 A[2][19]=0.20479923253002796 A[3][0]=0.13703856910806955 A[3][1]=0.09878453179402824 A[3][2]=0.6452220649011405 A[3][3]=0.2323814783446393 A[3][4]=0.03533310368852338 A[3][5]=0.1747178176274392 A[3][6]=0.12728693667754787 A[3][7]=0.9379071137869781 A[3][8]=0.9222083625563899 A[3][9]=0.15467105294792682 A[3][10]=0.22945522243337335 A[3][11]=0.7814553407435458 A[3][12]=0.4527749118508302 A[3][13]=0.3598256675252103 A[3][14]=0.4119034845141537 A[3][15]=0.7013165387757108 A[3][16]=0.3846521434444976 A[3][17]=0.6393976447178158 A[3][18]=0.23563564199547815 A[3][19]=0.651390197394771 A[4][0]=0.6811664368401644 A[4][1]=0.8307064634265713 A[4][2]=0.383472908909656 A[4][3]=0.9765164275972983 A[4][4]=0.7074339203997252 A[4][5]=0.7578151971432497 A[4][6]=0.9737118211895617 A[4][7]=0.7489406260154297 A[4][8]=0.8458971947151314 A[4][9]=0.07407051199002601 A[4][10]=0.8665545355964885 A[4][11]=0.8424306368021581 A[4][12]=0.9565169752754288 A[4][13]=0.11031599009930027 A[4][14]=0.09017275589629425 A[4][15]=0.830137175181028 A[4][16]=0.11170294610493114 A[4][17]=0.9032478879807974 A[4][18]=0.3462747416085159 A[4][19]=0.7581070658097052 Y[0]=19.448636334041915 Y[1]=24.18256120813955 Y[2]=17.33973609289034 Y[3]=18.115040818801816 Y[4]=25.31771874141033 solve system of equations A X = Y for X the equations are for i=0,4 A[i][0]*X0+ A[i][1]*X1+ A[i][2]*X2+ A[i][3]*X3+ A[i][4]*X4+ A[i][5]*X1*X1+ A[i][6]*X1*X2+ A[i][7]*X1*X3+ A[i][8]*X2*X2+ A[i][9]*X2*X3+ A[i][10]*X3*X3+ A[i][11]*X1*X1*X1+ A[i][12]*X1*X1*X2+ A[i][13]*X1*X1*X3+ A[i][14]*X2*X2*X1+ A[i][15]*X2*X2*X2+ A[i][16]*X2*X2*X3+ A[i][17]*X3*X3*X1+ A[i][18]*X3*X3*X2+ A[i][19]*X3*X3*X3 = Y[i] desired solution, may not be unique X_soln[0]=1.1 X_soln[1]=1.2 X_soln[2]=1.4 X_soln[3]=1.5 X_soln[4]=1.7 initial guess X[0]=1.0 X[1]=1.0 X[2]=1.0 X[3]=1.0 X[4]=1.0 simeq_newton5 itr 1, prev=52.59533822425418, residual=23.484663432787766 simeq_newton5 itr 2, prev=23.484663432787766, residual=1.968862601983254 simeq_newton5 itr 3, prev=1.968862601983254, residual=0.07154908765420842 simeq_newton5 itr 4, prev=0.07154908765420842, residual=2.5418192741710754E-4 simeq_newton5 itr 5, prev=2.5418192741710754E-4, residual=3.757207878152258E-10 solution may not be unique Returned solution vs expected solution X[0]=1.1000000000166419 err=1.6641799049921246E-11 X[1]=1.2000000000075088 err=7.508882404749784E-12 X[2]=1.3999999999954993 err=-4.5006220972254596E-12 X[3]=1.5000000000040565 err=4.056532887375397E-12 X[4]=1.6999999999423838 err=-5.7616134085947124E-11 Returned solution in given equation, sum of errors=3.757207878152258E-10 give solution as initial guess, check Returned solution vs expected solution X[0]=1.1 err=0.0 X[1]=1.2 err=0.0 X[2]=1.4 err=0.0 X[3]=1.5 err=0.0 X[4]=1.7 err=0.0 Returned solution in given equation, sum of errors=0.0 test 5 finished test case 4, n=5, nlin=1 Y[0]=3.0297368421052635 Y[1]=2.009298245614035 Y[2]=1.5491478696741856 Y[3]=1.2721658312447786 Y[4]=1.083453216374269 solve system of equations A X = Y for X the equations are for i=0,4 A[i][0]*X0+ A[i][1]*X1+ A[i][2]*X2+ A[i][3]*X3+ A[i][4]*X4+ A[i][5]*X0*X1*X2/(X3*X4) = Y[i] desired solution, may not be unique X_soln[0]=1.1 X_soln[1]=1.2 X_soln[2]=1.4 X_soln[3]=1.5 X_soln[4]=1.9 initial guess X[0]=2.0 X[1]=2.0 X[2]=2.0 X[3]=2.0 X[4]=2.0 simeq_newton5 itr 1, prev=5.260166248955721, residual=0.29059753148663026 simeq_newton5 itr 2, prev=0.29059753148663026, residual=0.05938452502552072 simeq_newton5 itr 3, prev=0.05938452502552072, residual=0.0031103459030283886 simeq_newton5 itr 4, prev=0.0031103459030283886, residual=9.43170427492035E-6 simeq_newton5 itr 5, prev=9.43170427492035E-6, residual=8.730438594284351E-11 Returned solution vs expected solution X[0]=1.1000000000006032 err=6.03073146976385E-13 X[1]=1.1999999999849174 err=-1.5082601834137677E-11 X[2]=1.4000000000916684 err=9.166845060804008E-11 X[3]=1.4999999997818723 err=-2.1812773809415376E-10 X[4]=1.9000000002233002 err=2.2330026716588236E-10 Returned solution in given equation, sum of errors=8.730438594284351E-11 test 6 finished