test_simeq_newton5.java running
test case 1, n=2, nlin=2
equation X[0] + X[1] + X[0]*X[0] + X[1]*X[1] = Y
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]=0.9137809858754505
A[0][1]=0.8270365662564145
A[0][2]=0.13953474779856456
A[0][3]=0.289537922772098
A[0][4]=0.7896730800956286
A[0][5]=0.816596160886628
A[0][6]=0.8995839741113334
A[1][0]=0.5605349991045631
A[1][1]=0.7655277871312027
A[1][2]=0.07269556077198613
A[1][3]=0.29295349807751925
A[1][4]=0.7596103849248839
A[1][5]=0.0030874625077840223
A[1][6]=0.2291924932378715
A[2][0]=0.2733030431254091
A[2][1]=0.756708504998652
A[2][2]=0.6456334570181581
A[2][3]=0.9459811188816297
A[2][4]=0.7654548337177232
A[2][5]=0.8883516400427294
A[2][6]=0.6941946316806727
 
Y[0]=5.477953118742946
Y[1]=3.7133555910591776
Y[2]=6.137281501714905
 
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=2.9996173585001262, residual=0.9648662161991486
simeq_newton5 itr 2, prev=0.9648662161991486, residual=0.020499125205784896
simeq_newton5 itr 3, prev=0.020499125205784896, residual=1.6204177407486142E-4
simeq_newton5 itr 4, prev=1.6204177407486142E-4, residual=2.1620885526374423E-8
Returned solution vs expected solution
X[0]=1.1000000980733167       err=9.807331657896157E-8
X[1]=1.1999999389818508       err=-6.101814920000947E-8
X[2]=1.4000000948305746       err=9.483057472614576E-8
Returned solution in given equation, sum of errors=2.1620885526374423E-8
 
test 2 finished 

test case 3, n=4, nlin=3
first A generated 
A[0][0]=0.6923407079250855
A[0][1]=0.47688637992601446
A[0][2]=0.2732155964571109
A[0][3]=0.2041000603226788
A[0][4]=0.24696749848413557
A[0][5]=0.6704515529556835
A[0][6]=0.801313100992522
A[1][0]=0.6463883224097194
A[1][1]=0.5416738284261101
A[1][2]=0.8097375119595293
A[1][3]=0.6976945192109479
A[1][4]=0.35768847064723996
A[1][5]=0.2814017758429751
A[1][6]=0.08319143846018928
A[2][0]=0.007864382450594065
A[2][1]=0.36253828889818374
A[2][2]=0.11011347326818377
A[2][3]=0.6891278949485625
A[2][4]=0.8296509956065434
A[2][5]=0.49370785940047013
A[2][6]=0.9602836546481368
A[3][0]=0.42095369703880703
A[3][1]=0.6250561304649018
A[3][2]=0.6589472025578117
A[3][3]=0.6231345041524677
A[3][4]=0.5304240981673395
A[3][5]=0.4856501769015068
A[3][6]=0.30667911597108555
 
Y[0]=6.188664104708534
Y[1]=4.7708245386572825
Y[2]=6.80398523483427
Y[3]=5.628237488764662
 
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=9.504529128470212, residual=2.56835987813409
simeq_newton5 itr 2, prev=2.56835987813409, residual=0.27344440106524726
simeq_newton5 itr 3, prev=0.27344440106524726, residual=0.004314023267433242
simeq_newton5 itr 4, prev=0.004314023267433242, residual=2.393448018445099E-6
simeq_newton5 itr 5, prev=2.393448018445099E-6, residual=1.7852386235972517E-13
Returned solution vs expected solution
X[0]=1.8385955274941947       err=0.7385955274941947
X[1]=1.2198707390937673       err=0.019870739093767353
X[2]=0.5240720784478577       err=-0.8759279215521422
X[3]=1.3927599545801534       err=-0.10724004541984655
Returned solution in given equation, sum of errors=1.7852386235972517E-13
 
test 3 finished 

test case 4, n=4, nlin=6
first A generated 
A[0][0]=0.507416520316295
A[0][1]=0.06647074443866319
A[0][2]=0.7963677197783804
A[0][3]=0.62850932674213
A[0][4]=0.016453899408929717
A[0][5]=0.8881180115250771
A[0][6]=0.3450970827666844
A[0][7]=0.8030277983822777
A[0][8]=0.9663358086781076
A[0][9]=0.33223119251442756
A[1][0]=0.559246883646102
A[1][1]=0.6332269495511937
A[1][2]=0.9925503782784466
A[1][3]=0.08031667120038266
A[1][4]=0.2155115738600506
A[1][5]=0.25896321582620296
A[1][6]=0.9480211642580836
A[1][7]=0.11332037659885597
A[1][8]=0.6653466607729461
A[1][9]=0.23624115561834325
A[2][0]=0.8824206048897008
A[2][1]=0.7693477678531995
A[2][2]=0.3462041454820859
A[2][3]=0.1666997564651942
A[2][4]=0.31079858395568694
A[2][5]=0.826454943450479
A[2][6]=0.10736667195034333
A[2][7]=0.23353283606139563
A[2][8]=0.12897869859340272
A[2][9]=0.22113715848585325
A[3][0]=0.6692591022684354
A[3][1]=0.45417681603018334
A[3][2]=0.7138385668477031
A[3][3]=0.48286736822721743
A[3][4]=0.35640453570189556
A[3][5]=0.19545049515708324
A[3][6]=0.45850478266386774
A[3][7]=0.2160144832326265
A[3][8]=0.09673087293822802
A[3][9]=0.5134334629546965
 
Y[0]=10.532346321731335
Y[1]=8.4281384766299
Y[2]=6.348808226626579
Y[3]=7.276782114685221
 
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=14.383680352302179, residual=6.283518797473754
simeq_newton5 itr 2, prev=6.283518797473754, residual=0.48585636863702675
simeq_newton5 itr 3, prev=0.48585636863702675, residual=0.003612976012628444
simeq_newton5 itr 4, prev=0.003612976012628444, residual=3.860801509603107E-7
Returned solution vs expected solution
X[0]=1.1000001393382637       err=1.3933826359391333E-7
X[1]=1.1999999666368606       err=-3.336313936230795E-8
X[2]=1.3999999776591627       err=-2.2340837180223616E-8
X[3]=1.500000008630206       err=8.630206105308957E-9
Returned solution in given equation, sum of errors=3.860801509603107E-7
 
test 4 finished 

test case 5, n=5, nlin=15
first A generated 
A[0][0]=0.23565693530710985
A[0][1]=0.9926967792994803
A[0][2]=0.5637237724147625
A[0][3]=0.17822086467987297
A[0][4]=0.05654946939383465
A[0][5]=0.8336034242162509
A[0][6]=0.25295991329514234
A[0][7]=0.8227941136185248
A[0][8]=0.49902416189396415
A[0][9]=0.048542622453199624
A[0][10]=0.2308444458508706
A[0][11]=0.5155987131006271
A[0][12]=0.31469973792106964
A[0][13]=0.5844525661897131
A[0][14]=0.2709148133163676
A[0][15]=0.19802155460510862
A[0][16]=0.9936897256525172
A[0][17]=0.18583685039236042
A[0][18]=0.10186294366890014
A[0][19]=0.8508121511588813
A[1][0]=0.9646132145713544
A[1][1]=0.6110632843430575
A[1][2]=0.5314661550062928
A[1][3]=0.9575934439857055
A[1][4]=0.5383276824473561
A[1][5]=0.8676914596641254
A[1][6]=0.28190676587149444
A[1][7]=0.8189594410245895
A[1][8]=0.6657266622336883
A[1][9]=0.9309707754557712
A[1][10]=0.4744989827192333
A[1][11]=0.5372586657872839
A[1][12]=0.0731096227954956
A[1][13]=0.6918773067852724
A[1][14]=0.8356310878870985
A[1][15]=0.04001381172879004
A[1][16]=0.3630449211425031
A[1][17]=0.9445347248296618
A[1][18]=0.8607698424099591
A[1][19]=0.3390296324043104
A[2][0]=0.2243112837836061
A[2][1]=0.06759046689949744
A[2][2]=0.3696629001456434
A[2][3]=0.33259245944239335
A[2][4]=0.9814168451901987
A[2][5]=0.6800955240171361
A[2][6]=0.11341466292046887
A[2][7]=0.8497669314631128
A[2][8]=0.33235926419878425
A[2][9]=0.9596624467239133
A[2][10]=0.3528991853836799
A[2][11]=0.30864590000642045
A[2][12]=0.2727041855721545
A[2][13]=0.49915256903269345
A[2][14]=0.6180138157413838
A[2][15]=0.3145125236576969
A[2][16]=0.8847236996801162
A[2][17]=0.5478705970706844
A[2][18]=0.1785654049247568
A[2][19]=0.7592239044469569
A[3][0]=0.8822498988323012
A[3][1]=0.23422066582125223
A[3][2]=0.11012055930117837
A[3][3]=0.4997276421965391
A[3][4]=0.5450636375920865
A[3][5]=0.8990047312283194
A[3][6]=0.22194041989451785
A[3][7]=0.4914745946600828
A[3][8]=0.9510517938585029
A[3][9]=0.9820210801217019
A[3][10]=0.5291590179571094
A[3][11]=0.3315918462483921
A[3][12]=0.22003082686605047
A[3][13]=0.9993464956542427
A[3][14]=0.39765421547386326
A[3][15]=0.5270324606134681
A[3][16]=0.8200483599742846
A[3][17]=0.024663221246396527
A[3][18]=0.9675981774125417
A[3][19]=0.4445192225644349
A[4][0]=0.8551387295660469
A[4][1]=0.7452174173067778
A[4][2]=0.9704646063037115
A[4][3]=0.8219518538981503
A[4][4]=0.6529222808942214
A[4][5]=0.6014731765400179
A[4][6]=0.5943078902723391
A[4][7]=0.9250482547200277
A[4][8]=0.9011024619745902
A[4][9]=0.7392521517164209
A[4][10]=0.6234192389906446
A[4][11]=0.9183421883637607
A[4][12]=0.04382855864591173
A[4][13]=0.5041257193378731
A[4][14]=0.6810033660104378
A[4][15]=0.7862613616039839
A[4][16]=0.6420564048994929
A[4][17]=0.9900531466971828
A[4][18]=0.037308943167103314
A[4][19]=0.18786103759227035
 
Y[0]=17.892891447525212
Y[1]=24.53331699330772
Y[2]=20.855941640767455
Y[3]=23.33324326662986
Y[4]=25.62311855258583
 
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=57.23307663297495, residual=30.730679341433103
simeq_newton5 itr 2, prev=30.730679341433103, residual=3.0979782482797695
simeq_newton5 itr 3, prev=3.0979782482797695, residual=0.11726963006275781
simeq_newton5 itr 4, prev=0.11726963006275781, residual=3.0791953829023555E-4
simeq_newton5 itr 5, prev=3.0791953829023555E-4, residual=2.1069084255032067E-9
solution may not be unique
Returned solution vs expected solution
X[0]=1.0999999998501107       err=-1.4988943419780298E-10
X[1]=1.199999999965145       err=-3.485500776889694E-11
X[2]=1.4000000000530404       err=5.3040460912257004E-11
X[3]=1.5000000000313258       err=3.132583081821849E-11
X[4]=1.6999999997222457       err=-2.777542640330921E-10
Returned solution in given equation, sum of errors=2.1069084255032067E-9
 
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