Python 3.5.2 (v3.5.2:4def2a2901a5, Jun 25 2016, 22:01:18) [MSC v.1900 32 bit (Intel)] on win32
Type "copyright", "credits" or "license()" for more information.
>>> 
================= RESTART: C:\Users\Admin\Desktop\8\NR\NR.py =================
>>> f1 = lambda x: x**3 - 4*x**2 + 3*x
>>> f1(2)
-2
>>> f1(1)
0
>>> f1(3)
0
>>> f1(0)
0
>>> f11 = lambda x: 3*x**2 - 8*x + 3
>>> f11(3)
6
>>> NR(f1, f11, x0=5)
5 40
3.947368421052632 11.022014870972447
3.340636586892667 2.663511124945501
3.0675810243556922 0.42863077610556743
3.0035059786544434 0.021097374453381335
3.0000101979512923 6.118822774503485e-05
3.000000000086664 5.199822794565989e-10 convergence in 6 iterations
3.000000000086664
>>> f1(5)
40
>>> NR(f1, f11, x0=4)
4 12
3.3684210526315788 2.9392039655926503
3.0771631246659057 0.4932089276860694
3.00452016332014 0.02722323165845708
3.000016929634699 0.00010157924126374951
3.0000000002388383 1.4330296949083277e-09 convergence in 5 iterations
3.0000000002388383
>>> NR(f1, f11, x0=1.5)
1.5 -1.125
1.0 0.0 convergence in 1 iterations
1.0
>>> NR(f1, f11, x0=1)
1 0 convergence in 0 iterations
1
>>> NR(f1, f11, x0=-1)
-1 -8
-0.4285714285714286 -2.099125364431487
-0.12781954887218044 -0.4508982898764238
-0.01707644468701397 -0.052400733489660165
-0.0003749431439753065 -0.0011253918140811683
-1.8729099961407088e-07 -5.618731391538933e-07
-4.677053907742991e-14 -1.403116172322985e-13 convergence in 6 iterations
-4.677053907742991e-14
>>> NR(f1, f11, x0=-100)
-100 -1040300
-66.22731552121547 -308219.713332865
-43.714721300088456 -91312.87237072227
-28.71009612498539 -27048.068775318116
-18.712619697719994 -8009.237285500867
-12.055936361790135 -2369.827538191346
-7.630358323771604 -700.0380790044833
-4.69776997833485 -206.04476758479447
-2.7683183340381365 -60.174547328052434
-1.5182577782389557 -17.274946207826037
-0.7352177131683565 -4.765251804345393
-0.2815301209486466 -1.183941053547825
-0.06587674325083545 -0.2152750992448425
-0.005065138335694455 -0.015298167461818852
-3.383623929994681e-05 -0.00010151329750293909
-1.526409549518009e-09 -4.579228657873731e-09 convergence in 15 iterations
-1.526409549518009e-09
>>> NR(f1, f11, x0=-100000)
-100000 -1000040000300000
-66666.22222740731 -296308148219753.06
-44443.70371493805 -87795006868404.23
-29628.69137718064 -26013335360734.4
-19752.016491175465 -7707654916578.032
-13167.566575921548 -2283749601498.0415
-8777.93331220964 -676666546316.0984
-5851.511156087157 -200493789983.85406
-3900.563081532355 -59405566391.21271
-2599.931076116429 -17601648626.890217
-1732.8431389299687 -5215302847.447095
-1154.7846137600336 -1545274618.2198637
-769.4124130441114 -457858946.5082912
-512.4978365859797 -135661777.05308574
-341.2217881363312 -40195993.47125907
-227.0382592313489 -11909864.976075971
-150.91666084613706 -3528809.601618618
-100.17005795293787 -1045547.091633408
-66.3406789955014 -309774.3777597209
-43.7902842677245 -91773.49409216132
-28.760452547121247 -27184.536230391623
-18.746162607763686 -8049.663391523245
-12.078256899545803 -2381.799858608273
-7.645178007963377 -703.581594543054
-4.707561809531958 -207.0921659925094
-2.7747205698135593 -60.48323833539264
-1.5223496356513133 -17.365361542014792
-0.7377030099488675 -4.791394159104298
-0.2828630233497016 -1.1912673219212826
-0.06638462948941617 -0.21707411628519563
-0.00513861435120129 -0.0155216001703541
-3.4819550498594795e-05 -0.00010446350114238735
-1.6164128500593348e-09 -4.849238560629167e-09 convergence in 32 iterations
-1.6164128500593348e-09
>>> NR(f1, f11)
-95.8090804606884 -916472.8941322183
-63.43358785010389 -271530.92478080734
-41.85256264942704 -80442.60298436883
-27.46914321418602 -23827.569934784457
-17.886039244499862 -7055.229683700944
-11.505947740035863 -2087.301163334085
-7.265259219871901 -616.4211249263717
-4.456630456939815 -181.3317225573661
-2.610784041398605 -52.89273408646339
-1.4177557265207974 -15.143125766070476
-0.674430480383648 -4.1494864021366915
-0.24927876276988287 -1.011886052363517
-0.053958467037294955 -0.17367856672096277
-0.0034764151305679628 -0.010477629254427568
-1.5993498869676208e-05 -4.798151978114401e-05
-3.410441900708486e-10 -1.0231325706777904e-09 convergence in 15 iterations
-3.410441900708486e-10
>>> NR(f1, f11)
6.228189231136412 105.11678800196063
4.716707198189266 30.09494084790267
3.7764848366240775 8.141717521565784
3.253696303423879 1.8603152467855377
3.040602956736085 0.2519276789334306
3.001306646192646 0.007848416008110704
3.0000014204193284 8.52252605909598e-06
3.0000000000016813 1.0089706847793423e-11 convergence in 7 iterations
3.0000000000016813
>>> NR(f1, f11)
3.442251714967881 3.7179416869282775
3.1045418249541425 0.6830384524389181
3.0080430049373095 0.04858199956738041
3.0000533646281324 0.00032020200785964903
3.0000000023729934 1.4237961920571252e-08
2.9999999999999996 -5.329070518200751e-15 convergence in 5 iterations
2.9999999999999996
>>> NR(f1, f11, epsilon = 10**(-15))
-27.259071539683674 -23309.048548186056
-17.746119705874367 -6901.629988784561
-11.412857279765156 -2041.81426894251
-7.203475933300224 -602.959528048916
-4.415842590360824 -177.35364556414763
-2.584163853935097 -51.720897955576426
-1.400809354363634 -14.800257207598726
-0.6642317217920396 -4.050571832921918
-0.24393740325797109 -0.9843496431959695
-0.05205696454598688 -0.16715167447172474
-0.0032476489314323675 -0.009785169942303834
-1.3964713309732885e-05 -4.189491998479325e-05
-2.600097566840819e-10 -7.80029270322666e-10
-9.014009439779966e-20 -2.70420283193399e-19 convergence in 13 iterations
-9.014009439779966e-20
>>> NR(f11, lambda x: 6*x-8)
-78.94535754810144 19331.671295577544
-38.8108563429417 4832.334560960907
-18.748448806802926 1207.5005884383536
-8.726922994567747 301.29293881588785
-3.735450792872398 74.74438422089227
-1.277781051968721 18.12042166606064
-0.1211598427728584 4.013317864685098
0.3387160244838847 0.6344574398554252
0.44503119284234804 0.03390874506926522
0.45139328210672885 0.00012142853942398446
0.4514162293465961 1.5797274599549382e-09 convergence in 10 iterations
0.4514162293465961
>>> NR(f1, f11, x0=0.4514162293465961)
zero derivative, x0= 0.4514162293465961  i= 0  xi= 0.4514162293465961
>>> f1 = lambda x: x**3 - 4*x**2 + 3*x
>>> f111 = diff_param(f1)
>>> f11 = lambda x: 3*x**2 - 8*x + 3
>>> f11(5)
38
>>> f111(5)
38.0110010000152
>>> NR(f1, f11, x0=10)
10 630
7.174887892376681 184.96476913841624
5.325941795893695 53.58903426358909
4.147887247022127 14.988057184494256
3.448550201901587 3.787534711731766
3.106995269084695 0.7004364330551365
3.008401915343808 0.050765046079604303
3.0000582073774584 0.0003492612054412092
3.0000000028232074 1.693924644996514e-08
2.9999999999999996 -5.329070518200751e-15 convergence in 9 iterations
2.9999999999999996
>>> NR(f1, f111, x0=10)
10 630
7.175217251911281 184.99771949071396
5.326479016163002 53.61347556642001
4.148530681260346 15.001850639468746
3.449180272840524 3.7945241469244166
3.1074371608417377 0.7035768022922522
3.008541343571467 0.05161345730870792
3.0000671443168527 0.00040288844321523243
3.000000059667697 3.580061971319992e-07
3.000000000049695 2.9816682456385024e-10 convergence in 9 iterations
3.000000000049695
>>> NR(f1, f11, x0=100)
100 960300
67.11639215149128 284516.0864493552
45.19664661407067 84289.49869925735
30.587496588509335 24966.889966032766
20.85413834428969 7392.344361123709
14.374469307909242 2186.7519452719994
10.068825372748655 645.4715443743399
7.220232637985668 189.53709083760052
5.3553234717718965 54.93595567590363
4.166127490268248 15.381793902741265
3.4586204422482596 3.89984908423099
3.1109536272884264 0.7286412184143067
3.008995404271178 0.054377740000884245
3.0000666714510746 0.00040005093215533805
3.0000000037039225 2.222353678860145e-08
2.9999999999999996 -5.329070518200751e-15 convergence in 15 iterations
2.9999999999999996
>>> NR(f1, f111, x0=100)
100 960300
67.1167254558865 284520.41272871493
45.19720204556927 84292.70337821353
30.588199913474767 24968.694097673724
20.85493979852538 7393.258739529663
14.375335064249981 2187.1916752296206
10.069731331916852 645.6768500080994
7.221159006449133 189.6312559863578
5.356247905758664 54.978671030165316
4.167012340410871 15.40103793816413
3.459386451112332 3.908445302427337
3.1114541946057472 0.7322198432949563
3.009148036937578 0.055307420092447046
3.000076428207293 0.00045859845055851167
3.0000000685078754 4.1104727799279317e-07
3.0000000000570575 3.4234659551657387e-10 convergence in 15 iterations
3.0000000000570575
>>> f111 = diff_param(f1, h=000001)
SyntaxError: invalid token
>>> f1111 = diff_param(f1, h=0.00001)
>>> f1111(5)
38.00010999839287
>>> NR(f1, f1111, x0=100)
100 960300
67.11639549551657 284516.1298544684
45.196652177455476 84289.53079797457
30.587503635970428 24966.908043372947
20.85414636767711 7392.353514626278
14.374477972011588 2186.756345602261
10.068834436686478 645.473598202536
7.2202419045746815 189.53803263422185
5.355332718243837 54.93638282584977
4.16613634039854 15.381986312628207
3.4586281029889587 3.8999350166852924
3.1109586311716977 0.7286769786414897
3.0089969265712235 0.054387011119391815
3.000066767603176 0.00040062790891681743
3.0000000042709356 2.562561540742081e-08
3.0000000000000355 2.1316282072803006e-13 convergence in 15 iterations
3.0000000000000355
>>> NR(sin_by_million, sin_by_million_deriv, x0=5)
5 -0.9765424686570843
4.9999954647951625 -0.03982982671627804
4.99999550465662 2.109114325154512e-05
4.999995504635528 4.122283666762455e-10 convergence in 3 iterations
4.999995504635528
>>> NR(sin_by_million, diff_param(sin_by_million), x0=5)
5 -0.9765424686570843
5.003917017291797 0.7208476850575305
5.001119203982546 -0.8364772493081046
5.0021403052173365 0.7877825243769632
5.003062692178523 0.8377300463606889
4.993199847085811 0.38262884947637
4.993610656575995 -0.9051733726778727
4.994821458365334 -0.15618816592664206
4.994612756766101 0.931913591866192
4.995929543622435 -0.6743760415609281
4.996674151806115 0.6360701290854601
4.997368245613877 -0.7755357225460957
4.9982685628152055 0.8040875922450342
4.992512882024309 0.606053484865707
4.990968789078038 0.7955190554690399
4.9919056133457875 0.2861503327233335
4.992217484052843 0.5335797727339134
4.991072039033316 -0.9740456894777609
4.992659911438145 -0.025645936547006542
4.992628458865095 0.010997543557186632
4.992641682751949 -0.602411157477693
4.991121885101731 -0.9817989858806241
4.994723332636274 -0.5476278363382436
4.995311217835878 0.1713040649761819
4.995503775875139 0.680712074805523
4.993292506122869 0.9168869904936133
5.00616967525505 -0.8081800054857476
5.000106912929725 -0.9930172010500578
5.003053390500079 -0.8984438901533383
5.032897389781341 0.014714702134653623
5.03291504962478 0.9336343616288479
5.034239750437033 0.774470321836184
5.0300345133048125 -0.783503627170586
5.030949084118539 0.5080616117936206
5.031492728982468 -0.3742593515842665
5.0318949123140175 -0.3184804757646629
5.032239887892363 -0.7978615834987902
5.033181164714741 -0.8504706305334684
5.019632927900758 0.6228750386470001
5.020310357228375 0.9673341555957037
5.024836790368521 -0.6538192408147583
5.022911153730609 0.7657970232536732
5.019016402705778 0.9921540840980064
5.020862048362695 0.08521853973989105
5.020753707522779 -0.9916357975652605
5.022587747227897 -0.8673338500762209
4.9954807587443275 0.2737097735029886
4.995779867629079 0.3712312433443165
4.995166599352619 0.2738312951146224
4.995465832998817 0.48378097927962593
4.994520880509187 -0.9214781303221409
5.005748411332706 -0.6056229306968859
5.004207219726695 0.9170653955451066
5.0054616962323 -0.17865616742984208
5.005662037313776 -0.7836182517777995
5.006576815999568 0.31954116904462204
5.0069228771769 -0.16004891510311575
5.00670838602041 0.645834527533009
5.0074150389446075 -0.7879907372372479
5.008337809237813 -0.9811078209510321
5.011979854412808 0.7353589228004829
5.012813437429311 0.23261651576622738
5.012482263182836 0.8782789029191305
5.013608659489714 -0.5922804422710986
5.012153599810481 0.1312259872826521
5.011981455419086 -0.699580403186685
5.00952419185268 -0.23449477001396618
5.009189774596132 0.9214266893949534
5.010461547312717 -0.9850300225422783
5.0138755092461045 0.43340442171737203
5.0130953266037945 -0.5805444516875296
5.013721367087343 -0.24172995224685087
5.013374338717636 0.935272966797552
5.0147067309146465 0.7526763279249663
5.015568116981659 0.2594355678718969
5.015852554005257 -0.9902787925967691
5.018963210254924 -0.9427635533761648
5.0203328970569405 -0.9575610573324355
5.021789528074605 -0.7140044350912347
5.019110026606001 0.8782862282380337
4.9392934774547195 -0.17305255581557968
4.9394878889320095 -0.515160911539841
4.940039359634964 -0.91308766399948
4.9546686280714365 0.02224006813864488
4.954641404523174 -0.8786500680571989
4.869264714239293 -0.30000471491679787
4.868808435553889 -0.4286997150253045
4.869267109698217 -0.42723836856157
4.869724253250044 -0.9212106949093908
4.881036897607216 0.8077895409242027
4.875004831774772 0.6686970024727052
4.872929280954845 -0.9793485094254142
4.874573141295245 0.5310430194882607
4.87514229016016 -0.039226335573540466
4.875188799406593 0.6082704682284867
4.875848163440396 0.8543522865389104
4.876911310302181 -0.26117731252913
4.8765294065724785 -0.9979514608142147
4.878567603783331 0.8066100698264109
4.872626414229649 -0.47990691863169127
no convergence, x0= 5  i= 99  xi= 4.871695315771791
>>> NR(sin_by_million, diff_param(sin_by_million, h=10**(-6)), x0=5)
5 -0.9765424686570843
5.00000364756242 0.9585449483296722
5.000005056336291 -0.12658230151194205
5.000004893322469 0.03608318566306196
5.000004935401477 -0.005987952117038359
5.000004928261941 0.0011515483964375912
5.000004929629576 -0.0002160864410055609
5.000004929372749 4.073972709037373e-05
5.000004929421163 -7.674145617092516e-06
5.000004929412043 1.446296356041036e-06
5.000004929413762 -2.729251166986298e-07
5.000004929413437 5.117513926755329e-08
5.000004929413498 -8.429505507837314e-09 convergence in 12 iterations
5.000004929413498
>>> f2 = lambda x: x**2+1
>>> NR(f2, diff_param(f2))
-89.3866686465658 7990.976531730948
-44.687490615417026 1997.9718175029848
-22.3323063661395 499.7319076311148
-11.143513586971517 125.17789506301881
-5.526635617378501 31.543701247276644
-2.6725886457416483 8.142730069347177
-1.1489247354283032 2.3200280476789965
-0.13883327009003232 1.0192746768838918
3.545293752354989 13.569107790487319
1.6318846910584344 3.6630476449108818
0.5098919203052665 1.2599897703925924
-0.724443617019761 1.524818554240674
0.3286898856403364 1.1080370409222575
-1.3542856389066633 2.834089591748829
-0.3075580365816697 1.0945919458659716
1.4748280524648778 3.175117784337344
0.3987562665889828 1.1590065601439838
-1.0527006761483964 2.108178713563291
-0.05090569475723883 1.002591389758717
9.894313735185865 98.89744429028765
4.8968753327493255 24.979388024488816
2.3465921374386784 6.506494659489025
0.9605164577276031 1.9225918655655823
-0.039774354206915996 1.0015819992525772
12.711320087418711 162.57765836481443
6.316576563407812 40.89913948139285
3.0793877252752875 10.482628762576109
1.377600241830625 2.897782426291797
0.32623172075583806 1.1064271356273152
-1.3669420137500587 2.8685304689550657
-0.3173071078811962 1.100683800711929
1.4198442585659716 3.0159577185827535
0.3581447091806629 1.1282676327141017
-1.214815387305876 2.4757764252351255
-0.19540294671744962 1.0381823115858624
2.46792854485577 7.090671302513918
1.0316562012038386 2.064314517482335
0.03165517661328221 1.001002050206418
-15.533522123543424 242.290309562613
-7.734321567602954 60.81973011108822
-3.8022596768912442 15.457178650513109
-1.769361760635276 4.130641039998364
-0.6017631579851954 1.3621188983083152
0.53095126183127 1.2819092424402179
-0.6750946491549663 1.455752785317667
0.4038886982086627 1.1631260805406882
-1.0342401190566997 2.0696526238664164
-0.03318937829832436 1.0011015348318293
15.279147333865932 234.45234324998242
7.607100390396851 58.86797634957592
3.738076432207869 14.97321541302791
1.7355474369420425 4.012124905876092
0.5800130833004502 1.336415176799695
-0.5710507042732005 1.3260989068509184
0.5910711693121222 1.3493651271919995
-0.5494214689288024 1.301863950519883
0.6364166010052945 1.4050260900351321
-0.4665740321617793 1.217691327487701
0.839754194106942 1.7051871065201996
-0.17493107523143636 1.0306008810816265
2.7792468994033444 8.724213327843103
1.210000913425892 2.464102210491493
0.19219820747090388 1.0369401509550287
-2.4983824797197394 7.241915014970554
-1.0487716445887356 2.099921962493361
-0.04716009984588165 1.0022240750174736
10.692466243943976 115.32883437788139
5.299723400335276 29.087068120061303
2.5557760302853234 7.531991116981007
1.08254093600203 2.171894878120151
0.07985728577112017 1.0063771860907305
-6.182034068785486 39.21754522762443
-3.0098809437507086 10.059383295553657
-1.3385433026251004 2.791698173002511
-0.29534157382996784 1.0872266452323625
1.54840561404004 3.397559945590713
0.4516441604066004 1.203982447629383
-0.8797701904352013 1.7739955879783904
0.1290184659278213 1.0166457645503684
-3.7956951155207266 15.407301409987902
-1.765851992702094 4.118233260129956
-0.59944629084913 1.35933585561278
0.5353264562075639 1.2865744147157487
-0.6652249534984673 1.442524238757038
0.4198285194944018 1.1762559857808612
-0.9793817781979115 1.959188667466103
0.021346149884003296 1.0004556581148702
-22.876410741437812 524.3301684109713
-11.416098311975341 131.32730066868623
-5.663999425884573 33.080889496420774
-2.743465052276232 8.526600493061029
-1.1891979853323165 2.41419184831844
-0.17372059826337694 1.0301788462609855
2.799883166501006 8.839345746055702
1.2216445433372733 2.492415390265735
0.2019552586884803 1.040785926511931
-2.3684544536953167 6.609576499229181
-0.9728244640823571 1.9463874379171253
0.02806953263203238 1.0007878986621808
-17.48688094895533 306.79100532293694
no convergence, x0= -89.3866686465658  i= 99  xi= -8.714596786267563
>>> f3 = lambda x: x**2-2
>>> NR(f3, diff_param(f3))
-3.0971462439375586 7.592314856336527
-1.8712530907884009 1.501588129785143
-1.469920564016396 0.16066646451827937
-1.4152505571944056 0.002934139639075628
-1.4142135759314702 3.834887651876784e-08
-1.4142135623682996 -1.3563372647240612e-11 convergence in 5 iterations
-1.4142135623682996
>>> NR(f3, diff_param(f3))
59.04930404283127 3484.820307942729
29.5418368764053 870.72012603214
14.80501815969132 217.18856270878976
7.470301455884514 53.805403841790294
3.869255158541797 12.971135481902307
2.1932918287593264 2.81052904610243
1.5527276217871089 0.41096306746065103
1.420434369434352 0.017633797870364898
1.4142293686089493 4.4707036067404005e-05
1.4142135680477044 1.605021893169578e-08
1.4142135623751007 5.6727955666247e-12 convergence in 10 iterations
1.4142135623751007
>>> NR(f3, diff_param(f3))
-7.136933199802911 48.93581549844902
-3.7083426050088186 11.751804876123591
-2.1236198796900663 2.509761393414852
-1.532564843791314 0.3487550004250948
-1.4187462277456477 0.01284085874250529
-1.414219207510622 1.5966891971697095e-05
-1.4142135603878103 -5.615233167333145e-09 convergence in 6 iterations
-1.4142135603878103
>>>