CoCalc Shared Filessupport / 2017-01-26-110805-3d-random.sagews
Author: William A. Stein
Description: Examples for support purposes.
import numpy
a = numpy.ndarray(dtype='float', shape=(3,3))
list_plot(a)

3D rendering not yet implemented
a[0] = NaN
list_plot(a)

3D rendering not yet implemented
a

Error in lines 1-1 Traceback (most recent call last): File "/projects/sage/sage-7.5/local/lib/python2.7/site-packages/smc_sagews/sage_server.py", line 976, in execute exec compile(block+'\n', '', 'single') in namespace, locals File "", line 1, in <module> NameError: name 'a' is not defined
var("J","R","T","Jprime","Rprime","Tprime")
Jprime=R+0.1*J
Rprime=-J-T
Tprime=0.1-14*R+R*T
t=srange(0,100,0.1)
sol=desolve_odeint([Jprime,Rprime,Tprime],ics=[5,5,1],dvars=[J,R,T],times=t)
#list_plot(sol,svg=False)

(J, R, T, Jprime, Rprime, Tprime)
/projects/sage/sage-7.5/local/lib/python2.7/site-packages/scipy/integrate/odepack.py:218: ODEintWarning: Excess work done on this call (perhaps wrong Dfun type). Run with full_output = 1 to get quantitative information. warnings.warn(warning_msg, ODEintWarning)
sol

array([[ 5.00000000e+000, 5.00000000e+000, 1.00000000e+000], [ 5.53376083e+000, 4.74557948e+000, -7.01874559e+000], [ 6.09211657e+000, 5.47544467e+000, -2.06510734e+001], ..., [ 5.98147386e-154, 6.01347002e-154, 7.73006220e+199], [ 6.01347002e-154, 2.68887286e+161, 2.17236024e-153], [ 5.57098308e+228, 1.06170575e-153, 2.43902493e-154]])
type(sol)

<type 'numpy.ndarray'>
import numpy
list_plot(numpy.clip(sol,-1000,1000),svg=False)

3D rendering not yet implemented
print matrix(sol).str()

[ 5.0 5.0 1.0] [ 5.533760829211794 4.745579480736711 -7.018745593406078] [ 6.092116574448896 5.475444665274792 -20.651073413842422] [ 6.816048670201431 8.229092480359924 -53.00282850016212] [ 8.08707017880845 18.056225461981203 -207.83590012191442] [ 17.204769581288573 1913.1165775598138 -1830293.0098799956] [ 55.483463036557964 392152068261.65265 -7.689162851010864e+22] [ 4.766917259204937e+180 6.013470016991625e-154 6.013470015088885e-154] [ 6.775053765336764e+78 2.427685338487549e-154 6.013470016999068e-154] [ 2.1612345949029867e-27 1.1752162493704188e+180 3.872782905583987e+233] [ 5.0404289121114015e+180 1.3974094257924031e+131 1.405301055147568e-259] [ 6.013470016999068e-154 1.0513283999777445e-153 6.0134700151096e-154] [ 3.523379244718934e+246 1.363805933637625e-153 1.2593365540250805e+180] [ 4.7448120454499445e+170 7.564550558653537e-96 2.04090178263832e-153] [ 6.013469529568927e-154 6.013470016999068e-154 2.4579047541936786e-154] [ 6.013470016999068e-154 2.1612345949029867e-27 8.092639614406094e-96] [ 6.013345032851368e-154 6.013470016999068e-154 6.013470015094651e-154] [ 3.523379244718934e+246 1.6776569888275035e+243 8.093001931499498e-96] [ 5.981475028990901e-154 6.013470016999068e-154 8.442496253210508e-53] [ 1.9656736896151727e-62 6.01346952610273e-154 1.64648843218695e+98] [ 6.013469526090846e-154 6.463219892103749e+170 4.716128733756977e+164] [ 7.249639671252237e+228 8.784151121954508e+247 2.080119123007088e-115] [ 7.347813742080329e-71 3.3020612083411976e-28 6.013470016991578e-154] [ 2.68887286470431e+161 1.1712536321805225e+214 1.051182747774098e-153] [ 4.576691564698975e-72 3.01478098881154e-110 6.013470016991619e-154] [ 1.0417589990380593e-76 6.013345032837478e-154 7.171329878379635e-309] [ 7.54792494673878e+168 9.946465036555735e+86 5.063081957248e-311] [ 2.866985836356745e-298 3.25096386413e-313 1.4916329294242185e+195] [ 5.075883677618858e-116 4.31592723924427e-310 6.465782802950641e+170] [ 2.256434201738322e-80 1.5773245994608127e-52 1.3223291959820418e+213] [ 4.6346186269741005e+228 5.830866908319191e+252 9.701582850787976e+189] [ 2.2564342017383164e-80 1.5075604632706485e+161 8.963834467249818e+276] [ 4.7357331615231793e+170 6.31023299525e-312 7.397341118287489e-159] [ 2.781342323583014e-309 2.113820165659551e-307 1.9490642722282976e+289] [ 7.11632542779945e-310 1.1665807608282908e-301 -3.133358684668045e-294] [ 3.8398198491917154e-297 3.256774513235363e-292 7.235460222410689e+221] [ 2.06971017861683e-309 3.3821188218980186e-306 1.3363436648421038e+241] [ 7.496586853363076e-309 1.9597358661828344e+289 6.7360646433422e-310] [ 2.216502004835012e-301 2.0642776288849e-309 1.9497713934287315e+289] [ 7.1163295723225e-310 -9.632043412039107e-196 8.984492158533331e-44] [ 1.6332312954652363e-301 3.919570104976637e+202 2.10230371244174e-309] [ 1.949769135353762e+289 4.4779612031761805e-305 1.9848374002590737e-263] [ 2.0642776288849e-309 -2.671230065842518e+161 6.0134695252028e-154] [ 6.124867780442012e+257 2.1817436837603085e+243 1.7492893263717827e+243] [ 9.750252643751416e+199 6.01346952610852e-154 9.417712718064014e+78] [ 6.013344344494569e-154 2.1684072415445323e+243 6.013345148603757e-154] [ 5.981422459169693e-154 1.6647733912155063e+117 3.322716988464221e-28] [ 6.013470016991578e-154 2.68887286470431e+161 1.1712536321805225e+214] [ 6.199766032789154e+223 4.141168355830618e-114 5.981474049404359e-154] [ 6.013470016999068e-154 8.157661252630055e+140 6.01347001699904e-154] [ 9.71841563247969e+189 7.39993629755735e+93 6.967697927431608e+252] [ 6.01346952877902e-154 6.013470016999068e-154 6.013469536072557e-154] [ 7.89648723907e-312 1.27733780502578e+294 1.1873136513722142e-301] [ 1.8740538452647e-311 1.331415044818e-311 7.3202693655e-314] [ 3.087133273e-314 3.172427296687537e-115 1.26683148720666e-310] [ 8.706226791584796e+252 5.853508358538666e-259 1.34116765226e-313] [ 7.398805164297606e-309 5.075883888688675e-116 8.322467492167e-311] [ 7.71534318557696e-114 8.48798316386e-313 2.4064030445020393e+232] [ 4.10189366693419e-80 9.718545405370387e+189 5.341406131046291e+228] [ 1.941009141592981e-80 3.706118295345568e-86 2.2819149662860552e+232] [ 4.0895523473911005e-80 4.9144226141587085e+252 5.4927406051471365e+247] [ 8.9767517531673e-309 6.035820639360468e+151 1.32815716558137e-310] [ 1.6638368940093042e-207 1.7363343944550864e-260 3.067837328316723e-188] [ 4.172013485150014e-309 2.1138201657113577e-307 1.9490632048870596e+289] [ 2.02081906597388e-309 2.492084742729333e-306 2.570591039691454e+207] [ 6.192832722607844e-309 1.6332117009085165e-301 1.950211522855537e+289] [ 4.433771222433894e-303 7.18187817643e-312 6.01347001699904e-154] [ 1.8166790500066507e-152 1.0985490440286722e+248 6.013344348238326e-154] [ 1.8206370822469567e+98 5.981297855847215e-154 3.6728541568058204e+194] [ 2.2885605930170483e+243 2.9603621256064966e+222 6.091147045071277e+247] [ 5.063241882477111e+45 3.0441852555152547e+156 6.013470016991578e-154] [ 4.093116842456173e+59 5.981297853589032e-154 6.013470016999068e-154] [ 1.9687117276479163e-153 6.561786040550808e-85 7.976954399057514e-72] [ 5.379881931517835e+228 2.4389494525292936e-154 6.013470016999068e-154] [ 4.576687245821699e-72 6.013470016991688e-154 2.68887286470431e+161] [ 1.1712536321805225e+214 6.199766032789154e+223 1.3969865722268647e+131] [ 5.83641794042478e+257 6.013345031992708e-154 6.013470016999068e-154] [ 4.576959623340131e-72 6.013470016991688e-154 2.68887286470431e+161] [ 1.1712536321805225e+214 6.199766032789154e+223 1.4104731212356358e+131] [ 5.83641794042478e+257 6.013345031992708e-154 6.013470016999068e-154] [ 5.906933293363405e+228 6.013470016991619e-154 9.946464919270843e+86] [ 3.433389189786e-311 4.841908629161761e-283 1.55336723136e-313] [ 2.1305516779948435e-308 9.946465369973387e+86 8.4879831648e-313] [ 5.371215076936573e+74 4.9297696781922865e+204 9.718545871802856e+189] [ 6.590835519630863e-43 1.1707577171540347e+214 1.165636520289639e+253] [ 6.820519247765693e+246 1.991107113700565e+209 9.71854586985979e+189] [ 1.0485784368215569e+242 6.561942883074621e-85 7.547925059263728e+168] [ 6.531759755115567e-302 5.34578713e-316 1.928492238486905e-309] [ 6.953355808158795e-309 4.366729495482322e-186 2.492083336906845e-306] [ 1.9502301105932614e+289 3.41149047621226e-309 6.28798745519e-312] [ 2.423960745485911e-154 4.009790486504005e+87 1.4692289033754833e+195] [ 8.800914600256003e+199 6.013469526109877e-154 9.417712718064014e+78] [ 6.013344344494569e-154 3.1547489851700675e+180 4.822596611192164e+228] [ 2.960362125606505e+222 6.091147045071277e+247 5.063241882477111e+45] [ 3.0441852555152547e+156 6.013470016991578e-154 4.093116842456173e+59] [ 5.981297853589032e-154 6.013470016999068e-154 1.9687117276479163e-153] [ 6.561786040550808e-85 1.0532745880498113e-76 2.3476796472048928e-85] [ 1.6756401164864824e+243 6.013470015091948e-154 2.046277810792539e-115] [ 5.981474049404359e-154 6.013470016999068e-154 1.9687117276479163e-153] [ 6.561786040550808e-85 5.3800238236174793e+228 1.1773211082066835e-94] [ 4.5394832287706866e+198 7.485995570688392e-114 6.013470016991619e-154] [ 3.701071445896031e-91 2.4389618706738323e-154 6.013470016999068e-154] [ 2.1612345949029867e-27 4.885996909062988e+252 3.3382516401632256e+151] [ 1.0511829032373475e-153 4.539483228779159e+198 7.485995570688392e-114] [ 6.013470016991619e-154 1.0417589990380593e-76 2.4390505087074376e-154] [ 2.046277810792539e-115 3.976620112271e-311 2.1519593906875644e-282] [ 5.037345731938626e+180 1.607963530573633e-309 5.075883964325236e-116] [ 8.48798316386e-313 2.4064030445020393e+232 4.10189366693419e-80] [ 9.718545405370387e+189 5.341406131046291e+228 1.941009141592981e-80] [ 3.706118295345568e-86 2.2819149662860552e+232 4.0895523473911005e-80] [ 4.9144226141587085e+252 5.4927406051471365e+247 1.1758094076301304e-308] [ 8.800914600241908e+199 7.263030818411355e-297 3.319501675680704e-309] [ 4.172013485996166e-309 -8.780465451415595e-273 2.492083336906845e-306] [ 3.920526918121022e+202 3.460381184440423e-309 4.96944352846091e-297] [ -3.132594155157336e-294 4.84562011773027e-309 3.63507850220015e-27] [ 4.84738108620961e-309 2.642115821253676e+108 3.10838233300797e+231] [ 7.52918070871229e-309 1.627320508094186e-260 5.010816335017306e-292] [ 3.32457345165708e-309 2.4922612344241762e-306 2.0111308881934194e+289] [ 1.433170541261355e-277 8.739900012827466e+245 6.0133441171554e-154] [ 7.456398453547549e+247 3.171095115862742e+180 7.266114961837434e+223] [ 2.3178568504574654e-152 8.801194498973139e+223 5.981810938032583e-154] [ 2.435660095649793e-154 1.4245637510526894e+73 2.665363458480551e-260] [ 6.013470016999068e-154 4.88703549349692e-85 1.1419922141881063e+243] [ 4.9143701748166794e+252 4.9137513899053655e+252 9.08364589302932e+223] [ 1.277346576716442e-152 5.298747663254974e+180 5.981896445918433e-154] [ 1.6959140725508421e+161 1.693756675540309e+190 3.9461098342228253e+180] [ 1.3849676200040272e+219 1.2379686250135101e-259 6.01347001699904e-154] [ 6.845827475144456e+25 6.013344344485748e-154 6.013470016999068e-154] [ 1.8094947084803123e+44 1.1712536322233136e+214 6.199766032789154e+223] [ 9.38264644059913e-76 2.4419094263314548e-154 6.013470016999068e-154] [ 4.576686385578347e-72 6.013470016991619e-154 2.68887286470431e+161] [ 2.8770636206848006e-14 4.885996909062988e+252 4.141168355830583e-114] [ 7.791080197933814e+140 5.981525795223992e-154 6.013470016999068e-154] [ 8.634002313032808e+140 6.01347001699904e-154 9.71841563247969e+189] [ 8.802980817763379e+247 4.443890999807684e+252 2.4389635209844413e-154] [ 6.013470016999068e-154 1.3956569253897155e-258 6.013470016999068e-154] [ 3.0318257756379346e+180 6.353933038956714e+151 5.287589321213929e+180] [ 6.967469844781447e+252 2.0922214302803854e-110 6.01347001699904e-154] [ 1.1630490526066296e+214 6.013470015112398e-154 3.523379244718934e+246] [ 3.4757370551828e-86 4.354520336227911e-114 9.076802042129502e+223] [ 2.7198181829175607e+44 8.800914600262008e+199 5.981473872302097e-154] [ 6.013470016999068e-154 2.460909669272632e-154 6.013470016999068e-154] [ 2.1612345949029867e-27 4.747769071372815e+170 4.2451081093505425e+175] [ 6.013345032764552e-154 6.013470016999068e-154 5.98181698375755e-154] [ 6.013470016999068e-154 1.9687117276479163e-153 1.1444878477968752e+243] [ 8.802937461523402e+247 4.443890999807684e+252 2.4389620984188416e-154] [ 6.013470016999068e-154 5.037345733878472e+180 6.01347001699904e-154] [ 9.71841563247969e+189 1.291415025811071e+214 2.5293205824834367e-86] [ 3.946109836126552e+180 3.475762104026347e-86 1.6756401164864824e+243] [ 6.013469528776645e-154 6.013470016999068e-154 6.013346372337969e-154] [ 6.013470016999068e-154 1.8094947084803123e+44 1.171253632223314e+214] [ 1.0985490733232308e+248 1.0514780917375053e-153 9.65779389659629e-23] [ 6.013469529655753e-154 6.013470016999068e-154 2.5203330636250547e-81] [ 6.013470015109598e-154 3.523379244718934e+246 3.4757370551828e-86] [ 3.946109836126552e+180 3.207736138797751e-110 6.01347001699904e-154] [ 5.504095481329775e+257 6.013470016991698e-154 2.68887286470431e+161] [ 4.5150120533669324e+198 6.470495594206439e+170 1.0240600089101663e-259] [ 6.013470016999068e-154 5.56206153980199e+180 6.01347001699904e-154] [ 1.1570384064176382e-306 2.992345627e-314 3.7993570718757505e-308] [ 9.94646503649217e+86 2.1903240554348e-310 5.853508358159958e-259] [ 9.4495125066e-314 2.2586445180523e-311 2.9110857211824667e-172] [ 1.36935040886e-313 1.4426524569184872e-277 2.3603009116846072e+257] [ 6.675221575531829e-308 1.68590907783e-312 4.443877029786676e+252] [ 6.859971167502369e+246 2.7911166736331363e-81 6.742003838095426e+199] [ 9.082542836895048e+223 5.293722137970542e+180 3.0318104663121697e+180] [ 6.859971167502369e+246 1.1712865691218597e+214 1.1656358702172098e+253] [ 4.7477686557053244e+170 4.2451081093505425e+175 1.2195109810874e-310] [ 7.892257250782088e-251 5.166682750304744e-246 8.520907073194384e+168] [ 1.69759663287e-313 1.42173717997e-312 6.3014787047138e-310] [ 1.63321259093806e-301 1.278121077742171e+294 6.73606381443766e-310] [ 4.9694464449100586e-297 4.950820715199598e+173 3.1203484852211645e-282] [ 9.023150503764175e-309 5.832908671482839e-302 1.9944800162757624e+289] [ 6.241723416589183e-309 2.0449515033510318e-277 4.949608335307381e+173] [ -1.049923723015552e-301 1.2777787735888277e+294 6.138509547144887e-309] [ 1.0703678774607871e-296 8.74505925406295e+245 2.096871812813013e-309] [ 4.761266232030341e-287 3.10838233300797e+231 6.13850954714571e-309] [ 3.822657943391627e-297 9.36756102641521e-305 3.1203450796381246e-282] [ 1.279338023812064e+294 4.845626329657974e-309 -2.93028578637873e+238] [ 1.2780906236371925e+294 8.919851870278894e-309 7.014762921727242e-292] [ 8.74505925406295e+245 2.096871812813566e-309 3.1203450796381246e-282] [ 3.1098984639574825e+231 8.919851870280267e-309 4.597099889101935e-287] [ 1.951672517138292e+289 8.178864302161644e-284 1.6009380666845e-311] [ 6.01347001699904e-154 1.8166790500066507e-152 2.9948912958412346e+262] [ 1.6959471157868914e-152 2.347835254829746e+251 1.1444878476259614e+243] [ 5.981299124907658e-154 8.714144126796682e+102 2.4276854830112164e-154] [ 1.722191900334663e+97 5.81746188400515e+180 7.21562943697059e+159] [ 2.7919506924929237e-152 3.5464965024964953e+155 5.298622204059182e+180] [ 2.6606186087081223e-260 6.013470016999068e-154 1.388319889752532e+93] [ 6.013469526090813e-154 6.013470016999068e-154 2.844150074421577e-71] [ 7.399936297557997e+93 6.171512528534769e-114 7.791080169541675e+140] [ 5.981520104961593e-154 6.013470016999068e-154 2.848454422645535e-110] [ 6.01347001699904e-154 9.71841563247969e+189 2.1722989656684752e-153] [ 6.561786040550808e-85 6.902740340243243e-72 9.657793896591768e-23] [ 6.01334523488276e-154 6.013470016999068e-154 9.494326627216567e-259] [ 6.013470016999068e-154 3.0318257756379346e+180 9.076584688799293e+223] [ 1.9161117317875743e+214 6.013345032851379e-154 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2.1700283942725964e+169 2.1219957915e-314] [ 1.421737179957e-312 6.3014787010206e-310 2.2165036110599987e-301] [ 8.739899915151473e+245 6.013344117154633e-154 5.260975359551115e+180] [ 5.818162359689694e+180 3.624793801911698e+228 2.4381298212991525e-152] [ 1.175757901364407e+214 1.1701941238057303e+171 1.9430199455870494e+227] [ 6.013346659902673e-154 5.981422459169693e-154 8.714144126796682e+102] [ 2.4276854830112164e-154 528400.062745098 3.997271709791954e+252] [ 2.1952985611849662e-152 5.298747662647602e+180 2.66064807106119e-260] [ 6.013470016999068e-154 1.388319889752532e+93 6.013469526090813e-154] [ 6.013470016999068e-154 2.282358596285389e-152 1.2593365540250805e+180] [ 1.2593365540255649e+180 4.7448120454499445e+170 7.564550558653537e-96] [ 1.1712536319573654e+214 1.0985490733232308e+248 6.171512530848184e-114] [ 5.981473873233366e-154 6.013470016999068e-154 1.9687117276479163e-153] [ 1.1444835460416174e+243 6.013469528801744e-154 6.013470016999068e-154] [ 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1.330491361291e-311] [ 2.9429999e-314 6.3659873744e-314 3.5554039477656e-310] [-3.1325762364488675e-294 8.474402415471776e-308 1.905366161008285e+141] [ 3.45494887327297e-309 3.006861603198089e-51 8.973544514280794e-44] [ 5.010506685614584e-292 1.6530341483972464e-301 8.739899980268801e+245] [ 6.01334411715467e-154 4.884835359022017e+252 1.2773465768277607e-152] [ 1.1736445966258326e+214 2.3484091[...]

numpy.clip(sol,-1000,1000)

array([[ 5.00000000e+000, 5.00000000e+000, 1.00000000e+000], [ 5.53376083e+000, 4.74557948e+000, -7.01874559e+000], [ 6.09211657e+000, 5.47544467e+000, -2.06510734e+001], ..., [ 1.06149315e-248, 9.94235500e-280, 1.00000000e+003], [ 2.12199579e-314, 1.42173718e-312, 6.73606344e-310], [ 5.83289989e-302, 1.00000000e+003, 4.96944353e-297]])