0
$\begingroup$

The following example shows two functionally identical versions of the same WhenEvent. The two versions rely on two conditions Condition A and Condition B being satisfied and differ only in the order of the two conditions in the test:

event1: WhenEvent[Condition A && Condition B, actions]

event2: WhenEvent[Condition B && Condition A, actions]

event1 catches the event. event2 does not. Specifically:

event1 = WhenEvent[Evaluate[(toggle[t] == 1) && 
                            (f[S[3][t]][3][t] - f[s[2][t]][2][t] -         
                             f[S[3][t]][2][t] + f[s[2][t]][2][t] < 1/100)],
                   Print[Row[{"End at ", t}]]; Endt = t; "StopIntegration"];

event2 = WhenEvent[Evaluate[(f[S[3][t]][3][t] - f[s[2][t]][2][t] - 
                             f[S[3][t]][2][t] + f[s[2][t]][2][t] < 1/100) &&
                            (toggle[t] == 1)],
                   Print[Row[{"End at ", t}]]; Endt = t; "StopIntegration"];

The behavior is not consistent. In some cases, putting the toggle first, fails in others, as here, putting it second fails.

The example relies on an InterpolatingFunctions and requires precision beyond $MachinePrecision

The variables are:

vars = {s[2], S[3], Cee[3], toggle};

with discrete variables:

dvars = {toggle};

The initial conditions are: (sorry, the example relies on precision beyond Machine Precision)

initconds = {s[2][
 2.144916158191085905678582630234886355478648729751836407222758673\
1192795799034279814104188519292500682575419414653357410794722550959999\
4740103335481901550805513733884265574044`150.] == 0, 
S[3][2.144916158191085905678582630234886355478648729751836407222758\
6731192795799034279814104188519292500682575419414653357410794722550959\
9994740103335481901550805513733884265574044`150.] == 
0.5141981056084164574889912336386378969597921282604537374345128696\
7276225511023895075588192194971707237837697231024424087411575040786155\
697463394392200504350102087030477646296`150., 
Cee[3][2.\
1449161581910859056785826302348863554786487297518364072227586731192795\
7990342798141041885192925006825754194146533574107947225509599994740103\
335481901550805513733884265574044`150.] == \
-3.7705276082859175241150830989671843407151051321395010246298084465953\
1541552336488269236183953197224497473620271066746924871297392088887135\
59000071618940582406013351697741357`150.72211305893404, 
toggle[2.\
1449161581910859056785826302348863554786487297518364072227586731192795\
7990342798141041885192925006825754194146533574107947225509599994740103\
335481901550805513733884265574044`150.] == 0};

The structural equations are:

eqns = {1/6 + E^(-4 s[2][t]) Derivative[1][Cee[2]][t] - 
              E^(-6 s[2][t]) Derivative[1][Cee[3]][t] - 
       1/6 Derivative[1][s[2]][t] - 
            4 E^(-4 s[2][t]) Cee[2][t] Derivative[1][s[2]][t] + 
            6 E^(-6 s[2][t]) Cee[3][t] Derivative[1][s[2]][t] == 0,

       1/3 + Derivative[1][Cee[3]][t] == 0,

       Derivative[1][S[3]][t] == (1 + 1/3 (-1 + E^(-6 S[3][t])) + 
                                 E^(-2 S[3][t]) Derivative[1][Cee[1]][t]) /
 (2/3 + 2 E^(-2 S[3][t]) Cee[1][t] -  6 E^(-6 S[3][t]) Cee[3][t]) (1 - toggle[t]) + 
 (1/2 + 1/3 (-1 + E^(-6 S[3][t])) + E^(-4 S[3][t]) Derivative[1][Cee[2]][t])/
  (1/6 + 4 E^(-4 S[3][t]) Cee[2][t] - 6 E^(-6 S[3][t]) Cee[3][t])toggle[t]};

The values of Cee1[t], Cee1[t], s1[t] and S[2][t] are given by (interpolating) functions ( trimmed these down for simplicity ):

Cee[1][t_] := (E^2  (3 - 2 t))/2;

c2points = \
{{1.907617896260767860011475497054036028318446809225144603058751249769\
4806815561571210736776933039564694633481296201461582370798924245736942\
3524758084468476006289788603675904564`150., \
-1.6831025439612610072201840729072758709522572250885761853047264124789\
1694241040816825546302252301433218634695817852766422718211647004164240\
745029965081096221365240085691615911`148.69639563085175}, \
{2.0413599262202311288072004258652563764328000038571304180020184499212\
4962733206272105034877743504054988781268826264296400206168659646195075\
76239092536031285484207595334058418`150., \
-2.9802757705333724103451089062908125112436423335851539685538595957120\
2338717379906886248580943245246548769431104777619881113407633292773814\
612688264309365198046850807694808338`150.}, \
{2.1394604850920685589650768423895210777029979995549773439374302764608\
0056809835998881873742408196150766674393824047905104371427542515405132\
966977252364434006623176591046317048`150., \
-4.1290963519258740800612276198173942460010650856221724269232975381140\
4900572369657119634822748960849090051135145287106739101240762847312401\
951640176423245809950065109807886723`150.}, \
{2.1433148556815212671537742657567336649611712343085516174662774029292\
7460921208246166328403525510432875056666575741050789208701128187287638\
520397966617725098222519176200496852`150., \
-4.1773462467078870788521151457077965227474892220344787423604223110122\
2726494814089345409587051196090635066927105048223158578001067150156773\
688524331255056708978911047703185954`150.}, \
{2.1449020728573698382827764277176392396912721240247133546700032241770\
6876700338027284581284655739244983125293596229770212201148191454691173\
642596838659032585171623606134361551`150., \
-4.1972810022299009595088425923374635051700681629514865849548865245995\
9246305764261381958227988898592942518117173506455750283004345251488660\
317405946505439657136177859108646252`150.}, \
{2.1524976456510253553962129239426156378722267983024141518610312867259\
7452105861449613310586508219833000268794054716280380487156080986214508\
113456303415163509006374736040187426`150., \
-4.2012488228255126776981064619713078189361133991512070759305156433629\
8726052930724806655293254109916500134397027358140190243578040493107254\
056728151707581754503187368028951726`150.}, \
{2.1704528697691028131628080771602455975585625465337067996509753587849\
0582284287752664906109596552119666892247042888895590631488377717233411\
383140967127700376963250532987180038`150., \
-4.2102264348845514065814040385801227987792812732668533998254876793924\
5291142143876332453054798276059833446123521444447795315744188858616705\
69157048356385018848162526650020244`150.}, \
{2.1997385373007056885504600897448336068263923196982653614879777587903\
7527453125485508254295651193074534301956318153762896616668903160238654\
423316201040305376342962332116725601`150., \
-4.2248692686503528442752300448724168034131961598491326807439888793951\
8763726562742754127147825596537267150978159076881448308334451580119327\
211658100520152688171481166059616834`150.}, \
{2.2426677524724705445204419922936684446643779334834943318368757760847\
7341792656130123831289308271205103044971736676542624140572644717873036\
922204315569577969701784100632101874`150., \
-4.2463338762362352722602209961468342223321889667417471659184378880423\
8670896328065061915644654135602551522485868338271312070286322358936518\
461102157784788984850892050316050932`150.}, \
{2.2772837446481053037681387264688332430308241721896523291778067433461\
6942613300774020831581745654555806249277125056899052504484167960112328\
376380723793629828293879072055725864`150., \
-4.2636418723240526518840693632344166215154120860948261645889033716730\
8471306650387010415790872827277903124638562528449526252242083980056164\
188190361896814914146939536027862927`150.}, \
{2.2825727937800136574760942092141594475729150546101098966785798733491\
8875391625084559228420170724077132249695456997820494325046387000946429\
985522474100794875187322697576350482`150., \
-4.2662863968900068287380471046070797237864575273050549483392899366745\
9437695812542279614210085362038566124847728498910247162523193500473214\
992761237050397437593661348788175241`150.}};
Cee[2] = Interpolation[c2points];

s1points = \
{{1.907617896260767860011475497054036028318446809225144603058751249769\
4806815561571210736776933039564694633481296201461582370798924245736942\
3524758084468476006289788603675904564`150., 
2.0552220905714129556973373980828549801740262538921295191524341804\
9357017940349356907852781700252741951426269368691848649449318994193148\
135437153310684034`128.62020399867365*^-21}, \
{2.0413599262202311288072004258652563764328000038571304180020184499212\
4962733206272105034877743504054988781268826264296400206168659646195075\
76239092536031285484207595334058418`150., 
0.1438911828442204935725243878882738952493618527856549839220804593\
5625748917823332280795156471990694299579743967873377464043981372658187\
524781886978853732783626102783057079565`150.}, \
{2.1394604850920685589650768423895210777029979995549773439374302764608\
0056809835998881873742408196150766674393824047905104371427542515405132\
966977252364434006623176591046317048`150., 
0.2234978924877639547733243542118064814045564346472745970093807492\
3106902407513938078883672651374541881865391290691918123330278702259751\
423488704780286016712273654093855760828`150.}, \
{2.1433148556815212671537742657567336649611712343085516174662774029292\
7460921208246166328403525510432875056666575741050789208701128187287638\
520397966617725098222519176200496852`150., 
0.2262938229965847979922893729604833117843691848353531586328403386\
0486328621807791334911808768322184596347570247516659382434374484076681\
633773206568249700412229013808699810722`150.}, \
{2.1449020728573698382827764277176392396912721240247133546700032241770\
6876700338027284581284655739244983125293596229770212201148191454691173\
642596838659032585171623606134361551`150., 
0.2274386983268234349722641495898086400088320534399941587258955730\
5406110760801461717549401883533381074453413492879710513146814248351680\
41226531551182106648792918210844384504`150.}, \
{2.1524976456510253553962129239426156378722267983024141518610312867259\
7452105861449613310586508219833000268794054716280380487156080986214508\
113456303415163509006374736040187426`150., 
0.2046194556266479114894462269693918112977027039898001156890038526\
2565704565770804156414009373920895948170755267352449123979716471628646\
757660551036602908857693542011191711511`150.}, \
{2.1704528697691028131628080771602455975585625465337067996509753587849\
0582284287752664906109596552119666892247042888895590631488377717233411\
383140967127700376963250532987180038`150., 
0.1613330783228310701053250413789435602236932564847625997844096722\
8734393416493934926628151042712058371531306154120554045894457390890492\
011488656451096244233403803609571098293`150.}, \
{2.1997385373007056885504600897448336068263923196982653614879777587903\
7527453125485508254295651193074534301956318153762896616668903160238654\
423316201040305376342962332116725601`150., 
0.1072742122004427274716358126528535424620851032575048041371412699\
6926598049700959551847229520969989786682939626764366707779527657393690\
074470140594612486017532911281477680022`150.}, \
{2.2426677524724705445204419922936684446643779334834943318368757760847\
7341792656130123831289308271205103044971736676542624140572644717873036\
922204315569577969701784100632101874`150., 
0.0461581812070294184757151282685988408076323405225660223909810006\
8259742850683984420496093581369244617360175653055392146635436195290941\
716705040628010198357611733708446053393`150.}, \
{2.2772837446481053037681387264688332430308241721896523291778067433461\
6942613300774020831581745654555806249277125056899052504484167960112328\
376380723793629828293879072055725864`150., 
0.0057055457060056295448370160812683374085937984973857263036062713\
4059080640127104859541121073382728776777258674316217064121230695841395\
818832069770391596715596071342029335437`150.}, \
{2.2825727937800136574760942092141594475729150546101098966785798733491\
8875391625084559228420170724077132249695456997820494325046387000946429\
985522474100794875187322697576350482`150., 
0.0000164205526152212166032480779119018332708249265010096431085712\
5736237769346524344259994646299987529478525153698171936862785409026397\
3395186010914832598911887191079997827526871447302897069324`150.}};
s[1] = Interpolation[s1points];

S2points = \
{{1.907617896260767860011475497054036028318446809225144603058751249769\
4806815561571210736776933039564694633481296201461582370798924245736942\
3524758084468476006289788603675904564`150., 
0.2555972772662321381648526908078933136183388957477167001636844734\
8106055126214072298836985577295125918675149302587323259236044938508514\
08136012742005788664176488519436371095`148.6888889906263}, \
{2.0413599262202311288072004258652563764328000038571304180020184499212\
4962733206272105034877743504054988781268826264296400206168659646195075\
76239092536031285484207595334058418`150., 
0.3999868938550802741951986141677280118318714064484576040266690718\
5426342229089866502111739344909276314161774503913459055657635665039189\
236127563582095935477123023992146439785`150.}, \
{2.1394604850920685589650768423895210777029979995549773439374302764608\
0056809835998881873742408196150766674393824047905104371427542515405132\
966977252364434006623176591046317048`150., 
0.4786883136209545792859937066712261354487123832746058194147770848\
9476802055809089568124582464557017161429451151946658066813533189216531\
161719436988864538022072595642290059281`150.}, \
{2.1433148556815212671537742657567336649611712343085516174662774029292\
7460921208246166328403525510432875056666575741050789208701128187287638\
520397966617725098222519176200496852`150., 
0.4814328302943097155888637601093749856568653260556738826950734954\
1428100138210863079268986240945507210792842670431641423429828289097095\
435224906310845297605899884630887554937`150.}, \
{2.1449020728573698382827764277176392396912721240247133546700032241770\
6876700338027284581284655739244983125293596229770212201148191454691173\
642596838659032585171623606134361551`150., 
0.4825562314583134967424318439985141484171820541242716736730865677\
4775559791157070311649761481292739413011096464080394070060557858837201\
550684616671990166917913854807197380287`150.}, \
{2.1524976456510253553962129239426156378722267983024141518610312867259\
7452105861449613310586508219833000268794054716280380487156080986214508\
113456303415163509006374736040187426`150., 
0.5049446981665887677211361351007665672082848309076926933805753238\
0844959149718694228670770833245587891243111649979967964839562076167648\
703690230083593851202554304237309283617`150.}, \
{2.1704528697691028131628080771602455975585625465337067996509753587849\
0582284287752664906109596552119666892247042888895590631488377717233411\
383140967127700376963250532987180038`150., 
0.5471155211735693496040709470801262540842240615192902139672243256\
2667020191603502168031800239131106228156059140677344800835317639098258\
510839323365008647966856963668557884889`150.}, \
{2.1997385373007056885504600897448336068263923196982653614879777587903\
7527453125485508254295651193074534301956318153762896616668903160238654\
423316201040305376342962332116725601`150., 
0.5992196256999047609374999588954923738405068718024291297459980081\
9872182816586916310037570042577026988538056540954459830320780335184626\
701872248236090193240415654537092937973`150.}, \
{2.2426677524724705445204419922936684446643779334834943318368757760847\
7341792656130123831289308271205103044971736676542624140572644717873036\
922204315569577969701784100632101874`150., 
0.6571975539248695315054172282033106166532344527205321922749750742\
2786060606343431743664022280579770911400633855278635579856002294580584\
273623182129252075459227931295787830937`150.}, \
{2.2772837446481053037681387264688332430308241721896523291778067433461\
6942613300774020831581745654555806249277125056899052504484167960112328\
376380723793629828293879072055725864`150., 
0.6949121779118717653475440036590601284112194802917932849675618170\
4633427302282746532760537267282667430336368821047010698945410350813400\
592488862761056162417239350916136729806`150.}, \
{2.2825727937800136574760942092141594475729150546101098966785798733491\
8875391625084559228420170724077132249695456997820494325046387000946429\
985522474100794875187322697576350482`150., 
0.7001682321237943327529007467937328937872073090037677451471472609\
5449029110817622825435024260497168894490291415805249103115677923448857\
534581655219099259204098776288774974834`150.}};
S[2] = Interpolation[S2points];

The Event trigger is defined by :

f[S[3][t]][3][t]- f[s[2][t]][3][t] - f[S[3][t]][2][t] + f[s[2][t]][2][t] < 1/100 when toggle[3][2] == 1, where

f[x_][i_][t_] := x +  x /(2 i^2) - x^2/(2 i) + (x t)/i - (E^(-2 x i)  Cee[i][t])/(2 i);

There are two flavors of events:

toggle events trigger a change in the discrete variable toggle[t]

toggleevent = WhenEvent[Evaluate[(S[3][t] < S[2][t])], {Print[Row[{"toggle event at ", t}]], toggle[t] -> 1, "RemoveEvent"}];

The event triggered by f can be written testing the toggle first or testing the toggle second:

event1 = WhenEvent[Evaluate[(toggle[t] ==1) && 
                            (f[S[3][t]][3][t] - f[s[2][t]][2][t] - f[S[3][t]][2][t] + f[s[2][t]][2][t] < 1/100)],
         Print[Row[{"End at ", t}]]; Endt = t; "StopIntegration"];

event2 = WhenEvent[Evaluate[(f[S[3][t]][3][t] - f[s[2][t]][2][t] - f[S[3][t]][2][t] + f[s[2][t]][2][t] < 1/100) && 
                            (toggle[t] == 1)],
         Print[Row[{"End at ", t}]]; Endt = t; "StopIntegration"];

Testing the toggle first

Dynamic[dynreport]

startt = 2.14491615819108590567858263023488635547864872975183640722275867311927957990342798141041885192925006825754194146533574107947225509599994740103335481901550805513733884265574044`150.;
Print[f[S[3][t]][3][t] - f[s[2][t]][3][t] - f[S[3][t]][2][t] + f[s[2][t]][2][t] /.t -> startt /. (initconds /. Equal -> Rule)]; 
sol1 = First[NDSolve[Join[eqns, initconds, {toggleevent, event1}], vars,       
                     {t, -\[Infinity], startt}, DiscreteVariables ->dvars,
                     EvaluationMonitor :> {Pause[0.005];
                     dynreport = Column[{Row[{"Stop Criterion = ", Style[f[S[3][t]][3][t] - f[s[2][t]][3][t] - f[S[3][t]][2][t] + f[s[2][t]][2][t], 
                      If[f[S[3][t]][3][t] - f[s[2][t]][2][t] - f[S[3][t]][2][t] + f[s[2][t]][2][t] < 1/100, Red, Black]]}], 
                                         Row[{"t = ", t}],
                                         Row[{"s[2] = ", s[2][t]}],                                        
                                         Row[{"S[3] = ", Style[S[3][t], If[S[3][t] <= S[2][t], Green, Black]]}],                                      
                                         Row[{"C[3] = ", Cee[3][t]}],                                    
                                         Row[{"toggle = ", toggle[t]}]
                                      }]}]];
Print[f[S[3][t]][3][t] - f[s[2][t]][3][t] - f[S[3][t]][2][t] + f[s[2][t]][2][t] /. sol1 /. t -> Endt];

This yields roughly the expected result:

(Output)

   0.1180039500392493987880273545540440553287906640253476084874518519607305453545644587291707233055968411834327367482888605333490514238621090923567733881

toggle event at 2.09444

End at 2.09444

0.0212756

The precision of the event location is pretty poor (probably due to the trimmed InterpolatingFunctions), but it did capture the event.

Testing the toggle second does not work:

Endt = -\[Infinity]; startt =2.14491615819108590567858263023488635547864872975183640722275867311927957990342798141041885192925006825754194146533574107947225509599994740103335481901550805513733884265574044`150.;
Print[f[S[3][t]][3][t] - f[s[2][t]][3][t] - f[S[3][t]][2][t] + f[s[2][t]][2][t] /.t -> startt /. (initconds /. Equal -> Rule)]; 
sol2 = First[NDSolve[Join[eqns, initconds, {toggleevent, event2}], vars,       
                     {t, -\[Infinity], startt}, DiscreteVariables ->dvars,
             EvaluationMonitor :> {Pause[0.005];
             dynreport2 = 
                       Column[{Row[{"Stop Criterion = ", Style[f[S[3][t]][3][t] - f[s[2][t]][3][t] - f[S[3][t]][2][t] + f[s[2][t]][2][t], 
                             If[f[S[3][t]][3][t] - f[s[2][t]][2][t] - f[S[3][t]][2][t] +f[s[2][t]][2][t] < 1/100, Red, Black]]}], 
                              Row[{"t = ", t}],
                              Row[{"s[2] = ", s[2][t]}],
                              Row[{"S[3] = ", Style[S[3][t], If[S[3][t] <= S[2][t], Green, Black]]}],
                              Row[{"C[3] = ", Cee[3][t]}],
                              Row[{"toggle = ", toggle[t]}]
                                      }]}]];
Print[Endt];

That yields

(Output)

0.1180039500392493987880273545540440553287906640253476084874518519607305453545644587291707233055968411834327367482888605333490514238621090923567733881

toggle event at 2.09444

NDSolve::ndsz: At t == 2.0667528920546507`, step size is effectively zero; singularity or stiff system suspected. >>

-\[Infinity]

event2 did not catch a point at which toggle[t]==1 and the function value was less than 1

A plot of the toggle value, the f test value and the cut off

Plot[{f[S[3][t]][3][t] - f[s[2][t]][3][t] - f[S[3][t]][2][t] + f[s[2][t]][2][t] /. sol2 /. t -> time, 
      toggle[t] /. sol2 /. t -> time, 1/100}, 
    {time, 2.06676, startt}, 
   PlotLegends -> {"f trigger value", "toggle value", "f trigger target"}]

enter image description here

$\endgroup$
5
  • 1
    $\begingroup$ Dt is an internal, Protected symbol. I cannot set it to a value at all. $\endgroup$ – Michael E2 Mar 29 '19 at 23:50
  • 1
    $\begingroup$ Your 2nd WhenEvent is incomplete. it has an odd number of [ brackets. $\endgroup$ – m_goldberg Mar 29 '19 at 23:54
  • $\begingroup$ A strict reading of the syntax in the docs suggests that multiple actions need separate codes: WhenEvent[<event>, <single action code>] or WhenEvent[< event>, {<single action>, <single action>,...}]. What you have is not a list of codes, but a single code that evaluates to a list of actions. The problem has nothing to do specifically with If[]: even, Null; {Dt = t, Dtoggle[t] -> 1, "RemoveEvent"} fails. I guess you would need to repeat the If[] test for each action. $\endgroup$ – Michael E2 Mar 30 '19 at 13:18
  • 2
    $\begingroup$ Related: The difference in switching the event and condition in WhenEvent[event && condition, action] is discussed here $\endgroup$ – Michael E2 Apr 2 '19 at 20:06
  • $\begingroup$ Note that WhenEvent[expr < 1/100 && condition, action] triggers an event only when the value of expr changes from greater than 1/100 to less than 1/100. Your f trigger value does not do that in the last plot. Perhaps WhenEvent[expr == 1/100 && condition, action] is what you're after. $\endgroup$ – Michael E2 Apr 2 '19 at 20:24

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