Items tagged with fsolve fsolve Tagged Items Feed

As part of a project, I am numerically estimating the roots of many large polynomials. Occasionally, "fsolve" fails with strange errors related to "fsolve/refine2". Searches for these error messages have turned up nothing.

I've inluded the code below that causes the error on Maple 18.02. I apologize for the polynomial in question being so long, it's the shortest example I have. The error it generates is:

    Error, (in fsolve/refine2) invalid input: evalf expects its 2nd argument, n, to be of type posint, but received undefined

Is this a bug? Or am I missing some fsolve option to prevent this? Note that it only happens when the "complex" flag is used.

=========

P := x^14-22702264347017701018473605850972699930097274504938699916055555261201515180511538865331807292689345943133521696082918467714371257277276696385067641909170155322906230250853577229812913946663078548646992393337618113886746876557117483839533553328895358682670189394678910311793504505447628428181885141769168591937690303328913335175451328463754619536253583902806843310134957600949886784187209785783810122275010505534415815566439121541947044486358488039865870455952098827525405324562601732796858645293515431747164008309785658410612354201118685855495413079021176507985235094746401708925593687656572387531020719291601076812080687859808747213536777976702071405128537760507468013438105233313663196919816564525291458692028177366393652501832447863872200682143768513389322886600569382594287138458765510827267842205096062437750804878586024353928794905249283675708441066101095406513448522689302522442783437142289641259057413952301148939774149714785/3195755849586795631956816504521213454239300164039404772924331154185577854140658969534719471406093912112781063157828311505891258148739680804289213024862131311540960306206602785748866445362483281617891374949555209869677857419473553982132073059025609434698683760348542259396937054082293168625919023158753310878489047944378154369352523436731294817697449949932655665007647918855300664365159027040571937825740235967492228453331261542499260943085539271304638576578246276634403350307801994081681247214869084246168101721298760198550961832560608341435638093413744839736250679074198753022491225840288065341597851066663786665723409977381822591654466626645542917017628998630902708076612502066607817250779545511895971357711983287763127653752300554550391349040027472903180009282594974618980021621163037989247901106508257414514187962209356325857887950302223210328647697948055097831009797738621154319922212951316644741457327450027692469090867369598*x^13+19088859498864751331345860430721481446264521641744903691362655800372349704990331481604867685549645823662978708926030541236042951546550966879612333115396628902751820387999904934599090760358886795430484312266737008386396041896213971568537362589851823779617430207078749426022658232278071527361264481524611089324107754031784837527081637219350016169914382322455035364613935875393571579561406195287363628553419822536428710010055920488818415526206620047517917895155637033562338042275152771173240104076821411360366799172066699958543868065037999702280159896040588223787643434915579465270491451613199185385049196526456210057933748521047167538262357063585093474544299142560492581751607753970282443057122762426600024763892341448332834018680513343674283251162037067303651651086278409136799357849452879897251530675098741236156640469815784447341282424004221641529187217962536022784563163918511210513153785881467158114512281634789894107114727680109/1065251949862265210652272168173737818079766721346468257641443718061859284713552989844906490468697970704260354385942770501963752716246560268096404341620710437180320102068867595249622148454161093872630458316518403289892619139824517994044024353008536478232894586782847419798979018027431056208639674386251103626163015981459384789784174478910431605899149983310885221669215972951766888121719675680190645941913411989164076151110420514166420314361846423768212858859415425544801116769267331360560415738289694748722700573766253399516987277520202780478546031137914946578750226358066251007497075280096021780532617022221262221907803325793940863884822208881847639005876332876967569358870834022202605750259848503965323785903994429254375884584100184850130449680009157634393336427531658206326673873721012663082633702169419138171395987403118775285962650100741070109549232649351699277003265912873718106640737650438881580485775816675897489696955789866*x^12-127688837609696458957114129756229560761957972259253280819996356067917173759565012901801561924391178368568146719627801670086606489531437386224078360185442651606983719684283163392876990522586784115059551865746707609765679864632874671595399416688286257053075135779925094175440416074968471245768830366824397599424731191899057489251725430472639828977416853808059394673266682604308077331301860791811476274942568803494246399367164616630866928631772760003749091917886558963952047434319195736393271420111064778587861639539510320744497931007588784407172972776901653630399291814617861650330433072614870207218474263898528043868017109168847074788133295715653324601280999334137328493510780499508083274179117783232296907665583279993325725716354393277745170409349317876378784871325009748734263290375761397883657890413900529632709410443413043575189427898559331856967020187201932742096158736566419271039506140015010172468151681141071869870925420155369/639151169917359126391363300904242690847860032807880954584866230837115570828131793906943894281218782422556212631565662301178251629747936160857842604972426262308192061241320557149773289072496656323578274989911041973935571483894710796426414611805121886939736752069708451879387410816458633725183804631750662175697809588875630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fsolve(P,complex);

 

Let us define a piecewise-linear continuous function:

restart; VP := Vector[row](16, {(1) = 10, (2) = 177.9780267, (3) = 355.9560534, (4) = 533.9340801, (5) = 711.9121068, (6) = 889.8901335, (7) = 1067.868160, (8) = 1245.846187, (9) = 1423.824214, (10) = 1601.802240, (11) = 1779.780267, (12) = 1957.758294, (13) = 2135.736320, (14) = 2313.714347, (15) = 2491.692374, (16) = 2669.670400}); VE := Vector[row](16, {(1) = 5.444193931, (2) = .4793595141, (3) = .3166653569, (4) = .2522053489, (5) = .2123038784, (6) = .1822258228, (7) = .1544240625, (8) = .1277082078, (9) = .1055351619, (10) = 0.8639065510e-1, (11) = 0.6936612570e-1, (12) = 0.5388339810e-1, (13) = 0.3955702170e-1, (14) = 0.2612014630e-1, (15) = 0.1338216460e-1, (16) = 0.1203297900e-2}); for i to 15 do p[i] := VE[i+1] < x and x <= VE[i], (VP[i+1]-VP[i])*(x-VE[i])/(VE[i+1]-VE[i])+VP[i] end do; g := unapply(piecewise(seq(p[i], i = 1 .. 15)), x);

for i to 15 do print(fsolve(g(x) = VP[i])) end do;

Why doesn't the fsolve command work if i = 4, 7, 9, 11, 14? There are workarounds:

print(DirectSearch:-SolveEqutions(g(x) = VP[i]));

and/or

VP := convert(VP, rational); VE := convert(VE, rational); print(solve(g(x) = VP[i]));

 How to explain such behavior of the fsolve command? That was asked but not answered in http://forum.exponenta.ru/viewtopic.php?t=13524&sid=025a140e7e00b99803c86060a5c0c33c .

NULL

 

strange_behavior.mw

Edit. Replaced worksheet.

I know 1st root of a function locates in a small interval (by drawing plots of function).

but fsolve command uses unreasonable time to find roots.

Also NextZero dosent work.

Please help me.

Thanks for your attention.

--------------------------------------------------------------------------------------------------

restart; s := sqrt(n)*Pi*(sqrt(n)*Pi-tan(sqrt(n)*Pi))/(sqrt(n)*Pi*tan(sqrt(n)*Pi)+2*(1-sec(sqrt(n)*Pi)));

C := (tan(sqrt(n)*Pi)-sqrt(n)*Pi*sec(sqrt(n)*Pi))/(sqrt(n)*Pi-tan(sqrt(n)*Pi));

S := s*(-C^2+1);

Gamma[b] := E[b2]/E[b1];

Gamma[c] := E[c2]/E[c1];

alpha[b] := t[b1]*t[b2]/(t[b1]+t[b2])^2;

alpha[c] := t[c1]*t[c2]/(t[c1]+t[c2])^2;

EIb := b*E[b1]*(t[b1]^4+2*Gamma[b]*alpha[b]*(2-alpha[b])*(t[b1]+t[b2])^4+Gamma[b]^2*t[b2]^4)/(12*(Gamma[b]*t[b2]+t[b1]));

EIc := b*E[c1]*(t[c1]^4+2*Gamma[c]*alpha[c]*(2-alpha[c])*(t[c1]+t[c2])^4+Gamma[c]^2*t[c2]^4)/(12*(Gamma[c]*t[c2]+t[c1]));

b := 1;Lb := 2; Lc1 := 2.5; Lc2 := 3; E[b1] := 180; E[b2] := 200; t[b1] := 0.3e-1; t[b2] := 0.4e-1; E[c2] := 220; t[c1] := 0.5e-1; t[c2] := 0.2e-1;

for k from 0 by 10 to 100 do

E[c1] := 150+k; nce := (1/2)*(Lc1/Lc2)^2*n; nb := (1/2)*(Lb/Lc2)^2*n; q[k] := 1000*fsolve((subs(n = nce, C*s)*EIc/Lc1)^2/(S*EIc/Lc2+subs(n = nce, s)*EIc/Lc1+subs(n = nb, s*(1-C))*EIb/Lb)-subs(n = nce, s)*EIc/Lc1-2*EIb/Lb, n = 1.45 .. 1.56)*evalf(Pi^2)*EIc/(2*Lc2^2); print(q[k], k)

end do;

with(CurveFitting); F := PolynomialInterpolation([seq([10*i, q[10*i]], i = 0 .. 10)], z)

Hi, the fsolve works perfectly fine when otaining SOL2 below. However, as soon as I change the values of paramters (from 0 values in SOL2 to t_prof = .16, t_r = .16, t_w = .16 in SOL3) fsolve simplmy reproduces the eval results and would not solve! Please your help is highly appreciated. Thanks in advance!

restart;
eq1 := ((1-s)*w)^(1-gamma)*r^gamma-P_v = 0;
eq2 := (1-s)*w*H/M-(1-gamma)*P_v*q/phi = 0;
eq3 := r*(K+K_f)/M-gamma*P_v*q/phi = 0;
eq4 := prof-M*p_d*q+(1-s)*w*H+r*(K+K_f) = 0;
eq5 := -tau*y_x+q-y_d-y_g = 0;
eq6 := p_d-sigma*P_v/((sigma-1)*phi) = 0;
eq7 := y_d-M^(lambda-1)*Y*(p_d/P)^(-sigma) = 0;
eq8 := y_x-F_f*(tau*p_d)^(-sigma_x) = 0;
eq9 := y_f-M_f^(lambda-1)*Y*((1+z)*tau*p_f/P)^(-sigma) = 0;
eq10 := (G*alpha_g+Y)^(-alpha_c)/P-A*H^alpha_h/((1-t_w)*w) = 0;
eq11 := P*Y-(1-t_w)*w*H-(1-t_r)*r*K-(1-t_prof)*prof+T = 0;
eq12 := P*Y-M*p_d*y_d-M_f*(1+z)*tau*p_f*y_f = 0;
eq13 := (1-t_r)*r-r_f = 0;
eq14 := G-y_g*M^((lambda_g-1+sigma_g)/(sigma_g-1)) = 0;
eq15 := s*w*H+M*p_d*y_g-T-t_w*w*H-t_r*r*(K+K_f)-t_prof*prof-z*M_f*tau*p_f*y_f = 0;

SOL2 := fsolve(eval({eq1, eq10, eq11, eq12, eq13, eq14, eq15, eq2, eq3, eq4, eq5, eq6, eq7, eq8, eq9}, [A = 7.716049383, K = 3.2, K_f = 0, alpha_c = .8, alpha_g = .2, alpha_h = 4, lambda = .5, p_f = 1, phi = .625, s = 0, sigma = 5, sigma_g = 5, sigma_x = 5, t_prof = 0, t_r = 0, t_w = 0, tau = 1.1, y_d = 1, y_f = 1, y_g = .4, y_x = 1, z = 0, lambda_g = .5, gamma = .25, gamma = .25]), {F_f, G, H, M, M_f, P, P_v, T, Y, p_d, prof, q, r, r_f, w}, {F_f = 2 .. 4, G = .1 .. .4, H = .4 .. .8, M = .4 .. .6, M_f = .3 .. .7, P = .8 .. 2, P_v = .4 .. .8, T = -.2 .. .3, Y = .7 .. 3, p_d = .9 .. 1.6, prof = .1 .. .4, q = 1.5 .. 2.7, r = 0.4e-1 .. 0.9e-1, r_f = 0.4e-1 .. 0.9e-1, w = .8 .. 3});

 

SOL3 := fsolve(eval({eq1, eq10, eq11, eq12, eq13, eq14, eq15, eq2, eq3, eq4, eq5, eq6, eq7, eq8, eq9}, [A = 7.716049383, K = 3.2, K_f = 0, alpha_c = .8, alpha_g = .2, alpha_h = 4, lambda = .5, p_f = 1, phi = .625, s = 0, sigma = 5, sigma_g = 5, sigma_x = 5, t_prof = .16, t_r = .16, t_w = .16, tau = 1.1, y_d = 1, y_f = 1, y_g = .4, y_x = 1, z = 0, lambda_g = .5, gamma = .25, gamma = .25]), {F_f, G, H, M, M_f, P, P_v, T, Y, p_d, prof, q, r, r_f, w}, {F_f = 2 .. 4, G = .1 .. .4, H = .4 .. .8, M = .4 .. .6, M_f = .3 .. .7, P = .8 .. 2, P_v = .4 .. .8, T = -.2 .. .3, Y = .7 .. 3, p_d = .9 .. 1.6, prof = .1 .. .4, q = 1.5 .. 2.7, r = 0.4e-1 .. 0.9e-1, r_f = 0.4e-1 .. 0.9e-1, w = .8 .. 3});

If there is  an equation or are several equations, I need to obtain all the roots, how can I do???

 

fsolve ? rootfindings? or what?

 

If an examples of actual is given,  That will be perfect  !!!

 

Thanks 

Hi Everyone,

I have a bunch polynomial systems of equations (all form zero-dimensional ideals, i.e. there is a finite number of complex solutions), and I would like to get a real solution for each of them, if available.

fsolve would be the tool to use. But it lead to some strange behaviour for me. Among some other inputs, the input

fsolve({81*x3^12+72*x3^10-614*x3^9+16*x3^8-384*x3^7+1884*x3^6+480*x3^4-2760*x3^3+1600, 81*x2*x3^11+72*x2*x3^9-452*x2*x3^8+16*x2*x3^7-240*x2*x3^6+980*x2*x3^5+32*x2*x3^4-144*x2*x3^3-800*x2*x3^2-220*x3^3+160*x2^2+480*x2+520, 81*x3^11+72*x3^9-452*x3^8+16*x3^7-240*x3^6+980*x3^5+32*x3^4-144*x3^3-800*x3^2+160*x1+160*x2+480},{x1, x2, x3});

somehow outputs itself, i.e.

fsolve({81*x3^12+72*x3^10-614*x3^9+16*x3^8-384*x3^7+1884*x3^6+480*x3^4-2760*x3^3+1600, 81*x2*x3^11+72*x2*x3^9-452*x2*x3^8+16*x2*x3^7-240*x2*x3^6+980*x2*x3^5+32*x2*x3^4-144*x2*x3^3-800*x2*x3^2-220*x3^3+160*x2^2+480*x2+520, 81*x3^11+72*x3^9-452*x3^8+16*x3^7-240*x3^6+980*x3^5+32*x3^4-144*x3^3-800*x3^2+160*x1+160*x2+480},{x1, x2, x3})

I know that this system has no real solutions, but only complex ones. But wouldn't the expected output then be just nothing (as e.g. "solve" does)?

I am confused by this output. Furthermore, how can I "check" with Maple if the output was a solution? By checking the type? There must be less hacky solutions. Thank you all in advance for your help.

Albert

PS.: When I add the keyword "complex" to the function call, then I receive a complex solution; hence, the syntax at least is correct (if someonw might have doubted that).

When I use fsolve with equation 

-x^2 + 2*x + 5 + (x^2 + 2*x - 1)* sqrt(2 - x^2)=0

I got only one solution.

fsolve(-x^2 + 2*x + 5 + (x^2 + 2*x - 1)* sqrt(2 - x^2)=0,x);

In fact, it have two reals solutions.  

I posted at here

http://mathematica.stackexchange.com/questions/83985/does-the-equation-have-two-roots/83991#83991

 

Dear Colleges

I have a problem with the following code. As you can see, procedure Q1 converges but I couldn't get the resutls from Q2.

I would be most grateful if you could help me on this problem.

 

Sincerely yours

Amir

 

restart;

Eq1:=diff(f(x),x$3)+diff(f(x),x$2)*f(x)+b^2*sqrt(2*reynolds)*diff(diff(f(x),x$2)^2*x^2,x$1);
Eq2:=diff(g(x),x$3)+diff(g(x),x$2)*g(x)+c*a^2*sqrt(2*reynolds)*diff(diff(g(x),x$2)^2*x,x$1);
eq1:=isolate(Eq1,diff(f(x),x,x,x));
eq2:=subs(g=f,isolate(Eq2,diff(g(x),x,x,x)));
EQ:=diff(f(x),x,x,x)=piecewise(x<c*0.1,rhs(eq1),rhs(eq2));
Eq11:=diff(theta(x),x$2)+pr*diff(theta(x),x$1)*f(x)+pr/prt*b^2*sqrt(2*reynolds)*diff(diff(f(x),x$2)*diff(theta(x),x$1)*x^2,x$1);
Eq22:=diff(g(x),x$2)+pr*diff(g(x),x$1)*f(x)+pr/prt*a^2*c*sqrt(2*reynolds)*diff(diff(f(x),x$2)*diff(g(x),x$1)*x^1,x$1);
eq11:=isolate(Eq11,diff(theta(x),x,x));
eq22:=subs(g=theta,isolate(Eq22,diff(g(x),x,x)));
EQT:=diff(theta(x),x,x)=piecewise(x<c*0.1,rhs(eq11),rhs(eq22));
EQT1a:=eval(EQT,EQ):
EQT2:=eval(EQT1a,{f(x)=G0(x),diff(f(x),x)=G1(x),diff(f(x),x,x)=G2(x)}):
bd:=c;
a:=0.13:
b:=0.41:
pr:=1;
prt:=0.86;
reynolds:=12734151.135786774055543653356602;     #10^6;   #1.125*10^8:

c:=88.419896050808975395120916434619:
;
Q:=proc(pp2) local res,F0,F1,F2;
print(pp2);
if not type(pp2,numeric) then return 'procname(_passed)' end if:
res:=dsolve({EQ,f(0)=0,D(f)(0)=0,(D@@2)(f)(0)=pp2},numeric,output=listprocedure);
F0,F1,F2:=op(subs(subs(res),[f(x),diff(f(x),x),diff(f(x),x,x)])):
F1(bd)-1;
end proc;
fsolve(Q(pp2)=0,pp2=(0..1002));
se:=%;
res2:=dsolve({EQ,f(0)=0,D(f)(0)=0,(D@@2)(f)(0)=se},numeric,output=listprocedure):
G0,G1,G2:=op(subs(subs(res2),[f(x),diff(f(x),x),diff(f(x),x,x)])):
plots:-odeplot(res2,[seq([x,diff(f(x),[x$i])],i=1..1)],0..c);



Q2:=proc(rr2) local solT,T0,T1;
print(rr2);
if not type(rr2,numeric) then return 'procname(_passed)' end if:
solT:=dsolve({EQT2,theta(0)=1,D(theta)(0)=-rr2},numeric,known=[G0,G1,G2],output=listprocedure):
T0,T1:=op(subs(subs(res),[theta(x),diff(theta(x),x)])):
T0(bd);
end proc;
fsolve(Q2(rr2)=0,rr2=(0..100));


shib:=%;
sol:=dsolve({EQT2,theta(0)=1,D(theta)(0)=-shib},numeric,known=[G0,G1,G2],output=listprocedure):
plots:-odeplot(sol,[x,theta(x)],0..c);
#fsolve(Q2(pp3)=0,pp3=-2..2):

Amir

Hi,

we want to know what is the meaning of this statement?

We expect to have the following statement . But unfortunately we don,t get it

> with(difforms);
> sol := fsolve({diff(S, x) = 0, diff(S, y) = 0}, {x, y});


I do not take values above code.

Hello there

I'm quite an amature so please don't judge.  I'm trying to use fsolve to solve a system of non-linear equations but Maple is just "spitting" on me the equations with no intention to solve them:

> delta5 := P*(1+mu5)*((1-2*mu5)*x/(sqrt(x^2+zeq^2)*(sqrt(x^2+zeq^2)*x))+x*zeq/sqrt(x^2+zeq^2)^3)/(2*Pi*E5);
print(`output redirected...`); # input placeholder
> shrinkage := P*(1+mu5)*((1-2*mu5)*x/(sqrt(x^2+Zb^2)*(sqrt(x^2+Zb^2)*x))+x*Zb/sqrt(x^2+Zb^2)^3)/(2*Pi*E5)-P*(1+mu5)*((1-2*mu5)*x/(sqrt(x^2+Za^2)*(sqrt(x^2+Za^2)*x))+x*Za/sqrt(x^2+Za^2)^3)/(2*Pi*E5);
> eq10 := subs(x = 1800, delta5)+subs(x = 1800, Zb = z2, Za = z1, shrinkage)+subs(x = 1800, Zb = z3, Za = z2, shrinkage)+subs(x = 1800, Zb = z4, Za = z3, shrinkage)+subs(x = 1800, Zb = z5, Za = z4, shrinkage) = 36.7*10^(-3);
print(`output redirected...`); # input placeholder
> eq9 := subs(x = 1500, delta5)+subs(x = 1500, Zb = z2, Za = z1, shrinkage)+subs(x = 1500, Zb = z3, Za = z2, shrinkage)+subs(x = 1500, Zb = z4, Za = z3, shrinkage)+subs(x = 1500, Zb = z5, Za = z4, shrinkage) = 47.2*10^(-3);
print(`output redirected...`); # input placeholder
> eq8 := subs(x = 1200, delta5)+subs(x = 1200, Zb = z2, Za = z1, shrinkage)+subs(x = 1200, Zb = z3, Za = z2, shrinkage)+subs(x = 1200, Zb = z4, Za = z3, shrinkage)+subs(x = 1200, Zb = z5, Za = z4, shrinkage) = 63.8*10^(-3);
> eq7 := subs(x = 900, delta5)+subs(x = 900, Zb = z2, Za = z1, shrinkage)+subs(x = 900, Zb = z3, Za = z2, shrinkage)+subs(x = 900, Zb = z4, Za = z3, shrinkage)+subs(x = 900, Zb = z5, Za = z4, shrinkage) = 91.1*10^(-3);
print(`output redirected...`); # input placeholder
> eq6 := subs(x = 600, delta5)+subs(x = 600, Zb = z2, Za = z1, shrinkage)+subs(x = 600, Zb = z3, Za = z2, shrinkage)+subs(x = 600, Zb = z4, Za = z3, shrinkage)+subs(x = 600, Zb = z5, Za = z4, shrinkage) = 137.9*10^(-3);
> eq5 := subs(x = 450, delta5)+subs(x = 450, Zb = z2, Za = z1, shrinkage)+subs(x = 450, Zb = z3, Za = z2, shrinkage)+subs(x = 450, Zb = z4, Za = z3, shrinkage)+subs(x = 450, Zb = z5, Za = z4, shrinkage) = 175.2*10^(-3);
> eq4 := subs(x = 300, delta5)+subs(x = 300, Zb = z2, Za = z1, shrinkage)+subs(x = 300, Zb = z3, Za = z2, shrinkage)+subs(x = 300, Zb = z4, Za = z3, shrinkage)+subs(x = 300, Zb = z5, Za = z4, shrinkage) = 230.9*10^(-3);
print(`output redirected...`); # input placeholder
> sys := {eq10, eq5, eq6, eq7, eq8, eq9};
print(`output redirected...`); # input placeholder
> fsolve(sys, {E1 = 1000 .. 2000, E2 = 0 .. 2000, E3 = 0 .. 2000, E4 = 0 .. 2000, E5 = 0 .. 2000, h4 = 100 .. 400});

and this is what Maple gives after the fsolve

 

fsolve({(3937.500000*(.2/(202500+(146.0507832*(E1/E5)^(1/3)+197.1094212*(E2/E5)^(1/3)+295.6641318*(E3/E5)^(1/3)+1.*h4*(E4/E5)^(1/3))^2)+(450*(146.0507832*(E1/E5)^(1/3)+197.1094212*(E2/E5)^(1/3)+295.6641318*(E3/E5)^(1/3)+1.*h4*(E4/E5)^(1/3)))/(202500+(146.0507832*(E1/E5)^(1/3)+197.1094212*(E2/E5)^(1/3)+295.6641318*(E3/E5)^(1/3)+1.*h4*(E4/E5)^(1/3))^2)^(3/2)))/E5-0.3888888889e-2/E5+(3937.500000*(.2/(202500+(650+h4)^2)+(450*(650+h4))/(202500+(650+h4)^2)^(3/2)))/E5 = .1752000000, (3937.500000*(.2/(360000+(146.0507832*(E1/E5)^(1/3)+197.1094212*(E2/E5)^(1/3)+295.6641318*(E3/E5)^(1/3)+1.*h4*(E4/E5)^(1/3))^2)+(600*(146.0507832*(E1/E5)^(1/3)+197.1094212*(E2/E5)^(1/3)+295.6641318*(E3/E5)^(1/3)+1.*h4*(E4/E5)^(1/3)))/(360000+(146.0507832*(E1/E5)^(1/3)+197.1094212*(E2/E5)^(1/3)+295.6641318*(E3/E5)^(1/3)+1.*h4*(E4/E5)^(1/3))^2)^(3/2)))/E5-0.2187500000e-2/E5+(3937.500000*(.2/(360000+(650+h4)^2)+(600*(650+h4))/(360000+(650+h4)^2)^(3/2)))/E5 = .1379000000, (3937.500000*(.2/(810000+(146.0507832*(E1/E5)^(1/3)+197.1094212*(E2/E5)^(1/3)+295.6641318*(E3/E5)^(1/3)+1.*h4*(E4/E5)^(1/3))^2)+(900*(146.0507832*(E1/E5)^(1/3)+197.1094212*(E2/E5)^(1/3)+295.6641318*(E3/E5)^(1/3)+1.*h4*(E4/E5)^(1/3)))/(810000+(146.0507832*(E1/E5)^(1/3)+197.1094212*(E2/E5)^(1/3)+295.6641318*(E3/E5)^(1/3)+1.*h4*(E4/E5)^(1/3))^2)^(3/2)))/E5-0.9722222220e-3/E5+(3937.500000*(.2/(810000+(650+h4)^2)+(900*(650+h4))/(810000+(650+h4)^2)^(3/2)))/E5 = 0.9110000000e-1, (3937.500000*(.2/(1440000+(146.0507832*(E1/E5)^(1/3)+197.1094212*(E2/E5)^(1/3)+295.6641318*(E3/E5)^(1/3)+1.*h4*(E4/E5)^(1/3))^2)+(1200*(146.0507832*(E1/E5)^(1/3)+197.1094212*(E2/E5)^(1/3)+295.6641318*(E3/E5)^(1/3)+1.*h4*(E4/E5)^(1/3)))/(1440000+(146.0507832*(E1/E5)^(1/3)+197.1094212*(E2/E5)^(1/3)+295.6641318*(E3/E5)^(1/3)+1.*h4*(E4/E5)^(1/3))^2)^(3/2)))/E5-0.5468750000e-3/E5+(3937.500000*(.2/(1440000+(650+h4)^2)+(1200*(650+h4))/(1440000+(650+h4)^2)^(3/2)))/E5 = 0.6380000000e-1, (3937.500000*(.2/(2250000+(146.0507832*(E1/E5)^(1/3)+197.1094212*(E2/E5)^(1/3)+295.6641318*(E3/E5)^(1/3)+1.*h4*(E4/E5)^(1/3))^2)+(1500*(146.0507832*(E1/E5)^(1/3)+197.1094212*(E2/E5)^(1/3)+295.6641318*(E3/E5)^(1/3)+1.*h4*(E4/E5)^(1/3)))/(2250000+(146.0507832*(E1/E5)^(1/3)+197.1094212*(E2/E5)^(1/3)+295.6641318*(E3/E5)^(1/3)+1.*h4*(E4/E5)^(1/3))^2)^(3/2)))/E5-0.3500000000e-3/E5+(3937.500000*(.2/(2250000+(650+h4)^2)+(1500*(650+h4))/(2250000+(650+h4)^2)^(3/2)))/E5 = 0.4720000000e-1, (3937.500000*(.2/(3240000+(146.0507832*(E1/E5)^(1/3)+197.1094212*(E2/E5)^(1/3)+295.6641318*(E3/E5)^(1/3)+1.*h4*(E4/E5)^(1/3))^2)+(1800*(146.0507832*(E1/E5)^(1/3)+197.1094212*(E2/E5)^(1/3)+295.6641318*(E3/E5)^(1/3)+1.*h4*(E4/E5)^(1/3)))/(3240000+(146.0507832*(E1/E5)^(1/3)+197.1094212*(E2/E5)^(1/3)+295.6641318*(E3/E5)^(1/3)+1.*h4*(E4/E5)^(1/3))^2)^(3/2)))/E5-0.2430555555e-3/E5+(3937.500000*(.2/(3240000+(650+h4)^2)+(1800*(650+h4))/(3240000+(650+h4)^2)^(3/2)))/E5 = 0.3670000000e-1}, {E1, E2, E3, E4, E5, h4}, {E1 = 1000 .. 2000, E2 = 0 .. 2000, E3 = 0 .. 2000, E4 = 0 .. 2000, E5 = 0 .. 2000, h4 = 100 .. 400})

Hi everyone,

 

i'm trying to find out the euler angles from a rotation matrix.

I have a matrix that contains the result of multpilying the 3 axis rotation R(z,c)*R(y,b)*R(x,a) without knowing the values of the angles a,c,b (that's what I want to find out), so there are sinus and cosinus everywhere. There is another matrix containing the expected values that each equation in the first matrix will match.

My problem is that I eventually will change the order of the multiplication of the axis (i.e. R(x,a)*R(z,c)*R(y,b)) and I'm try to make maple compute this for me.

I defined R(x,a), R(y,b) and R(z,c) as follows:

Rx := Matrix (3,3, [1,0,0,0,cos(a),-sin(a),0,sin(a),cos(a)]);    
Ry := Matrix (3,3, [sin(b), 0, cos(b), 0, 1, 0, -sin(b), 0, cos(b)]);
Rz := Matrix (3,3, [cos(c), -sin(c), 0, sin(c), cos(c), 0, 0, 0, 1]);
and
RT := Multiply(Multiply(Rx,Rz),Ry);

Since here is alright. Now I want to match RT to the solution matrix.

g1 := RT[1,1] = mat[1,1];
g2 := RT[1,2] = mat[1,2];
g3 := RT[1,3] = mat[1,3];
g4 := RT[2,1] = mat[2,1];
g5 := RT[2,2] = mat[2,2];
g6 := RT[2,3] = mat[2,3];
g7 := RT[3,1] = mat[3,1];
g8 := RT[3,2] = mat[3,2];
g9 := RT[3,3] = mat[3,3];

soll := fsolve({g1,g2,g3,g4,g5,g6,g7,g8,g9},{a,b,c});

At this point I'm getting an error. I know that there are more equations than variables but the system is solvable anyway.
What maple trick can I do to solve this system or to find the good 3 equations?

 

Extra question:

Is there any method to match RT to mat without all those gX equations?

 

Thank you everyone.

The issue I am currently having is that, while analyticity (and physics) indicates a certain function must have roots, fsolve is having trouble finding them. In fact, I have even found roots manually in a certain region myself, simply inputting into the function various values until I found them. However, fsolve does not seem to want to find these roots, and I believe it is a numerics issue: when I changed the digits around, for extremely low values of Digits, it would find a root (even though it was incorrect). Further, this problem arose elsewhere in the domain of interest for other values of Digits (in particular, for Digits:=5, fsolve failed in a region it had not failed before).

The region of interest is the "peak" of the output of poleR(M0, 0.935, mK), which should be somewhere around M0 = 0.95 or so. However, because fsolve cannot find the roots, the plot cannot be made.

Anyone have any ideas as to why fsolve cannot find the roots? I was also experiencing issues with some of these functions having multiple roots, which itself is weird as well (note that I am working over the complex plane).

Attached is the document.

pole-dragging-mapleprimes.mw

Any ideas?

How can this error be corrected '' error, (in fsolve) fsolve cannot solve on 0=0 ''. See the worksheet p4.mw

Thanks.

Hi,

I have a problem solving two equations.  They are as follows:

s := 1/(273.16+50); s1 := 1/(273.16+145); s3 := 1/(273.16+250); s2 := 1/(273.16+197.5); gamma0 := 0.1e-3; gamma1 := .5; gamma2 := 0.15e-2; beta := -3800:

c := 300; n := 200; tau1 := 99; tau2 := 120;


Delta := solve(1-exp(-(gam0*tau1+(1/2)*gam1*tau1^2)*exp(beta*s1)) = 1-exp(-(gam0*a+(1/2)*gam1*a^2)*exp(beta*s2)), a);
a := Delta[1];


Theta := solve(1-exp(-(gam0*(a+tau2-tau1)+(1/2)*gam1*(a+tau2-tau1)^2)*exp(beta*s2)) = 1-exp(-(gam0*b+(1/2)*gam1*b^2)*exp(beta*s3)), b);
b := Theta[1];

n1 := int((gam1*t+gam0)*exp(beta*s1)*exp(-(gam0*t+(1/2)*gam1*t^2)*exp(beta*s1)), t = 0 .. tau1);
n22 := (n-n1)*(int((gam1*t+gam0)*exp(beta*s2)*exp(-(gam0*t+(1/2)*gam1*t^2)*exp(beta*s2)), t = a1 .. a1+tau2-tau1));
n2 := eval(n22, a1 = a);
n33 := (n-n1-n2)*(Int((gam1*t+gam0)*exp(beta*s3)*exp(-(gam0*t+(1/2)*gam1*t^2)*exp(beta*s3)), t = b1 .. c));
n3 := eval(n33, a1 = a);
n4 := n-n1-n2-n3;

g1 := -n1*(Int((1/(gam1*t+gam0)-t*exp(beta*s1))*(gamma2*t^2+gamma1*t+gamma0)*exp(beta*s1)*exp(-(gamma0*t+(1/2)*gamma1*t^2+(1/3)*gamma2*t^3)*exp(beta*s1)), t = 0 .. tau1))-n2*(Int((1/(gam0+gam1*(a+t-tau1))-(a+t-tau1)*exp(beta*s2))*(gamma0+gamma1*(a+t-tau1)+gamma2*(a+t-tau1)^2)*exp(beta*s2)*exp(-(gamma0*(a+t-tau1)+(1/2)*gamma1*(a+t-tau1)^2+(1/3)*gamma2*(a+t-tau1)^3)*exp(beta*s2)), t = tau1 .. tau2))-n3*(Int((1/(gam0+gam1*(b+t-tau2))-(b+t-tau2)*exp(s3))*(gamma0+gamma1*(b+t-tau2)+gamma2*(b+t-tau2)^2)*exp(beta*s3)*exp(-(gamma0*(b+t-tau2)+(1/2)*gamma1*(b+t-tau2)^2+(1/3)*gamma2*(b+t-tau2)^3)*exp(beta*s3)), t = tau2 .. c))+(n-n1-n2-n3)*(1/(gam0+gam1*(b+c-tau2))-(b+c-tau2)*exp(s3))*(gamma0+gamma1*(b+c-tau2)+gamma2*(b+c-tau2)^2)*exp(beta*s3)*exp(-(gamma0*(b+c-tau2)+(1/2)*gamma1*(b+c-tau2)^2+(1/3)*gamma2*(b+c-tau2)^3)*exp(beta*s3));

g2 := -n1*(Int((t/(gam1*t+gam0)-(1/2)*t^2*exp(beta*s1))*(gamma2*t^2+gamma1*t+gamma0)*exp(beta*s1)*exp(-(gamma0*t+(1/2)*gamma1*t^2+(1/3)*gamma2*t^3)*exp(beta*s1)), t = 0 .. tau1))-n2*(Int(((a+t-tau1)/(gam0+gam1*(a+t-tau1))-(1/2)*(a+t-tau1)^2*exp(beta*s2))*(gamma0+gamma1*(a+t-tau1)+gamma2*(a+t-tau1)^2)*exp(beta*s2)*exp(-(gamma0*(a+t-tau1)+(1/2)*gamma1*(a+t-tau1)^2+(1/3)*gamma2*(a+t-tau1)^3)*exp(beta*s2)), t = tau1 .. tau2))-n3*(Int(((b+t-tau2)/(gam0+gam1*(b+t-tau2))-(1/2)*(b+t-tau2)^2*exp(s3))*(gamma0+gamma1*(b+t-tau2)+gamma2*(b+t-tau2)^2)*exp(beta*s3)*exp(-(gamma0*(b+t-tau2)+(1/2)*gamma1*(b+t-tau2)^2+(1/3)*gamma2*(b+t-tau2)^3)*exp(beta*s3)), t = tau2 .. c))+(n-n1-n2-n3)*((b+c-tau2)/(gam0+gam1*(b+c-tau2))-(1/2)*(b+c-tau2)^2*exp(s3))*(gamma0+gamma1*(b+c-tau2)+gamma2*(b+c-tau2)^2)*exp(beta*s3)*exp(-(gamma0*(b+c-tau2)+(1/2)*gamma1*(b+c-tau2)^2+(1/3)*gamma2*(b+c-tau2)^3)*exp(beta*s3));


solve({g1 = 0, g2 = 0}, {gam0, gam1});

Warning, solutions may have been lost.

What do I do wrong?

Thanks for advice in advance.

 

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