hello i was wondering is it possible to find the standard error of the coefficents in the NonlinearFit function within the statistical package? or in any other package for that matter?

does someone have angorithme that can find it? 

i've searched around the internet and it does not seem like maple employs this function at all?

hope someone can help:)

hello agian i have the following problem. i need to fit data using the following model:

ode_sub := diff(S(t), t) = -k1*S(t)-S(t)/T1_s;

ode_P1 := diff(P1(t), t) = 2*k1*S(t)-k2*(P1(t)-P2(t)/keq)-P1(t)/T1_p1;

ode_P2 := diff(P2(t), t) = -k2*(-keq*P1(t)+P2(t))/keq-k4*P2(t)-P2(t)/T1_p2;

ode_P2e := diff(P2_e(t), t) = k4*P2(t)-P2_e(t)/T1_p2_e;

ode_system := ode_sub, ode_P1, ode_P2, ode_P2e

known paramters: s0 := 10000; k2 := 1000; T1_s := 14; T1_p2_e := 35; T1_p2 := T1_p1

initial conditions: init := S(0) = s0, P1(0) = 0, P2(0) = 0, P2_e(0) = 0

using the following data the fitting is fine:

T := [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100]

data_s := [10000.00001377746, 7880.718836217512, 6210.572917625112, 4894.377814704496, 3857.121616806618, 3039.689036293312, 2395.493468824973, 1887.821030424934, 1487.738721378254, 1172.445015238064, 923.970970533911, 728.1555148262845, 573.8389058920359, 452.2263410725434, 356.3868133709972, 280.8584641247961, 221.3366863178145, 174.4291648589732, 137.4627967029932, 108.3305246342751, 85.37230370803576, 67.2794974831867, 53.0210755540487, 41.78436556408739, 32.92915589156605, 25.95049906181449, 20.45092590987601, 16.11678944747619, 12.70115104646253, 10.009439492356, 7.888058666357939, 6.216464754698855, 4.899036441885205, 3.860793948052506, 3.042584031379331, 2.397778731385364, 1.889601342133927, 1.489145259940784, 1.173591417634974, .9248694992255094, .7288443588090404, .5743879613705721, .4526024635132348, .3567687570029392, .2810508404011898, .2215650452813882, .174603181767829, .1376243372528356, .1084232889842753, 0.8542884707952822e-1, 0.6738282660463157e-1]

data_p1 := [0.1194335334401124e-4, 244.8746046039949, 374.8721199398692, 430.5392805383767, 439.6598364813143, 421.0353424914179, 387.1842556288343, 346.2646897222593, 303.4377508746471, 261.8283447091155, 223.1996547160051, 188.4213144493491, 157.7924449350029, 131.2622073983344, 108.5771635112278, 89.37951009190863, 73.26979150957087, 59.84578653950572, 48.72563358658898, 39.56010490461378, 32.03855466968536, 25.88922670933322, 20.87834763772145, 16.80708274458702, 13.50774122768974, 10.84014148654258, 8.687656394505874, 6.954093898245485, 5.560224107929433, 4.441209458524726, 3.544128529596104, 2.825755811619965, 2.251247757181308, 1.792233305651086, 1.425861347838012, 1.133566009019768, .90081361320016, .7153496336919163, .5678861241754847, .4505952916932289, .3572989037753538, .2832489239941939, .2244289868248577, .1778450590752305, .1408633578784151, .1114667192753896, 0.8826814044702111e-1, 0.6979315954603076e-1, 0.5526502783606788e-1, 0.4370354298880999e-1, 0.3456334307662573e-1]

data_p2_p2e := [-0.1821397630630296e-4, 1000.40572909871, 1568.064904416198, 1848.900129881268, 1944.147939710225, 1923.352973299286, 1833.705314342611, 1706.726235937363, 1563.036042115902, 1415.741121363331, 1272.825952816517, 1138.833091575137, 1016.03557293539, 905.2470623752856, 806.3754051707843, 718.7979384094563, 641.6091822001032, 573.7825966275556, 514.2718125966452, 462.0710416682647, 416.2491499591012, 375.9656328260581, 340.4748518743264, 309.124348579787, 281.3484612079911, 256.6599441255977, 234.6416876403397, 214.9378461256197, 197.2453333305823, 181.3059798685686, 166.90059218783, 153.8422174795751, 141.9717783871606, 131.1529759058513, 121.2692959115991, 112.2199678247825, 103.9187616370328, 96.29007054510998, 89.26877137303566, 82.79743967408479, 76.82586273439793, 71.30944943617081, 66.2085909515396, 61.48838150744805, 57.11714763242225, 53.06666224006544, 49.31130738219119, 45.82807853990728, 42.59597194910467, 39.59575450632008, 36.81013335261527]

the fitting is done the following way: 

P1fu, P2fu, P2e_fu, Sfu := op(subs(res, [P1(t), P2(t), P2_e(t), S(t)]))

making residuals:

Q := proc (T1_p1, k1, keq, k4) local P1v, P2v, P2e_v, Sv, resid; option remember;

res(parameters = [T1_p1, k1, keq, k4]);

try P1v := `~`[P1fu](T); P2v := `~`[P2fu](T); P2e_v := `~`[P2e_fu](T); Sv := `~`[Sfu](T); resid := [P1v-data_p1, P2v+P2e_v-data_p2_p2e, Sv-data_s]; return [seq(seq(resid[i][j], i = 1 .. 3), j = 1 .. nops(T))] catch: return [1000000$3*nops(T)] end try end proc;
q := [seq(subs(_nn = n, proc (T1_p1, k1, keq, k4) Q(args)[_nn] end proc), n = 1 .. 3*nops(T))];

finding inital point for the LSsolve:

L := fsolve(q[2 .. 5], [10, 0.2e-1, 4, 4])

fitting the data with the intial point: 

solLS := Optimization:-LSSolve(q, initialpoint = L)

this is all good however, when i used the following data it did not turn out so well (using the same approch as above):

data_s := [96304.74567, 77385.03700, 62621.83067, 51239.94333, 42663.82367, 35084.74100, 28480.28367, 23066.01467, 18774.73700, 15179.13700, 12278.50767, 9937.652000, 8046.848333, 6521.242000, 5287.811667, 4277.779000, 3466.518333, 2835.467000, 2297.796333, 1861.249667, 1529.654000, 1235.353000, 999.6626667, 826.2343333, 667.9480000, 559.9230000, 449.2790000, 376.4860000, 289.1203333, 236.1483333]

data_p1 := [0.86e-1, 3.904, 26.975, 31.719, 41.067, 46.779, 52.115, 43.101, 44.344, 41.094, 36.523, 27.742, 26.543, 28.062, 22.178, 21.303, 14.951, 17.871, 11.422, 12.051, 9.232, 6.817, 6.1, .717, 1.215, 6.146, .772, .375, 2.595, .518]

data_p2_p2e := [-3.024, 22.238, 61.731, 103.816, 132.695, 159.069, 167.302, 160.188, 158.398, 152.943, 146.745, 135.22, 132.145, 120.413, 107.864, 95.339, 90.775, 81.828, 71.065, 70.475, 62.872, 49.955, 40.858, 42.938, 41.311, 35.583, 31.573, 29.841, 29.558, 21.762]

the known parameters is the case are:

s0 := 96304.74567; k2 := 10^5; T1_s := 14; T1_p2_e := 35; T1_p2 := T1_p1

additionally the following fuction affects the solution: 

K:=t->cos((1/180)*beta*Pi)^(t/Tr)

i included this by doing this:

P1fu_K := proc (t) options operator, arrow; P1fu(t)*K(t) end proc;

P2fu_K := proc (t) options operator, arrow; P2fu(t)*K(t) end proc;

P2e_fu_K := proc (t) options operator, arrow;

P2e_fu(t)*K(t) end proc;

Sfu_K := proc (t) options operator, arrow; Sfu(t)*K(t) end proc

resulting in the following residuals:

Q := proc (T1_p1, k1, keq, k4) local P1v, P2v, P2e_v, Sv, resid; option remember;

res(parameters = [T1_p1, k1, keq, k4]);

try P1v := `~`[P1fu_K](T); P2v := `~`[P2fu_K](T); P2e_v := `~`[P2e_fu_K](T); Sv := `~`[Sfu_K](T); resid := [P1v-data_p1, P2v+P2e_v-data_p2_p2e, Sv-data_s]; return [seq(seq(resid[i][j], i = 1 .. 3), j = 1 .. nops(T))] catch: return [1000000$3*nops(T)] end try end proc;
q := [seq(subs(_nn = n, proc (T1_p1, k1, keq, k4) Q(args)[_nn] end proc), n = 1 .. 3*nops(T))];

i think my problem is that the inital point in this case is not known. all i know is that all the fitted parameters should be positive and that k1<1, k4>10, keq>1 and T1_p1>100 (more i do not know) - is there a way to determin the inital point without guessing?

i also know the results, which should be close to these values:

k1=0.000438, k4=0.0385, keq=2.7385 and T1_p1=36.8 the output fit should look something like this

where the red curve is (PP2(t)+PP2_e(t))*K(t)

the blue cure is PP1(t)*K(t) 

anyone able to help - i've tried for 2 days now. it might be that  ode_P1 := diff(P1(t), t) = 2*k1*S(t)-k2*(P1(t)-P2(t)/keq)-P1(t)/T1_p1 should be changed into ode_P1 := diff(P1(t), t) = k1*S(t)-k2*(P1(t)-P2(t)/keq)-P1(t)/T1_p1;

i've tried this but it didnt seem to do much 

anyone able to help?:)

NB stiff=true can be used within the dsolve to speed up the process if needed:)

hello i have the following set of ode's:

ode_sub := diff(S(t), t) = -k1*S(t)-S(t)/T1_s;
ode_P1 := diff(P1(t), t) = k1*S(t)-k2*(P1(t)-P2(t)/keq)-P1(t)/T1_p1;
ode_P2 := diff(P2(t), t) = -k2*(-keq*P1(t)+P2(t))/keq-k4*P2(t)-P2(t)/T1_p2;
ode_P2e := diff(P2_e(t), t) = k4*P2(t)-P2_e(t)/T1_p2_e;

ode_system := ode_sub, ode_P1, ode_P2, ode_P2e;

with these parameters:
s0 := 10000;
k2 := 1000; T1_s := 14; T1_p2_e := 35; T1_p2 := T1_p1;
 

i want to find the unkown parameters : T1_p1, k1, keq and k4

my idea was this:

init:=S(0)=s0,P1(0)=0,P2(0)=0,P2_e(0)=0

dsolve({ode_system,init})

sol := combine(expand(%));
PS := subs(sol, [S(t), P1(t), P2(t), P2_e(t)]);
 

P1fu := unapply(PS[2],t);
Sfu := unapply(PS[1],t);
P2fu := unapply(PS[3],t);
P2e_fu := unapply(PS[4],t);
P2_total := unapply(P2fu+P2e_fu, t);
 

the following data is given:

T:=<0,2,4,6,8>

S:=<9999.99913146527,8328.870587730016,6937.009129218748,5777.745632133724,4812.209983843559>

P1:=<0.0,67.86790056712294,114.88787098501874,145.95438088662502,164.85650644237887>

P2_P2e:=<0.0,271.68492651947497,461.9130396605823,589.3710176125417,668.9967533337124> # data from P2(t)+P2_e(t)

making the rediduals:

RP1 := convert(P1-P1fu~(T), list);
RS := convert(S-Sfu~(T), list);
RP2_P2e := convert(P2_P2_e-P2_total~(T), list);
 

RPs := [op(RS), op(RP2_P2_e), op(RP1)]

res := Optimization:-LSSolve(RPs, k1 = 0 .. 1, keq = 0 .. 10, k4 = 0 .. 1, T1_p1 = 0 .. 100)

i dont know wheter or not the last step work to get the parameters becuase it takes to long to compute. is there a smarter way to obtain the parameters of the ode's? a numeric approch ?

i tried with dsolve({ode_sysytem,init},numeric,'parameters'=[k1,keq,k4,T1_p1]) however it doesnt seem to get my anywhere since i need to know the parameters to use this (i think)

hope someone can help:)

hello im currently working on a project and im fitting some non-linear data with the follwing model:

model:= 1.*10^5*exp(-t*k-*t/B)

where B and k are the unkown parameters.

i have the following data:

X=<0,2,4,6,8,10>

Y := <100000, 86089.76983, 74114.4849, 63804.98946, 54929.56828>

if i do the fit like this: fit(model,X,Y,t) i get a fit that looks like this:

100000*exp(-0.520664970792415e-1*t) which i alright. however when i try to get the parameters i get something like this

fit(model,X,Y,t,output=[parametervalues])

[B = .999563650781966, k = -.948370042622550] - when i define k=0.05 however i get [B = 483.910474528817], which is the right parameter.

insereting the two different sets yields:

1) k=0.05, B = 483.910474528817 -> 100000*exp(-0.520664970792415e-1*t) (good aprox to the fit)

2) B = .999563650781966 and k = -.948370042622550 -> 100000*exp(-0.5206649794e-1*S) (way off)

how is this possible anyone able to help, been sitting with this for days now?