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How do I solve this in Maple:

 

M(k,n)=M(k,n-1)+M(k-1,n-1)+M(k-2,n-2) and

M(k,1)=1 and M(1,n)=n

 

?

 

Thank you, Jan

 

Hej hej,

is there a way to obtain confidence intervals for the parameters in a NonlinearFit? To give you an impression of the problem which I was working on, I created a minimial working example (not sure wheather that actually helps). In this particular case, I have two parameters to fit the coefficients of a binomial series to some data I obtained. Beyond the values of the parameters (in a least square fit), I'm also interested in some kind of confidence interval, to get a feeling about how realiable my values are. Is there a direct (or even indirect) way to obtain such a thing. Either directly as a Maple function (confidenceintervals is not supported for NonlinearFit, if I'm not mistaken) or as something I can implement myself (within a reasonable time frame, as in hours rather than days).
Thanks in advance!

Cheer,

Sören

restart; with(plots); with(Statistics)

alpha[0] := 1.000000000:

m__max := 4:

model := Fit(pochhammer(z__1, m)*h__exp^m/factorial(m), [seq(m, m = 0 .. m__max)], [seq(alpha[m], m = 0 .. m__max)], m, output = [leastsquaresfunction, residuals], weights = [seq(1/abs(alpha[m]), m = 0 .. m__max)], iterationlimit = 10000)

model := [pochhammer(1.42349754368085, m)*16.2763580438677^m/factorial(m), Vector[row](5, {(1) = 0., (2) = -0.120508651249829e-1, (3) = 0.113910530162494e-1, (4) = 0.348907003220054e-3, (5) = -0.305508272150429e-2})]

(1)

plots[multiple](logplot, [{seq([m, alpha[m]], m = 0 .. m__max)}, style = point, color = black], [{seq([m, model[1]], m = 0 .. m__max)}])

 

``

Download nonlinearfit-problem.mw

Hi,

 

I'm trying to create interactive plots by using Explore to help demonstrate the effects parameters have on functions. I created one successfully to illustrate shifts and stretches of a polynomial:

 

transform(A,B,X,H,P,K):=Explore(plot(a*(b*x+h)^(p)+k,x=X),parameters=[a=A, b= B,h=H,p=P,k=K],placement=right)

 

However when I try to do the same with a solved ODE it returns an error message:

 

Explore(plot(1/(-p*x+x+1)^(1/(p-1)), x = -5 .. 5), parameters = [p = -20 .. 20], placement = right);

 

Executing this gives the error message: 

Warning, expecting only range variable x in expression 1/((-p*x+x+1)^(1/(p-1))) to be plotted but found name p
INTERFACE_PLOT(AXESLABELS(x, ""),

VIEW(-5. .. 5., DEFAULT, _ATTRIBUTE("source" = "mathdefault"))),

parameters = [p = -20 .. 20], placement = right

 

I'm not sure why it is having difficulty dealing with "p" when it had no difficulty with the first. Any help would be appreciated!

Hi there,

I am trying to maximize a function given a set of values to a parameter in the function. The function is an differential equation belonging to a system of two differential equations.

I have a for loop to state different values to the parameter.

Maple yields the error:

Error, (in Optimization:-NLPSolve) cannot evaluate the solution further right of 0.17757507e-4, probably a singularity

When trying to maximize the function.

Supposed that I was doing something wrong in the loop, if I reproduce the contents of the loop outside, and set a value for the parameter. If I plot the solution of the ordinary differential equation, I can see where the maximum lies.

Having plot it, the Optimizamtion:-Maximize works as expected.

However, omitting the plot has a weird effect: I only get the same result depending on the bounds I set for the Maximization:

de1 := diff(A(t), t) = r*m*(1-g)*A(t)-piecewise(t < 8, r*A(t), t >= 8, (r+k)*A(t));
de2 := diff(G(t), t) = r*m*g*A(t)-l*G(t);

ics := A(0) = 25.0, G(0) = 0.;
num := dsolve({de1, de2, ics}, {A(t), G(t)}, type = numeric, output = listprocedure, parameters = [g]);

num(parameters = [g = .15]);
val := eval(G(t), num);

# odeplot(val, [t, G(t)], t = 0 .. 100);


Maximize(val);
Error, (in Optimization:-NLPSolve) cannot evaluate the solution further right of 0.17757507e-4, probably a singularity

val2 := Maximize(val);

Error, (in Optimization:-NLPSolve) cannot evaluate the solution further right of 0.17757507e-4, probably a singularity

val3 := Maximize(val(t), t = 0 .. 60);

  [10267.824035766165, [t = 8.25727747134303]]

val4 := Maximize(val(t), t = 0 .. 100);

[6.863211343195069e-9, [t = 59.84184367042171]]

 

The right answer is [10267.824035766165, [t = 8.25727747134303]]: Why do I get two different answers even if in that range there is only one relative maximum?

I ignore whether the way I am specifying the arguments for the Maximize function is correct. val is a procedure.

 

What am I missing?

Attached is the worksheet: MaplePrimes_malaria_param_variation_2.mw

 

Thanks,

jon

I have solved ODE's with either i.c. or b.c. (mechanics stuff) where the results were in terms of expressions, not functions.  I could plot these expressions, substitute values in for parameters, etc. 

Then I thought that the real way to solve an ODE or system of ODE's was to define functions.  I wanted this to be in three levels: the solutions in generality, the solutions with i.c./m.c. applied, and then further with the parameter values defined. 

So far, no joy.  Lots of confusion--input eqns as sequence, list, set?  I looked on the Maple help page, thought I was doing things right. I even tried out "union" for the ode's and the ic's.

The code is below; statement (11) produces an error. Yes, I am using Maple 18, even though the file says Maple 15.  I'd like to solve the 4-ODE system at the three levels listed above, and then (if possible), plot the result! Am I asking too much?  Should I be using MapleSim or some other product instead?

 

Thanks for any and all help!

 

robert w.


NULL

restart

assume(m1 > 0);

eqn1 := diff(z1(t), t) = z2(t);

diff(z1(t), t) = z2(t)

(1)

eqn2 := diff(z2(t), t) = -(k1+k2)*z1(t)/m1-(c1+c2)*z2(t)/m1+k2*z3(t)/m1+c2*z4(t)/m1;

diff(z2(t), t) = -(k1+k2)*z1(t)/m1-(c1+c2)*z2(t)/m1+k2*z3(t)/m1+c2*z4(t)/m1

(2)

eqn3 := diff(z3(t), t) = z4(t);

diff(z3(t), t) = z4(t)

(3)

eqn4 := diff(z4(t), t) = k2*z1(t)/m2+c2*z2(t)/m2-k2*z3(t)/m2-c2*z4(t)/m2;

diff(z4(t), t) = k2*z1(t)/m2+c2*z2(t)/m2-k2*z3(t)/m2-c2*z4(t)/m2

(4)

eqns := eqn1, eqn2, eqn3, eqn4;

diff(z1(t), t) = z2(t), diff(z2(t), t) = -(k1+k2)*z1(t)/m1-(c1+c2)*z2(t)/m1+k2*z3(t)/m1+c2*z4(t)/m1, diff(z3(t), t) = z4(t), diff(z4(t), t) = k2*z1(t)/m2+c2*z2(t)/m2-k2*z3(t)/m2-c2*z4(t)/m2

(5)

var := z1(t), z2(t), z3(t), z4(t);

z1(t), z2(t), z3(t), z4(t)

(6)

ic1 := z1(0) = -2;

z1(0) = -2

(7)

ic2 := z2(0) = 0;

z2(0) = 0

(8)

ic3 := z3(0) = 1;

z3(0) = 1

(9)

ic4 := z4(0) = 0;

z4(0) = 0

(10)

ics := ic1, ic2, ic3, ic4;

z1(0) = -2, z2(0) = 0, z3(0) = 1, z4(0) = 0

(11)

dsolve(`union`(eqns, ics), var)

Error, invalid input: `union` received diff(z1(t), t) = z2(t), which is not valid for its 1st argument

 

var;

z1(t), z2(t), z3(t), z4(t)

(12)

data:=(m1=1,m2=2,m3=1,c1=0,c2=0,c3=0,k1=5,k2=2,k3=2);

m1 = 1, m2 = 2, m3 = 1, c1 = 0, c2 = 0, c3 = 0, k1 = 5, k2 = 2, k3 = 2

(13)

eqnsev := subs(data, eqns);

diff(z4(t), t) = z1(t)-z3(t)

(14)

NULL


Download mae340_state_space_4-ode_system.mw

I am trying to fit an experimental data C[A](t)  vs t, with modelled ODE equation by solving it with numerical method. But the process gives problems here ha code and also find attached maple file.

Input is time =[0, 30, 60, 90, 120, 150, 180, 210, 240]

and output exptal data = [7647.5, 7397.5, 6755, 6252.5, 5860, 5530, 5440, 5107.5, 4857.5]

I want to find k,K[A] parameters;

 

EXPT_datafittinh_LHHW.mw

Dear all,

I want to know how can I solve a fourth or higher order equation to find out its roots, actually coefficients of each power terms itself are functins of other parameters not constant.

Please reply as soon as possible, as this is very urgent,

Regards.

Dear all;

I need your help to get all the solution of this nonlinear  system  with four parameters: r1, r2, q1, q2  assumed to be positives. Let the system:

the first equation is: r1*x*(1-x/q1)=x*y/(1+x)

the second equation: r2*y*(exp(-y)-q2)=-x*y/(1+x)

How can get the positive solution ( x, y) of the previous system.

Thank you for your help.

Hej everyone,

I am trying to run a Maple script for multiple parameters on our cluster, so far so good. I found that I can pass for example a:=1 and b:=2 to a Maple script using

maple -c "a:=1;" -c "b:=2;" < script.mpl

Is that the best/only way? For convenience I would like to read the parameters from a file, my first idea was to work with sed, so I tried

maple $(sed -n 1'p' data) < script.mpl

This should take the first line from data (which is -c "a:=1;" -c "b:=2;"), so that I would expect to get the same result.
Unfortunately, this is not the case, only the first parameter a:=1 is passed correctly and non of the further parameters.

I've appended the files, I used.

This may be not a Maple problem but rather me making a mistake using sed, but maybe you can see where I made a mistake.

Thanks in advance,

Sören

 

a

b

c

Download script.mw

The mw-file has to be exported as an mpl-file first. In my case data just contains one line: -c "a:=1;" -c "b:=2;" -c "c:=3;" (I couldn't upload either)

Is it possible in Maple 15 to solve an equation with a parameter for a given set of parameters? How can this be passed to the solve function, should I use some kind of list?  After obtaining the solution how can I assign the solutions to variables such as x1 for the first value of the parameter, x2 for the second value of the parameters and so on. Furthermore, is this possible with the fsolve command?

 

Thanks

Hi,

I need to build a multibody model in MapleSim 6.4 in which with few global parameters I can describe all the other parameters. In other words the final user will enter this few parameters, that are coordinates of specific points, and then the model will calculate all the relative distances on the base of those coordinates.

The problem is that if I apply trigonometric function and square root (like in the screenshot) the model is not calculating any value. Is it possible to make those calculculations?

 

this is the model (don't worry about the nonsense plots, it's because it's not ultimated):

DWS.msim

 

 

Thanks.

 

Hi everyone,

I have to create a double wishbone suspesione model that can be edited by different users, only introducing some reference point values (called Hard Points). So I need some tool that, in some way, passes from the entered reference point values to the actual values of the bodyframes link. 

I found an already done model (from this link) that seems to be perfect to me because contains an attached Maple document that does exactly what I need working on the base of symbolic parameters applied to the MapleSim model. Now my problem is that I need to deeply change the model and so having the possibility to change the parameter set and insert for example nex parameters. But when I try to do that some problems come out with the Maple document: the syntax of the nex parameter set is different from the default (in the sense of already built in the model I downloaded) one and there are some syntax errors. Below I'll put a screenshot of the error.

 

under the XData code line, you can also see the syntax of one of the parameters that is very long and complicated: below I'll insert another image from which it can be seen the syntax with the original parameter set.

Now if you another idea for solving the initial problem, that would be great! Instead do you have an idea on how to fix the problem with the downloaded model? In my opinion there is a different MapleSim version problem, in the sense that could be thatn the model I downloaded has been done in another MapleSim version in which the parameter set syntax was different.

Hello,

In my model, it seems that I have parameters which are not evaluated.

Indeed, I'm not sure that the parameters defined with relations as you can see in the printscreen are evaluated.

 

One point which helps me to debug my model is to follow the evaluation of the construction of my model with the 3D visualization.

Questions :
1) How can I do to be sure that my parameters are evaluated ?

2) Is it possible to launch the update of the 3D visualization even if I still have some bugs in my model ?

Thank you for help.

Hello,

In a subsystem, i defined parameters like this in the "parameters" area :

 

In the "diagram" area, the parameters are not updated because i see this panel :

 

Do you know why the parameters are not updated (possibly only on visualization) ? And if yes, how i can do to visualize in this last panel the value of the parameters updated ?

Thanks a lot for your help

Hi,

 

I want to calculate a new position (X,Y,Z) for a cartesian model with 3 points (dX,dY,dZ) but  I got a problem, my point is a parameters, so I can't change it in the simulation in real time with a Input signal on the components. Does It exist a solution for convert a parameters to a variable to get a Input signal?

Exemple of my calcul:

eq:= [x(t)= dx+sin(dy/dz), y(t)=dy+20,z(t)=dz]

 

Thanks!

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