In Maple 2015 is there a way to fit data to an exponential model and determine the goodness of fit?

Thanks in advance!

Les

I am trying to solve the particular system of partial differential equation. But I get the following error.pdsolve.mw
 

Download pdsolve.mw

Of course, with Maple.

What would be the IBC conditions for the 1D heat equation describing the temperature distribution along a circular rod with a heat source at its base?

Hi,

I have 6 by 6 Hessian matrix H. I want to check whether it is a negative definite. The rule of negative definite is "if and only if its n leading principlal minors alternate in sign with the kth order leading principal minor should have same sign as (-1)^k".

In my Hessian H, some leading principal minor of H is zero while the nonzero ones follows above rule. So negative definite test fails and Now I have to check negative semidefinite test which state that "H is negative semidefinite if and only if every principal minor of odd order is <=0 and every principal minor of even orderis >=0". So I have to check sign of every principal minor ( instead of just leading principal minor) to check for negative semidefinite of H matrix.

Can anyone help me how can I compute sign of all principal minor of a 6 by 6 square Hessian matrix.

Thanks and Regards,

Nilesh

Hello people in mapleprimes,

I want to single out omega^epsilon from and modify the rhs of the following expression
to the expression where the  the part without omega^epsilon and  another part of  omega^epsilon
are multiplied.

Y = -L*epsilon^epsilon*(1-epsilon)^(1-epsilon)*(-omega^(-1+epsilon)*k*theta+(1-theta)*omega^epsilon)/(1-epsilon-theta)

I am glad if you teach me this.

taro

I found this error extremely confusing when using the solve function:

Error, (in Engine:-Dispatch) cannot determine if this expression is true or false: 1000 < 5^(1/2)
 

Hi, i encountered this, error, and the link to the help page was broken.

Error, (in RootOf) expression independent of _S000100
 

when I enter a trig function as cos(pi/2) I get as a return the same input.  What I would like is the numeric answer displayed. also there are times when I don't want pi in the answer but a numeric value calculated based on pi * whatever.

Thanks

Bill

I am trying to prove the equation of the least square estimator. For example, I have: 

X := Matrix(2,3,symbol=p)

Y:= Matrix(2,1,symbol=f)

b:= Matrix(2,1,symbol=n)

or Y=X.b

The known estimation of b results from the minimization of the objective function: 

S:=Transpose(X.b-Y).(X.b-Y).

We take the derivative of the above expression and set it equals with zero. 

Then the estimator is: b=MatrixInverse(Transpose(X).X).Transpose(X).Y

How can I get this expression using commands οn maple?

My final task is to change the objective function to see the different estimations. For example if I have the below objective function which is the results of estimation as equation:

S:=Transpose(X.b-Y).MatrixInverse(C).(X.b-Y)

where C:=Matrix(2,2,symbol=w)

Ofcorsse I know the answer, but I am not sure for more complicated objective functions.

Hello people in maple primes,

I have an expression,

e1_1:=-gamma*r*theta/(w*beta*(theta-1))

, which I want to put in order as 

gamma*r*theta/(w*beta*(1-theta))

Isn't there any ways to do the modification above?

 I am very glad if you answer to my question.

taro

Hi!

Here below is the code I got problems:

#################################

Dens := proc(v)
local theta, r;
evalf[8](
    Int(
        Int(
            4*r/(1-0.84*cos(theta)^2)^(1/2)*exp(-r*(6.25-5.245*cos(theta)^2)^(1/2))
        , theta = 0. .. 2*Pi)
    , r = 0. .. v)
) assuming v>=0
end proc;
#
#
FitFinalDens := NonlinearFit(
  b*(1+a*u)/u*Dens(u/(1+a*u))
, depth
, veloc
, [u]
, initialvalues = [a = 1.4, b = 0.13]
, parameternames = [a, b]
, output = [leastsquaresfunction, residuals, parametervector]
, parameterranges=[a=1.1..3.0,b=0.02..0.8]
);

#################################

Then, I obtain two sort of errors:

First error message:

Error, (in Statistics:-NonlinearFit) invalid input: no implementation of NonlinearFit matches the arguments in call, 'NonlinearFit(0.13*(1.+1.4*u)*(int(int(4*r/..........

etc...

Second error message:

Error, (in Statistics:-NonlinearFit) complex value encountered

So, really I don't known how to correct the code.

I tried a lot  of things such as using  "value" command,  "Re" command, etc.

Do you have a solution?

Sincerely yours.

Jacqr

invalid input: LinearAlgebra:-Basis expects its 1st argument, V, to be of type {Vector, set(Vector), list(Vector)

A:=<<5,5,5>|<1,2,3>|<-5,1,2>>;
Basis(A);
 

restart;
with(Student[Calculus1]);
a := Int(exp(cos(x)), y = 0 .. sin(x), x = 0 .. (1/2)*Pi);
ShowSolution(a);
i get error 

Trying to solve:

solve (arctan((2*x^2-1)/(2*x^2+1)) = 0, x);

The answer I get is the original function:

 
            arctan((2*x^2-1)/(2*x^2+1))

This example is from the Maple book by Keck, and he shows the Maple V answer as

1/2 sqrt(2) -1/2 sqrt(2)     

Suggestions?