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?

Hi every body : 

I want to slove this below PDE with conditions 1&2, can every body help me, tnx.

PDE := diff(u(x, t), t)+6*u(x, t)*(diff(u(x, t), x))+diff(u(x, t), x, x, x) = 0;

1.x=0

2.assume t is step function(Heaviside).

with regards....

restart;
sol:=dsolve(diff(y(x),x)= x/(sqrt(x^2-16))*1/(2*y(x)),y(x));

Gives

But the solution can also be written as

I just do not know how to transform the first solution to the second simpler one. I tried:

sol:=map(x->rhs(x),[sol]);
simplify(sol,radical);

Also tried simplify(sol,sqrt); simplify(sol,radical,symbolic); simplify(sol,size);

The simpler solution can be found as follows

restart;
sol:=dsolve(diff(y(x),x)= x/(sqrt(x^2-16))*1/(2*y(x)),y(x),'implicit');

But the term in the middle above is

Therefore the solution is really

eq:=y(x)^2-sqrt(x^2-16)-_C1 = 0;
solve(eq,y(x));

Which gives

What command to simplify the long solution to the shorter one obtained from the implicit?

The solution by Maple below is correct, but non-the-less, a little strange.

restart;
dsolve(diff(y(x),x)=3*x^2*(y(x)^2+1),y(x));

Gives

Ofcourse 3*constant is still constant. But it is a little strange and have no reason for it to be there.  When I solve it by hand

What could made Maple put the 3 in there? Again, solution is 100% correct, but it could be simpler.

Maple 2017.1

I have Imported a CAD model (.sty) into maple. What I want to do is rotate the model along several axes. At first I want to rotate it around its center. This can be done via 

rotate(Zylinder, 2, 3, 56)

where Zylinder is the Object I importet via

Zylinder := Import("C:/...")

this works fine, but I want the rotation to be a continuous animation. I tried:

animate(rotate(Zylinder, A, 0, 0), A = 0 .. 360)

but that does not work. Can you please tell me how to make it work? And it would be great if the aproach would work for rotations around an axis away from the center, too.