Data.xlsx

XY.mw

XYZ.mw

Hello,

I'm using the Global Optimization Toolbox to solve some examples and fit equations to a given data, finding "unknown" parameters. I generated the data on Excel, and I already know the values of these parameters.

The XY case is (there is no problem here, I just put as a example I follow):

> with(GlobalOptimization);
> with(plots);
> 
> X := ExcelTools:-Import("F:\\Data.xlsx", "Plan1", "I5:I25");
> Y := ExcelTools:-Import("F:\\Data.xlsx", "Plan1", "J5:J25");
> 
> XY := zip( (X, Y) -> [X, Y] , X, Y);
> fig1 := plot(XY, style = point, view = [.9 .. 3.1, 6 .. 40]);

> Model := A+B*x+C*x^2+D*cos(x)+E*exp(x):
> VarInterv := [A = 0 .. 10, B = 0 .. 10, C = -10 .. 10, D = 0 .. 10, E = 0 .. 10];

> ModelSubs := proc (x, val)

    subs({x = val}, Model)

    end proc;

> SqEr := expand(add((ModelSubs(x, X(i))-Y(i))^2, i = 1 .. 21));
> CoefList := GlobalSolve(SqEr, op(VarInterv), timelimit = 5000);
> 
> Model := subs(CoefList[2], Model):

I could find the right values of A, B, C, D and E. 

My problem is in the XYZ case, where I don't know how to "write" the right instruction. My last attempt was:

> with(GlobalOptimization);
> with(plots);

> X := ExcelTools:-Import("F:\\Data.xlsx", "Plan1", "Q5:Q25"); X2 := convert(X, list);
> Y := ExcelTools:-Import("F:\\Data.xlsx", "Plan1", "R5:R25"); Y2 := convert(Y, list);
> Z := ExcelTools:-Import("F:\\Data.xlsx", "Plan1", "S5:S25"); Z2 := convert(Z, list);
> NElem := numelems(X);

> pointplot3d(X2, Y2, Z2, axes = normal, labels = ["X", "Y", "Z"], symbol = box, color = red);

> Model := A*x+B*y+C*sin(x*y)+D*exp(x/y);

> VarInterv := [A = 0 .. 10, B = 0 .. 10, C = 0 .. 10, D = 0 .. 10];

> ModelSubs:=proc({x,y},val)

subs({(x,y)=val},Model)

end proc:
Error, missing default value for option(s)

> SqEr := expand(add((ModelSubs(x, y, X(i), Y(i))-Z(i))^2, i = 1 .. NElem));
> CoefList := GlobalSolve(SqEr, op(Range), timelimit = 5000);
Error, (in GlobalOptimization:-GlobalSolve) finite bounds must be provided for all variables

My actual problem involves six equations, six parameters and four or five independent variables on each equation, but I alread developed a way to solve two or more equations simultaneously.

Thanks

Hi guys! Maple noob here.

I want to get an array of the sums of each and every row of a matrix which I imported from Excel. I can't manage to work my way around with LinearAlgebra-Add, Sum and eval. Maple always shows me the table and not the scalar I am looking for.

I'd also like to know how to tell Maple how to do something on a certain interval of cells of the matrix.

I hope I have been clear and you can help me out :D

Cheers from Italy!

Dear Primers,

I am new to Maple and want to ask how to merge two point plots. Suppose, I have two different point plots with same x coordinates but varying y coordinates. How can I merge them just like you would merge two different line plots on a single graph?

Please keep it simple thanks.

Find the points (both x and y coordinates) of intersection y=cosh(x) and y=x^2. Give the answers in numeric form. To find the y-coordinates define one of the functions as f(x) and use f(?).

Is it possible to display each element of a sequence on a new line?

The default behaviour, obviously, is to display each element on the same line separated by commas, and wrapping to a new line as required by screen space. This is somewhat unsightly when the elements of the sequence contain long equations or expressions, and impacts readability because the commas don't stand out as effective separators between elements.

For example:

B := b=2;

C := c=3;

A := B,C;

>A

b=2, c=3

Is there a way to display each element on a new line?

For example:

>A

b=2,

c=3

Is there another data type or a simple expression that could achieve this effect?

Hi,

I'm currently writing a programme for synchronising automatas, its creates an array and adds words or matrices to the array that aren't already in. I am currently getting an error when i try and run my procedure though and i'm unsure of the problem, any help would be appreciated, here is my code so far.

Thanks!

proc_cerny1:=proc(A::Matrix,B::Matrix,C::Vector[row],N)
local x, S, i, j, T, R, y, found;
x:=2^N;
S:=Array(0..(x-1));
S[0]:=C;
i:=0;
j:=1;
found:=false;

while (i<(x-1) and i<>j) do
T:=S[i].A;
for y from 0 to j do
if LinearAlgebra:-Equal(S[y],T) then
found:=true;
if (found=false) then
S[j]:=T;
j:=j+1;
end if:
end if:
od:

R:=S[i].B;
for y from 0 to j do
if LinearAlgebra:-Equal(S[y],T) then
found:=true;
if (found=false) then
S[j]:=R;
j:=j+1;
i:=i+1;

end if:
end if:
od:
od:
print(S);
end proc:

The error i'm getting is when i input this:

proc_cerny1(Matrix([[1,0,0],[1,0,0],[1,0,0]]),Matrix([[0,1,0],[0,0,1],[0,0,1]]),Vector(1..3,1,orientation=row),3);

and the error is:

Error, (in LinearAlgebra:-Equal) invalid input: LinearAlgebra:-Equal expects its 1st argument, X, to be of type {Matrix, Vector} but received 0

Is there a simple way, given a functional equation satisfied by a formal power series, to obtain the explicit form (the Taylor expansion) of this formal power series? For example, my input is "f(x)=1+x*f²(x)", and I want to have as the output: "1+x+2x²+5x³+O(x⁴)".

Many thanks!

I have equation like :

Now I compute second derivative of F respect to x( u and w are functions of x,y):

I must change variables x and y so define them as function of r and s:

And my problem is I want change partial derivative of F respect to x to partial derivative of f respect to r and s. Can anybody help me ?

How to calculate category theory in maple?

Expect to draw commutative diagram for asso property, distributive property and

 to calculate hom, disjoint union, adjoint, closure.

In a trivial example of where x goes from 0 to 1 of d n(x)/dx =a, where n(0)=1, n(1)=2, so that the integral is solved easily, how can i do this in maple however I can only solve an eqation with the initial condition, if i try anything else then i get errors such as, 

fx := diff(n(x), x)-a

A := rhs(dsolve({fx, x = 0 .. 1, n(0) = 1, n(1) = 2}, n(x)));

Error, (in dsolve) invalid terms in sum: 0 .. 1

Hello, Mapleprimes' users.

I am using spline to fit a function to a given data (instead of polynomial). I created two examples with data of y=cos(x). 

The first example has a domain X=0..10 and its result is satisfactory.

Ths second example has a larger domain, X=0..15, but I couldn't plot the spline function. The function fits well, but its line ends at X=~10.

Then I ckecked this spline assigning several values of X, and all the results are correct. The problem is on the plot step.

My mw file is:

> restart;
> with(plots);
> with(CurveFitting);
> plotsetup(default);

First Exemple Data (Y=cos(X)):
> X := [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10];
> Y := [1, .54, -.41, -.99, -.65, .28, .96, .75, -.14, -.91, -.83];
> Piece1 := spline(X, Y, x, 2);
> fig1 := plot(Piece1, view = [0 .. 15, -1 .. 1]);
> fig2 := pointplot(X, Y);
> display(fig1, fig2);
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

Second Example Data (Y=cos(X))::
> X := [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15];
> Y := [1, .54, -.41, -.99, -.65, .28, .96, .75, -.14, -.91, -.83, 0., .84, .91, .13, -.76];
> Piece2 := spline(X, Y, x, 2);
> fig3 := plot(Piece2, view = [0 .. 15, -1 .. 1]);
> fig4 := pointplot(X, Y);
> display(fig3, fig4);
> test := unapply(Piece2, x);
> test(15);

    test(15)=-0.76    #correct value!
 

My actual problem involves data from X=0 to X=300, and I have the same issue in this case.

Thanks.

A linear homogenous ODE with constant real coefficients has a partial solution
y := t-> 3*t^7*cosh(5*t)*sin(2*t).
What can be its minimal order? How to determine that with Maple?

Hi,

I have a system of differential equations with boundary conditions:

diff(S(t), t) = -K(t)*S(t)/N, diff(K(t), t) = K(t)*S(t)/N, where S(T)=10, K(T)=20; If I would like to solve this system backward in time, is it right to re-write the system of original diff. equations in the following way:

diff(S(t), t) = K(t)*S(t)/N, diff(K(t), t) = -K(t)*S(t)/N and S(0)=10, K(0)=20 ( I simply changed the sign of the right hand of the equations and changed the boundary conditions to the inotoal ones).

Thanks,

Dmitry

Hi everyone,

restart:with(plots):

lambda1:=(S+sqrt(S^2+4*alpha))/(2);

lambda2:=(S-sqrt(S^2+4*alpha))/(2);

plot3d({lambda1,lambda2}, S=-10..10, alpha=-5..5, contours=50,grid=[100,100]);

plot([subs(alpha=-5,lambda1),subs(alpha=-4,lambda1),subs(alpha=-3,lambda1),subs(alpha=-2,lambda1)

,subs(alpha=-1,lambda1),subs(alpha=-0.5,lambda1),subs(alpha=0.0,lambda1),subs(alpha=0.5,lambda1)

,subs(alpha=1,lambda1),subs(alpha=2,lambda1),subs(alpha=3,lambda1),subs(alpha=4,lambda1)

,subs(alpha=5,lambda1),subs(alpha=-5,lambda2),subs(alpha=-4,lambda2),subs(alpha=-3,lambda2)

,subs(alpha=-2,lambda2),subs(alpha=-1,lambda2),subs(alpha=-0.5,lambda2),subs(alpha=0.0,lambda2)

,subs(alpha=0.5,lambda2),subs(alpha=1,lambda2),subs(alpha=2,lambda2),subs(alpha=3,lambda2)

,subs(alpha=4,lambda2),subs(alpha=5,lambda2)],S=-10...10,axes=box,color=[red,green]);

contourplot({lambda1,lambda2}, S=-10..10, alpha=-5..5, contours=50,grid=[100,100]);

How to minimize the disconnect in the 3d plot and countourplot to get a smooth plot?

I am trying to illustrate the chain rule for multivariet functions

diff(f(u(x,y),v(x,y),x)

The Maple responce is D1(f)(u(x,y),v(x,y)*(partial of u(x,y) wrt x) +..etc

I would like to replace the D- notation with the standard notation for the "partial of f wrt u" for obvious reasons - this is what students are familar with. The convert cmnd Doe Not Work in this case.

Similarly the cmnd diff(u(x,y),v(x,y),x,x) gives rise to D1,D11, D12 symbols which I would likee to convert to standard partial notation.

All this is a BIG DEAL when trying to illstrate the chain rule in Cal III.

Joe Salacuse

Mathematics

Kettering University