## 5 Reputation

10 years, 187 days

## Global Optimization - XYZ problem...

Maple 16 , Global Optimization

Data.xlsx

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

## Plotting a Spline...

Maple 16

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.

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