F1(u,v)=0,F2(u,v)=0 with 4 parameters a,b,c,d, 3 of which (a,c,d) are given

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Atom 2024-6-10

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2127071-f1-u-v-0-f2-u-v-0-with-4-parameters-a-b-c-d-3-of-which-a-c-d-are-given

评论： Star Strider 2024-6-10

I have two equations F1(u,v)=0,F2(u,v)=0 with 4 parameters a,b,c,d, 3 of which (a,c,d) are given. For the range b=0.1:0.1:9, I have to collect all positive real solutions of the system F1(u,v)=0,F2(u,v)=0. How to then plot each solutions obtained for b=0.1:0.1:9

How to do that. Note that the solutions (u,v) should be positive.

a = 1.5; c = 0.4; d = 0.9;
b=0.1:0.1:9;
syms u v
F1= u*(1 - u) - b*u*v/(c*u + 1);
F2= 0.5*b*u*v/(c*u + 1) + u*v/(u + 1) - d*v^2;
E=[F1==0,F2==0];
solve(E,u,v)
plot(u,v)

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Answer 1

Star Strider 2024-6-10

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2127071-f1-u-v-0-f2-u-v-0-with-4-parameters-a-b-c-d-3-of-which-a-c-d-are-given#answer_1469606

在 MATLAB Online 中打开

a = 1.5; c = 0.4; d = 0.9;

b=0.1:0.1:9;

syms u v

F1 = @(u,v,b) u*(1 - u) - b*u*v/(c*u + 1);

F2 = @(u,v,b) 0.5*b*u*v/(c*u + 1) + u*v/(u + 1) - d*v^2;

% E=[F1==0,F2==0];

for k = 1:numel(b)

[uv(:,k),fv(k)] = fmincon(@(p)norm([F1(p(1),p(2),b(k)); F2(p(1),p(2),b(k))]), rand(2,1), [],[],[],[], zeros(2,1));

end

Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. 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Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance.

format shortG

uv

uv = 2x90

1.9593e-06 0.91147 0.86145 0.8088 0.75463 0.70008 0.6463 0.59434 0.54505 0.49901 0.45659 0.4179 0.38287 0.35132 0.323 0.29762 0.27487 0.25447 0.23614 0.21965 0.20479 0.19135 0.17917 0.16811 0.99999 0.14884 0.14042 0.1327 0.1256 0.11906 0.0012415 0.60404 0.62098 0.63263 0.63888 0.63985 0.63591 0.62762 0.61571 0.60098 0.58423 0.56617 0.54742 0.52845 0.50964 0.49125 0.47345 0.45634 0.44001 0.42445 0.40969 0.3957 0.38246 0.36993 5.7414e-06 0.34686 0.33624 0.32619 0.31666 0.30763

<mw-icon class=""></mw-icon>

fv

fv = 1x90

1.0e+00 * 2.399e-06 2.6284e-09 1.6137e-09 2.9782e-09 5.5332e-09 5.0974e-09 1.6383e-09 1.7269e-09 5.4861e-09 3.6968e-09 2.5587e-09 2.2643e-09 1.7091e-09 2.8115e-09 2.2959e-09 4.0353e-09 5.9438e-09 6.0736e-09 3.0128e-09 3.4053e-09 5.7217e-09 8.3134e-10 3.362e-09 5.8099e-09 7.9969e-06 4.2445e-09 2.3542e-09 6.0049e-09 3.598e-09 1.9788e-09

<mw-icon class=""></mw-icon>

figure

plot(b, uv(1,:), 'DisplayName','u(b)')

hold on

plot(b,uv(2,:), 'DisplayName','v(b)')

hold off

grid

xlabel('b')

ylabel('Parameter Value')

legend('Location','best')

If you want to elimiinate the ‘spike’ discontinuities, use the ismissing function to detect the ‘outlier’ values (that appear to be either 0 or 1 in the ‘uv’ matrix, other functions may also be useful), set them to NaN, and then use the fillmissing function to interpolate them. I leave that to you.

.

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Star Strider 2024-6-10

在 MATLAB Online 中打开

As always, my pleasure!

Sure!

This generally works, although not as well as I would like it to. The reason is that the outliers change from run to run, and the isoutlier calls do no always work as I would like them to. (The ismissing approach failed because the outlier spikes are not always single isolated values.)

Try this —

a = 1.5; c = 0.4; d = 0.9;

b=0.1:0.1:9;

syms u v

F1 = @(u,v,b) u*(1 - u) - b*u*v/(c*u + 1);

F2 = @(u,v,b) 0.5*b*u*v/(c*u + 1) + u*v/(u + 1) - d*v^2;

% E=[F1==0,F2==0];

for k = 1:numel(b)

[uv(:,k),fv(k)] = fmincon(@(p)norm([F1(p(1),p(2),b(k)); F2(p(1),p(2),b(k))]), rand(2,1), [],[],[],[], zeros(2,1));

end

Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance. Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance.

format shortG

uv

uv = 2x90

9.8128e-06 1.9595e-06 0.86145 0.8088 0.75463 0.70008 0.6463 0.59434 0.54505 0.49901 0.45659 0.4179 0.38287 0.35132 1 0.29762 9.8747e-06 0.25447 0.23614 0.21965 0.20479 0.19135 1 0.16811 0.15804 0.14884 0.99999 0.1327 0.1256 0.11906 0.0027794 0.0012416 0.62098 0.63263 0.63888 0.63985 0.63591 0.62762 0.61571 0.60098 0.58423 0.56617 0.54742 0.52845 1.5443e-06 0.49125 0.0027873 0.45634 0.44001 0.42445 0.40969 0.3957 9.6446e-07 0.36993 0.35808 0.34686 4.3672e-06 0.32619 0.31666 0.30763

<mw-icon class=""></mw-icon>

fv

fv = 1x90

1.0e+00 * 1.2007e-05 2.399e-06 5.3921e-09 5.1788e-09 3.3437e-09 4.1734e-09 4.9515e-09 3.9618e-10 2.296e-09 4.9309e-09 4.2973e-09 2.1425e-09 7.2797e-09 5.6279e-09 1.5995e-06 5.0248e-09 1.2032e-05 6.9628e-09 1.9764e-09 3.4825e-09 1.538e-09 3.1273e-09 1.2745e-06 5.1597e-09 7.7891e-10 4.6436e-09 6.3948e-06 1.1631e-09 4.1181e-09 5.8897e-10

<mw-icon class=""></mw-icon>

figure

plot(b, uv(1,:), 'DisplayName','u(b)')

hold on

plot(b,uv(2,:), 'DisplayName','v(b)')

hold off

grid

xlabel('b')

ylabel('Parameter Value')

legend('Location','best')

Lvu = isoutlier(uv(1,:), 'movmedian', 7);

Nru = nnz(Lvu)

Nru =

13

uv(1,Lvu) = NaN;

Lvv = isoutlier(uv(2,:), 'movmedian', 7);

Nrv = nnz(Lvv)

Nrv =

13

uv(2,Lvv) = NaN;

uv(1,:) = fillmissing(uv(1,:), 'linear');

uv(2,:) = fillmissing(uv(2,:), 'linear');

uv = [uv(1,:); uv(2,:)]

uv = 2x90

9.8128e-06 0.43073 0.86145 0.8088 0.75463 0.70008 0.6463 0.59434 0.54505 0.49901 0.45659 0.4179 0.38287 0.35132 0.32447 0.29762 0.27604 0.25447 0.23614 0.21965 0.20479 0.19135 0.17973 0.16811 0.15804 0.14884 0.14077 0.1327 0.1256 0.11906 0.0027794 0.31188 0.62098 0.63263 0.63888 0.63985 0.63591 0.62762 0.61571 0.60098 0.58423 0.56617 0.54742 0.52845 0.50985 0.49125 0.4738 0.45634 0.44001 0.42445 0.40969 0.3957 0.38282 0.36993 0.35808 0.34686 0.33653 0.32619 0.31666 0.30763

<mw-icon class=""></mw-icon>

save('uvb.mat', 'uv','b')

whos('-file', 'uvb')

Name Size Bytes Class Attributes b 1x90 720 double uv 2x90 1440 double

which('uvb.mat')

/users/mss.system.z28zz/uvb.mat

figure

plot(b, uv(1,:), 'DisplayName','u(b)')

hold on

plot(b,uv(2,:), 'DisplayName','v(b)')

hold off

grid

xlabel('b')

ylabel('Parameter Value')

legend('Location','best')

It may be necesssary to run it several times to get good data. Those values.will have been saved in ‘uvb.mat’, so you can use them in other applications.

.

Atom 2024-6-10

This is amazing... Thank you greatly.

Star Strider 2024-6-10

As always, my pleasure!

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F1(u,v)=0,F2(u,v)=0 with 4 parameters a,b,c,d, 3 of which (a,c,d) are given

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F1(u,v)=0,F2(u,v)=0 with 4 parameters a,b,c,d, 3 of which (a,c,d) are given

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