plot system in 3-D

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hasan s 2021-3-9

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链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/767216-plot-system-in-3-d

评论： hasan s 2021-3-21

采纳的回答： Walter Roberson

在 MATLAB Online 中打开

I need to plot in 3-D ,the first equation ,and the second equation, then the third equation

after that plot all in one drawing

if any prof. can help me....thanks a lots....

there is my equations:

And this is my matlab :

N = 1000;
Q1 = rand(10,N);
Q=reshape(Q1,1,[]); % convert matrix to row vector
    sum1=0;sum2=0;sum3=0;sum4=0;sum5=0;sum6=0;
    for j=1:10000
        sum1=sum1+1/(A+(G*B*((Q(j))^(G-1))));
        sum2=sum2+(Q(j));
        sum3=sum3+(G*((Q(j))^(G-1)))/(A+(G*B*((Q(j))^(G-1))));
        sum4=sum4+(Q(j))^(G);
        sum5=sum5+(((G*log(Q(j)))*((Q(j))^(G-1)))+((Q(j))^(G-1)))/(A+(B*G*((Q(j))^(G-1))));
        sum6=sum6+((Q(j))^(G))*log(Q(j));
        
    end
    f(A,B,G)=sum1-sum2;
    g(A,B,G)=sum3-sum4;
    h(A,B,G)=B*sum5-B*sum6;
    plot3d(f(A,B,G)=0,color=red);
    plot3d(g(A,B,G)=0,color=yellow);
    plot3d(h(A,B,G)=0,color=blue);
    display({plotf,plotg,ploth},axes=    );

my variable : A,B,G in matlab ...INSTEAD OF x, y, z for the 3-D

what I add to this program to plot all the three eqations, in different colors please, and then put them in one drawing .

I write

plot ( .,)

but I dont know what write between the Parentheses.

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hasan s 2021-3-9

I searched a lot and could not find a way to write it in Matlab, and find this in Maple

I thought the same way .

I hope to help me write it in matlab

These are the same equations for the program that you helped me with while you are the person he knows best

I really appreciate your time

If you can help me, thanks a lot

hasan s 2021-3-9

The coordinates x, y, z , or ( A, B, G) THAT I want are all greater than zero

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采纳的回答

Walter Roberson 2021-3-10

2
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/767216-plot-system-in-3-d#answer_643667

在 MATLAB Online 中打开

digits(16);
syms A B G
N = 1000;
Q1 = rand(10,N);
Q = vpa(reshape(Q1,1,[])); % convert matrix to row vector
sum1=0;sum2=0;sum3=0;sum4=0;sum5=0;sum6=0;
for j=1:10000
    sum1=sum1+1/(A+(G*B*((Q(j))^(G-1))));
    sum2=sum2+(Q(j));
    sum3=sum3+(G*((Q(j))^(G-1)))/(A+(G*B*((Q(j))^(G-1))));
    sum4=sum4+(Q(j))^(G);
    sum5=sum5+(((G*log(Q(j)))*((Q(j))^(G-1)))+((Q(j))^(G-1)))/(A+(B*G*((Q(j))^(G-1))));
    sum6=sum6+((Q(j))^(G))*log(Q(j));
    
end
sum1m2 = vpa(sum1 - sum2);
sum3m4 = vpa(sum3 - sum4);
sum5m6 = vpa(B*sum5-B*sum6);
f = matlabFunction(sum1m2, 'vars', [A, B, G]);  %really long
g = matlabFunction(sum3m4, 'vars', [A, B, G]);  %really long
h = matlabFunction(sum5m6, 'vars', [A, B, G]);  %really long
fimplicit3(f, 'r');
drawnow();
hold on
fimplicit3(g, 'y');
drawnow();
fimplicit3(h, 'b');

However, that fimplicit3 of h takes at least an hour! And the g is in the same place as f it looks like!

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Walter Roberson 2021-3-10

在 MATLAB Online 中打开

You can get a fairly different view with this, but be warned that computation will take about half an hour.

digits(16);
syms A B G
N = 1000;
Q1 = rand(10,N);
Q = vpa(reshape(Q1,1,[])); % convert matrix to row vector
sum1=0;sum2=0;sum3=0;sum4=0;sum5=0;sum6=0;
for j=1:10000
    sum1=sum1+1/(A+(G*B*((Q(j))^(G-1))));
    sum2=sum2+(Q(j));
    sum3=sum3+(G*((Q(j))^(G-1)))/(A+(G*B*((Q(j))^(G-1))));
    sum4=sum4+(Q(j))^(G);
    sum5=sum5+(((G*log(Q(j)))*((Q(j))^(G-1)))+((Q(j))^(G-1)))/(A+(B*G*((Q(j))^(G-1))));
    sum6=sum6+((Q(j))^(G))*log(Q(j));
    
end
sum1m2 = vpa(sum1 - sum2);
sum3m4 = vpa(sum3 - sum4);
sum5m6 = vpa(B*sum5-B*sum6);
f = matlabFunction(sum1m2, 'vars', [A, B, G]);  %really long
g = matlabFunction(sum3m4, 'vars', [A, B, G]);  %really long
h = matlabFunction(sum5m6, 'vars', [A, B, G]);  %really long
[Ag, Bg, Gg] = meshgrid(linspace(-5,5));  %do not use ndgrid
Fgrid = f(Ag,Bg,Gg);    %several minutes
Ggrid = g(Ag,Bg,Gg);    %about 10 minutes!
Hgrid = h(Ag,Bg,Gg);    %about 15 minutes!
p(1) = patch(isosurface(Ag, Bg, Gg, Fgrid, 0), 'facecolor',[0.6 0 0], 'edgecolor','none','FaceAlpha', 0.5);
p(2) = patch(isosurface(Ag, Bg, Gg, Ggrid, 0), 'facecolor',[0 0.6 0], 'edgecolor','none','FaceAlpha', 0.5);
p(3) = patch(isosurface(Ag, Bg, Gg, Hgrid, 0), 'facecolor',[0 0 0.6], 'edgecolor','none','FaceAlpha', 0.5);

Walter Roberson 2021-3-10

在 MATLAB Online 中打开

On my system the below takes under 13 minutes. You can increase the resolution (which would make it slower) by increasing NumPoints.

As you add more equations, add their evaluated values to the grids cell array, and add legend labels for them to the gridnames variable.

NumPoints = 50;
tic
digits(16);
syms A B G
N = 1000;
Q1 = rand(10,N);
Q = vpa(reshape(Q1,1,[])); % convert matrix to row vector
sum1=0;sum2=0;sum3=0;sum4=0;sum5=0;sum6=0;
for j=1:10000
    sum1=sum1+1/(A+(G*B*((Q(j))^(G-1))));
    sum2=sum2+(Q(j));
    sum3=sum3+(G*((Q(j))^(G-1)))/(A+(G*B*((Q(j))^(G-1))));
    sum4=sum4+(Q(j))^(G);
    sum5=sum5+(((G*log(Q(j)))*((Q(j))^(G-1)))+((Q(j))^(G-1)))/(A+(B*G*((Q(j))^(G-1))));
    sum6=sum6+((Q(j))^(G))*log(Q(j));
    
end
sum1m2 = vpa(sum1 - sum2);
sum3m4 = vpa(sum3 - sum4);
sum5m6 = vpa(B*sum5-B*sum6);
f = matlabFunction(sum1m2, 'vars', [A, B, G]);  %really long
g = matlabFunction(sum3m4, 'vars', [A, B, G]);  %really long
h = matlabFunction(sum5m6, 'vars', [A, B, G]);  %really long
[Ag, Bg, Gg] = meshgrid(linspace(0.1, 4.9,NumPoints));
Fgrid = f(Ag,Bg,Gg);
Ggrid = g(Ag,Bg,Gg);
Hgrid = h(Ag,Bg,Gg);
grids = {Fgrid, Ggrid, Hgrid};
gridnames = {'f', 'g', 'h'};
ngrid = length(grids);
cmap = parula(ngrid);
patches = gobjects(1,ngrid);
view(3);
for K = 1 : ngrid
  patches(K) = patch(isosurface(Ag, Bg, Gg, grids{K}, 0), 'facecolor', cmap(K,:), 'edgecolor','none','FaceAlpha', 0.5, 'displayname', gridnames{K});
end
legend show
toc
beep

Walter Roberson 2021-3-10

在 MATLAB Online 中打开

Here is a modified version that is "ready" to work towards intersection.

NumPoints = 50;
tic
digits(16);
syms A B G
N = 1000;
Q1 = rand(10,N);
Q = vpa(reshape(Q1,1,[])); % convert matrix to row vector
sum1=0;sum2=0;sum3=0;sum4=0;sum5=0;sum6=0;
for j=1:10000
    sum1=sum1+1/(A+(G*B*((Q(j))^(G-1))));
    sum2=sum2+(Q(j));
    sum3=sum3+(G*((Q(j))^(G-1)))/(A+(G*B*((Q(j))^(G-1))));
    sum4=sum4+(Q(j))^(G);
    sum5=sum5+(((G*log(Q(j)))*((Q(j))^(G-1)))+((Q(j))^(G-1)))/(A+(B*G*((Q(j))^(G-1))));
    sum6=sum6+((Q(j))^(G))*log(Q(j));
    
end
sum1m2 = vpa(sum1 - sum2);
sum3m4 = vpa(sum3 - sum4);
sum5m6 = vpa(B*sum5-B*sum6);
f = matlabFunction(sum1m2, 'vars', [A, B, G]);  %really long
g = matlabFunction(sum3m4, 'vars', [A, B, G]);  %really long
h = matlabFunction(sum5m6, 'vars', [A, B, G]);  %really long
[Ag, Bg, Gg] = meshgrid(linspace(0.1, 4.9,NumPoints));
Fgrid = f(Ag,Bg,Gg);    %several minutes
Ggrid = g(Ag,Bg,Gg);    %about 10 minutes!
Hgrid = h(Ag,Bg,Gg);    %about 15 minutes!
grids = {Fgrid, Ggrid, Hgrid};
gridnames = {'f', 'g', 'h'};
ngrid = length(grids);
cmap = parula(ngrid);
view(3);
patches = gobjects(1,ngrid);
surfaces = cell(ngrid, 1);
for K = 1 : ngrid
  surfaces{K} = isosurface(Ag, Bg, Gg, grids{K}, 0);
  patches(K) = patch(surfaces{K}, 'facecolor', cmap(K,:), 'edgecolor','none','FaceAlpha', 0.5, 'displayname', gridnames{K});
end
xlabel('A');
ylabel('B');
zlabel('G');
legend show
toc
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