plot system in 3-D

Hi

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.

[Walter Roberson]

    plot3d(f(A,B,G)=0,color=red);

It looks to me as if you wrote your original code in Maple rather than in MATLAB ?

[hasan s]

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]

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

Answer 1

[Walter Roberson]

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!

[Walter Roberson]

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);

[hasan s]

thanks a lot prof. Walter

I try now to run it .

please what mean :

linspace(-5,5)? I want to plot in positive coordinates. can I put as (0.1,4.9),or only integer

[0.6 0 0]? what mean 0.6 in different place

(Ag, Bg, Gg, Fgrid, 0)? is 0 mean f(A,B,G)=0

[hasan s]

Thank you very much prof. Walter

Your programming is excellent and the graphic is good .. I expected it to be in a specific, but random appearance. I need the positive coordinates what I change please?

In the case of 9 different equations, do they follow the same programming in the drawing ??

Because I am required to draw from 3 to 9 equations like this

[Walter Roberson]

The 0.6 are color components.

linspace is fine with 0.1,4.9

isosurface accepts 3d grids of coordinates and a 3d grid of result values, and it effectively creates a 3d contour of the locations that match the last value (0 in this case), so it is drawing surfaces around all the places with value 0.

[hasan s]

pardon .. what mean 0.6 are color components? is there are any number else.

in case of 9 equations is [0.6 0 0] become

[0.6 0 0 0 0 0 0 0 0]

[0 0.6 0 0 0 0 0 0 0]

and so on

?? or not

I want to try please,because I am required to draw from 3 to 9 equations like this

[Walter Roberson]

There are three color components, Red, Green, and Blue. You can use any sets of colors you want. I will post an update in a few minutes.

[Walter Roberson]

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]

[Walter Roberson]

You should probably add xlabel(), ylabel(), zlabel() calls to the code.

[hasan s]

PLEASE YOU SAY "You should probably add xlabel(), ylabel(), zlabel() calls to the code"

Where add it ? in the program?

[hasan s]

I will try for 4 to 9 equations.thanks alot Porf. Walter for your help

Colors became many in the drawing

How can I recognize the points of intersection at the main colars only of 3(or 9 ) equations?

Can you advise me?

or add something in the program?to know the intersection points of these 3(or 9) equations

[Walter Roberson]

Put the xlabel(), ylabel(), zlabel() calls after the "legend show" call.

[Walter Roberson]

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
beep

[Walter Roberson]

The code was modified so that the objects returned by isosurface() are explicitly saved. Those are struct() with Faces and Vertices information about the polyhedra created.

I am not finding direct code to compute the intersection of polyhedra of these types. I do see

https://www.mathworks.com/matlabcentral/fileexchange/30892-analyze-n-dimensional-polyhedra-in-terms-of-vertices-or-in-equalities from @Matt J

which accepts lists of vertices, but does not accept face information. To use that routine, you would need to first break out the information returned by isosurface() into disjoint cycles at the very least, asking about the intersection of each member of one set with each member of the other set. However, the polyhedra returned by isosurface are by no means guaranteed to be convex, and if you just submit the vertices without the face information you can get distorted ideas of where the intersections are.

I tagged Matt; if he happens to notice, then perhaps he will have some ideas.

[hasan s]

Thank you very very much Prof. Walter for your help

I will try the last program.

[hasan s]

please prof. Walter , if you can :

I am trying to drawing 4 equations containing sums , I write the sums , but I donot know which of these sums is true ,since it is difficult equations.... this one:

for j=1:10000
sum1=sum1+((log((Q(j))/(A)))^2)*(((Q(j))/(A))^(2*(C)))*exp(2*(((Q(j))/(A))^(C))); 
sum2=sum2+exp(2*(B)*(1-exp(((Q(j))/(A))^(C))))*exp(2*(((Q(j))/(A))^(C)))*(((Q(j))/(A))^(2*(C)))*(log((Q(j))/(A))^2);
end

where, exp(2*(B)*(1-exp(((Q(j))/(A))^(C)))) ,is very long.

or I must separate these functions like this:

for j=1:10000
    m(j)=((Q(j))/(A)))
    n(j)=log(m(j))
    v(j)=(((Q(j))/(A))^(2*(C)))
    z(j)=2*(((Q(j))/(A))^(C))
    x(j)=exp(z(j))
    sum1=sum1+((n(j))^2)*v(j)*x(j)
    w(j)=((Q(j))/(A))^(C)   
    d(j)=exp(w(j))
    q(j)=((Q(j))/(A))^2
    l(j)=log(q(j))
    sum2=sum2+exp(2*(B)*(1-d(j)))*(x(j))*(v(j))*(l(j))
end

which one is right ,please??

[Walter Roberson]

sum1 is the same for both of them.

sum2 is different between the two of them.

I do not know which one is "right" as you have not indicated which equation sum2 corresponds to.

[hasan s]

thanks alot for your reply

Yes,,,you are right. I should print the equations.

both of them is same ..but

I donot know how to write difficult functions

The first write ....I wrote it in its full form, and I noticed that the long function was not calculated by the program like

exp( 2*(B)*(1-exp(((Q(j))/(A))^(C))) ) ,is very long

the output still as exp(..)

The second write....I divided it up and then collected in the second writing. Is that permissible ??

But when I write seprate the functions, a warning appears to me for its writing .like those

m(j)=((Q(j))/(A)))

n(j)=log(m(j))

v(j)=(((Q(j))/(A))^(2*(C)))

z(j)=2*(((Q(j))/(A))^(C))

x(j)=exp(z(j))

w(j)=((Q(j))/(A))^(C)

d(j)=exp(w(j))

q(j)=((Q(j))/(A))^2

l(j)=log(q(j))

[Walter Roberson]

    m(j)=((Q(j))/(A)))
     1 0 12 3 21 2 10!

You have too many close brackets

[hasan s]

thanks alot for your note, I donot understand these numbers and how you get it , ...I change it.

like this sum... how can I write these sum in matlab , please

I write it as follows:

for j=1:10000
    m(j)=(Q(j)/A);
    n(j)=log(m(j));
    v(j)=((Q(j)/A)^(2*C));
    z(j)=2*((Q(j)/A)^(C));
    x(j)=exp(z(j));
    sum1=sum1+((n(j))^2)*v(j)*x(j);
    w(j)=(Q(j)/A)^(C);   
    d(j)=exp(w(j));
    q(j)=(A/(Q(j)))^2;
    l(j)=log(q(j));
    sum2=sum2+exp(2*(B)*(1-d(j)))*x(j)*v(j)*(l(j))^2;
    sum3=....
end

is right ???please..

I have line warining in m "the variable m appears to change size on every loop iteration"

also , for n,v,z,x,w,d,q,l the same line warining.

thank you very much prof. Walter for your help

[Walter Roberson]

maxj = 10000;
m = zeros(1,maxj);
n = zeros(1,maxj);
v = zeros(1,maxj);
z = zeros(1,maxj);
x = zeros(1,maxj);
w = zeros(1,maxj);
d = zeros(1,maxj);
q = zeros(1,maxj);
l = zeros(1,maxj);

for j=1:maxj
    m(j)=(Q(j)/A);
    n(j)=log(m(j));
    v(j)=((Q(j)/A)^(2*C));
    z(j)=2*((Q(j)/A)^(C));
    x(j)=exp(z(j));
    sum1=sum1+((n(j))^2)*v(j)*x(j);
    w(j)=(Q(j)/A)^(C);   
    d(j)=exp(w(j));
    q(j)=(A/(Q(j)))^2;
    l(j)=log(q(j));
    sum2=sum2+exp(2*(B)*(1-d(j)))*x(j)*v(j)*(l(j))^2;
    sum3=....
end

I did not attempt to verify the equations yet: I am just showing here how to get rid of the warning.

[hasan s]

thanks alot prof. Walter. I will try to attempt it

[hasan s]

please prof. Walter , when you can...

https://ch.mathworks.com/matlabcentral/answers/777102-how-add-another-loop-in-program

Is there a similar formula to "zeros(1,maxj);"

To get rid of the warning؟؟

if the warning remains ... is this thing that may make these results that obtained scientifically incorrect??

[Walter Roberson]

Sorry, I do not have the resources to assist you further for the next while.

[hasan s]

Ok prof., I appreciate your time,,,,thanks for your previous help