How to plot a multivariable function with constraints
7 views (last 30 days)
Show older comments
Hello,
I plotted a 2-variables function and I would like to highlight (or plot/intersect) only the z points for which x (k in the function) and y satisfy the following constraints: 250020*((pi/4)*k^2*y)-325.33=0
I have been trying several approaches but I cannot make it happen. I hope you can help.
Thank you!
f=@(k,y) (8120*(((pi*((((k+(2*(5*0.0026))+(2*0.0026))+(((pi*((k+(2*(5*0.0026)))/2)*((1.49*(5*0.0026))/((5*0.0026)+0.0026)))/(8*0.97*2.350))*2)+((4.5*(((pi*(k+(2*(5*0.0026))+(2*0.0026)))/24)-((2*pi()*((k+(2*(5*0.0026)))/2)*((1.49*(5*0.0026))/((5*0.0026)+0.0026)))/(24*0.97*2.350))))*2)).^2)-((((k+(2*(5*0.0026))+(2*0.0026))+(((pi*((k+(2*(5*0.0026)))/2)*((1.49*(5*0.0026))/((5*0.0026)+0.0026)))/(8*0.97*2.350))*2)+((4.5*(((pi*(k+(2*(5*0.0026))+(2*0.0026)))/24)-((2*pi()*((k+(2*(5*0.0026)))/2)*((1.49*(5*0.0026))/((5*0.0026)+0.0026)))/(24*0.97*2.350))))*2))-(2*((pi*((k+(2*(5*0.0026)))/2)*((1.49*(5*0.0026))/((5*0.0026)+0.0026)))/(8*0.97*2.350)))).^2))*y)/4)+(((2*pi()*((k+(2*(5*0.0026)))/2)*((1.49*(5*0.0026))/((5*0.0026)+0.0026)))/(24*0.97*2.350))*(4.5*(((pi*(k+(2*(5*0.0026))+(2*0.0026)))/24)-((2*pi()*((k+(2*(5*0.0026)))/2)*((1.49*(5*0.0026))/((5*0.0026)+0.0026)))/(24*0.97*2.350))))*y.*24)))+(8120*(pi*((k.^2)-((k-(2*((pi*((k+(2*(5*0.0026)))/2)*((1.49*(5*0.0026))/((5*0.0026)+0.0026)))/(8*0.97*2.350)))).^2))*y)/4)+(7450*((pi*y.*(((k+(2*(5*0.0026))).^2)-(k.^2)))/4)+(8933*pi*(0.003/2).^2*((15*(2*4))*((2*y)+((2*(pi*((k+(2*(5*0.0026))+(2*0.0026))+(4.5*(((pi*(k+(2*(5*0.0026))+(2*0.0026)))/24)-((2*pi()*((k+(2*(5*0.0026)))/2)*((1.49*(5*0.0026))/((5*0.0026)+0.0026)))/(24*0.97*2.350)))))))/8)+(4*(((pi*((k+(2*(5*0.0026))+(2*0.0026))+(4.5*(((pi*(k+(2*(5*0.0026))+(2*0.0026)))/24)-((2*pi()*((k+(2*(5*0.0026)))/2)*((1.49*(5*0.0026))/((5*0.0026)+0.0026)))/(24*0.97*2.350))))))/24)-((2*pi()*((k+(2*(5*0.0026)))/2)*((1.49*(5*0.0026))/((5*0.0026)+0.0026)))/(24*0.97*2.350))))))*3));
fsurf(f);
xlim([0.02 0.1]);
ylim([0.04 0.4]);
zlim([0 100]);
0 Comments
Answers (1)
John D'Errico
on 28 Aug 2021
Can you solve for y, as a function of k, given the constraint? (YES.)
If so, then do you really have a TWO variable problem? (NO.)
syms k y
ysol = solve(250020*((pi/4)*k^2*y)-325.33==0,y)
z = (8120*(((pi*((((k+(2*(5*0.0026))+(2*0.0026))+(((pi*((k+(2*(5*0.0026)))/2)*((1.49*(5*0.0026))/((5*0.0026)+0.0026)))/(8*0.97*2.350))*2)+((4.5*(((pi*(k+(2*(5*0.0026))+(2*0.0026)))/24)-((2*pi()*((k+(2*(5*0.0026)))/2)*((1.49*(5*0.0026))/((5*0.0026)+0.0026)))/(24*0.97*2.350))))*2)).^2)-((((k+(2*(5*0.0026))+(2*0.0026))+(((pi*((k+(2*(5*0.0026)))/2)*((1.49*(5*0.0026))/((5*0.0026)+0.0026)))/(8*0.97*2.350))*2)+((4.5*(((pi*(k+(2*(5*0.0026))+(2*0.0026)))/24)-((2*pi()*((k+(2*(5*0.0026)))/2)*((1.49*(5*0.0026))/((5*0.0026)+0.0026)))/(24*0.97*2.350))))*2))-(2*((pi*((k+(2*(5*0.0026)))/2)*((1.49*(5*0.0026))/((5*0.0026)+0.0026)))/(8*0.97*2.350)))).^2))*y)/4)+(((2*pi()*((k+(2*(5*0.0026)))/2)*((1.49*(5*0.0026))/((5*0.0026)+0.0026)))/(24*0.97*2.350))*(4.5*(((pi*(k+(2*(5*0.0026))+(2*0.0026)))/24)-((2*pi()*((k+(2*(5*0.0026)))/2)*((1.49*(5*0.0026))/((5*0.0026)+0.0026)))/(24*0.97*2.350))))*y.*24)))+(8120*(pi*((k.^2)-((k-(2*((pi*((k+(2*(5*0.0026)))/2)*((1.49*(5*0.0026))/((5*0.0026)+0.0026)))/(8*0.97*2.350)))).^2))*y)/4)+(7450*((pi*y.*(((k+(2*(5*0.0026))).^2)-(k.^2)))/4)+(8933*pi*(0.003/2).^2*((15*(2*4))*((2*y)+((2*(pi*((k+(2*(5*0.0026))+(2*0.0026))+(4.5*(((pi*(k+(2*(5*0.0026))+(2*0.0026)))/24)-((2*pi()*((k+(2*(5*0.0026)))/2)*((1.49*(5*0.0026))/((5*0.0026)+0.0026)))/(24*0.97*2.350)))))))/8)+(4*(((pi*((k+(2*(5*0.0026))+(2*0.0026))+(4.5*(((pi*(k+(2*(5*0.0026))+(2*0.0026)))/24)-((2*pi()*((k+(2*(5*0.0026)))/2)*((1.49*(5*0.0026))/((5*0.0026)+0.0026)))/(24*0.97*2.350))))))/24)-((2*pi()*((k+(2*(5*0.0026)))/2)*((1.49*(5*0.0026))/((5*0.0026)+0.0026)))/(24*0.97*2.350))))))*3));
z_k = subs(z,y,ysol)
It may look messy, but who cares?
fplot(z_k,[0.02,0.1])
xlabel 'k'
ylabel 'z'
Again, this is not a 2 variable problem, due to the constraint.
Can you plot it in 3-dimensions anyway? Well, yes.
K = linspace(0.02,0.1,100);
yfun = matlabFunction(ysol);
Y = yfun(K);
f = @(k,y) (8120*(((pi*((((k+(2*(5*0.0026))+(2*0.0026))+(((pi*((k+(2*(5*0.0026)))/2)*((1.49*(5*0.0026))/((5*0.0026)+0.0026)))/(8*0.97*2.350))*2)+((4.5*(((pi*(k+(2*(5*0.0026))+(2*0.0026)))/24)-((2*pi()*((k+(2*(5*0.0026)))/2)*((1.49*(5*0.0026))/((5*0.0026)+0.0026)))/(24*0.97*2.350))))*2)).^2)-((((k+(2*(5*0.0026))+(2*0.0026))+(((pi*((k+(2*(5*0.0026)))/2)*((1.49*(5*0.0026))/((5*0.0026)+0.0026)))/(8*0.97*2.350))*2)+((4.5*(((pi*(k+(2*(5*0.0026))+(2*0.0026)))/24)-((2*pi()*((k+(2*(5*0.0026)))/2)*((1.49*(5*0.0026))/((5*0.0026)+0.0026)))/(24*0.97*2.350))))*2))-(2*((pi*((k+(2*(5*0.0026)))/2)*((1.49*(5*0.0026))/((5*0.0026)+0.0026)))/(8*0.97*2.350)))).^2))*y)/4)+(((2*pi()*((k+(2*(5*0.0026)))/2)*((1.49*(5*0.0026))/((5*0.0026)+0.0026)))/(24*0.97*2.350))*(4.5*(((pi*(k+(2*(5*0.0026))+(2*0.0026)))/24)-((2*pi()*((k+(2*(5*0.0026)))/2)*((1.49*(5*0.0026))/((5*0.0026)+0.0026)))/(24*0.97*2.350))))*y.*24)))+(8120*(pi*((k.^2)-((k-(2*((pi*((k+(2*(5*0.0026)))/2)*((1.49*(5*0.0026))/((5*0.0026)+0.0026)))/(8*0.97*2.350)))).^2))*y)/4)+(7450*((pi*y.*(((k+(2*(5*0.0026))).^2)-(k.^2)))/4)+(8933*pi*(0.003/2).^2*((15*(2*4))*((2*y)+((2*(pi*((k+(2*(5*0.0026))+(2*0.0026))+(4.5*(((pi*(k+(2*(5*0.0026))+(2*0.0026)))/24)-((2*pi()*((k+(2*(5*0.0026)))/2)*((1.49*(5*0.0026))/((5*0.0026)+0.0026)))/(24*0.97*2.350)))))))/8)+(4*(((pi*((k+(2*(5*0.0026))+(2*0.0026))+(4.5*(((pi*(k+(2*(5*0.0026))+(2*0.0026)))/24)-((2*pi()*((k+(2*(5*0.0026)))/2)*((1.49*(5*0.0026))/((5*0.0026)+0.0026)))/(24*0.97*2.350))))))/24)-((2*pi()*((k+(2*(5*0.0026)))/2)*((1.49*(5*0.0026))/((5*0.0026)+0.0026)))/(24*0.97*2.350))))))*3));
f = str2func(vectorize(func2str(f)));
plot3(K,Y,f(K,Y),'o-')
grid on
box on
xlabel 'k'
ylabel 'y'
zlabel 'z'
4 Comments
See Also
Categories
Find more on Synchronous in Help Center and File Exchange
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!