how to plot the drivative ?

s= [0,5*10^-2,1*10^-1,1.5*10^-1,2*10^-1,2.5*10^-1,3*10^-1,3.5*10^-1,4*10^-1,4.5*10^-1,5*10^-1,5.5*10^-1,6*10^-1,6.5*10^-1,7*10^-1,7.5*10^-1,8*10^-1,8.5*10^-1,9*10^-1,9.5*10^-1,9.9*10^-1,9.99*10^-1,1,1,1,1,1];
omega= [3.74*10^-1, 3.8*10^-1,3.87*10^-1,3.94*10^-1,4.02*10^-1,4.11*10^-1,4.2*10^-1,4.29*10^-1,4.4*10^-1,4.51*10^-1,4.64*10^-1,4.78*10^-1,4.94*10^-1,5.12*10^-1,5.33*10^-1,5.57*10^-1,5.86*10^-1,6.23*10^-1,6.72*10^-1,7.46*10^-1,8.71*10^-1,9.56*10^-1,9.68*10^-1,9.72*10^-1,9.75*10^-1,9.8*10^-1,9.86*10^-1];
Z1= 1+((1-(s.^2)).^(1/3)).*(((1+s).^(1/3))+(1-s).^(1/3));
Z2= sqrt(3*(s.^2)+(Z1.^2));
Ri= 3+Z2-sqrt((3-Z1).*(3+Z1+2.*Z2));R= 3+Z2+(sqrt((3-Z1).*(3+Z1+2.*Z2)));
Wi= (s+((Ri).^(3/2))).^-1;
WR= (s+((R).^(3/2))).^-1;
Rlr= 2*(1+cos((2/3)*acos(-s)));
Wlr= (s+((Rlr).^2)).^-1;
plot(s,Wi,'r');
hold on 
plot(s,WR,'y'),plot(s,Wlr,'b'),plot(s,omega,'g');
hold off 
xlabel('spin'),ylabel('angular velocity'),legend('r-prograde Isco angular velocity','y-retrograde ISCO angular velocity','b-LR angular velocity','g-given angular velocity');
y= diff(Wi);
s=diff(s);
c=diff(omega);
plot(s,y,'r');

how can I plot this ? because it doesn't give me to plot y over s

[Constantino Carlos Reyes-Aldasoro]

I ran your code and obtained this:

What is exactly the problem?

[Tomer Segev]

but s is variable that goes to one, and here it goes just until 0.05

[VBBV]

you are using hold off in your program. So its plotting only the last figure. Use the legend function in the last line preferably to match the variables. You are taking the diff of the vector s . The max value in s is 0.05

s= [0,5*10^-2,1*10^-1,1.5*10^-1,2*10^-1,2.5*10^-1,3*10^-1,3.5*10^-1,4*10^-1,4.5*10^-1,5*10^-1,5.5*10^-1,6*10^-1,6.5*10^-1,7*10^-1,7.5*10^-1,8*10^-1,8.5*10^-1,9*10^-1,9.5*10^-1,9.9*10^-1,9.99*10^-1,1,1,1,1,1,1];
omega= [3.74*10^-1, 3.8*10^-1,3.87*10^-1,3.94*10^-1,4.02*10^-1,4.11*10^-1,4.2*10^-1,4.29*10^-1,4.4*10^-1,4.51*10^-1,4.64*10^-1,4.78*10^-1,4.94*10^-1,5.12*10^-1,5.33*10^-1,5.57*10^-1,5.86*10^-1,6.23*10^-1,6.72*10^-1,7.46*10^-1,8.71*10^-1,9.56*10^-1,9.68*10^-1,9.72*10^-1,9.75*10^-1,9.8*10^-1,9.86*10^-1,9.92*10^-1];
Z1= 1+((1-(s.^2)).^(1/3)).*(((1+s).^(1/3))+(1-s).^(1/3));
Z2= sqrt(3*(s.^2)+(Z1.^2));
Ri= 3+Z2-sqrt((3-Z1).*(3+Z1+2.*Z2));R= 3+Z2+(sqrt((3-Z1).*(3+Z1+2.*Z2)));
Wi= (s+((Ri).^(3/2))).^-1;
WR= (s+((R).^(3/2))).^-1;
Rlr= 2*(1+cos((2/3)*acos(-s)));
Wlr= (s+((Rlr).^2)).^-1;
plot(s,Wi,'r');
hold on 
plot(s,WR,'y'),plot(s,Wlr,'b'),plot(s,omega,'g');
hold on 
xlabel('spin'),ylabel('angular velocity'),legend('r-prograde Isco angular velocity','y-retrograde ISCO angular velocity','b-LR angular velocity','g-given angular velocity');
y= diff(Wi);
s=diff(s);
c=diff(omega);
plot(s,y,'r');

Answer 1

[Karan Singh]

HI @Tomer Segev,

I think you are incorrectly reassigns s to diff(s), which causes issues because s is no longer the original x-axis values.The derivative is not computed correctly because y is just the difference in Wi, not the actual derivative (dWi/ds). Also the derivative plot was attempted in the same figure as the original data.

Here is my attempt for you to check.

s = [0,5e-2,1e-1,1.5e-1,2e-1,2.5e-1,3e-1,3.5e-1,4e-1,4.5e-1,5e-1,5.5e-1,6e-1,6.5e-1,7e-1,7.5e-1,8e-1,8.5e-1,9e-1,9.5e-1,9.9e-1,9.99e-1,1,1,1,1,1];
omega = [3.74e-1,3.8e-1,3.87e-1,3.94e-1,4.02e-1,4.11e-1,4.2e-1,4.29e-1,4.4e-1,4.51e-1,4.64e-1,4.78e-1,4.94e-1,5.12e-1,5.33e-1,5.57e-1,5.86e-1,6.23e-1,6.72e-1,7.46e-1,8.71e-1,9.56e-1,9.68e-1,9.72e-1,9.75e-1,9.8e-1,9.86e-1];

Z1 = 1 + ((1 - (s.^2)).^(1/3)) .* (((1 + s).^(1/3)) + (1 - s).^(1/3));
Z2 = sqrt(3 * (s.^2) + (Z1.^2));
Ri = 3 + Z2 - sqrt((3 - Z1) .* (3 + Z1 + 2 .* Z2));
R = 3 + Z2 + sqrt((3 - Z1) .* (3 + Z1 + 2 .* Z2));
Wi = (s + ((Ri).^(3/2))).^-1;
WR = (s + ((R).^(3/2))).^-1;
Rlr = 2 * (1 + cos((2/3) * acos(-s)));
Wlr = (s + ((Rlr).^2)).^-1;

figure;
plot(s, Wi, 'r');
hold on;
plot(s, WR, 'y');
plot(s, Wlr, 'b');
plot(s, omega, 'g');
hold off;
xlabel('spin');
ylabel('angular velocity');

legend('r-prograde ISCO angular velocity', 'y-retrograde ISCO angular velocity', 'b-LR angular velocity', 'g-given angular velocity');

% Compute the derivative of Wi with respect to s
dWi = diff(Wi); % Differences in Wi
ds = diff(s);   % Differences in s
derivative_Wi = dWi ./ ds; % Derivative of Wi

figure;
plot(s(1:end-1), derivative_Wi, 'r');
xlabel('spin');
ylabel('d(Wi)/ds');
title('Derivative of Wi with respect to s');