I'm having some problems with my code. Here is it:
syms I t v;
v = t*exp(-t);
I = int(v,t)
t = linspace(0,10);
plot(t, I)
When i try to plot, i get ??? Error using ==> plot
Conversion to double from sym is not possible.
I tried many ways but it doesn't work.
I'm new to matlab so I don't know much. Hope to get help from everybody. Thank you so much.
because I is a symbolic expression the correct plotting function is :
fplot(I,[0 10])
Alternatively you can create from I an anonymous function (say It), and then use the t you had as an input to It :
It = matlabFunction(I);
plot(t, It(t))
Related
Hello I'm trying to integrate the following function in MATLAB
And this is my attempt at evaluating it at a given (x,y)
fun = #(t,x,y) exp(1i.*(t.^4+x.*t.^2+y.*t));
P = #(x,y) integral(#(t)fun(t,x,y),-Inf,Inf);
P(1,1)
According to WolframAlpha the answer is 1.20759 + 0.601534 i for P(1,1)
but MATLAB returns -6.459688464052636e+07 - 8.821747942103466e+07i
I am wondering how to enter an integral like this correctly.
I have now also tried evaluating this symbolically and using a taylor series to approximate but still no luck.
syms x y t
x=1
y=1
f = exp(1i*(t^4+x*t^2+y*t));
fApprox = taylor(f, t, 'ExpansionPoint', 0, 'Order', 10)
sol=int(fApprox,t,[-inf inf])
Any additional suggestions
Many thanks in advance.
I need to draw the curve of x^3+y^3-3*axy=0 and calculate its area. I'm new to matlab so I don't know much. Any help would be appreciated.
Here's what I came up with already`
function makeres(a)
syms x y;
k=y.^3+x.^3-3.*x.*a.*y==0;
ezplot(k)
fun=#(x)(k);
integral(integral(k,0,5),0,5)
But I get an error on integral.
Try this:
syms x y;
k=y.^3+x.^3-3.*x.*a.*y==0;
ezplot(k)
fun=#(x,y)y.^3+x.^3-3.*x.*a.*y;
g = integral2(fun,0,5,0,5);
Your erros where in the last 2 lines:
a - you were defining k (which is an equation) as the function to be integrated
b - then you integrated k, not fun
c - it is better use integral2 for double integral
I'm don't know what a should be, it works for me when a is a number, an the code as a single script (not a defined function).
I am going to devise a 2D function as a probability density function, is which a function of two variables, i.e. f = f(x,n). Then, as the target is plotting the probability variation, the integration in related to parameter x should be taken into account. The t parameter is the variable planned to be the upper bound of the integration. It is suffice to say that n is the other tuning factor. Finally, with due attention to the considered meshgrid, the probability surface is supposed to be drawn.
My option for the integration process is the symbolic int function. But there is an error: Error using mupadmex
Here is my code:
clear;
syms x;
syms n;
syms t;
sigma = 1;
mu = 0;
[t,n] = meshgrid(0:0.01:20, 1:1:100);
f = (n./(2*sigma*sqrt(pi))).*exp(-((n.*x)./(2.*sigma)).^2);
ff = int(f, x, -inf, t);
mesh(n,t,ff);
And the error trace:
Error using mupadmex
Error in MuPAD command: The argument is invalid. [Dom::Interval::new]
Error in sym/int (line 153)
rSym = mupadmex('symobj::intdef',f.s,x.s,a.s,b.s,options);
Error in field (line 14)
ff = int(f, x, -inf, t);
Would you please helping me to overcome this tie?!
PS. I know that there are some ideas to do this stuff more numerically by integral function, but I am prone to handle this case by int function, if it is possible. Because this code should be used as a service by the other snippets and the generated ff parameter is completely deserving, however it won't be a closed form function.
Thanks in advance.
I have changed several details in your code, Ill try to explain all of them.
No need of defining symbolic variables that are not going to be symbolic.
code:
clear;
syms x;
sigma = 1;
mu = 0; % This is never used!
You want to integrate a function f(n,x) dx for different n. If you create a meshgrid of n (instead of a vector), you will have tons of repeated f(ni,x) that you are not going to use.
Just do:
t=(0:1:20);
n=(1:10:100);
% are you sure you dont want ((n.*x)-mu) here?
f = (n./(2*sigma*sqrt(pi))).*exp(-((n.*x)./(2.*sigma)).^2);
int does not accept a mesh of symbolic functions! (or I haven't managed to make it work...).
So put a couple of for's there!
for ii=1:length(n)
for jj=1:length(t)
ff(ii,jj) = int(f(ii), x, -inf, t(jj));
end
end
Now we DO want a meshgrid for the plot!
Like this:
[t,n] = meshgrid(t, n);
And you want to plot the numerical value, so use double() to convert from symbolic to numerical:
plot!:
mesh(n,t,double(ff));
Result (with low amount of points due to the obvious computational effort needed)
I am using the code below and am trying to plot a velocity and acceleration curve after differentiation of a position function but I am getting errors. Could someone give me a hand?
clc,clear,close all
t=0:.0001:2*pi/150;
theta= (150*t) ;
r=.2.*cos(theta)+sqrt(.75^2 - (.2.*sin(theta)).^2);
plot(t,r)
hold on
syms t
theta= (150*t);
r=.2.*cos(theta)+sqrt(.75^2 - (.2.*sin(theta)).^2);
v=diff(r,t);
a=diff(r,t,2);
t=0:.0001:2*pi/150;
plot(t,v);
plot(t,a);
hold off
The reason why you're getting errors is because when you are using diff, you are using it symbolically. When you're plotting stuff, you need to get the numerical output. As such, you'll need an additional call to subs, plus a cast using double if you want to get this working. So:
syms t;
theta= (150*t);
r=.2.*cos(theta)+sqrt(.75^2 - (.2.*sin(theta)).^2);
v=diff(r,t);
a=diff(r,t,2);
%// Change
t_vec=0:.0001:2*pi/150;
v = double(subs(v, t, t_vec));
a = double(subs(a, t, t_vec));
hold on;
%// Change
plot(t_vec,v);
plot(t_vec,a);
hold off
I want to plot relations like y^2=x^2(x+3) in MATLAB without using ezplot or doing algebra to find each branch of the function.
Does anyone know how I can do this? I usually create a linspace and then create a function over the linspace. For example
x=linspace(-pi,pi,1001);
f=sin(x);
plot(x,f)
Can I do something similar for the relation I have provided?
What you could do is use solve and allow MATLAB's symbolic solver to symbolically solve for an expression of y in terms of x. Once you do this, you can use subs to substitute values of x into the expression found from solve and plot all of these together. Bear in mind that you will need to cast the result of subs with double because you want the numerical result of the substitution. Not doing this will still leave the answer in MATLAB's symbolic format, and it is incompatible for use when you want to plot the final points on your graph.
Also, what you'll need to do is that given equations like what you have posted above, you may have to loop over each solution, substitute your values of x into each, then add them to the plot.
Something like the following. Here, you also have control over the domain as you have desired:
syms x y;
eqn = solve('y^2 == x^2*(x+3)', 'y'); %// Solve for y, as an expression of x
xval = linspace(-1, 1, 1000);
%// Spawn a blank figure and remember stuff as we throw it in
figure;
hold on;
%// For as many solutions as we have...
for idx = 1 : numel(eqn)
%// Substitute our values of x into each solution
yval = double(subs(eqn(idx), xval));
%// Plot the points
plot(xval, yval);
end
%// Add a grid
grid;
Take special care of how I used solve. I specified y because I want to solve for y, which will give me an expression in terms of x. x is our independent variable, and so this is important. I then specify a grid of x points from -1 to 1 - exactly 1000 points actually. I spawn a blank figure, then for as many solutions to the equation that we have, we determine the output y values for each solution we have given the x values that I made earlier. I then plot these on a graph of these points. Note that I used hold on to add more points with each invocation to plot. If I didn't do this, the figure would refresh itself and only remember the most recent call to plot. You want to put all of the points on here generated from all of the solution. For some neatness, I threw a grid in.
This is what I get:
Ok I was about to write my answer and I just saw that #rayryeng proposed a similar idea (Good job Ray!) but here it goes. The idea is also to use solve to get an expression for y, then convert the symbolic function to an anonymous function and then plot it. The code is general for any number of solutions you get from solve:
clear
clc
close all
syms x y
FunXY = y^2 == x^2*(x+3);
%//Use solve to solve for y.
Y = solve(FunXY,y);
%// Create anonymous functions, stored in a cell array.
NumSol = numel(Y); %// Number of solutions.
G = cell(1,NumSol);
for k = 1:NumSol
G{k} = matlabFunction(Y(k))
end
%// Plot the functions...
figure
hold on
for PlotCounter = 1:NumSol
fplot(G{PlotCounter},[-pi,pi])
end
hold off
The result is the following:
n = 1000;
[x y] = meshgrid(linspace(-3,3,n),linspace(-3,3,n));
z = nan(n,n);
z = (y .^ 2 <= x .^2 .* (x + 3) + .1);
z = z & (y .^ 2 >= x .^2 .* (x + 3) - .1);
contour(x,y,z)
It's probably not what you want, but I it's pretty cool!