When I ran a simple exercise of integration of defined functions as below,
clear all;
syms z tau;
deltav=tau^(1/(3*z))-tau^(1/(4*z));
deltax=1/(0.5+12*z)*(tau^(1/(3*z))-tau^(1/(4*z)));
a=1;
b=9;
tau=0.5;
mu_vx=int(deltav*deltax,a,b);
mu_x2=int(deltax^2,a,b);
ratio=double(mu_vx/mu_x2);
I got error message from MATLAB by saying "??? Error using ==> mupadmex
Error in MuPAD command: DOUBLE cannot convert the input expression into
a double array.If the input expression contains a symbolic variable, use the VPA
function instead."
So I plug in the expression of "deltav" and "deltax" in to integration, and run
clear all;
syms z tau;
deltav=tau^(1/(3*z))-tau^(1/(4*z));
deltax=1/(0.5+12*z)*(tau^(1/(3*z))-tau^(1/(4*z)));
a=1;
b=9;
tau=0.5;
mu_vx=int((tau^(1/(3*z))-tau^(1/(4*z)))*1/(0.5+12*z)*(tau^(1/(3*z))- tau^(1/(4*z))),a,b);
mu_x2=int((1/(0.5+12*z)*(tau^(1/(3*z))-tau^(1/(4*z))))^2,a,b);
ratio=double(mu_vx/mu_x2)
It works this time. I wonder how I should make the first way work without plugging the long expression. Thank you.
Sometimes a solve is necessary to find a explicit solution
mu_vx=int(solve(deltav*deltax),a,b);
mu_x2=int(solve(deltax^2),a,b);
ratio=double(mu_vx/mu_x2);
Related
Using Matlab, I have the following code:
s = tf('s')
K=0.5;
H= 1/(s*(s+2));
Hcl=feedback(K*H,1)
ilaplace(Hcl)
rltool(H)
I want to get the inverse laplace transform of the unity closed-loop system.
rltool(H) generates automatically the unity closed-loop system. That's why I pass the open-loop system as an argument.
When I run this code, Matlab gives an error about ilaplace:
"Check for incorrect argument data type or missing argument in call to function 'ilaplace'."
Can someone help me how to use ilaplace and rltool concurrently
I have found a solution for this problem.
syms s;
K=1/2;
H= 1/(s*(s+2))
Hcl=simplify(K*H/(1+K*H))
P=poles(Hcl)
ilaplace(Hcl)
H = syms2tf(Hcl)
rltool(H)
ilaplace works with symbolic expressions and not with a transfer function. By converting the symbolic expression to a transfer function midway of the code, I can use both functions in the same code.
Notice I've added the function simplify and changed the beginning from s=tf('s') to syms s
The function syms2tf() can be found here
How do i find the integral of the movmean function on the top graph
The intz doesnt work, and im not so sure what the trap gives me:
subplot(3,1,1);
Fz1=detrend(Fz(500:1200000));
plot(Fz1,'Color','k');
hold on
M1 = movmean(Fz(500:1200000),[2000,2000]);
M11=detrend(M1);
plot(M11,'Color','r')
trapz(M11)
intz = int(M11)
this line intz = int(M11)throwing an exception. Please tell me what is wrong on here
You are confusing your commands. The trapz is the command that is doing the integration using the trapezoidal integration method. The command int does not do integration; it creates variables of integer type given integer-valued floating-point (a.k.a. double) variables.
Most likely you are seeing this kind of error
M11 = [1.2 3.4]; % as an example
int(M11)
Undefined function 'int' for input arguments of type 'double'.
because your data in M11 contains non-integer values. In short int is not necessary for integration; just use trapz. See help trapz in MATLAB for details on using this command.
I am trying to find use to Newton-Raphson method to find the roots. It does this by making a guess and then improving the guess after each iteration until you get one of the zeros.
Because the Newton-Raphson method quickly finds the zeros, it gives me a small error immediately and after two or three iterations max it should fail to meet the conditions of the while loop. However, the problem is that when I remove the semi-colon after "error" in my loop, I start getting fractions that should break the while loop, but its like Matlab doesn't know that 123/8328423 is less than 1. It continues to run until I manually force the program to stop running.
How do I fix this? I tried format long, format longe, and using double both in the command window, in the scrip file, and somewhere in the loop.
Thank you in advance for any tips, suggestions, or advice that may help!!
A = [1,2,-4;2,-2,-2;-4,-2,1;];
format longe
% syms x y z
% P = x^4 + 3*x^2*y^2-z^3+y+1;
% feval(symengine,'degree',P,x)
syms x
B = mateigenvalue(A);
f(x) = simplify(matdet(B));
x0 = 1;
error = 10;
while(error > .01)
x1 = x0 - f(x0)/(27*(x0)-3*(x0)^2);
error = abs(((f(x0)-f(x1))/f(x0))*100)
x0 = x1;
end
x0 = double(x0)
I reckon the main problem is with error.
It starts as double but inside the while-loop it turns into a symbolic variable and you can't easily compare symbolic variables with scalar values (the .01 in the while-loop condition).
Check in your workspace if error is symbolic (or type class(error) and check if sym is returned). I guess it is symbolic because a fraction is returned (123/8328423), as instead Matlab treats double values with decimals, not fractions.
If so, try doing (inside the while-loop) a conversion for error that is, under the line
error = abs(((f(x0)-f(x1))/f(x0))*100);
try putting
error=double(error);
So error will be temporarily converted in double and you can easily compare its value with .01 to check the while-loop condition.
Also, it is bad practice to call a variable error since error() is a built-in function in Matlab. By naming a variable error you cannot use the error() function. Same story goes for other built-in functions.
I hope this is the right area. I'm trying to get this code to work in MatLab.
function y=test(x)
y=-x+(B/(B-1))*(r-a)*p+(B/(B-1))*(r-a)*(b((1-(b/x)^(B-1))/r- a)+p* ((b/x)^B))/(1-(b/x)^B);
end
I then jump to the command value and type this:
B=3.0515;
b=1.18632*10^5;
a=.017;
r=.054;
p=5931617;
I then try to find the zeros of the first equation by typing this and I get errors:
solution=fzero(#test,5000000)
I'm getting the following error:
Error: File: test.m Line: 5 Column: 1 This statement is not
inside any function. (It follows the END that terminates the
definition of the function "test".)
New error
Error using fzero (line 289)
FZERO cannot continue because user supplied function_handle ==> #(x)
(test(x,B,b,a,r,p))
failed with the error below.
Subscript indices must either be real positive integers or logicals.
I would guess that this is a problem of scoping, you are defining variables (B, b, etc...) in the command line but trying to use them inside your test function where they are out of scope. You should alter your test function to take these in as parameters and then use an anonymous function so that your call to test in fsolve still only takes a single parameter:
function y=test(x, B, b, r, a, p)
y=-x+(B/(B-1))*(r-a)*p+(B/(B-1))*(r-a)*(b((1-(b/x)^(B-1))/r- a)+p* ((b/x)^B))/(1-(b/x)^B);
end
and
B=3.0515;
b=1.18632*10^5;
a=.017;
r=.054;
p=5931617;
solution=fzero(#(x)(test(x,B,b,a,r,p)),5000000)
As an aside, unless you really do mean matrix multiplication, I would suggest that you replace all your *s and /s in test with the element-wise operators .* and ./. If you are dealing with scalars, it doesn't matter now, but it makes a big difference if you later want to scale your project and need a vectorized solution.
Regarding the errors you have added to your question:
You can't put code after the end in your function file. (With the exception of local functions). Your objective function should be an .m-file containing the code for one single function.
This is because in your test function you have ...b((1-(b/x)^(B-1))... which in MATLAB means you are trying to index the variable b in which case the value of (1-(b/x)^(B-1) has to be a positive integer. I'm guess you are missing a *
Your
function y=test(x)
y=-x+(B/(B-1))*(r-a)*p+(B/(B-1))*(r-a)*(b((1-(b/x)^(B-1))/r- a)+p* ((b/x)^B))/(1-(b/x)^B);
end
cannot access variables in your workspace. You need to pass the values in somehow. You could do something like:
function y=test(x,B,b,a,r,p)
y=-x+(B/(B-1))*(r-a)*p+(B/(B-1))*(r-a)*(b((1-(b/x)^(B-1))/r- a)+p* ((b/x)^B))/(1-(b/x)^B);
end
and then you can create an implicit wrapper function:
B=3.0515;
b=1.18632*10^5;
a=.017;
r=.054;
p=5931617;
solution = fzero(#(x) test(x,B,b,a,r,p),5000000)
I haven't tested whether fzero returns sensible results, but this code shouldn't give an error.
I'm working on an assignment for a class of mine and I'm supposed to write a code using a program of my choice (I've chosen Matlab) to solve the Bessel function differential equation using the 4th order Runge-Kutta method. For reference the Bessel function DE is:
x^2*(J_n)''+x*(J_n)'+(x^2-n^2)*J_n=0.
I'm able to separate this into two coupled first order DEs by:
(J_n)'=Z_n and
(Z_n)'+(1/x)*Z_n+[(x^2-n^2)/x^2]*J_n=0.
I have no experience with Matlab nor any other programming language before this assignment. I know Matlab has the 'ode45' command but I'm supposed to write the code myself, not rely on Matlab's commands. So far I've been working on the n=0 case for the Bessel function but I keep getting an error when I try and plot the function. The current error I have says: "Undefined function or method 'J' for input arguments of type 'double'." But I don't know how to fix this error nor if my code is even correct. Could someone tell me where I've gone wrong or what is the correct way to write this code?
h=0.01; %step size
J_0(1)=1; %initial condition for J_0
Z_0(1)=1; %initial condition for Z_0-This value should be zero
%but Matlab gives me an error. To fix this, I input
%Z_0(1)-1 to use the correct value for Z_0(1).
x(1)=0.001; %first value of x
dZ(Z_0,J_0)=(-1/x)*(Z_0-1)-J_0;
for i=[1:1:10]
dZ1=(-1/x)*(Z_0-1)-J_0;
dJ1=(Z_0(1)-1)*h;
dZ2=(-1/x)*(Z_0-1+0.5*h)-(J_0+0.5*h*dJ1);
dJ2=((Z_0(1)-1)+dZ1)*h;
dZ3=(-1/x)*(Z_0-1+0.5*h)-(J_0+0.5*h*dJ2);
dJ3=((Z_0(1)-1)+dZ1+dZ2)*h;
dZ4=(-1/x)*(Z_0-1+h)-(J_0+h*dJ3);
dJ4=((Z_0(1)-1)+dZ1+dZ2+dZ3)*h;
J(i+1)=J(i)+(h/6)*(dJ1+2*dJ2+2*dJ3+dJ4);
end
plot(J_0);
Thanks in advance for any help
Your problem is on the line:
J(i+1)=J(i)+(h/6)*(dJ1+2*dJ2+2*dJ3+dJ4);
In the right-hand side of your assignment operator you use the variable J that is never set before i is taking the value 1. Looks like a typo to me (should it be J_0 instead?)
Also, don't forget your index i when computing your dJ and dZ stuff in the for loop.