I want to make symbolic functions theta1(t), theta2(t), theta3(t),...,thetaN(t) where N is some parameter I can define in MATLAB. I know that I can use something like sym('theta',[1 N]) to get [theta1, theta2, theta3,..., thetaN]. However, how can I do the same thing with theta being a function of t? The way to hard-code it would be like syms theta1(t) theta2(t) theta3(t) ... thetaN(t), but I want to make this general.
I do not want to directly use the sym command here because "support of character vectors that are not valid variable names and do not define a number will be removed in a future release", meaning something like sym('theta1(t)') would not be valid in future releases.
Any suggestions?
Figured part of it out. I could do something like the following
for i = 1:N
syms(strcat('theta',num2str(i),'(t)'))
end
However, if I want to assign a variable that contains all the symbolic expressions I'm still stuck. If I try
for i = 1:N
my_array(i) = syms(strcat('theta',num2str(i),'(t)'))
end
I get Error using syms (line 133). Using input and output arguments simultaneously is not supported. It works if I use sym instead of syms, but this leads to the warning I mentioned in my original post.
Related
I have the following function that I wish to solve using fzero:
f = lambda* exp(lambda^2)* erfc(lambda) - frac {C (T_m - T_i)}/{L_f*sqrt(pi)}
Here, C, T_m, T_i, and L_f are all input by the user.
On trying to solve using fzero, MATLAB gives the following error.
Undefined function or variable 'X'.
(where X are the variables stated above)
This error is understandable. But is there a way around it? How do I solve this?
This is answered to the best of my understanding after reading your question as it's not really clear what you are exactly trying and what you want exactly.
Posting the exact lines of code helps a big deal in understanding(as clean as possible, remove clutter). If then the output that matlab gives is added it becomes a whole lot easier to make sure we answer your question properly and it allows us to try it out. Usually it's a good idea to give some example values for data that is to be entered by the user anyway.
First of to make it a function it either needs a handle.
Or if you have it saved it as a matlab file you generally do not want other inputs in your m file then the variable.
So,
function [out]=yourfun(in)
constants=your values; %you can set a input or inputdlg to get a value from the user
out= something something, your lambda thingy probably; %this is the equation/function you're solving for
end
Now since that is not all that convenient I suggest the following
%declare or get your constants here, above the function makes it easier
syms lambda
f = lambda* exp(lambda^2)* erfc(lambda) - frac {C (T_m - T_i)}/{L_f*sqrt(pi)};
hf=matlabFunction(f); %this way matlab automatically converts it to a function handle, alternatively put #(lambda) in front
fzero(hf,x0)
Also this matlab page might help you as well ;)
I'm using arrayfun to plot the result of a custom function, which does some logic, look-ups, and calculations. My original call looked similar to this:
plot(x, arrayfun(#Q, x.^2, someNumericVariable));
This worked great. However, in addition to the someNumericVariable parameter, I also wanted to add another parameter, someStringVariable, so I changed it to this:
plot(x, arrayfun(#Q, x.^2, someNumericVariable, someStringVariable));
However, when trying to use this, I get an error:
error: arrayfun: dimensions mismatch
I'm guessing that this happens due to this line in the GNU Octave documentation:
If given more than one array input argument then all input arguments must have the same sizes
(https://www.gnu.org/software/octave/doc/interpreter/Function-Application.html)
So I assume that the string I'm trying to pass is being treated as an array, which has different dimensions than the numeric constant value?
If this is so, are there any workarounds that I can do while keeping the code syntactically concise?
One workaround that would work in MATLAB would be:
plot(x, arrayfun(#(u,v) Q(u,v,someStringVariable), x.^2, someNumericVariable));
As part of a group project we have a system of 2 non linear differential equations and we have to draw the S=S(t) , I=I(t) graphic using the midpoint method.
And I'm getting the following error when trying to insert the matrix with the corresponding differential equations:
"Error in inline expression ==> matrix([[-(IS)/1000], [(IS)/1000 - (3*I)/10]])
Undefined function 'matrix' for input arguments of type 'double'.
Error in inline/subsref (line 23)
INLINE_OUT_ = inlineeval(INLINE_INPUTS_, INLINE_OBJ_.inputExpr, INLINE_OBJ_.expr);"
The code I have done is the following:
syms I S
u=[S;I];
F=[-0.001*S*I;0.001*S*I-0.3*I];
F1=inline(char(F),'I','S');
h=100; %Valores aleatórios
T=100000;
ni=(T/h);
u0=[799;1];
f=zeros(1,2);
k=zeros(1,2);
i=1;
while i<=ni
f(1)=F1(u0(1));
f(2)=F1(u0(2));
dx=h*f;
k(1)=F1((u0(1)+h*(1/2)),(u0(2)+h*(1/2)));
k(2)=F1((u0(1)+h*(1/2)),(u0(2)+h*(1/2)));
u1=u0+h*k;
disp('i:'),disp(i)
disp('u= '),disp(u1)
u0=u1;
i=i+1;
end
I'm new to this so the algorithm it's very likely to be wrong but if someone could help me with that error I'd apreciate it. Thank you!
The problem that specifically creates the error is that you are putting two symbolic functions into a matrix and then calling char (which outputs matrix([[-(IS)/1000], [(IS)/1000 - (3*I)/10]]) rather than converting nicely to string).
The secondary problem is that you are trying to pass two functions simultaneously to inline. inline creates a single function from a string (and using anonymous functions instead of inline is preferred anyway). You cannot put multiple functions in it.
You don't need sym here. In fact, avoid it (more trouble than it's worth) if you don't need to manipulate the equations at all. A common method is to create a cell array:
F{1} = #(I,S) -0.001*S*I;
F{2} = #(I,S) 0.001*S*I-0.3*I;
You can then pass in I and S as so:
F{1}(500,500)
Note that both your functions include both I and S, so they are always necessary. Reconsider what you were expecting when passing only one variable like this: f(1)=F1(u0(1));, because that will also give an error.
I'm trying to model the effect of different filter "building blocks" on a system which is a construct based on these filters.
I would like the basic filters to be "modular", i.e. they should be "replaceable", without rewriting the construct which is based upon the basic filters.
For example, I have a system of filters G_0, G_1, which is defined in terms of some basic filters called H_0 and H_1.
I'm trying to do the following:
syms z
syms H_0(z) H_1(z)
G_0(z)=H_0(z^(4))*H_0(z^(2))*H_0(z)
G_1(z)=H_1(z^(4))*H_0(z^(2))*H_0(z)
This declares the z-domain I'd like to work in, and a construct of two filters G_0,G_1, based on the basic filters H_0,H_1.
Now, I'm trying to evaluate the construct in terms of some basic filters:
H_1(z) = 1+z^-1
H_0(z) = 1+0*z^-1
What I would like to get at this point is an expanded polynomial of z.
E.g. for the declarations above, I'd like to see that G_0(z)=1, and that G_1(z)=1+z^(-4).
I've tried stuff like "subs(G_0(z))", "formula(G_0(z))", "formula(subs(subs(G_0(z))))", but I keep getting result in terms of H_0 and H_1.
Any advice? Many thanks in advance.
Edit - some clarifications:
In reality, I have 10-20 transfer functions like G_0 and G_1, so I'm trying to avoid re-declaring all of them every time I change the basic blocks H_0 and H_1. The basic blocks H_0 and H_1 would actually be of a much higher degree than they are in the example here.
G_0 and G_1 will not change after being declared, only H_0 and H_1 will.
H_0(z^2) means using z^2 as an argument for H_0(z). So wherever z appears in the declaration of H_0, z^2 should be plugged in
The desired output is a function in terms of z, not H_0 and H_1.
A workable hack is having an m-File containing the declarations of the construct (G_0 and G_1 in this example), which is run every time H_0 and H_1 are redefined. I was wondering if there's a more elegant way of doing it, along the lines of the (non-working) code shown above.
This seems to work quite nicely, and is very easily extendable. I redefined H_0 to H_1 as an example only.
syms z
H_1(z) = 1+z^-1;
H_0(z) = 1+0*z^-1;
G_0=#(Ha,z) Ha(z^(4))*Ha(z^(2))*Ha(z);
G_1=#(Ha,Hb,z) Hb(z^(4))*Ha(z^(2))*Ha(z);
G_0(H_0,z)
G_1(H_0,H_1,z)
H_0=#(z) H_1(z);
G_0(H_0,z)
G_1(H_0,H_1,z)
This seems to be a namespace issue. You can't define a symbolic expression or function in terms of arbitrary/abstract symfuns and then later on define these symfuns explicitly and be able to use them to obtain an exploit form of the original symbolic expression or function (at least not easily). Here's an example of how a symbolic function can be replaced by name:
syms z y(z)
x(z) = y(z);
y(z) = z^2; % Redefines y(z)
subs(x,'y(z)',y)
Unfortunately, this method depends on specifying the function(s) to be substituted exactly – because strings are used, Matlab sees arbitrary/abstract symfuns with different arguments as different functions. So the following example does not work as it returns y(z^2):
syms z y(z)
x(z) = y(z^2); % Function of z^2 instead
y(z) = z^2;
subs(x,'y(z)',y)
But if the last line was changed to subs(x,'y(z^2)',y) it would work.
So one option might be to form strings for case, but that seems overly complex and inelegant. I think that it would make more sense to simply not explicitly (re)define your arbitrary/abstract H_0, H_1, etc. functions and instead use other variables. In terms of the simple example:
syms z y(z)
x(z) = y(z^2);
y_(z) = z^2; % Create new explicit symfun
subs(x,y,y_)
which returns z^4. For your code:
syms z H_0(z) H_1(z)
G_0(z) = H_0(z^4)*H_0(z^2)*H_0(z);
G_1(z) = H_1(z^4)*H_0(z^2)*H_0(z);
H_0_(z) = 1+0*z^-1;
H_1_(z) = 1+z^-1;
subs(G_0, {H_0, H_1}, {H_0_, H_1_})
subs(G_1, {H_0, H_1}, {H_0_, H_1_})
which returns
ans(z) =
1
ans(z) =
1/z^4 + 1
You can then change H_0_ and H_1_, etc. at will and use subs to evaluateG_1andG_2` again.
I have a MATLAB function to solve a Inertia Tensor , and I have a nested function in my program . All the variables in it are symbolics but it told me
“Error using assignin: Attempt to add ”x“ to a static workspace”
and I don't understand why this happens . Here is my test.m code:
function test
syms x y z
f=x
f1=f+1
f2=f1^2
function r=test2
r=f2^3;
end
f3=test2
end
After searching this web-forum I have found some answers . But at the same time I just don't understand it
Andrew Janke explianed it like this : While syms A may look like a static variable declaration, it isn't. It's just a regular function call. It's using Matlab's "command" invocation style to look like syntax, but it's really equivalent to syms('a', 'b', 'c').
on this page : Matlab: "Error using assignin: Attempt to add "c" to a static workspace"
what does static variable mean ?
I also search the HELP doc and it said :In functions and scripts, do not use syms to create symbolic variables with the same names as MATLAB® functions. For these names MATLAB does not create symbolic variables, but keeps the names assigned to the functions.
I only know syms x to create a symbolic variable in the workspace but why does the documentation say MATLAB does not create ?
'Static' means fixed, 'workspace' is what Matlab calls the places where all of its variables are stored. For non-nested functions the workspace starts off as empty when Matlab is at the beginning of the function; as Matlab continues through function's lines of code it continuously add more variables to the workspace.
For functions with a nested function, Matlab first parses the function to see what variable will be created (it specifically looks for x = type lines), then it creates all of these variables (with value as 'unassigned'), and then only does it start to run through the code; but while running through the code, it can never create a new variable.
This is why the code
function TestNestedFunction
syms x;
function Nested()
end
end
generates an error, there is no x = to tell it to pre-create the unassigned variable x at the start of the code. It fails at syms x;, as that line tries to create a new variable x, which fails as it may not.
This is also why the following code runs
function TestNestedFunction
syms x;
x = x;
function Nested()
end
end
it sees the x = and then pre-creates x. (This is why your example of adding [x, y, z] = deal([]); also works).
You can test this with a break point at the beginning of simple non-nested function and a simple nested function. Just run it step by step.
This code works:
function test
x=sym('x')
y=sym('y')
z=sym('z')
f=x
f1=f+1
f2=f1^2
function r=test2
r=f2^3;
end
f3=test2
end
I think the pages you found are quite clear.
You need to declare the variables one by one and use:
x = sym('x')
Otherwise syms will try to assign the values into a workspace where this is not allowed.