Is it possible to have MATLAB do implicit differentiation with its symbols?
I have the following code
syms x;
y = symfun(sym('y(x)'), sym('x'));
yPrime = symfun(sym('y+(2*x)-1'), [sym('x'), sym('y')]);
diff(yPrime, x, 1)
From this I get
ans(x, y) =
2
but what I want to get (in some form) is
ans(x, y) =
dy/dx + 2
Is that possible?
It looks you're trying to use y as both a symbolic variable and an abstract symbolic function (symfun), which isn't possible. A symbolic function can only take symbolic variables as arguments. I think that you can accomplish what you want with (old-style strings not needed)
syms y(x) % Implicitly defines x too
yPrime = y+2*x-1 % Also a symfun because y is a symfun
diff(yPrime,x)
which returns this symfun
ans(x) =
diff(y(x), x) + 2
Related
I want to define a differntiable sym in MatLab so that
sym x y t;
eq = y == x;
diff(eq,'t') = dy/dt == dx/dt
With this Code dy/dt and dx/dt are calculated and 0 is returned. How can I tell matlab that y and x are functions of t?
I do not know the explicit functions, so substituting y and x with their explicit functions is not an option.
What you are looking for is this-
syms x(t) y(t)
Define your functions as-
x(t)='your function';
y(t)='your function';
And then calculate the differential as follows-
diff(x) %since x is only a function of t
diff(y) %since y is only a function of t
Consider the following MWE in MATLAB:
f = #(t) integral(#(x) x.^2,0,t);
integral(f,0,1);
This yields the error
Error using integral (line 85) A and B must be floating-point scalars.
(and a bit more). How do I fix this? Is this even possible? I think the problem is the variable upper bound.
If you want to use integral then set 'ArrayValued' to true otherwise t would be an invalid end point in integral(#(x) x.^2,0,t). So it would be:
f = #(t) integral(#(x) x.^2,0,t);
integral(f,0,1,'ArrayValued',true)
% ans =
% 0.0833
Alternately, since you're doing double integration, so use the function dedicated for this purpose i.e. integral2. For your example, it would be:
f = #(t,x) x.^2 ;
integral2(f,0,1,0, #(t) t)
% ans =
% 0.0833
If you have Symbolic Math Toolbox, you can also use int as int(expr,var,a,b) but it would be slower. For your case, it would be:
syms x t;
f = x.^2;
req = int(int(f,x,0,t),t,0,1); % It gives 1/12
req = double(req); % Convert to double if required
how can I differentiate a function in matlab? I tried with:
syms x;
f = 3x^2 + 2;
A = diff(f);
disp(A);
My problem is now I want to give x a value after (for example A(x = 1) and I don't know how.
First, there's an error in your code, you can't imply multiplication, you need to write 3*x^2 rather than 3x^2.
Also, in case you feed the function a vector rather than scalar, you should use element-wise operations (including a . before powers, multiplication etc.) so this becomes 3*x.^2.
Other than that, 2 options:
syms x;
f = 3*x.^2 + 2;
1) define A like you did and use subs to substitute x for, say, 1.
A = diff(f);
subs(A,x,1);
2) define A as an anonymous function and call it more easily.
A = #(y) subs(diff(f),x,y)
Now A can be easily called with different values
A(1)
ans = 6
A(2)
ans = 12
Links to documentation on element-wise ops, subs and anonymous functions:
https://uk.mathworks.com/help/matlab/matlab_prog/array-vs-matrix-operations.html
https://uk.mathworks.com/help/symbolic/subs.html
https://uk.mathworks.com/help/matlab/matlab_prog/anonymous-functions.html
Modify your code like this:
syms x;
f = 3*x^2 + 2; % You missed a * here
A(x) = diff(f); % This creates a symfun
A(1) % This gives the value of A at x=1
You need the matlabfunction function.
matlabFunction Generate a MATLAB file or anonymous function from a sym
I have a Matlab function that returns a polynomial of the form:
poly = ax^2 + bx*y + cy^2
where a, b, and c are constants, and x and y are symbolic (class sym).
I want to get the coefficients of the polynomial in the form [a b c], but I'm running into the following problem. If the function returns poly = y^2, then coeffs(poly) = 1. I don't want this – I want it to return [0 0 1].
How can I create a function that will give me the coefficients of a symbolic polynomial in the form that I want?
You can use sym2poly if your polynomial is a function of a single variable like your example y^2:
syms y
p = 2*y^2+3*y+4;
c = sym2poly(p)
which returns
c =
2 3 4
Use fliplr(c) if you really want the coefficients in the other order. If you're going to be working with polynomials it would probably also be a good idea not to create a variable called poly, which is the name of a function you might want to use.
If you actually need to handle polynomials in multiple variables, you can use MuPAD functions from within Matlab. Here is how you can use MuPAD's coeff to get the coefficients in terms of the order of variable they precede (x or y):
syms x y
p = 2*x^2+3*x*y+4*y;
v = symvar(p);
c = eval(feval(symengine,'coeff',p,v))
If you want to extract all of the information from the polynomial, the poly2list function is quite helpful:
syms x y
p = 2*x^2+3*x*y+4*y;
v = symvar(p);
m = eval(feval(symengine,'poly2list',p,v));
c = m(:,1); % Coefficients
degs = m(:,2:end); % Degree of each variable in each term
The polynomial can then be reconstructed via:
sum(c.*prod(repmat(v,[size(m,1) 1]).^degs,2))
By the way, good choice on where you go to school. :-)
There is also an alternative to this problem. For a given degree, this function returns a polynomial of that degree and its coefficients altogether.
function [polynomial, coefficeint] = makePoly(degree)
syms x y
previous = 0 ;
for i=0:degree
current = expand((x+y)^i);
previous= current + previous ;
end
[~,poly] = coeffs(previous);
for j= 1:length(poly)
coefficeint(j) = sym(strcat('a', int2str(j)) );
end
polynomial = fliplr(coefficeint)* poly.' ;
end
Hope this helps.
I am trying to do this: syms f(x, y) but it is not working and throws the error: Not a valid variable name. What am I doing wrong here? Thank you
Like this
syms x y;
f = sym('3*x + 4*y');
subs(f, {x,y}, {4,5}); % returns 32
Btw, quite a nice page on symbolic maths in MATLAB here
It looks valid since it is the same as an example in http://www.mathworks.co.uk/help/toolbox/symbolic/syms.html. You could check which x, which y and which f to make sure that x, y and f aren't existing functions (I don't think symbolic variables can have the same name as a function)
You could also try:
x = sym('x');
y = sym('y');
f(x, y) = sym('f(x, y)');
This should do the same as your original code, but I don't see why it would work if syms doesn't.