Working with an equation and variables from user.

Hello, I would like to get equation of two variables (x,y) from user's input. 'Enter the equation f(x,y): '. Then ask user for value of each variable 'Set value of x: ' and 'Set value of y: '. When all variables are in I want to evaluate the equation with variables. After this is it possible to countinue to work with the equation, to make a partial derivative evaluate that etc.? I'll be gratefull for any advice.

str1 = input('Enter and equation f(x,y); ','s');
x = input('Set the value of x: ');
y = input('Set the value of y: ');
% the rest was unsuccessful in my code

Answer 1

[James Tursa]

You can construct a function handle as follows:

f = str2func(['@(x,y)' str1]);

You can then use this function handle to evaluate at specific values of x and y.

If you want to take derivatives of this downstream in your code, you could create symbolic expressions to work with. E.g.,

syms x y
fxy = f(x,y)

[Patrik Matta]

Thank you for help! This happened so far. I am a beginner in matlab.

format long; % this enables higher decimal accuracy
 
str1 = input('Enter f(x,y); ','s');
x = input('Set x: ');
y = input('Set y: ');
f = str2func(['@(x,y) ' str1]);

syms x y 
F_xy = f(x,y);
disp(F_xy);

I don't fully understand how these variables and data types work so far, but I want to have my eqation and its value in two different variables, if that makes sense. Algorithm would be: Load equation, load x and y, put x and y into equation, load the result into other variable. Just like you would do on paper.

EDIT: I tried it without "syms x y" and now it gives me the numeric value. So if I understand correctly, as far as I want to work with the equation I use "syms x y" then I can differentiate etc. but if I want the equation to give me values I have to sort of "undo" syms?

I know, my explanation sounds dumb but you get the point.

[Patrik Matta]

It seems to work as I wanted it to. Except value of derivative with given x and y doesn't show up.

format long; % this enables higher decimal accuracy
 
str1 = input('Enter f(x,y); ','s');
x = input('Set x: ');
y = input('Set y: ');
f = str2func(['@(x,y) ' str1]);

F_xy = f(x,y);
syms x y
f_dx = diff(f,x);
disp(F_xy);
disp(f_dx); % this is only for check if derivative is correct
F_dx = f_dx(x,y);
disp(F_dx);

[James Tursa]

If you feed the function handle numeric values, then it will give you a numeric answer. If you feed the function handle symbolic variables, then it will give you a symbolic expression result. You can do both in your code, but you can't have the same variable mean two different things at the same time. E.g.,

str1 = input('Enter f(x,y); ','s');
f = str2func(['@(x,y) ' str1]);
% Use f with numeric variables x and y
x = input('Set x: ');
y = input('Set y: ');
disp('Numeric Results:');
fprintf('%s evaluated at x = %d and y = %d = %d\n',str1,x,y,f(x,y));
% Use f with symbolic variables x and y
disp('Symbolic Results:');
syms x y 
F_xy = f(x,y);
disp('Expression:')
disp(F_xy);
disp('Derivative with respect to x:')
disp(diff(F_xy,x));
disp('Derivative with respect to y:')
disp(diff(F_xy,y));

[Patrik Matta]

Thank you this was very helpful. I'm starting to understand this. My (hopefully) last question is how could I evaluate for instance derivative with respect to x with a variable x given by user, if variable types are different.

[James Tursa]

If you want to work with both numeric and symbolic at the same time, then pick different variable names for them. E.g., let small case x and y be the symbolic and upper case X and Y be numeric. Then you can work with both at the same time. You can use the subs( ) function to get numeric values into a symbolic expression. E.g.,

str1 = input('Enter f(x,y); ','s');
f = str2func(['@(x,y) ' str1]);
% Use f with numeric variables X and Y (uppercase)
X = input('Set x: ');
Y = input('Set y: ');
disp('Numeric Results:');
fprintf('%s evaluated at x = %d and y = %d = %d\n',str1,X,Y,f(X,Y));
% Use f with symbolic variables x and y (lowercase)
disp('Symbolic Results:');
syms x y 
F_xy = f(x,y);
disp('Expression:')
disp(F_xy);
disp('Derivative with respect to x:')
disp(diff(F_xy,x));
fprintf('Evaluated at x = %d and y = %d\n',X,Y);
subs(diff(F_xy,x),[x y],[X Y]);
disp('Derivative with respect to y:')
disp(diff(F_xy,y));
fprintf('Evaluated at x = %d and y = %d\n',X,Y);
subs(diff(F_xy,y),[x y],[X Y]);

[Patrik Matta]

Thank you, this was very helpful.