Use an input for a function

Good morning team!

I am trying to prompt the user to input an equation but it seems input just calculates the equation. How do I retain x and y as a variable? The bolded and underlined is the part I am having trouble with.

syms e i r

display("Hello! Welcome to Matt Baron's numerical solver. Press enter to continue.")

pause

choice = input('Press e for Euler, i for Improved Euler, or r for RK4.');

if choice == e

step = input('What step size would you like?');

initcondx = input('What is the initial condition for x?');

initcondy = input('What is the initial condition for y?');

n=0;%start at 0

x=initcondx;%start at the initial condition

y=initcondy;%start at the initial condition

dfeq=input('What differential equation do you want approximated? i.e. .2 * x * y');

f=@(x,y) (dfeq);%the function to be evaluated

actual=@(x) (exp(.1 .* (x .^2) - .1));%the solved function

while x < 1.5%what value do you want it estimated to

x = (initcondx) + ((n) .* (step));

abs = actual(x) - y;

rel = (abs ./ actual(x)) .* 100;

[x y actual(x) abs rel]

y = (y) + ((step) .* f(x,y));

if x >= 1.5

break

end

n=n+1;

end

end

I have also tried;

f=@(x,y) (input('What differential equation do you want approximated? i.e. .2 * x * y'));%the function to be evaluated

Please point me in the right direction.

Answer 1

[Stephen23]

Use the 's' option to return the input unevaluated (i.e. as a character vector):

https://www.mathworks.com/help/matlab/ref/input.html

You then need to use str2func to convert that character vector to a valid function handle:

https://www.mathworks.com/help/matlab/ref/str2func.html

For example:

pmt = 'What differential equation do you want approximated? i.e. .2 * x * y';
str = input(pmt,'s');
%               ^^^ you need this!
fun = str2func(sprintf('@(x,y)%s',str));
fun(2,3) % assuming user entered '0.2*x*y'

ans = 1.2000

Note that with the 's' option you can also get rid of those symbolic variables at the start.

[Matt Baron]

Thank you, perfect. After playing around with it and reading the references here is how I understand it;

's' causes the input to be stored as an unevaluated function

sprintf makes ('@(x,y)%s',dfeq) to input @(x,y) as a string along with dfeq (kind of like you were typing it yourself into the command line)

str2func makes the strings above into a function

Does that sound right?