Automating function creation from an input statement

Hello,

I am want to have a program in which I insert N equations with N variables and it itself produces N functions of the equations.

The psuedo code woud be something like this:

Input:

Equations: Equation1: x1^2+3*x2+3, Equation2: exp(x1+x2)

Output:

function f = f(x1,x2)

f = x1^2+3*x2+3

end

function g = g(x1,x2)

g = exp(x1+x2)

end

[Stephen23]

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

Answer 1

[Aakash]

To create a program that takes N equations with N variables and produces N functions based on those equations, you can use the concept of anonymous functions in MATLAB. Here's an example of how you can achieve this:

% Example input equations

equations = {'x1^2+3*x2+3', 'exp(x1+x2)'};

% Create N functions based on the equations

N = numel(equations);

functions = cell(1, N);

for i = 1:N

% Create anonymous function using eval and str2func

functions{i} = str2func(['@(x1, x2) ' equations{i}]);

end

% Example usage of the generated functions

x1 = 2;

x2 = 3;

% Evaluate the functions at the specified values

results = zeros(1, N);

for i = 1:N

results(i) = functions{i}(x1, x2);

end

[Fernando]

Great thank you very much!!

[Dyuman Joshi]

What if there are 3 variables instead of 2? How about 7?

What if functions don't have same amount of variables?

[Aakash]

Then you can modify the for loop as follows:

for i = 1:N

% Extract variables from the equation string

equation = equations{i};

variables = regexp(equation, 'x\d+', 'match')

% Create symbolic expression using str2sym

symExpression = str2sym(equation)

% Create anonymous function using matlabFunction

functions{i} = matlabFunction(symExpression, 'Vars', sym(variables))

end

x = [2, 3, 4]; % Values for x1, x2, x3

% Evaluate the functions at the specified values

results = zeros(1, N);

for i = 1:N

equation = equations{i};

variables = regexp(equation, 'x\d+', 'match')

xValues = num2cell(x(1:numel(variables)));

results(i) = functions{i}(xValues{:});

end

[Dyuman Joshi]

Extracting the variables and specifying them as input to matlabFunction() is not necessary, as matlabFunction automatically does that for you -

%(x2,x3) instead of (x1,x2)
y = 'x2^2+3*x3+3';
z = str2sym(y);
out = matlabFunction(z)

out = function_handle with value:
    @(x2,x3)x3.*3.0+x2.^2+3.0

Answer 2

[Swastik Sarkar]

You can use symvar to extract the variables in an equation, and then also use anonymous functions for the equations

The code will look something like this:

function generate_functions(equations)
    % Create N anonymous functions based on the given equations
    
    % Get the number of equations (N)
    N = numel(equations);
    
    % Create a cell array to store the functions
    functions = cell(1, N);
    
    % Loop through each equation and create an anonymous function
    for i = 1:N
        % Extract the equation from the input
        equation = equations{i};
        disp(equation)
        % Extract the variables from the equation
        variables = symvar(equation);
        
        % Create a cell array of variable names as strings
        variable_names = arrayfun(@char, variables, 'UniformOutput', false);
        
        % Create an anonymous function based on the equation
        input_args = strjoin(variable_names, ', ');
        functions{i} = str2func(['@(', input_args, ') ', equation]);
    end
    
    % Display the generated functions
    for i = 1:N
        fprintf('function %s = %s(%s)\n', char(96 + i), char(96 + i), input_args);
        fprintf('%s = %s\n', char(96 + i), equations{i});
        fprintf('end\n\n');
    end
    
    % Return the cell array of functions (optional)
    % You can use these functions later in your code
    % if you want to evaluate them for specific values of the variables.
    % Example: f_val = functions{1}(x1_value, x2_value, ...);
end

>> equations = {'x1^2+3*x2+3', 'exp(x1 + x2)'};

>> generate_functions(equations)

x1^2+3*x2+3

exp(x1 + x2)

function a = a(x1, x2)

a = x1^2+3*x2+3

end

function b = b(x1, x2)

b = exp(x1 + x2)

end

Answer 3

[Dyuman Joshi]

An efficient approach -

%Input, in the form of cell-strings
%Note that I have added an extra element
eqns  = {'x1^2+3*x2+3', 'exp(x1+x2)', 'sin(x1)+x2^3*log(x3)-x4'};

%Names you want to put for the functions
names = {'f', 'g', 'h'};

%Generating function files via loop
for k=1:numel(eqns)
    z = str2sym(eqns{k});
    matlabFunction(z,'File',names{k});
end

This generates function files in the current directory, each function file corresponding to each element of input, i.e. eqns variable.

You can also specify many others options, check out matlabFunction documentation for more info.

In case you don't want to store the function in the file, use this instead -

n = numel(eqns);
out = cell(n,1);
for k=1:numel(eqns)
    z = str2sym(eqns{k});
    out{k} = matlabFunction(z);
end
out

out = 3×1 cell array
    {               @(x1,x2)x2.*3.0+x1.^2+3.0}
    {                      @(x1,x2)exp(x1+x2)}
    {@(x1,x2,x3,x4)-x4+sin(x1)+x2.^3.*log(x3)}

Also, @Fernando, you should avoid using the same names for the output variables and the function name (as you have done in the examples posted above).