Coefficients in simple equations, y not represented all the time

I have the equations x=0, and z=50000. Written as a=x==0, and b=z==50000. Potentially in other examples maybe all variables (x,y,z) are represented in the equations, I would like matlab to tell me the coefficients of x,y and z in both equations. For example the x=0 equation would tell me I have 1 x, 0y, 0z as the coefficents. Another exmaple is the other equation would tell me I have 0x,0y and 1 z.

[katherine keogh]

Okay I have it so that I use children to seperate the equations from the numbers at the end

and then I can get the coefficients but I want it so that it will tell me if there are no xs or zs or ys rather than just omitting the 0s

[dpb]

More info on what you're doing and how to use this probably would lead to some other feedback, but if you have the Statistics or CurveFitting TB there are options to use a fitobject or linearmodel object that contains information on coefficients, variables, etc., ...

Other than that, a mechanism such as holding the coefficients vector where the terms are related positionally is about the best one can do in ordinary procedural code; one could write a special class of one's own to deal with somewhat similarly as do the two objects above without all the bells and whistles.

Or, there is the Symbolic TB to treat that way...I've never used/had it so not all that familiar.

Answer 1

[Zuber Khan]

Hi,

When working with symbolic expressions in MATLAB, you might find it necessary to extract the coefficients of specific variables, ensuring that even those variables which are not present in the expression are accounted for, with a zero coefficient. To accomplish this, the coeffs function of Symbolic Math Toolbox can be a valuable tool.

Firstly, you need to define the symbolic variables and equations involved as follows.

% Define symbolic variables
syms x y z

% Define the equations
eq1 = 2*x == 0;
eq2 = z == 50000;
eq3 = x+y-3*z == 23;

Then you can write a function to extract the coefficients. Kindly note that you need to take care of the use cases as mentioned below to eliminate any logical errors in the code.

• Case 1: When the mathematical expression has a single term. For instance, x, 4*z etc.
• Case 2: When the mathematical expression has more than one term. For instance, x-20, 4*z-3*x-5 etc.

I am attaching the code snippet below for your reference.

% Create a list of all variables
vars = [x, y, z];

% Extract coefficients for each equation
coeffs_eq1 = extractCoefficients(eq1, vars);
coeffs_eq2 = extractCoefficients(eq2, vars);
coeffs_eq3 = extractCoefficients(eq3, vars);

% Display results
disp('Coefficients for eq1 (2*x=0):');
disp(['x: ', num2str(coeffs_eq1(1)), ', y: ', num2str(coeffs_eq1(2)), ', z: ', num2str(coeffs_eq1(3))]);

disp('Coefficients for eq2 (z=50000):');
disp(['x: ', num2str(coeffs_eq2(1)), ', y: ', num2str(coeffs_eq2(2)), ', z: ', num2str(coeffs_eq2(3))]);

disp('Coefficients for eq3 (x+y-3*z==23):');
disp(['x: ', num2str(coeffs_eq3(1)), ', y: ', num2str(coeffs_eq3(2)), ', z: ', num2str(coeffs_eq3(3))]);

% Function to extract coefficients
function coff = extractCoefficients(eq, vars)
    % Convert equation to symbolic expression
    expr = lhs(eq) - rhs(eq);
    % Initialize coefficients array
    coff = zeros(1, length(vars));
    % Possible operators combining symoblic variables
    operators = {'+', '-'};
    % Extract coefficients for each variable
    for i = 1:length(vars)
        [cof,term] = coeffs(expr, vars(i));
        Operators = operators(cellfun(@(op) contains(char(expr), op), operators));
        if ~isempty(Operators)
            % Muti-term expression
            if length(term)==1
                  coff(i) = 0; % If no term found, coefficient is zero
            else     
                  coff(i) = cof(1); % If term exists, equal to coefficient
            end
        else 
            % Single term expression
            if contains(string(expr),string(vars(i)))
                 coff(i) = cof(1); % Extract the coefficient for term, if it exists
            else
                coff(i) = 0;
            end

        end
    end
end

This will address your query. If you have any concerns, drop a comment and I will be glad to assist you further.

Regards,

Zuber