MATLAB拟合方程求解遇问题：fit_eq为char类型需转sym

Let's break down why you're getting Empty sym: 0-by-1 and walk through reliable fixes for your MATLAB code:

Root Causes of the Issue #

Your current workflow uses string replacement to convert the fit formula into a character string, then tries to solve it directly. This fails for two key reasons:

1. Locale-Based Format Errors: If your system uses German locale, num2str outputs decimal commas (, instead of .), which the Symbolic Math Toolkit doesn't recognize as valid decimal separators.
2. Unreliable String Manipulation: Manual string replacement is prone to subtle bugs (like accidental partial matches or formatting quirks) that break the symbolic expression structure.

Solution 1: Build Symbolic Expression Directly from Fit Object (Recommended) #

Skip string operations entirely by constructing the symbolic equation using the fit object's native coefficients and terms. This is far more robust:

% Assuming fitobject_{1} is already generated from your fitting loop
syms x y

% Extract coefficients and their corresponding polynomial terms
coeff_values = coeffvalues(fitobject_{1});
coeff_terms = coeffnames(fitobject_{1});

% Build the symbolic polynomial step-by-step
fit_symbolic = 0;
for idx = 1:length(coeff_values)
    % Convert term name (e.g., 'x^9') to a symbolic term
    symbolic_term = str2sym(coeff_terms{idx});
    % Add the term multiplied by its coefficient to the equation
    fit_symbolic = fit_symbolic + coeff_values(idx) * symbolic_term;
end

% Solve for x when y=1 (use 'Real', true to filter for only real solutions)
erg = solve(fit_symbolic == y, x, 'Real', true);

This method leverages MATLAB's native symbolic tools, eliminating all risks associated with string formatting errors.

Solution 2: Fix the String-to-Symbol Conversion #

If you want to stick with your original string-based approach, fix the decimal separator issue and ensure proper conversion to a symbolic expression:

% ... your existing code up to the fit_eq generation loop ...
for ii=1:1:numel(cvalues)
    cname = cnames{ii};
    cvalue = num2str(cvalues(ii));
    % Replace German decimal commas with periods for symbolic compatibility
    cvalue = strrep(cvalue, ',', '.');
    fit_eq = strrep(fit_eq, cname , cvalue);
end

% Convert the cleaned string to a symbolic expression
fit_symbolic = str2sym(fit_eq);
syms x y=1;
% Solve with real solution filtering (critical for odd-degree polynomials)
erg = solve(fit_symbolic == y, x, 'Real', true);

Why This Works #

• The decimal comma replacement ensures the symbolic engine interprets coefficients correctly.
• Adding 'Real', true tells solve to return only real solutions—critical for a 9th-degree polynomial, which will have at least one real root per the Fundamental Theorem of Algebra.

Additional Notes #

• A 9th-degree polynomial can have up to 9 real roots, so erg may return a vector of solutions instead of a single value.
• Always verify your symbolic expression with disp(fit_symbolic) before solving to catch any remaining formatting issues.

内容的提问来源于stack exchange，提问作者Cassiopeia