BuildDesignMatrix.m

function [X, uX] = BuildDesignMatrix(modelStr, params, x_i, ux_i)
% Create design matrix from model string
%
% modelStr : string like 'a + b*x + c*sin(x)'
% params   : string array of parameter names, e.g. ["a","b","c"]
% x_i    : column vector of x values
% ux_i : scalar or vector of uncertainties in x (set to 0 to skip)


syms x
expr = str2sym(modelStr);

n = length(x_i);
p = length(params);
X = zeros(n, p);
uX = zeros(n, p);

for k = 1:p
    sym_param = sym(params(k));
    
    % Basis function (design matrix column)
    col_expr  = diff(expr, sym_param);
    
    % Uncertainty propagation: d/dx of basis function, times u_x
    dcol_dx   = diff(col_expr, x);
    
    % Evaluate basis function
    if isnumeric(col_expr)
        X(:, k) = double(col_expr) * ones(n, 1);
    else
        f = matlabFunction(col_expr, 'Vars', x);
        X(:, k) = f(x_i);
    end
    
    % Evaluate uncertainty column
    if isnumeric(dcol_dx) || dcol_dx == 0
        uX(:, k) = 0;
    else
        f = matlabFunction(dcol_dx, 'Vars', x);
        uX(:, k) = abs(f(x_i)) .* ux_i(:);
    end
end
end