Fixing fsolve Indexing Errors in MATLAB Coder

When compiling fsolve with MATLAB Coder, indexing errors occur when array sizes, vector dimensions (row vs. column), or objective function outputs lack fixed, static definitions at compile time.

Root Causes

• Row vs. Column mismatch: x0 is a row vector (e.g., [1, 2]), but the objective function returns a column vector (e.g., [F1; F2]).


• Dynamic output allocation: The objective function does not explicitly preallocate output arrays with static dimensions.


• Unsupported algorithm selection: Code generation only supports specific algorithms like 'trust-region-dogleg' and 'levenberg-marquardt'.

The 4-Step Solution

1. Enforce Column Vectors Everywhere

Ensure both the initial guess x0 and the objective function output F are strictly column vectors (N-by-1).

% Correct: Column vector
x0 = [1.0; 2.0];

% Avoid: Row vector
% x0 = [1.0, 2.0];

2. Preallocate the Objective Function Output

Inside the nonlinear system function, preallocate F explicitly with zeros(N, 1) before assigning values by index.

function F = myObjective(x)
%#codegen
% Fixed size preallocation for 2 equations
F = zeros(2, 1);

F(1) = 2*x(1) - x(2) - exp(-x(1));
F(2) = -x(1) + 2*x(2) - exp(-x(2));
end

3. Configure Coder-Compatible Options

Set solver options specifically for code generation. Disable plotting and graphical outputs.

opts = optimoptions('fsolve', ...
    'Algorithm', 'trust-region-dogleg', ...
    'Display', 'off');

Complete Coder-Ready Example

Save the following solver wrapper in a file named solve_system.m:

function x_sol = solve_system(x0_init)
%#codegen

% 1. Enforce static size and column shape
coder.varsize('x0_init', [2, 1], [0, 0]); % Fixed 2x1 vector
x0 = x0_init(:); % Guarantee column vector
% 2. Set code-gen compatible options
opts = optimoptions('fsolve', ...
    'Algorithm', 'trust-region-dogleg', ...
    'Display', 'off');
% 3. Call fsolve
x_sol = fsolve(@myObjective, x0, opts);
end
function F = myObjective(x)
% Fixed-size column output
F = zeros(2, 1);
F(1) = 3*x(1) + x(2) - 5;
F(2) = x(1)^2 + x(2)^2 - 9;
end

Generate C Code (or MEX)

Test the MEX compilation in MATLAB to confirm the indexing error is resolved:

% Compile to MEX
codegen solve_system -args {zeros(2,1)}

% Run MEX
x_sol = solve_system_mex([1.0; 2.0]);
disp('Solution:');
disp(x_sol);