feat(analysis): create solver analysis script

- Implements 'analyzeSolvers' function to run benchmarks. - Loops through specified matrix sizes and types. - Generates matrices using 'utils.generateMatrices'. - Runs each specified solver using 'tic'/'toc' for timing. - Calls 'linearSolvers.checkConvergence' for iterative methods to skip non-convergent cases (based on spectral radius). - Records time, iteration count (for iterative), convergence status, and any errors. - Stores results in a MATLAB table. - Optionally saves the results table to a .mat file.

Author: msmrexe

analyzeSolvers.m

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+% analyzeSolvers.m
+% Runs timing and iteration analysis for linear solvers.
+
+function results_table = analyzeSolvers(sizes, matrix_types, methods_to_test, tol, max_iter, results_file)
+ % Add package path
+ addpath(genpath(pwd));
+
+ % Define which methods are iterative
+ iterative_methods = {'Jacobi', 'GaussSeidel', 'SOR'};
+
+ results = []; % Use a cell array to accumulate results
+
+ for n = sizes
+ fprintf('Analyzing matrix size n = %d...\n', n);
+ for m_type = matrix_types
+ fprintf(' Matrix Type: %s...\n', m_type);
+
+ % Generate matrix and vector
+ try
+ A = utils.generateMatrices(n, m_type);
+ b = rand(n, 1);
+ catch ME
+ fprintf(' Skipping matrix generation error: %s\n', ME.message);
+ continue;
+ end
+
+ for method_name_cell = methods_to_test
+ method_name = method_name_cell{:}; % Get string from cell
+ fprintf(' Testing Method: %s...\n', method_name);
+
+ time_taken = NaN;
+ iterations = NaN; % Only for iterative methods
+ converged = true; % Assume success unless failure occurs
+ error_msg = '';
+
+ try
+ % Check applicability/convergence for iterative methods
+ is_iterative = ismember(method_name, iterative_methods);
+ can_run = true;
+ if is_iterative
+ % Use spectral radius check for convergence guarantee
+ % Using omega=1.2 as a default for SOR check if needed
+ omega_check = 1.2;
+ if ~linearSolvers.checkConvergence(A, method_name, omega_check)
+ warning('Skipping %s for n=%d (%s matrix): Convergence condition (spectral radius >= 1) not met.', method_name, n, m_type);
+ can_run = false;
+ error_msg = 'Convergence Fail';
+ end
+ end
+
+ if can_run
+ tic; % Start timer
+ switch method_name
+ case 'GaussianElimination'
+ x = linearSolvers.gaussianElimination(A, b);
+ case 'GaussJordanElimination'
+ x = linearSolvers.gaussJordanElimination(A, b);
+ case 'LUDecomposition'
+ x = linearSolvers.luDecomposition(A, b);
+ case 'Jacobi'
+ [x, iterations, final_error] = linearSolvers.jacobi(A, b, [], tol, max_iter);
+ if final_error >= tol; converged = false; error_msg = sprintf('Did not converge (err=%e)', final_error); end
+ case 'GaussSeidel'
+ [x, iterations, final_error] = linearSolvers.gaussSeidel(A, b, [], tol, max_iter);
+ if final_error >= tol; converged = false; error_msg = sprintf('Did not converge (err=%e)', final_error); end
+ case 'SOR'
+ omega = 1.2; % Example omega, could be optimized
+ [x, iterations, final_error] = linearSolvers.sor(A, b, omega, [], tol, max_iter);
+ if final_error >= tol; converged = false; error_msg = sprintf('Did not converge (err=%e)', final_error); end
+ case 'MATLAB Backslash'
+ x = A \ b;
+ end
+ time_taken = toc; % Stop timer
+ end
+
+ catch ME
+ warning('Error running %s for n=%d (%s matrix): %s', method_name, n, m_type, ME.message);
+ error_msg = ME.identifier; % Record error type
+ converged = false;
+ end
+
+ % Append result
+ results = [results; {method_name, n, m_type, time_taken, iterations, converged, error_msg}];
+ end % End methods loop
+ end % End matrix types loop
+ end % End sizes loop
+
+ % Convert cell array to table
+ results_table = cell2table(results, ...
+ 'VariableNames', {'Method', 'Size', 'MatrixType', 'Time_s', 'Iterations', 'Converged', 'Error'});
+
+ % Save results
+ if nargin >= 6 && ~isempty(results_file)
+ try
+ save(results_file, 'results_table');
+ fprintf('\nResults saved to %s\n', results_file);
+ catch ME
+ fprintf('\nError saving results: %s\n', ME.message);
+ end
+ end
+end