%使用fitnlm()通过噪声数据拟合非线性模型(指数衰减曲线，Y = a * exp(-b*x) + c)。%需要统计和机器学习工具箱，其中包含fitnlm()。%初始化步骤。clc;%清除命令窗口。关闭所有;%关闭所有数字(imtool.除外)清除;删除所有已存在的变量。或者clearvars，如果你想的话。工作空间; % Make sure the workspace panel is showing. format long g; format compact; fontSize = 20; % Create the X coordinates from 0 to 20 every 0.5 units. X = 0 : 0.5 : 20; % Define coefficients and function that the X values obey. a = 10 % Arbitrary sample values I picked. b = 0.4 c = 5 Y = a * exp(-X * b) + c; % Get a vector. No noise in this Y yet. % Add noise to Y. Y = Y + 0.5 * randn(1, length(Y)); %-------------------------------------------------------------------------------------------------------------------------------------- % Now we have noisy training data that we can send to fitnlm(). % Plot the noisy initial data. plot(X, Y, 'b*', 'LineWidth', 2, 'MarkerSize', 15); grid on; % Convert X and Y into a table, which is the form fitnlm() likes the input data to be in. % Note: it doesn't matter if X and Y are row vectors or column vectors since we use (:) to get them into column vectors for the table. tbl = table(X(:), Y(:)); % Define the model as Y = a * exp(-b*x) + c % Note how this "x" of modelfun is related to big X and big Y. % x((:, 1) is actually X and x(:, 2) is actually Y - the first and second columns of the table. modelfun = @(b,x) b(1) * exp(-b(2)*x(:, 1)) + b(3); % Guess values to start with. Just make your best guess. aGuessed = 11 % Arbitrary sample values I picked. bGuessed = 0.5 cGuessed = 6 beta0 = [aGuessed, bGuessed, cGuessed]; % Guess values to start with. Just make your best guess. % Now the next line is where the actual model computation is done. mdl = fitnlm(tbl, modelfun, beta0); % Now the model creation is done and the coefficients have been determined. % YAY!!!! % Extract the coefficient values from the the model object. % The actual coefficients are in the "Estimate" column of the "Coefficients" table that's part of the mode. coefficients = mdl.Coefficients{:, 'Estimate'} % Create smoothed/regressed data using the model: yFitted = coefficients(1) * exp(-coefficients(2)*X) + coefficients(3); % Now we're done and we can plot the smooth model as a red line going through the noisy blue markers. hold on; plot(X, yFitted, 'r-', 'LineWidth', 2); grid on; title('Exponential Regression with fitnlm()', 'FontSize', fontSize); xlabel('X', 'FontSize', fontSize); ylabel('Y', 'FontSize', fontSize); legendHandle = legend('Noisy Y', 'Fitted Y', 'Location', 'north'); legendHandle.FontSize = 30; % Place formula text roughly in the middle of the plot. formulaString = sprintf('Y = %.3f * exp(-%.3f * X) + %.3f', coefficients(1), coefficients(2), coefficients(3)) xl = xlim; yl = ylim; xt = xl(1) + abs(xl(2)-xl(1)) * 0.325; yt = yl(1) + abs(yl(2)-yl(1)) * 0.59; text(xt, yt, formulaString, 'FontSize', 25, 'FontWeight', 'bold'); % Set up figure properties: % Enlarge figure to full screen. set(gcf, 'Units', 'Normalized', 'OuterPosition', [0 0 1 1]); % Get rid of tool bar and pulldown menus that are along top of figure. % set(gcf, 'Toolbar', 'none', 'Menu', 'none'); % Give a name to the title bar. set(gcf, 'Name', 'Demo by ImageAnalyst', 'NumberTitle', 'Off')